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 (op_iterator I = op_begin(), E = op_end(); I != E; ++I)
344 if (!(*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 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
708 if (SCEVComplexityCompare(LI)(RHS, LHS))
713 // Do the rough sort by complexity.
714 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
716 // Now that we are sorted by complexity, group elements of the same
717 // complexity. Note that this is, at worst, N^2, but the vector is likely to
718 // be extremely short in practice. Note that we take this approach because we
719 // do not want to depend on the addresses of the objects we are grouping.
720 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
721 const SCEV *S = Ops[i];
722 unsigned Complexity = S->getSCEVType();
724 // If there are any objects of the same complexity and same value as this
726 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
727 if (Ops[j] == S) { // Found a duplicate.
728 // Move it to immediately after i'th element.
729 std::swap(Ops[i+1], Ops[j]);
730 ++i; // no need to rescan it.
731 if (i == e-2) return; // Done!
739 //===----------------------------------------------------------------------===//
740 // Simple SCEV method implementations
741 //===----------------------------------------------------------------------===//
743 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
745 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
747 const Type* ResultTy) {
748 // Handle the simplest case efficiently.
750 return SE.getTruncateOrZeroExtend(It, ResultTy);
752 // We are using the following formula for BC(It, K):
754 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
756 // Suppose, W is the bitwidth of the return value. We must be prepared for
757 // overflow. Hence, we must assure that the result of our computation is
758 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
759 // safe in modular arithmetic.
761 // However, this code doesn't use exactly that formula; the formula it uses
762 // is something like the following, where T is the number of factors of 2 in
763 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
766 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
768 // This formula is trivially equivalent to the previous formula. However,
769 // this formula can be implemented much more efficiently. The trick is that
770 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
771 // arithmetic. To do exact division in modular arithmetic, all we have
772 // to do is multiply by the inverse. Therefore, this step can be done at
775 // The next issue is how to safely do the division by 2^T. The way this
776 // is done is by doing the multiplication step at a width of at least W + T
777 // bits. This way, the bottom W+T bits of the product are accurate. Then,
778 // when we perform the division by 2^T (which is equivalent to a right shift
779 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
780 // truncated out after the division by 2^T.
782 // In comparison to just directly using the first formula, this technique
783 // is much more efficient; using the first formula requires W * K bits,
784 // but this formula less than W + K bits. Also, the first formula requires
785 // a division step, whereas this formula only requires multiplies and shifts.
787 // It doesn't matter whether the subtraction step is done in the calculation
788 // width or the input iteration count's width; if the subtraction overflows,
789 // the result must be zero anyway. We prefer here to do it in the width of
790 // the induction variable because it helps a lot for certain cases; CodeGen
791 // isn't smart enough to ignore the overflow, which leads to much less
792 // efficient code if the width of the subtraction is wider than the native
795 // (It's possible to not widen at all by pulling out factors of 2 before
796 // the multiplication; for example, K=2 can be calculated as
797 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
798 // extra arithmetic, so it's not an obvious win, and it gets
799 // much more complicated for K > 3.)
801 // Protection from insane SCEVs; this bound is conservative,
802 // but it probably doesn't matter.
804 return SE.getCouldNotCompute();
806 unsigned W = SE.getTypeSizeInBits(ResultTy);
808 // Calculate K! / 2^T and T; we divide out the factors of two before
809 // multiplying for calculating K! / 2^T to avoid overflow.
810 // Other overflow doesn't matter because we only care about the bottom
811 // W bits of the result.
812 APInt OddFactorial(W, 1);
814 for (unsigned i = 3; i <= K; ++i) {
816 unsigned TwoFactors = Mult.countTrailingZeros();
818 Mult = Mult.lshr(TwoFactors);
819 OddFactorial *= Mult;
822 // We need at least W + T bits for the multiplication step
823 unsigned CalculationBits = W + T;
825 // Calculate 2^T, at width T+W.
826 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
828 // Calculate the multiplicative inverse of K! / 2^T;
829 // this multiplication factor will perform the exact division by
831 APInt Mod = APInt::getSignedMinValue(W+1);
832 APInt MultiplyFactor = OddFactorial.zext(W+1);
833 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
834 MultiplyFactor = MultiplyFactor.trunc(W);
836 // Calculate the product, at width T+W
837 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
839 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
840 for (unsigned i = 1; i != K; ++i) {
841 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
842 Dividend = SE.getMulExpr(Dividend,
843 SE.getTruncateOrZeroExtend(S, CalculationTy));
847 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
849 // Truncate the result, and divide by K! / 2^T.
851 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
852 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
855 /// evaluateAtIteration - Return the value of this chain of recurrences at
856 /// the specified iteration number. We can evaluate this recurrence by
857 /// multiplying each element in the chain by the binomial coefficient
858 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
860 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
862 /// where BC(It, k) stands for binomial coefficient.
864 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
865 ScalarEvolution &SE) const {
866 const SCEV *Result = getStart();
867 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
868 // The computation is correct in the face of overflow provided that the
869 // multiplication is performed _after_ the evaluation of the binomial
871 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
872 if (isa<SCEVCouldNotCompute>(Coeff))
875 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
880 //===----------------------------------------------------------------------===//
881 // SCEV Expression folder implementations
882 //===----------------------------------------------------------------------===//
884 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
886 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
887 "This is not a truncating conversion!");
888 assert(isSCEVable(Ty) &&
889 "This is not a conversion to a SCEVable type!");
890 Ty = getEffectiveSCEVType(Ty);
893 ID.AddInteger(scTruncate);
897 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
899 // Fold if the operand is constant.
900 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
902 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
903 getEffectiveSCEVType(Ty))));
905 // trunc(trunc(x)) --> trunc(x)
906 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
907 return getTruncateExpr(ST->getOperand(), Ty);
909 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
910 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
911 return getTruncateOrSignExtend(SS->getOperand(), Ty);
913 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
914 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
915 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
917 // If the input value is a chrec scev, truncate the chrec's operands.
918 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
919 SmallVector<const SCEV *, 4> Operands;
920 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
921 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
922 return getAddRecExpr(Operands, AddRec->getLoop());
925 // As a special case, fold trunc(undef) to undef. We don't want to
926 // know too much about SCEVUnknowns, but this special case is handy
928 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
929 if (isa<UndefValue>(U->getValue()))
930 return getSCEV(UndefValue::get(Ty));
932 // The cast wasn't folded; create an explicit cast node. We can reuse
933 // the existing insert position since if we get here, we won't have
934 // made any changes which would invalidate it.
935 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
937 UniqueSCEVs.InsertNode(S, IP);
941 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
943 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
944 "This is not an extending conversion!");
945 assert(isSCEVable(Ty) &&
946 "This is not a conversion to a SCEVable type!");
947 Ty = getEffectiveSCEVType(Ty);
949 // Fold if the operand is constant.
950 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
952 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
953 getEffectiveSCEVType(Ty))));
955 // zext(zext(x)) --> zext(x)
956 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
957 return getZeroExtendExpr(SZ->getOperand(), Ty);
959 // Before doing any expensive analysis, check to see if we've already
960 // computed a SCEV for this Op and Ty.
962 ID.AddInteger(scZeroExtend);
966 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
968 // If the input value is a chrec scev, and we can prove that the value
969 // did not overflow the old, smaller, value, we can zero extend all of the
970 // operands (often constants). This allows analysis of something like
971 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
972 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
973 if (AR->isAffine()) {
974 const SCEV *Start = AR->getStart();
975 const SCEV *Step = AR->getStepRecurrence(*this);
976 unsigned BitWidth = getTypeSizeInBits(AR->getType());
977 const Loop *L = AR->getLoop();
979 // If we have special knowledge that this addrec won't overflow,
980 // we don't need to do any further analysis.
981 if (AR->hasNoUnsignedWrap())
982 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
983 getZeroExtendExpr(Step, Ty),
986 // Check whether the backedge-taken count is SCEVCouldNotCompute.
987 // Note that this serves two purposes: It filters out loops that are
988 // simply not analyzable, and it covers the case where this code is
989 // being called from within backedge-taken count analysis, such that
990 // attempting to ask for the backedge-taken count would likely result
991 // in infinite recursion. In the later case, the analysis code will
992 // cope with a conservative value, and it will take care to purge
993 // that value once it has finished.
994 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
995 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
996 // Manually compute the final value for AR, checking for
999 // Check whether the backedge-taken count can be losslessly casted to
1000 // the addrec's type. The count is always unsigned.
1001 const SCEV *CastedMaxBECount =
1002 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1003 const SCEV *RecastedMaxBECount =
1004 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1005 if (MaxBECount == RecastedMaxBECount) {
1006 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1007 // Check whether Start+Step*MaxBECount has no unsigned overflow.
1008 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
1009 const SCEV *Add = getAddExpr(Start, ZMul);
1010 const SCEV *OperandExtendedAdd =
1011 getAddExpr(getZeroExtendExpr(Start, WideTy),
1012 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1013 getZeroExtendExpr(Step, WideTy)));
1014 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
1015 // Return the expression with the addrec on the outside.
1016 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1017 getZeroExtendExpr(Step, Ty),
1020 // Similar to above, only this time treat the step value as signed.
1021 // This covers loops that count down.
1022 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1023 Add = getAddExpr(Start, SMul);
1024 OperandExtendedAdd =
1025 getAddExpr(getZeroExtendExpr(Start, WideTy),
1026 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1027 getSignExtendExpr(Step, WideTy)));
1028 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
1029 // Return the expression with the addrec on the outside.
1030 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1031 getSignExtendExpr(Step, Ty),
1035 // If the backedge is guarded by a comparison with the pre-inc value
1036 // the addrec is safe. Also, if the entry is guarded by a comparison
1037 // with the start value and the backedge is guarded by a comparison
1038 // with the post-inc value, the addrec is safe.
1039 if (isKnownPositive(Step)) {
1040 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1041 getUnsignedRange(Step).getUnsignedMax());
1042 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1043 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1044 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1045 AR->getPostIncExpr(*this), N)))
1046 // Return the expression with the addrec on the outside.
1047 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1048 getZeroExtendExpr(Step, Ty),
1050 } else if (isKnownNegative(Step)) {
1051 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1052 getSignedRange(Step).getSignedMin());
1053 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1054 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1055 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1056 AR->getPostIncExpr(*this), N)))
1057 // Return the expression with the addrec on the outside.
1058 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1059 getSignExtendExpr(Step, Ty),
1065 // The cast wasn't folded; create an explicit cast node.
1066 // Recompute the insert position, as it may have been invalidated.
1067 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1068 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1070 UniqueSCEVs.InsertNode(S, IP);
1074 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1076 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1077 "This is not an extending conversion!");
1078 assert(isSCEVable(Ty) &&
1079 "This is not a conversion to a SCEVable type!");
1080 Ty = getEffectiveSCEVType(Ty);
1082 // Fold if the operand is constant.
1083 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1085 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1086 getEffectiveSCEVType(Ty))));
1088 // sext(sext(x)) --> sext(x)
1089 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1090 return getSignExtendExpr(SS->getOperand(), Ty);
1092 // Before doing any expensive analysis, check to see if we've already
1093 // computed a SCEV for this Op and Ty.
1094 FoldingSetNodeID ID;
1095 ID.AddInteger(scSignExtend);
1099 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1101 // If the input value is a chrec scev, and we can prove that the value
1102 // did not overflow the old, smaller, value, we can sign extend all of the
1103 // operands (often constants). This allows analysis of something like
1104 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1105 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1106 if (AR->isAffine()) {
1107 const SCEV *Start = AR->getStart();
1108 const SCEV *Step = AR->getStepRecurrence(*this);
1109 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1110 const Loop *L = AR->getLoop();
1112 // If we have special knowledge that this addrec won't overflow,
1113 // we don't need to do any further analysis.
1114 if (AR->hasNoSignedWrap())
1115 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1116 getSignExtendExpr(Step, Ty),
1119 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1120 // Note that this serves two purposes: It filters out loops that are
1121 // simply not analyzable, and it covers the case where this code is
1122 // being called from within backedge-taken count analysis, such that
1123 // attempting to ask for the backedge-taken count would likely result
1124 // in infinite recursion. In the later case, the analysis code will
1125 // cope with a conservative value, and it will take care to purge
1126 // that value once it has finished.
1127 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1128 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1129 // Manually compute the final value for AR, checking for
1132 // Check whether the backedge-taken count can be losslessly casted to
1133 // the addrec's type. The count is always unsigned.
1134 const SCEV *CastedMaxBECount =
1135 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1136 const SCEV *RecastedMaxBECount =
1137 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1138 if (MaxBECount == RecastedMaxBECount) {
1139 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1140 // Check whether Start+Step*MaxBECount has no signed overflow.
1141 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1142 const SCEV *Add = getAddExpr(Start, SMul);
1143 const SCEV *OperandExtendedAdd =
1144 getAddExpr(getSignExtendExpr(Start, WideTy),
1145 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1146 getSignExtendExpr(Step, WideTy)));
1147 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1148 // Return the expression with the addrec on the outside.
1149 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1150 getSignExtendExpr(Step, Ty),
1153 // Similar to above, only this time treat the step value as unsigned.
1154 // This covers loops that count up with an unsigned step.
1155 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1156 Add = getAddExpr(Start, UMul);
1157 OperandExtendedAdd =
1158 getAddExpr(getSignExtendExpr(Start, WideTy),
1159 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1160 getZeroExtendExpr(Step, WideTy)));
1161 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1162 // Return the expression with the addrec on the outside.
1163 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1164 getZeroExtendExpr(Step, Ty),
1168 // If the backedge is guarded by a comparison with the pre-inc value
1169 // the addrec is safe. Also, if the entry is guarded by a comparison
1170 // with the start value and the backedge is guarded by a comparison
1171 // with the post-inc value, the addrec is safe.
1172 if (isKnownPositive(Step)) {
1173 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1174 getSignedRange(Step).getSignedMax());
1175 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1176 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1177 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1178 AR->getPostIncExpr(*this), N)))
1179 // Return the expression with the addrec on the outside.
1180 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1181 getSignExtendExpr(Step, Ty),
1183 } else if (isKnownNegative(Step)) {
1184 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1185 getSignedRange(Step).getSignedMin());
1186 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1187 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1188 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1189 AR->getPostIncExpr(*this), N)))
1190 // Return the expression with the addrec on the outside.
1191 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1192 getSignExtendExpr(Step, Ty),
1198 // The cast wasn't folded; create an explicit cast node.
1199 // Recompute the insert position, as it may have been invalidated.
1200 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1201 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1203 UniqueSCEVs.InsertNode(S, IP);
1207 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1208 /// unspecified bits out to the given type.
1210 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1212 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1213 "This is not an extending conversion!");
1214 assert(isSCEVable(Ty) &&
1215 "This is not a conversion to a SCEVable type!");
1216 Ty = getEffectiveSCEVType(Ty);
1218 // Sign-extend negative constants.
1219 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1220 if (SC->getValue()->getValue().isNegative())
1221 return getSignExtendExpr(Op, Ty);
1223 // Peel off a truncate cast.
1224 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1225 const SCEV *NewOp = T->getOperand();
1226 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1227 return getAnyExtendExpr(NewOp, Ty);
1228 return getTruncateOrNoop(NewOp, Ty);
1231 // Next try a zext cast. If the cast is folded, use it.
1232 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1233 if (!isa<SCEVZeroExtendExpr>(ZExt))
1236 // Next try a sext cast. If the cast is folded, use it.
1237 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1238 if (!isa<SCEVSignExtendExpr>(SExt))
1241 // Force the cast to be folded into the operands of an addrec.
1242 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1243 SmallVector<const SCEV *, 4> Ops;
1244 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1246 Ops.push_back(getAnyExtendExpr(*I, Ty));
1247 return getAddRecExpr(Ops, AR->getLoop());
1250 // As a special case, fold anyext(undef) to undef. We don't want to
1251 // know too much about SCEVUnknowns, but this special case is handy
1253 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1254 if (isa<UndefValue>(U->getValue()))
1255 return getSCEV(UndefValue::get(Ty));
1257 // If the expression is obviously signed, use the sext cast value.
1258 if (isa<SCEVSMaxExpr>(Op))
1261 // Absent any other information, use the zext cast value.
1265 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1266 /// a list of operands to be added under the given scale, update the given
1267 /// map. This is a helper function for getAddRecExpr. As an example of
1268 /// what it does, given a sequence of operands that would form an add
1269 /// expression like this:
1271 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1273 /// where A and B are constants, update the map with these values:
1275 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1277 /// and add 13 + A*B*29 to AccumulatedConstant.
1278 /// This will allow getAddRecExpr to produce this:
1280 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1282 /// This form often exposes folding opportunities that are hidden in
1283 /// the original operand list.
1285 /// Return true iff it appears that any interesting folding opportunities
1286 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1287 /// the common case where no interesting opportunities are present, and
1288 /// is also used as a check to avoid infinite recursion.
1291 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1292 SmallVector<const SCEV *, 8> &NewOps,
1293 APInt &AccumulatedConstant,
1294 const SCEV *const *Ops, size_t NumOperands,
1296 ScalarEvolution &SE) {
1297 bool Interesting = false;
1299 // Iterate over the add operands. They are sorted, with constants first.
1301 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1303 // Pull a buried constant out to the outside.
1304 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1306 AccumulatedConstant += Scale * C->getValue()->getValue();
1309 // Next comes everything else. We're especially interested in multiplies
1310 // here, but they're in the middle, so just visit the rest with one loop.
1311 for (; i != NumOperands; ++i) {
1312 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1313 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1315 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1316 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1317 // A multiplication of a constant with another add; recurse.
1318 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1320 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1321 Add->op_begin(), Add->getNumOperands(),
1324 // A multiplication of a constant with some other value. Update
1326 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1327 const SCEV *Key = SE.getMulExpr(MulOps);
1328 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1329 M.insert(std::make_pair(Key, NewScale));
1331 NewOps.push_back(Pair.first->first);
1333 Pair.first->second += NewScale;
1334 // The map already had an entry for this value, which may indicate
1335 // a folding opportunity.
1340 // An ordinary operand. Update the map.
1341 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1342 M.insert(std::make_pair(Ops[i], Scale));
1344 NewOps.push_back(Pair.first->first);
1346 Pair.first->second += Scale;
1347 // The map already had an entry for this value, which may indicate
1348 // a folding opportunity.
1358 struct APIntCompare {
1359 bool operator()(const APInt &LHS, const APInt &RHS) const {
1360 return LHS.ult(RHS);
1365 /// getAddExpr - Get a canonical add expression, or something simpler if
1367 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1368 bool HasNUW, bool HasNSW) {
1369 assert(!Ops.empty() && "Cannot get empty add!");
1370 if (Ops.size() == 1) return Ops[0];
1372 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1373 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1374 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1375 "SCEVAddExpr operand types don't match!");
1378 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1379 if (!HasNUW && HasNSW) {
1381 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1382 E = Ops.end(); I != E; ++I)
1383 if (!isKnownNonNegative(*I)) {
1387 if (All) HasNUW = true;
1390 // Sort by complexity, this groups all similar expression types together.
1391 GroupByComplexity(Ops, LI);
1393 // If there are any constants, fold them together.
1395 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1397 assert(Idx < Ops.size());
1398 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1399 // We found two constants, fold them together!
1400 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1401 RHSC->getValue()->getValue());
1402 if (Ops.size() == 2) return Ops[0];
1403 Ops.erase(Ops.begin()+1); // Erase the folded element
1404 LHSC = cast<SCEVConstant>(Ops[0]);
1407 // If we are left with a constant zero being added, strip it off.
1408 if (LHSC->getValue()->isZero()) {
1409 Ops.erase(Ops.begin());
1413 if (Ops.size() == 1) return Ops[0];
1416 // Okay, check to see if the same value occurs in the operand list more than
1417 // once. If so, merge them together into an multiply expression. Since we
1418 // sorted the list, these values are required to be adjacent.
1419 const Type *Ty = Ops[0]->getType();
1420 bool FoundMatch = false;
1421 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1422 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1423 // Scan ahead to count how many equal operands there are.
1425 while (i+Count != e && Ops[i+Count] == Ops[i])
1427 // Merge the values into a multiply.
1428 const SCEV *Scale = getConstant(Ty, Count);
1429 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1430 if (Ops.size() == Count)
1433 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1434 --i; e -= Count - 1;
1438 return getAddExpr(Ops, HasNUW, HasNSW);
1440 // Check for truncates. If all the operands are truncated from the same
1441 // type, see if factoring out the truncate would permit the result to be
1442 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1443 // if the contents of the resulting outer trunc fold to something simple.
1444 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1445 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1446 const Type *DstType = Trunc->getType();
1447 const Type *SrcType = Trunc->getOperand()->getType();
1448 SmallVector<const SCEV *, 8> LargeOps;
1450 // Check all the operands to see if they can be represented in the
1451 // source type of the truncate.
1452 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1453 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1454 if (T->getOperand()->getType() != SrcType) {
1458 LargeOps.push_back(T->getOperand());
1459 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1460 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1461 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1462 SmallVector<const SCEV *, 8> LargeMulOps;
1463 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1464 if (const SCEVTruncateExpr *T =
1465 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1466 if (T->getOperand()->getType() != SrcType) {
1470 LargeMulOps.push_back(T->getOperand());
1471 } else if (const SCEVConstant *C =
1472 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1473 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1480 LargeOps.push_back(getMulExpr(LargeMulOps));
1487 // Evaluate the expression in the larger type.
1488 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1489 // If it folds to something simple, use it. Otherwise, don't.
1490 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1491 return getTruncateExpr(Fold, DstType);
1495 // Skip past any other cast SCEVs.
1496 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1499 // If there are add operands they would be next.
1500 if (Idx < Ops.size()) {
1501 bool DeletedAdd = false;
1502 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1503 // If we have an add, expand the add operands onto the end of the operands
1505 Ops.erase(Ops.begin()+Idx);
1506 Ops.append(Add->op_begin(), Add->op_end());
1510 // If we deleted at least one add, we added operands to the end of the list,
1511 // and they are not necessarily sorted. Recurse to resort and resimplify
1512 // any operands we just acquired.
1514 return getAddExpr(Ops);
1517 // Skip over the add expression until we get to a multiply.
1518 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1521 // Check to see if there are any folding opportunities present with
1522 // operands multiplied by constant values.
1523 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1524 uint64_t BitWidth = getTypeSizeInBits(Ty);
1525 DenseMap<const SCEV *, APInt> M;
1526 SmallVector<const SCEV *, 8> NewOps;
1527 APInt AccumulatedConstant(BitWidth, 0);
1528 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1529 Ops.data(), Ops.size(),
1530 APInt(BitWidth, 1), *this)) {
1531 // Some interesting folding opportunity is present, so its worthwhile to
1532 // re-generate the operands list. Group the operands by constant scale,
1533 // to avoid multiplying by the same constant scale multiple times.
1534 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1535 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1536 E = NewOps.end(); I != E; ++I)
1537 MulOpLists[M.find(*I)->second].push_back(*I);
1538 // Re-generate the operands list.
1540 if (AccumulatedConstant != 0)
1541 Ops.push_back(getConstant(AccumulatedConstant));
1542 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1543 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1545 Ops.push_back(getMulExpr(getConstant(I->first),
1546 getAddExpr(I->second)));
1548 return getConstant(Ty, 0);
1549 if (Ops.size() == 1)
1551 return getAddExpr(Ops);
1555 // If we are adding something to a multiply expression, make sure the
1556 // something is not already an operand of the multiply. If so, merge it into
1558 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1559 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1560 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1561 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1562 if (isa<SCEVConstant>(MulOpSCEV))
1564 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1565 if (MulOpSCEV == Ops[AddOp]) {
1566 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1567 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1568 if (Mul->getNumOperands() != 2) {
1569 // If the multiply has more than two operands, we must get the
1571 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1572 Mul->op_begin()+MulOp);
1573 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1574 InnerMul = getMulExpr(MulOps);
1576 const SCEV *One = getConstant(Ty, 1);
1577 const SCEV *AddOne = getAddExpr(One, InnerMul);
1578 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1579 if (Ops.size() == 2) return OuterMul;
1581 Ops.erase(Ops.begin()+AddOp);
1582 Ops.erase(Ops.begin()+Idx-1);
1584 Ops.erase(Ops.begin()+Idx);
1585 Ops.erase(Ops.begin()+AddOp-1);
1587 Ops.push_back(OuterMul);
1588 return getAddExpr(Ops);
1591 // Check this multiply against other multiplies being added together.
1592 bool AnyFold = false;
1593 for (unsigned OtherMulIdx = Idx+1;
1594 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1596 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1597 // If MulOp occurs in OtherMul, we can fold the two multiplies
1599 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1600 OMulOp != e; ++OMulOp)
1601 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1602 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1603 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1604 if (Mul->getNumOperands() != 2) {
1605 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1606 Mul->op_begin()+MulOp);
1607 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1608 InnerMul1 = getMulExpr(MulOps);
1610 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1611 if (OtherMul->getNumOperands() != 2) {
1612 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1613 OtherMul->op_begin()+OMulOp);
1614 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1615 InnerMul2 = getMulExpr(MulOps);
1617 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1618 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1619 if (Ops.size() == 2) return OuterMul;
1620 Ops[Idx] = OuterMul;
1621 Ops.erase(Ops.begin()+OtherMulIdx);
1627 return getAddExpr(Ops);
1631 // If there are any add recurrences in the operands list, see if any other
1632 // added values are loop invariant. If so, we can fold them into the
1634 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1637 // Scan over all recurrences, trying to fold loop invariants into them.
1638 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1639 // Scan all of the other operands to this add and add them to the vector if
1640 // they are loop invariant w.r.t. the recurrence.
1641 SmallVector<const SCEV *, 8> LIOps;
1642 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1643 const Loop *AddRecLoop = AddRec->getLoop();
1644 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1645 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1646 LIOps.push_back(Ops[i]);
1647 Ops.erase(Ops.begin()+i);
1651 // If we found some loop invariants, fold them into the recurrence.
1652 if (!LIOps.empty()) {
1653 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1654 LIOps.push_back(AddRec->getStart());
1656 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1658 AddRecOps[0] = getAddExpr(LIOps);
1660 // Build the new addrec. Propagate the NUW and NSW flags if both the
1661 // outer add and the inner addrec are guaranteed to have no overflow.
1662 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1663 HasNUW && AddRec->hasNoUnsignedWrap(),
1664 HasNSW && AddRec->hasNoSignedWrap());
1666 // If all of the other operands were loop invariant, we are done.
1667 if (Ops.size() == 1) return NewRec;
1669 // Otherwise, add the folded AddRec by the non-liv parts.
1670 for (unsigned i = 0;; ++i)
1671 if (Ops[i] == AddRec) {
1675 return getAddExpr(Ops);
1678 // Okay, if there weren't any loop invariants to be folded, check to see if
1679 // there are multiple AddRec's with the same loop induction variable being
1680 // added together. If so, we can fold them.
1681 for (unsigned OtherIdx = Idx+1;
1682 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1684 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1685 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1686 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1688 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1690 if (const SCEVAddRecExpr *OtherAddRec =
1691 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1692 if (OtherAddRec->getLoop() == AddRecLoop) {
1693 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1695 if (i >= AddRecOps.size()) {
1696 AddRecOps.append(OtherAddRec->op_begin()+i,
1697 OtherAddRec->op_end());
1700 AddRecOps[i] = getAddExpr(AddRecOps[i],
1701 OtherAddRec->getOperand(i));
1703 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1705 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop);
1706 return getAddExpr(Ops);
1709 // Otherwise couldn't fold anything into this recurrence. Move onto the
1713 // Okay, it looks like we really DO need an add expr. Check to see if we
1714 // already have one, otherwise create a new one.
1715 FoldingSetNodeID ID;
1716 ID.AddInteger(scAddExpr);
1717 ID.AddInteger(Ops.size());
1718 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1719 ID.AddPointer(Ops[i]);
1722 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1724 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1725 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1726 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1728 UniqueSCEVs.InsertNode(S, IP);
1730 if (HasNUW) S->setHasNoUnsignedWrap(true);
1731 if (HasNSW) S->setHasNoSignedWrap(true);
1735 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1737 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1738 bool HasNUW, bool HasNSW) {
1739 assert(!Ops.empty() && "Cannot get empty mul!");
1740 if (Ops.size() == 1) return Ops[0];
1742 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1743 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1744 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1745 "SCEVMulExpr operand types don't match!");
1748 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1749 if (!HasNUW && HasNSW) {
1751 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1752 E = Ops.end(); I != E; ++I)
1753 if (!isKnownNonNegative(*I)) {
1757 if (All) HasNUW = true;
1760 // Sort by complexity, this groups all similar expression types together.
1761 GroupByComplexity(Ops, LI);
1763 // If there are any constants, fold them together.
1765 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1767 // C1*(C2+V) -> C1*C2 + C1*V
1768 if (Ops.size() == 2)
1769 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1770 if (Add->getNumOperands() == 2 &&
1771 isa<SCEVConstant>(Add->getOperand(0)))
1772 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1773 getMulExpr(LHSC, Add->getOperand(1)));
1776 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1777 // We found two constants, fold them together!
1778 ConstantInt *Fold = ConstantInt::get(getContext(),
1779 LHSC->getValue()->getValue() *
1780 RHSC->getValue()->getValue());
1781 Ops[0] = getConstant(Fold);
1782 Ops.erase(Ops.begin()+1); // Erase the folded element
1783 if (Ops.size() == 1) return Ops[0];
1784 LHSC = cast<SCEVConstant>(Ops[0]);
1787 // If we are left with a constant one being multiplied, strip it off.
1788 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1789 Ops.erase(Ops.begin());
1791 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1792 // If we have a multiply of zero, it will always be zero.
1794 } else if (Ops[0]->isAllOnesValue()) {
1795 // If we have a mul by -1 of an add, try distributing the -1 among the
1797 if (Ops.size() == 2)
1798 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1799 SmallVector<const SCEV *, 4> NewOps;
1800 bool AnyFolded = false;
1801 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1803 const SCEV *Mul = getMulExpr(Ops[0], *I);
1804 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1805 NewOps.push_back(Mul);
1808 return getAddExpr(NewOps);
1812 if (Ops.size() == 1)
1816 // Skip over the add expression until we get to a multiply.
1817 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1820 // If there are mul operands inline them all into this expression.
1821 if (Idx < Ops.size()) {
1822 bool DeletedMul = false;
1823 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1824 // If we have an mul, expand the mul operands onto the end of the operands
1826 Ops.erase(Ops.begin()+Idx);
1827 Ops.append(Mul->op_begin(), Mul->op_end());
1831 // If we deleted at least one mul, we added operands to the end of the list,
1832 // and they are not necessarily sorted. Recurse to resort and resimplify
1833 // any operands we just acquired.
1835 return getMulExpr(Ops);
1838 // If there are any add recurrences in the operands list, see if any other
1839 // added values are loop invariant. If so, we can fold them into the
1841 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1844 // Scan over all recurrences, trying to fold loop invariants into them.
1845 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1846 // Scan all of the other operands to this mul and add them to the vector if
1847 // they are loop invariant w.r.t. the recurrence.
1848 SmallVector<const SCEV *, 8> LIOps;
1849 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1850 const Loop *AddRecLoop = AddRec->getLoop();
1851 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1852 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1853 LIOps.push_back(Ops[i]);
1854 Ops.erase(Ops.begin()+i);
1858 // If we found some loop invariants, fold them into the recurrence.
1859 if (!LIOps.empty()) {
1860 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1861 SmallVector<const SCEV *, 4> NewOps;
1862 NewOps.reserve(AddRec->getNumOperands());
1863 const SCEV *Scale = getMulExpr(LIOps);
1864 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1865 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1867 // Build the new addrec. Propagate the NUW and NSW flags if both the
1868 // outer mul and the inner addrec are guaranteed to have no overflow.
1869 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop,
1870 HasNUW && AddRec->hasNoUnsignedWrap(),
1871 HasNSW && AddRec->hasNoSignedWrap());
1873 // If all of the other operands were loop invariant, we are done.
1874 if (Ops.size() == 1) return NewRec;
1876 // Otherwise, multiply the folded AddRec by the non-liv parts.
1877 for (unsigned i = 0;; ++i)
1878 if (Ops[i] == AddRec) {
1882 return getMulExpr(Ops);
1885 // Okay, if there weren't any loop invariants to be folded, check to see if
1886 // there are multiple AddRec's with the same loop induction variable being
1887 // multiplied together. If so, we can fold them.
1888 for (unsigned OtherIdx = Idx+1;
1889 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1891 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1892 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> -->
1893 // {A*C,+,F*D + G*B + B*D}<L>
1894 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1896 if (const SCEVAddRecExpr *OtherAddRec =
1897 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1898 if (OtherAddRec->getLoop() == AddRecLoop) {
1899 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1900 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1901 const SCEV *B = F->getStepRecurrence(*this);
1902 const SCEV *D = G->getStepRecurrence(*this);
1903 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1906 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1908 if (Ops.size() == 2) return NewAddRec;
1909 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
1910 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1912 return getMulExpr(Ops);
1915 // Otherwise couldn't fold anything into this recurrence. Move onto the
1919 // Okay, it looks like we really DO need an mul expr. Check to see if we
1920 // already have one, otherwise create a new one.
1921 FoldingSetNodeID ID;
1922 ID.AddInteger(scMulExpr);
1923 ID.AddInteger(Ops.size());
1924 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1925 ID.AddPointer(Ops[i]);
1928 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1930 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1931 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1932 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1934 UniqueSCEVs.InsertNode(S, IP);
1936 if (HasNUW) S->setHasNoUnsignedWrap(true);
1937 if (HasNSW) S->setHasNoSignedWrap(true);
1941 /// getUDivExpr - Get a canonical unsigned division expression, or something
1942 /// simpler if possible.
1943 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1945 assert(getEffectiveSCEVType(LHS->getType()) ==
1946 getEffectiveSCEVType(RHS->getType()) &&
1947 "SCEVUDivExpr operand types don't match!");
1949 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1950 if (RHSC->getValue()->equalsInt(1))
1951 return LHS; // X udiv 1 --> x
1952 // If the denominator is zero, the result of the udiv is undefined. Don't
1953 // try to analyze it, because the resolution chosen here may differ from
1954 // the resolution chosen in other parts of the compiler.
1955 if (!RHSC->getValue()->isZero()) {
1956 // Determine if the division can be folded into the operands of
1958 // TODO: Generalize this to non-constants by using known-bits information.
1959 const Type *Ty = LHS->getType();
1960 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1961 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1962 // For non-power-of-two values, effectively round the value up to the
1963 // nearest power of two.
1964 if (!RHSC->getValue()->getValue().isPowerOf2())
1966 const IntegerType *ExtTy =
1967 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1968 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1969 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1970 if (const SCEVConstant *Step =
1971 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1972 if (!Step->getValue()->getValue()
1973 .urem(RHSC->getValue()->getValue()) &&
1974 getZeroExtendExpr(AR, ExtTy) ==
1975 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1976 getZeroExtendExpr(Step, ExtTy),
1978 SmallVector<const SCEV *, 4> Operands;
1979 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1980 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1981 return getAddRecExpr(Operands, AR->getLoop());
1983 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1984 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1985 SmallVector<const SCEV *, 4> Operands;
1986 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1987 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1988 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1989 // Find an operand that's safely divisible.
1990 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1991 const SCEV *Op = M->getOperand(i);
1992 const SCEV *Div = getUDivExpr(Op, RHSC);
1993 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1994 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1997 return getMulExpr(Operands);
2001 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2002 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
2003 SmallVector<const SCEV *, 4> Operands;
2004 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2005 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2006 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2008 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2009 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2010 if (isa<SCEVUDivExpr>(Op) ||
2011 getMulExpr(Op, RHS) != A->getOperand(i))
2013 Operands.push_back(Op);
2015 if (Operands.size() == A->getNumOperands())
2016 return getAddExpr(Operands);
2020 // Fold if both operands are constant.
2021 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2022 Constant *LHSCV = LHSC->getValue();
2023 Constant *RHSCV = RHSC->getValue();
2024 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2030 FoldingSetNodeID ID;
2031 ID.AddInteger(scUDivExpr);
2035 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2036 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2038 UniqueSCEVs.InsertNode(S, IP);
2043 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2044 /// Simplify the expression as much as possible.
2045 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
2046 const SCEV *Step, const Loop *L,
2047 bool HasNUW, bool HasNSW) {
2048 SmallVector<const SCEV *, 4> Operands;
2049 Operands.push_back(Start);
2050 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2051 if (StepChrec->getLoop() == L) {
2052 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2053 return getAddRecExpr(Operands, L);
2056 Operands.push_back(Step);
2057 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
2060 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2061 /// Simplify the expression as much as possible.
2063 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2065 bool HasNUW, bool HasNSW) {
2066 if (Operands.size() == 1) return Operands[0];
2068 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2069 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2070 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2071 "SCEVAddRecExpr operand types don't match!");
2074 if (Operands.back()->isZero()) {
2075 Operands.pop_back();
2076 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
2079 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2080 // use that information to infer NUW and NSW flags. However, computing a
2081 // BE count requires calling getAddRecExpr, so we may not yet have a
2082 // meaningful BE count at this point (and if we don't, we'd be stuck
2083 // with a SCEVCouldNotCompute as the cached BE count).
2085 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
2086 if (!HasNUW && HasNSW) {
2088 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2089 E = Operands.end(); I != E; ++I)
2090 if (!isKnownNonNegative(*I)) {
2094 if (All) HasNUW = true;
2097 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2098 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2099 const Loop *NestedLoop = NestedAR->getLoop();
2100 if (L->contains(NestedLoop) ?
2101 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2102 (!NestedLoop->contains(L) &&
2103 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2104 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2105 NestedAR->op_end());
2106 Operands[0] = NestedAR->getStart();
2107 // AddRecs require their operands be loop-invariant with respect to their
2108 // loops. Don't perform this transformation if it would break this
2110 bool AllInvariant = true;
2111 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2112 if (!Operands[i]->isLoopInvariant(L)) {
2113 AllInvariant = false;
2117 NestedOperands[0] = getAddRecExpr(Operands, L);
2118 AllInvariant = true;
2119 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2120 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2121 AllInvariant = false;
2125 // Ok, both add recurrences are valid after the transformation.
2126 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2128 // Reset Operands to its original state.
2129 Operands[0] = NestedAR;
2133 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2134 // already have one, otherwise create a new one.
2135 FoldingSetNodeID ID;
2136 ID.AddInteger(scAddRecExpr);
2137 ID.AddInteger(Operands.size());
2138 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2139 ID.AddPointer(Operands[i]);
2143 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2145 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2146 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2147 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2148 O, Operands.size(), L);
2149 UniqueSCEVs.InsertNode(S, IP);
2151 if (HasNUW) S->setHasNoUnsignedWrap(true);
2152 if (HasNSW) S->setHasNoSignedWrap(true);
2156 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2158 SmallVector<const SCEV *, 2> Ops;
2161 return getSMaxExpr(Ops);
2165 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2166 assert(!Ops.empty() && "Cannot get empty smax!");
2167 if (Ops.size() == 1) return Ops[0];
2169 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2170 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2171 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2172 "SCEVSMaxExpr operand types don't match!");
2175 // Sort by complexity, this groups all similar expression types together.
2176 GroupByComplexity(Ops, LI);
2178 // If there are any constants, fold them together.
2180 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2182 assert(Idx < Ops.size());
2183 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2184 // We found two constants, fold them together!
2185 ConstantInt *Fold = ConstantInt::get(getContext(),
2186 APIntOps::smax(LHSC->getValue()->getValue(),
2187 RHSC->getValue()->getValue()));
2188 Ops[0] = getConstant(Fold);
2189 Ops.erase(Ops.begin()+1); // Erase the folded element
2190 if (Ops.size() == 1) return Ops[0];
2191 LHSC = cast<SCEVConstant>(Ops[0]);
2194 // If we are left with a constant minimum-int, strip it off.
2195 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2196 Ops.erase(Ops.begin());
2198 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2199 // If we have an smax with a constant maximum-int, it will always be
2204 if (Ops.size() == 1) return Ops[0];
2207 // Find the first SMax
2208 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2211 // Check to see if one of the operands is an SMax. If so, expand its operands
2212 // onto our operand list, and recurse to simplify.
2213 if (Idx < Ops.size()) {
2214 bool DeletedSMax = false;
2215 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2216 Ops.erase(Ops.begin()+Idx);
2217 Ops.append(SMax->op_begin(), SMax->op_end());
2222 return getSMaxExpr(Ops);
2225 // Okay, check to see if the same value occurs in the operand list twice. If
2226 // so, delete one. Since we sorted the list, these values are required to
2228 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2229 // X smax Y smax Y --> X smax Y
2230 // X smax Y --> X, if X is always greater than Y
2231 if (Ops[i] == Ops[i+1] ||
2232 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2233 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2235 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2236 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2240 if (Ops.size() == 1) return Ops[0];
2242 assert(!Ops.empty() && "Reduced smax down to nothing!");
2244 // Okay, it looks like we really DO need an smax expr. Check to see if we
2245 // already have one, otherwise create a new one.
2246 FoldingSetNodeID ID;
2247 ID.AddInteger(scSMaxExpr);
2248 ID.AddInteger(Ops.size());
2249 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2250 ID.AddPointer(Ops[i]);
2252 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2253 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2254 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2255 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2257 UniqueSCEVs.InsertNode(S, IP);
2261 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2263 SmallVector<const SCEV *, 2> Ops;
2266 return getUMaxExpr(Ops);
2270 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2271 assert(!Ops.empty() && "Cannot get empty umax!");
2272 if (Ops.size() == 1) return Ops[0];
2274 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2275 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2276 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2277 "SCEVUMaxExpr operand types don't match!");
2280 // Sort by complexity, this groups all similar expression types together.
2281 GroupByComplexity(Ops, LI);
2283 // If there are any constants, fold them together.
2285 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2287 assert(Idx < Ops.size());
2288 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2289 // We found two constants, fold them together!
2290 ConstantInt *Fold = ConstantInt::get(getContext(),
2291 APIntOps::umax(LHSC->getValue()->getValue(),
2292 RHSC->getValue()->getValue()));
2293 Ops[0] = getConstant(Fold);
2294 Ops.erase(Ops.begin()+1); // Erase the folded element
2295 if (Ops.size() == 1) return Ops[0];
2296 LHSC = cast<SCEVConstant>(Ops[0]);
2299 // If we are left with a constant minimum-int, strip it off.
2300 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2301 Ops.erase(Ops.begin());
2303 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2304 // If we have an umax with a constant maximum-int, it will always be
2309 if (Ops.size() == 1) return Ops[0];
2312 // Find the first UMax
2313 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2316 // Check to see if one of the operands is a UMax. If so, expand its operands
2317 // onto our operand list, and recurse to simplify.
2318 if (Idx < Ops.size()) {
2319 bool DeletedUMax = false;
2320 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2321 Ops.erase(Ops.begin()+Idx);
2322 Ops.append(UMax->op_begin(), UMax->op_end());
2327 return getUMaxExpr(Ops);
2330 // Okay, check to see if the same value occurs in the operand list twice. If
2331 // so, delete one. Since we sorted the list, these values are required to
2333 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2334 // X umax Y umax Y --> X umax Y
2335 // X umax Y --> X, if X is always greater than Y
2336 if (Ops[i] == Ops[i+1] ||
2337 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2338 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2340 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2341 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2345 if (Ops.size() == 1) return Ops[0];
2347 assert(!Ops.empty() && "Reduced umax down to nothing!");
2349 // Okay, it looks like we really DO need a umax expr. Check to see if we
2350 // already have one, otherwise create a new one.
2351 FoldingSetNodeID ID;
2352 ID.AddInteger(scUMaxExpr);
2353 ID.AddInteger(Ops.size());
2354 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2355 ID.AddPointer(Ops[i]);
2357 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2358 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2359 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2360 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2362 UniqueSCEVs.InsertNode(S, IP);
2366 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2368 // ~smax(~x, ~y) == smin(x, y).
2369 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2372 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2374 // ~umax(~x, ~y) == umin(x, y)
2375 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2378 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2379 // If we have TargetData, we can bypass creating a target-independent
2380 // constant expression and then folding it back into a ConstantInt.
2381 // This is just a compile-time optimization.
2383 return getConstant(TD->getIntPtrType(getContext()),
2384 TD->getTypeAllocSize(AllocTy));
2386 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2387 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2388 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2390 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2391 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2394 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2395 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2396 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2397 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2399 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2400 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2403 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2405 // If we have TargetData, we can bypass creating a target-independent
2406 // constant expression and then folding it back into a ConstantInt.
2407 // This is just a compile-time optimization.
2409 return getConstant(TD->getIntPtrType(getContext()),
2410 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2412 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2413 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2414 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2416 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2417 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2420 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2421 Constant *FieldNo) {
2422 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2423 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2424 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2426 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2427 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2430 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2431 // Don't attempt to do anything other than create a SCEVUnknown object
2432 // here. createSCEV only calls getUnknown after checking for all other
2433 // interesting possibilities, and any other code that calls getUnknown
2434 // is doing so in order to hide a value from SCEV canonicalization.
2436 FoldingSetNodeID ID;
2437 ID.AddInteger(scUnknown);
2440 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2441 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2442 "Stale SCEVUnknown in uniquing map!");
2445 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2447 FirstUnknown = cast<SCEVUnknown>(S);
2448 UniqueSCEVs.InsertNode(S, IP);
2452 //===----------------------------------------------------------------------===//
2453 // Basic SCEV Analysis and PHI Idiom Recognition Code
2456 /// isSCEVable - Test if values of the given type are analyzable within
2457 /// the SCEV framework. This primarily includes integer types, and it
2458 /// can optionally include pointer types if the ScalarEvolution class
2459 /// has access to target-specific information.
2460 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2461 // Integers and pointers are always SCEVable.
2462 return Ty->isIntegerTy() || Ty->isPointerTy();
2465 /// getTypeSizeInBits - Return the size in bits of the specified type,
2466 /// for which isSCEVable must return true.
2467 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2468 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2470 // If we have a TargetData, use it!
2472 return TD->getTypeSizeInBits(Ty);
2474 // Integer types have fixed sizes.
2475 if (Ty->isIntegerTy())
2476 return Ty->getPrimitiveSizeInBits();
2478 // The only other support type is pointer. Without TargetData, conservatively
2479 // assume pointers are 64-bit.
2480 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2484 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2485 /// the given type and which represents how SCEV will treat the given
2486 /// type, for which isSCEVable must return true. For pointer types,
2487 /// this is the pointer-sized integer type.
2488 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2489 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2491 if (Ty->isIntegerTy())
2494 // The only other support type is pointer.
2495 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2496 if (TD) return TD->getIntPtrType(getContext());
2498 // Without TargetData, conservatively assume pointers are 64-bit.
2499 return Type::getInt64Ty(getContext());
2502 const SCEV *ScalarEvolution::getCouldNotCompute() {
2503 return &CouldNotCompute;
2506 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2507 /// expression and create a new one.
2508 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2509 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2511 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2512 if (I != ValueExprMap.end()) return I->second;
2513 const SCEV *S = createSCEV(V);
2515 // The process of creating a SCEV for V may have caused other SCEVs
2516 // to have been created, so it's necessary to insert the new entry
2517 // from scratch, rather than trying to remember the insert position
2519 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2523 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2525 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2526 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2528 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2530 const Type *Ty = V->getType();
2531 Ty = getEffectiveSCEVType(Ty);
2532 return getMulExpr(V,
2533 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2536 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2537 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2538 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2540 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2542 const Type *Ty = V->getType();
2543 Ty = getEffectiveSCEVType(Ty);
2544 const SCEV *AllOnes =
2545 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2546 return getMinusSCEV(AllOnes, V);
2549 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2551 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2553 // Fast path: X - X --> 0.
2555 return getConstant(LHS->getType(), 0);
2558 return getAddExpr(LHS, getNegativeSCEV(RHS));
2561 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2562 /// input value to the specified type. If the type must be extended, it is zero
2565 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2567 const Type *SrcTy = V->getType();
2568 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2569 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2570 "Cannot truncate or zero extend with non-integer arguments!");
2571 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2572 return V; // No conversion
2573 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2574 return getTruncateExpr(V, Ty);
2575 return getZeroExtendExpr(V, Ty);
2578 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2579 /// input value to the specified type. If the type must be extended, it is sign
2582 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2584 const Type *SrcTy = V->getType();
2585 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2586 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2587 "Cannot truncate or zero extend with non-integer arguments!");
2588 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2589 return V; // No conversion
2590 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2591 return getTruncateExpr(V, Ty);
2592 return getSignExtendExpr(V, Ty);
2595 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2596 /// input value to the specified type. If the type must be extended, it is zero
2597 /// extended. The conversion must not be narrowing.
2599 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2600 const Type *SrcTy = V->getType();
2601 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2602 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2603 "Cannot noop or zero extend with non-integer arguments!");
2604 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2605 "getNoopOrZeroExtend cannot truncate!");
2606 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2607 return V; // No conversion
2608 return getZeroExtendExpr(V, Ty);
2611 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2612 /// input value to the specified type. If the type must be extended, it is sign
2613 /// extended. The conversion must not be narrowing.
2615 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2616 const Type *SrcTy = V->getType();
2617 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2618 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2619 "Cannot noop or sign extend with non-integer arguments!");
2620 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2621 "getNoopOrSignExtend cannot truncate!");
2622 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2623 return V; // No conversion
2624 return getSignExtendExpr(V, Ty);
2627 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2628 /// the input value to the specified type. If the type must be extended,
2629 /// it is extended with unspecified bits. The conversion must not be
2632 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2633 const Type *SrcTy = V->getType();
2634 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2635 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2636 "Cannot noop or any extend with non-integer arguments!");
2637 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2638 "getNoopOrAnyExtend cannot truncate!");
2639 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2640 return V; // No conversion
2641 return getAnyExtendExpr(V, Ty);
2644 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2645 /// input value to the specified type. The conversion must not be widening.
2647 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2648 const Type *SrcTy = V->getType();
2649 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2650 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2651 "Cannot truncate or noop with non-integer arguments!");
2652 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2653 "getTruncateOrNoop cannot extend!");
2654 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2655 return V; // No conversion
2656 return getTruncateExpr(V, Ty);
2659 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2660 /// the types using zero-extension, and then perform a umax operation
2662 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2664 const SCEV *PromotedLHS = LHS;
2665 const SCEV *PromotedRHS = RHS;
2667 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2668 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2670 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2672 return getUMaxExpr(PromotedLHS, PromotedRHS);
2675 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2676 /// the types using zero-extension, and then perform a umin operation
2678 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2680 const SCEV *PromotedLHS = LHS;
2681 const SCEV *PromotedRHS = RHS;
2683 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2684 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2686 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2688 return getUMinExpr(PromotedLHS, PromotedRHS);
2691 /// PushDefUseChildren - Push users of the given Instruction
2692 /// onto the given Worklist.
2694 PushDefUseChildren(Instruction *I,
2695 SmallVectorImpl<Instruction *> &Worklist) {
2696 // Push the def-use children onto the Worklist stack.
2697 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2699 Worklist.push_back(cast<Instruction>(*UI));
2702 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2703 /// instructions that depend on the given instruction and removes them from
2704 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2707 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2708 SmallVector<Instruction *, 16> Worklist;
2709 PushDefUseChildren(PN, Worklist);
2711 SmallPtrSet<Instruction *, 8> Visited;
2713 while (!Worklist.empty()) {
2714 Instruction *I = Worklist.pop_back_val();
2715 if (!Visited.insert(I)) continue;
2717 ValueExprMapType::iterator It =
2718 ValueExprMap.find(static_cast<Value *>(I));
2719 if (It != ValueExprMap.end()) {
2720 // Short-circuit the def-use traversal if the symbolic name
2721 // ceases to appear in expressions.
2722 if (It->second != SymName && !It->second->hasOperand(SymName))
2725 // SCEVUnknown for a PHI either means that it has an unrecognized
2726 // structure, it's a PHI that's in the progress of being computed
2727 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2728 // additional loop trip count information isn't going to change anything.
2729 // In the second case, createNodeForPHI will perform the necessary
2730 // updates on its own when it gets to that point. In the third, we do
2731 // want to forget the SCEVUnknown.
2732 if (!isa<PHINode>(I) ||
2733 !isa<SCEVUnknown>(It->second) ||
2734 (I != PN && It->second == SymName)) {
2735 ValuesAtScopes.erase(It->second);
2736 ValueExprMap.erase(It);
2740 PushDefUseChildren(I, Worklist);
2744 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2745 /// a loop header, making it a potential recurrence, or it doesn't.
2747 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2748 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2749 if (L->getHeader() == PN->getParent()) {
2750 // The loop may have multiple entrances or multiple exits; we can analyze
2751 // this phi as an addrec if it has a unique entry value and a unique
2753 Value *BEValueV = 0, *StartValueV = 0;
2754 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2755 Value *V = PN->getIncomingValue(i);
2756 if (L->contains(PN->getIncomingBlock(i))) {
2759 } else if (BEValueV != V) {
2763 } else if (!StartValueV) {
2765 } else if (StartValueV != V) {
2770 if (BEValueV && StartValueV) {
2771 // While we are analyzing this PHI node, handle its value symbolically.
2772 const SCEV *SymbolicName = getUnknown(PN);
2773 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2774 "PHI node already processed?");
2775 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2777 // Using this symbolic name for the PHI, analyze the value coming around
2779 const SCEV *BEValue = getSCEV(BEValueV);
2781 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2782 // has a special value for the first iteration of the loop.
2784 // If the value coming around the backedge is an add with the symbolic
2785 // value we just inserted, then we found a simple induction variable!
2786 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2787 // If there is a single occurrence of the symbolic value, replace it
2788 // with a recurrence.
2789 unsigned FoundIndex = Add->getNumOperands();
2790 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2791 if (Add->getOperand(i) == SymbolicName)
2792 if (FoundIndex == e) {
2797 if (FoundIndex != Add->getNumOperands()) {
2798 // Create an add with everything but the specified operand.
2799 SmallVector<const SCEV *, 8> Ops;
2800 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2801 if (i != FoundIndex)
2802 Ops.push_back(Add->getOperand(i));
2803 const SCEV *Accum = getAddExpr(Ops);
2805 // This is not a valid addrec if the step amount is varying each
2806 // loop iteration, but is not itself an addrec in this loop.
2807 if (Accum->isLoopInvariant(L) ||
2808 (isa<SCEVAddRecExpr>(Accum) &&
2809 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2810 bool HasNUW = false;
2811 bool HasNSW = false;
2813 // If the increment doesn't overflow, then neither the addrec nor
2814 // the post-increment will overflow.
2815 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2816 if (OBO->hasNoUnsignedWrap())
2818 if (OBO->hasNoSignedWrap())
2822 const SCEV *StartVal = getSCEV(StartValueV);
2823 const SCEV *PHISCEV =
2824 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2826 // Since the no-wrap flags are on the increment, they apply to the
2827 // post-incremented value as well.
2828 if (Accum->isLoopInvariant(L))
2829 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2830 Accum, L, HasNUW, HasNSW);
2832 // Okay, for the entire analysis of this edge we assumed the PHI
2833 // to be symbolic. We now need to go back and purge all of the
2834 // entries for the scalars that use the symbolic expression.
2835 ForgetSymbolicName(PN, SymbolicName);
2836 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2840 } else if (const SCEVAddRecExpr *AddRec =
2841 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2842 // Otherwise, this could be a loop like this:
2843 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2844 // In this case, j = {1,+,1} and BEValue is j.
2845 // Because the other in-value of i (0) fits the evolution of BEValue
2846 // i really is an addrec evolution.
2847 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2848 const SCEV *StartVal = getSCEV(StartValueV);
2850 // If StartVal = j.start - j.stride, we can use StartVal as the
2851 // initial step of the addrec evolution.
2852 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2853 AddRec->getOperand(1))) {
2854 const SCEV *PHISCEV =
2855 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2857 // Okay, for the entire analysis of this edge we assumed the PHI
2858 // to be symbolic. We now need to go back and purge all of the
2859 // entries for the scalars that use the symbolic expression.
2860 ForgetSymbolicName(PN, SymbolicName);
2861 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2869 // If the PHI has a single incoming value, follow that value, unless the
2870 // PHI's incoming blocks are in a different loop, in which case doing so
2871 // risks breaking LCSSA form. Instcombine would normally zap these, but
2872 // it doesn't have DominatorTree information, so it may miss cases.
2873 if (Value *V = PN->hasConstantValue(DT)) {
2874 bool AllSameLoop = true;
2875 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2876 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2877 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2878 AllSameLoop = false;
2885 // If it's not a loop phi, we can't handle it yet.
2886 return getUnknown(PN);
2889 /// createNodeForGEP - Expand GEP instructions into add and multiply
2890 /// operations. This allows them to be analyzed by regular SCEV code.
2892 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2894 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2895 // Add expression, because the Instruction may be guarded by control flow
2896 // and the no-overflow bits may not be valid for the expression in any
2899 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2900 Value *Base = GEP->getOperand(0);
2901 // Don't attempt to analyze GEPs over unsized objects.
2902 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2903 return getUnknown(GEP);
2904 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2905 gep_type_iterator GTI = gep_type_begin(GEP);
2906 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2910 // Compute the (potentially symbolic) offset in bytes for this index.
2911 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2912 // For a struct, add the member offset.
2913 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2914 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2916 // Add the field offset to the running total offset.
2917 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2919 // For an array, add the element offset, explicitly scaled.
2920 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2921 const SCEV *IndexS = getSCEV(Index);
2922 // Getelementptr indices are signed.
2923 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2925 // Multiply the index by the element size to compute the element offset.
2926 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2928 // Add the element offset to the running total offset.
2929 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2933 // Get the SCEV for the GEP base.
2934 const SCEV *BaseS = getSCEV(Base);
2936 // Add the total offset from all the GEP indices to the base.
2937 return getAddExpr(BaseS, TotalOffset);
2940 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2941 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2942 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2943 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2945 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2946 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2947 return C->getValue()->getValue().countTrailingZeros();
2949 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2950 return std::min(GetMinTrailingZeros(T->getOperand()),
2951 (uint32_t)getTypeSizeInBits(T->getType()));
2953 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2954 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2955 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2956 getTypeSizeInBits(E->getType()) : OpRes;
2959 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2960 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2961 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2962 getTypeSizeInBits(E->getType()) : OpRes;
2965 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2966 // The result is the min of all operands results.
2967 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2968 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2969 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2973 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2974 // The result is the sum of all operands results.
2975 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2976 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2977 for (unsigned i = 1, e = M->getNumOperands();
2978 SumOpRes != BitWidth && i != e; ++i)
2979 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2984 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2985 // The result is the min of all operands results.
2986 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2987 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2988 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2992 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(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 SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3001 // The result is the min of all operands results.
3002 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3003 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3004 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3008 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3009 // For a SCEVUnknown, ask ValueTracking.
3010 unsigned BitWidth = getTypeSizeInBits(U->getType());
3011 APInt Mask = APInt::getAllOnesValue(BitWidth);
3012 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3013 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3014 return Zeros.countTrailingOnes();
3021 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3024 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3026 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3027 return ConstantRange(C->getValue()->getValue());
3029 unsigned BitWidth = getTypeSizeInBits(S->getType());
3030 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3032 // If the value has known zeros, the maximum unsigned value will have those
3033 // known zeros as well.
3034 uint32_t TZ = GetMinTrailingZeros(S);
3036 ConservativeResult =
3037 ConstantRange(APInt::getMinValue(BitWidth),
3038 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3040 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3041 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3042 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3043 X = X.add(getUnsignedRange(Add->getOperand(i)));
3044 return ConservativeResult.intersectWith(X);
3047 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3048 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3049 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3050 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3051 return ConservativeResult.intersectWith(X);
3054 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3055 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3056 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3057 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3058 return ConservativeResult.intersectWith(X);
3061 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3062 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3063 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3064 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3065 return ConservativeResult.intersectWith(X);
3068 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3069 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3070 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3071 return ConservativeResult.intersectWith(X.udiv(Y));
3074 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3075 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3076 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3079 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3080 ConstantRange X = getUnsignedRange(SExt->getOperand());
3081 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3084 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3085 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3086 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3089 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3090 // If there's no unsigned wrap, the value will never be less than its
3092 if (AddRec->hasNoUnsignedWrap())
3093 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3094 if (!C->getValue()->isZero())
3095 ConservativeResult =
3096 ConservativeResult.intersectWith(
3097 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3099 // TODO: non-affine addrec
3100 if (AddRec->isAffine()) {
3101 const Type *Ty = AddRec->getType();
3102 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3103 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3104 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3105 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3107 const SCEV *Start = AddRec->getStart();
3108 const SCEV *Step = AddRec->getStepRecurrence(*this);
3110 ConstantRange StartRange = getUnsignedRange(Start);
3111 ConstantRange StepRange = getSignedRange(Step);
3112 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3113 ConstantRange EndRange =
3114 StartRange.add(MaxBECountRange.multiply(StepRange));
3116 // Check for overflow. This must be done with ConstantRange arithmetic
3117 // because we could be called from within the ScalarEvolution overflow
3119 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3120 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3121 ConstantRange ExtMaxBECountRange =
3122 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3123 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3124 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3126 return ConservativeResult;
3128 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3129 EndRange.getUnsignedMin());
3130 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3131 EndRange.getUnsignedMax());
3132 if (Min.isMinValue() && Max.isMaxValue())
3133 return ConservativeResult;
3134 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3138 return ConservativeResult;
3141 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3142 // For a SCEVUnknown, ask ValueTracking.
3143 APInt Mask = APInt::getAllOnesValue(BitWidth);
3144 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3145 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3146 if (Ones == ~Zeros + 1)
3147 return ConservativeResult;
3148 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3151 return ConservativeResult;
3154 /// getSignedRange - Determine the signed range for a particular SCEV.
3157 ScalarEvolution::getSignedRange(const SCEV *S) {
3159 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3160 return ConstantRange(C->getValue()->getValue());
3162 unsigned BitWidth = getTypeSizeInBits(S->getType());
3163 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3165 // If the value has known zeros, the maximum signed value will have those
3166 // known zeros as well.
3167 uint32_t TZ = GetMinTrailingZeros(S);
3169 ConservativeResult =
3170 ConstantRange(APInt::getSignedMinValue(BitWidth),
3171 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3173 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3174 ConstantRange X = getSignedRange(Add->getOperand(0));
3175 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3176 X = X.add(getSignedRange(Add->getOperand(i)));
3177 return ConservativeResult.intersectWith(X);
3180 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3181 ConstantRange X = getSignedRange(Mul->getOperand(0));
3182 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3183 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3184 return ConservativeResult.intersectWith(X);
3187 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3188 ConstantRange X = getSignedRange(SMax->getOperand(0));
3189 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3190 X = X.smax(getSignedRange(SMax->getOperand(i)));
3191 return ConservativeResult.intersectWith(X);
3194 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3195 ConstantRange X = getSignedRange(UMax->getOperand(0));
3196 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3197 X = X.umax(getSignedRange(UMax->getOperand(i)));
3198 return ConservativeResult.intersectWith(X);
3201 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3202 ConstantRange X = getSignedRange(UDiv->getLHS());
3203 ConstantRange Y = getSignedRange(UDiv->getRHS());
3204 return ConservativeResult.intersectWith(X.udiv(Y));
3207 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3208 ConstantRange X = getSignedRange(ZExt->getOperand());
3209 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3212 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3213 ConstantRange X = getSignedRange(SExt->getOperand());
3214 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3217 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3218 ConstantRange X = getSignedRange(Trunc->getOperand());
3219 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3222 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3223 // If there's no signed wrap, and all the operands have the same sign or
3224 // zero, the value won't ever change sign.
3225 if (AddRec->hasNoSignedWrap()) {
3226 bool AllNonNeg = true;
3227 bool AllNonPos = true;
3228 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3229 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3230 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3233 ConservativeResult = ConservativeResult.intersectWith(
3234 ConstantRange(APInt(BitWidth, 0),
3235 APInt::getSignedMinValue(BitWidth)));
3237 ConservativeResult = ConservativeResult.intersectWith(
3238 ConstantRange(APInt::getSignedMinValue(BitWidth),
3239 APInt(BitWidth, 1)));
3242 // TODO: non-affine addrec
3243 if (AddRec->isAffine()) {
3244 const Type *Ty = AddRec->getType();
3245 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3246 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3247 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3248 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3250 const SCEV *Start = AddRec->getStart();
3251 const SCEV *Step = AddRec->getStepRecurrence(*this);
3253 ConstantRange StartRange = getSignedRange(Start);
3254 ConstantRange StepRange = getSignedRange(Step);
3255 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3256 ConstantRange EndRange =
3257 StartRange.add(MaxBECountRange.multiply(StepRange));
3259 // Check for overflow. This must be done with ConstantRange arithmetic
3260 // because we could be called from within the ScalarEvolution overflow
3262 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3263 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3264 ConstantRange ExtMaxBECountRange =
3265 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3266 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3267 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3269 return ConservativeResult;
3271 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3272 EndRange.getSignedMin());
3273 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3274 EndRange.getSignedMax());
3275 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3276 return ConservativeResult;
3277 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3281 return ConservativeResult;
3284 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3285 // For a SCEVUnknown, ask ValueTracking.
3286 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3287 return ConservativeResult;
3288 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3290 return ConservativeResult;
3291 return ConservativeResult.intersectWith(
3292 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3293 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3296 return ConservativeResult;
3299 /// createSCEV - We know that there is no SCEV for the specified value.
3300 /// Analyze the expression.
3302 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3303 if (!isSCEVable(V->getType()))
3304 return getUnknown(V);
3306 unsigned Opcode = Instruction::UserOp1;
3307 if (Instruction *I = dyn_cast<Instruction>(V)) {
3308 Opcode = I->getOpcode();
3310 // Don't attempt to analyze instructions in blocks that aren't
3311 // reachable. Such instructions don't matter, and they aren't required
3312 // to obey basic rules for definitions dominating uses which this
3313 // analysis depends on.
3314 if (!DT->isReachableFromEntry(I->getParent()))
3315 return getUnknown(V);
3316 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3317 Opcode = CE->getOpcode();
3318 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3319 return getConstant(CI);
3320 else if (isa<ConstantPointerNull>(V))
3321 return getConstant(V->getType(), 0);
3322 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3323 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3325 return getUnknown(V);
3327 Operator *U = cast<Operator>(V);
3329 case Instruction::Add: {
3330 // The simple thing to do would be to just call getSCEV on both operands
3331 // and call getAddExpr with the result. However if we're looking at a
3332 // bunch of things all added together, this can be quite inefficient,
3333 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3334 // Instead, gather up all the operands and make a single getAddExpr call.
3335 // LLVM IR canonical form means we need only traverse the left operands.
3336 SmallVector<const SCEV *, 4> AddOps;
3337 AddOps.push_back(getSCEV(U->getOperand(1)));
3338 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3339 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3340 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3342 U = cast<Operator>(Op);
3343 const SCEV *Op1 = getSCEV(U->getOperand(1));
3344 if (Opcode == Instruction::Sub)
3345 AddOps.push_back(getNegativeSCEV(Op1));
3347 AddOps.push_back(Op1);
3349 AddOps.push_back(getSCEV(U->getOperand(0)));
3350 return getAddExpr(AddOps);
3352 case Instruction::Mul: {
3353 // See the Add code above.
3354 SmallVector<const SCEV *, 4> MulOps;
3355 MulOps.push_back(getSCEV(U->getOperand(1)));
3356 for (Value *Op = U->getOperand(0);
3357 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3358 Op = U->getOperand(0)) {
3359 U = cast<Operator>(Op);
3360 MulOps.push_back(getSCEV(U->getOperand(1)));
3362 MulOps.push_back(getSCEV(U->getOperand(0)));
3363 return getMulExpr(MulOps);
3365 case Instruction::UDiv:
3366 return getUDivExpr(getSCEV(U->getOperand(0)),
3367 getSCEV(U->getOperand(1)));
3368 case Instruction::Sub:
3369 return getMinusSCEV(getSCEV(U->getOperand(0)),
3370 getSCEV(U->getOperand(1)));
3371 case Instruction::And:
3372 // For an expression like x&255 that merely masks off the high bits,
3373 // use zext(trunc(x)) as the SCEV expression.
3374 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3375 if (CI->isNullValue())
3376 return getSCEV(U->getOperand(1));
3377 if (CI->isAllOnesValue())
3378 return getSCEV(U->getOperand(0));
3379 const APInt &A = CI->getValue();
3381 // Instcombine's ShrinkDemandedConstant may strip bits out of
3382 // constants, obscuring what would otherwise be a low-bits mask.
3383 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3384 // knew about to reconstruct a low-bits mask value.
3385 unsigned LZ = A.countLeadingZeros();
3386 unsigned BitWidth = A.getBitWidth();
3387 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3388 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3389 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3391 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3393 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3395 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3396 IntegerType::get(getContext(), BitWidth - LZ)),
3401 case Instruction::Or:
3402 // If the RHS of the Or is a constant, we may have something like:
3403 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3404 // optimizations will transparently handle this case.
3406 // In order for this transformation to be safe, the LHS must be of the
3407 // form X*(2^n) and the Or constant must be less than 2^n.
3408 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3409 const SCEV *LHS = getSCEV(U->getOperand(0));
3410 const APInt &CIVal = CI->getValue();
3411 if (GetMinTrailingZeros(LHS) >=
3412 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3413 // Build a plain add SCEV.
3414 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3415 // If the LHS of the add was an addrec and it has no-wrap flags,
3416 // transfer the no-wrap flags, since an or won't introduce a wrap.
3417 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3418 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3419 if (OldAR->hasNoUnsignedWrap())
3420 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3421 if (OldAR->hasNoSignedWrap())
3422 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3428 case Instruction::Xor:
3429 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3430 // If the RHS of the xor is a signbit, then this is just an add.
3431 // Instcombine turns add of signbit into xor as a strength reduction step.
3432 if (CI->getValue().isSignBit())
3433 return getAddExpr(getSCEV(U->getOperand(0)),
3434 getSCEV(U->getOperand(1)));
3436 // If the RHS of xor is -1, then this is a not operation.
3437 if (CI->isAllOnesValue())
3438 return getNotSCEV(getSCEV(U->getOperand(0)));
3440 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3441 // This is a variant of the check for xor with -1, and it handles
3442 // the case where instcombine has trimmed non-demanded bits out
3443 // of an xor with -1.
3444 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3445 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3446 if (BO->getOpcode() == Instruction::And &&
3447 LCI->getValue() == CI->getValue())
3448 if (const SCEVZeroExtendExpr *Z =
3449 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3450 const Type *UTy = U->getType();
3451 const SCEV *Z0 = Z->getOperand();
3452 const Type *Z0Ty = Z0->getType();
3453 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3455 // If C is a low-bits mask, the zero extend is serving to
3456 // mask off the high bits. Complement the operand and
3457 // re-apply the zext.
3458 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3459 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3461 // If C is a single bit, it may be in the sign-bit position
3462 // before the zero-extend. In this case, represent the xor
3463 // using an add, which is equivalent, and re-apply the zext.
3464 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3465 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3467 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3473 case Instruction::Shl:
3474 // Turn shift left of a constant amount into a multiply.
3475 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3476 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3478 // If the shift count is not less than the bitwidth, the result of
3479 // the shift is undefined. Don't try to analyze it, because the
3480 // resolution chosen here may differ from the resolution chosen in
3481 // other parts of the compiler.
3482 if (SA->getValue().uge(BitWidth))
3485 Constant *X = ConstantInt::get(getContext(),
3486 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3487 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3491 case Instruction::LShr:
3492 // Turn logical shift right of a constant into a unsigned divide.
3493 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3494 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3496 // If the shift count is not less than the bitwidth, the result of
3497 // the shift is undefined. Don't try to analyze it, because the
3498 // resolution chosen here may differ from the resolution chosen in
3499 // other parts of the compiler.
3500 if (SA->getValue().uge(BitWidth))
3503 Constant *X = ConstantInt::get(getContext(),
3504 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3505 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3509 case Instruction::AShr:
3510 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3511 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3512 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3513 if (L->getOpcode() == Instruction::Shl &&
3514 L->getOperand(1) == U->getOperand(1)) {
3515 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3517 // If the shift count is not less than the bitwidth, the result of
3518 // the shift is undefined. Don't try to analyze it, because the
3519 // resolution chosen here may differ from the resolution chosen in
3520 // other parts of the compiler.
3521 if (CI->getValue().uge(BitWidth))
3524 uint64_t Amt = BitWidth - CI->getZExtValue();
3525 if (Amt == BitWidth)
3526 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3528 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3529 IntegerType::get(getContext(),
3535 case Instruction::Trunc:
3536 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3538 case Instruction::ZExt:
3539 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3541 case Instruction::SExt:
3542 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3544 case Instruction::BitCast:
3545 // BitCasts are no-op casts so we just eliminate the cast.
3546 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3547 return getSCEV(U->getOperand(0));
3550 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3551 // lead to pointer expressions which cannot safely be expanded to GEPs,
3552 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3553 // simplifying integer expressions.
3555 case Instruction::GetElementPtr:
3556 return createNodeForGEP(cast<GEPOperator>(U));
3558 case Instruction::PHI:
3559 return createNodeForPHI(cast<PHINode>(U));
3561 case Instruction::Select:
3562 // This could be a smax or umax that was lowered earlier.
3563 // Try to recover it.
3564 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3565 Value *LHS = ICI->getOperand(0);
3566 Value *RHS = ICI->getOperand(1);
3567 switch (ICI->getPredicate()) {
3568 case ICmpInst::ICMP_SLT:
3569 case ICmpInst::ICMP_SLE:
3570 std::swap(LHS, RHS);
3572 case ICmpInst::ICMP_SGT:
3573 case ICmpInst::ICMP_SGE:
3574 // a >s b ? a+x : b+x -> smax(a, b)+x
3575 // a >s b ? b+x : a+x -> smin(a, b)+x
3576 if (LHS->getType() == U->getType()) {
3577 const SCEV *LS = getSCEV(LHS);
3578 const SCEV *RS = getSCEV(RHS);
3579 const SCEV *LA = getSCEV(U->getOperand(1));
3580 const SCEV *RA = getSCEV(U->getOperand(2));
3581 const SCEV *LDiff = getMinusSCEV(LA, LS);
3582 const SCEV *RDiff = getMinusSCEV(RA, RS);
3584 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3585 LDiff = getMinusSCEV(LA, RS);
3586 RDiff = getMinusSCEV(RA, LS);
3588 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3591 case ICmpInst::ICMP_ULT:
3592 case ICmpInst::ICMP_ULE:
3593 std::swap(LHS, RHS);
3595 case ICmpInst::ICMP_UGT:
3596 case ICmpInst::ICMP_UGE:
3597 // a >u b ? a+x : b+x -> umax(a, b)+x
3598 // a >u b ? b+x : a+x -> umin(a, b)+x
3599 if (LHS->getType() == U->getType()) {
3600 const SCEV *LS = getSCEV(LHS);
3601 const SCEV *RS = getSCEV(RHS);
3602 const SCEV *LA = getSCEV(U->getOperand(1));
3603 const SCEV *RA = getSCEV(U->getOperand(2));
3604 const SCEV *LDiff = getMinusSCEV(LA, LS);
3605 const SCEV *RDiff = getMinusSCEV(RA, RS);
3607 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3608 LDiff = getMinusSCEV(LA, RS);
3609 RDiff = getMinusSCEV(RA, LS);
3611 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3614 case ICmpInst::ICMP_NE:
3615 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3616 if (LHS->getType() == U->getType() &&
3617 isa<ConstantInt>(RHS) &&
3618 cast<ConstantInt>(RHS)->isZero()) {
3619 const SCEV *One = getConstant(LHS->getType(), 1);
3620 const SCEV *LS = getSCEV(LHS);
3621 const SCEV *LA = getSCEV(U->getOperand(1));
3622 const SCEV *RA = getSCEV(U->getOperand(2));
3623 const SCEV *LDiff = getMinusSCEV(LA, LS);
3624 const SCEV *RDiff = getMinusSCEV(RA, One);
3626 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3629 case ICmpInst::ICMP_EQ:
3630 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3631 if (LHS->getType() == U->getType() &&
3632 isa<ConstantInt>(RHS) &&
3633 cast<ConstantInt>(RHS)->isZero()) {
3634 const SCEV *One = getConstant(LHS->getType(), 1);
3635 const SCEV *LS = getSCEV(LHS);
3636 const SCEV *LA = getSCEV(U->getOperand(1));
3637 const SCEV *RA = getSCEV(U->getOperand(2));
3638 const SCEV *LDiff = getMinusSCEV(LA, One);
3639 const SCEV *RDiff = getMinusSCEV(RA, LS);
3641 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3649 default: // We cannot analyze this expression.
3653 return getUnknown(V);
3658 //===----------------------------------------------------------------------===//
3659 // Iteration Count Computation Code
3662 /// getBackedgeTakenCount - If the specified loop has a predictable
3663 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3664 /// object. The backedge-taken count is the number of times the loop header
3665 /// will be branched to from within the loop. This is one less than the
3666 /// trip count of the loop, since it doesn't count the first iteration,
3667 /// when the header is branched to from outside the loop.
3669 /// Note that it is not valid to call this method on a loop without a
3670 /// loop-invariant backedge-taken count (see
3671 /// hasLoopInvariantBackedgeTakenCount).
3673 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3674 return getBackedgeTakenInfo(L).Exact;
3677 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3678 /// return the least SCEV value that is known never to be less than the
3679 /// actual backedge taken count.
3680 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3681 return getBackedgeTakenInfo(L).Max;
3684 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3685 /// onto the given Worklist.
3687 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3688 BasicBlock *Header = L->getHeader();
3690 // Push all Loop-header PHIs onto the Worklist stack.
3691 for (BasicBlock::iterator I = Header->begin();
3692 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3693 Worklist.push_back(PN);
3696 const ScalarEvolution::BackedgeTakenInfo &
3697 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3698 // Initially insert a CouldNotCompute for this loop. If the insertion
3699 // succeeds, proceed to actually compute a backedge-taken count and
3700 // update the value. The temporary CouldNotCompute value tells SCEV
3701 // code elsewhere that it shouldn't attempt to request a new
3702 // backedge-taken count, which could result in infinite recursion.
3703 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3704 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3706 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3707 if (BECount.Exact != getCouldNotCompute()) {
3708 assert(BECount.Exact->isLoopInvariant(L) &&
3709 BECount.Max->isLoopInvariant(L) &&
3710 "Computed backedge-taken count isn't loop invariant for loop!");
3711 ++NumTripCountsComputed;
3713 // Update the value in the map.
3714 Pair.first->second = BECount;
3716 if (BECount.Max != getCouldNotCompute())
3717 // Update the value in the map.
3718 Pair.first->second = BECount;
3719 if (isa<PHINode>(L->getHeader()->begin()))
3720 // Only count loops that have phi nodes as not being computable.
3721 ++NumTripCountsNotComputed;
3724 // Now that we know more about the trip count for this loop, forget any
3725 // existing SCEV values for PHI nodes in this loop since they are only
3726 // conservative estimates made without the benefit of trip count
3727 // information. This is similar to the code in forgetLoop, except that
3728 // it handles SCEVUnknown PHI nodes specially.
3729 if (BECount.hasAnyInfo()) {
3730 SmallVector<Instruction *, 16> Worklist;
3731 PushLoopPHIs(L, Worklist);
3733 SmallPtrSet<Instruction *, 8> Visited;
3734 while (!Worklist.empty()) {
3735 Instruction *I = Worklist.pop_back_val();
3736 if (!Visited.insert(I)) continue;
3738 ValueExprMapType::iterator It =
3739 ValueExprMap.find(static_cast<Value *>(I));
3740 if (It != ValueExprMap.end()) {
3741 // SCEVUnknown for a PHI either means that it has an unrecognized
3742 // structure, or it's a PHI that's in the progress of being computed
3743 // by createNodeForPHI. In the former case, additional loop trip
3744 // count information isn't going to change anything. In the later
3745 // case, createNodeForPHI will perform the necessary updates on its
3746 // own when it gets to that point.
3747 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3748 ValuesAtScopes.erase(It->second);
3749 ValueExprMap.erase(It);
3751 if (PHINode *PN = dyn_cast<PHINode>(I))
3752 ConstantEvolutionLoopExitValue.erase(PN);
3755 PushDefUseChildren(I, Worklist);
3759 return Pair.first->second;
3762 /// forgetLoop - This method should be called by the client when it has
3763 /// changed a loop in a way that may effect ScalarEvolution's ability to
3764 /// compute a trip count, or if the loop is deleted.
3765 void ScalarEvolution::forgetLoop(const Loop *L) {
3766 // Drop any stored trip count value.
3767 BackedgeTakenCounts.erase(L);
3769 // Drop information about expressions based on loop-header PHIs.
3770 SmallVector<Instruction *, 16> Worklist;
3771 PushLoopPHIs(L, Worklist);
3773 SmallPtrSet<Instruction *, 8> Visited;
3774 while (!Worklist.empty()) {
3775 Instruction *I = Worklist.pop_back_val();
3776 if (!Visited.insert(I)) continue;
3778 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3779 if (It != ValueExprMap.end()) {
3780 ValuesAtScopes.erase(It->second);
3781 ValueExprMap.erase(It);
3782 if (PHINode *PN = dyn_cast<PHINode>(I))
3783 ConstantEvolutionLoopExitValue.erase(PN);
3786 PushDefUseChildren(I, Worklist);
3790 /// forgetValue - This method should be called by the client when it has
3791 /// changed a value in a way that may effect its value, or which may
3792 /// disconnect it from a def-use chain linking it to a loop.
3793 void ScalarEvolution::forgetValue(Value *V) {
3794 Instruction *I = dyn_cast<Instruction>(V);
3797 // Drop information about expressions based on loop-header PHIs.
3798 SmallVector<Instruction *, 16> Worklist;
3799 Worklist.push_back(I);
3801 SmallPtrSet<Instruction *, 8> Visited;
3802 while (!Worklist.empty()) {
3803 I = Worklist.pop_back_val();
3804 if (!Visited.insert(I)) continue;
3806 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3807 if (It != ValueExprMap.end()) {
3808 ValuesAtScopes.erase(It->second);
3809 ValueExprMap.erase(It);
3810 if (PHINode *PN = dyn_cast<PHINode>(I))
3811 ConstantEvolutionLoopExitValue.erase(PN);
3814 PushDefUseChildren(I, Worklist);
3818 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3819 /// of the specified loop will execute.
3820 ScalarEvolution::BackedgeTakenInfo
3821 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3822 SmallVector<BasicBlock *, 8> ExitingBlocks;
3823 L->getExitingBlocks(ExitingBlocks);
3825 // Examine all exits and pick the most conservative values.
3826 const SCEV *BECount = getCouldNotCompute();
3827 const SCEV *MaxBECount = getCouldNotCompute();
3828 bool CouldNotComputeBECount = false;
3829 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3830 BackedgeTakenInfo NewBTI =
3831 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3833 if (NewBTI.Exact == getCouldNotCompute()) {
3834 // We couldn't compute an exact value for this exit, so
3835 // we won't be able to compute an exact value for the loop.
3836 CouldNotComputeBECount = true;
3837 BECount = getCouldNotCompute();
3838 } else if (!CouldNotComputeBECount) {
3839 if (BECount == getCouldNotCompute())
3840 BECount = NewBTI.Exact;
3842 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3844 if (MaxBECount == getCouldNotCompute())
3845 MaxBECount = NewBTI.Max;
3846 else if (NewBTI.Max != getCouldNotCompute())
3847 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3850 return BackedgeTakenInfo(BECount, MaxBECount);
3853 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3854 /// of the specified loop will execute if it exits via the specified block.
3855 ScalarEvolution::BackedgeTakenInfo
3856 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3857 BasicBlock *ExitingBlock) {
3859 // Okay, we've chosen an exiting block. See what condition causes us to
3860 // exit at this block.
3862 // FIXME: we should be able to handle switch instructions (with a single exit)
3863 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3864 if (ExitBr == 0) return getCouldNotCompute();
3865 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3867 // At this point, we know we have a conditional branch that determines whether
3868 // the loop is exited. However, we don't know if the branch is executed each
3869 // time through the loop. If not, then the execution count of the branch will
3870 // not be equal to the trip count of the loop.
3872 // Currently we check for this by checking to see if the Exit branch goes to
3873 // the loop header. If so, we know it will always execute the same number of
3874 // times as the loop. We also handle the case where the exit block *is* the
3875 // loop header. This is common for un-rotated loops.
3877 // If both of those tests fail, walk up the unique predecessor chain to the
3878 // header, stopping if there is an edge that doesn't exit the loop. If the
3879 // header is reached, the execution count of the branch will be equal to the
3880 // trip count of the loop.
3882 // More extensive analysis could be done to handle more cases here.
3884 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3885 ExitBr->getSuccessor(1) != L->getHeader() &&
3886 ExitBr->getParent() != L->getHeader()) {
3887 // The simple checks failed, try climbing the unique predecessor chain
3888 // up to the header.
3890 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3891 BasicBlock *Pred = BB->getUniquePredecessor();
3893 return getCouldNotCompute();
3894 TerminatorInst *PredTerm = Pred->getTerminator();
3895 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3896 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3899 // If the predecessor has a successor that isn't BB and isn't
3900 // outside the loop, assume the worst.
3901 if (L->contains(PredSucc))
3902 return getCouldNotCompute();
3904 if (Pred == L->getHeader()) {
3911 return getCouldNotCompute();
3914 // Proceed to the next level to examine the exit condition expression.
3915 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3916 ExitBr->getSuccessor(0),
3917 ExitBr->getSuccessor(1));
3920 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3921 /// backedge of the specified loop will execute if its exit condition
3922 /// were a conditional branch of ExitCond, TBB, and FBB.
3923 ScalarEvolution::BackedgeTakenInfo
3924 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3928 // Check if the controlling expression for this loop is an And or Or.
3929 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3930 if (BO->getOpcode() == Instruction::And) {
3931 // Recurse on the operands of the and.
3932 BackedgeTakenInfo BTI0 =
3933 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3934 BackedgeTakenInfo BTI1 =
3935 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3936 const SCEV *BECount = getCouldNotCompute();
3937 const SCEV *MaxBECount = getCouldNotCompute();
3938 if (L->contains(TBB)) {
3939 // Both conditions must be true for the loop to continue executing.
3940 // Choose the less conservative count.
3941 if (BTI0.Exact == getCouldNotCompute() ||
3942 BTI1.Exact == getCouldNotCompute())
3943 BECount = getCouldNotCompute();
3945 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3946 if (BTI0.Max == getCouldNotCompute())
3947 MaxBECount = BTI1.Max;
3948 else if (BTI1.Max == getCouldNotCompute())
3949 MaxBECount = BTI0.Max;
3951 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3953 // Both conditions must be true at the same time for the loop to exit.
3954 // For now, be conservative.
3955 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3956 if (BTI0.Max == BTI1.Max)
3957 MaxBECount = BTI0.Max;
3958 if (BTI0.Exact == BTI1.Exact)
3959 BECount = BTI0.Exact;
3962 return BackedgeTakenInfo(BECount, MaxBECount);
3964 if (BO->getOpcode() == Instruction::Or) {
3965 // Recurse on the operands of the or.
3966 BackedgeTakenInfo BTI0 =
3967 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3968 BackedgeTakenInfo BTI1 =
3969 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3970 const SCEV *BECount = getCouldNotCompute();
3971 const SCEV *MaxBECount = getCouldNotCompute();
3972 if (L->contains(FBB)) {
3973 // Both conditions must be false for the loop to continue executing.
3974 // Choose the less conservative count.
3975 if (BTI0.Exact == getCouldNotCompute() ||
3976 BTI1.Exact == getCouldNotCompute())
3977 BECount = getCouldNotCompute();
3979 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3980 if (BTI0.Max == getCouldNotCompute())
3981 MaxBECount = BTI1.Max;
3982 else if (BTI1.Max == getCouldNotCompute())
3983 MaxBECount = BTI0.Max;
3985 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3987 // Both conditions must be false at the same time for the loop to exit.
3988 // For now, be conservative.
3989 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3990 if (BTI0.Max == BTI1.Max)
3991 MaxBECount = BTI0.Max;
3992 if (BTI0.Exact == BTI1.Exact)
3993 BECount = BTI0.Exact;
3996 return BackedgeTakenInfo(BECount, MaxBECount);
4000 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4001 // Proceed to the next level to examine the icmp.
4002 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4003 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
4005 // Check for a constant condition. These are normally stripped out by
4006 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4007 // preserve the CFG and is temporarily leaving constant conditions
4009 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4010 if (L->contains(FBB) == !CI->getZExtValue())
4011 // The backedge is always taken.
4012 return getCouldNotCompute();
4014 // The backedge is never taken.
4015 return getConstant(CI->getType(), 0);
4018 // If it's not an integer or pointer comparison then compute it the hard way.
4019 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4022 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4023 /// backedge of the specified loop will execute if its exit condition
4024 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4025 ScalarEvolution::BackedgeTakenInfo
4026 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4031 // If the condition was exit on true, convert the condition to exit on false
4032 ICmpInst::Predicate Cond;
4033 if (!L->contains(FBB))
4034 Cond = ExitCond->getPredicate();
4036 Cond = ExitCond->getInversePredicate();
4038 // Handle common loops like: for (X = "string"; *X; ++X)
4039 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4040 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4041 BackedgeTakenInfo ItCnt =
4042 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4043 if (ItCnt.hasAnyInfo())
4047 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4048 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4050 // Try to evaluate any dependencies out of the loop.
4051 LHS = getSCEVAtScope(LHS, L);
4052 RHS = getSCEVAtScope(RHS, L);
4054 // At this point, we would like to compute how many iterations of the
4055 // loop the predicate will return true for these inputs.
4056 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
4057 // If there is a loop-invariant, force it into the RHS.
4058 std::swap(LHS, RHS);
4059 Cond = ICmpInst::getSwappedPredicate(Cond);
4062 // Simplify the operands before analyzing them.
4063 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4065 // If we have a comparison of a chrec against a constant, try to use value
4066 // ranges to answer this query.
4067 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4068 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4069 if (AddRec->getLoop() == L) {
4070 // Form the constant range.
4071 ConstantRange CompRange(
4072 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4074 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4075 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4079 case ICmpInst::ICMP_NE: { // while (X != Y)
4080 // Convert to: while (X-Y != 0)
4081 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4082 if (BTI.hasAnyInfo()) return BTI;
4085 case ICmpInst::ICMP_EQ: { // while (X == Y)
4086 // Convert to: while (X-Y == 0)
4087 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4088 if (BTI.hasAnyInfo()) return BTI;
4091 case ICmpInst::ICMP_SLT: {
4092 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4093 if (BTI.hasAnyInfo()) return BTI;
4096 case ICmpInst::ICMP_SGT: {
4097 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4098 getNotSCEV(RHS), L, true);
4099 if (BTI.hasAnyInfo()) return BTI;
4102 case ICmpInst::ICMP_ULT: {
4103 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4104 if (BTI.hasAnyInfo()) return BTI;
4107 case ICmpInst::ICMP_UGT: {
4108 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4109 getNotSCEV(RHS), L, false);
4110 if (BTI.hasAnyInfo()) return BTI;
4115 dbgs() << "ComputeBackedgeTakenCount ";
4116 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4117 dbgs() << "[unsigned] ";
4118 dbgs() << *LHS << " "
4119 << Instruction::getOpcodeName(Instruction::ICmp)
4120 << " " << *RHS << "\n";
4125 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4128 static ConstantInt *
4129 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4130 ScalarEvolution &SE) {
4131 const SCEV *InVal = SE.getConstant(C);
4132 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4133 assert(isa<SCEVConstant>(Val) &&
4134 "Evaluation of SCEV at constant didn't fold correctly?");
4135 return cast<SCEVConstant>(Val)->getValue();
4138 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4139 /// and a GEP expression (missing the pointer index) indexing into it, return
4140 /// the addressed element of the initializer or null if the index expression is
4143 GetAddressedElementFromGlobal(GlobalVariable *GV,
4144 const std::vector<ConstantInt*> &Indices) {
4145 Constant *Init = GV->getInitializer();
4146 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4147 uint64_t Idx = Indices[i]->getZExtValue();
4148 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4149 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4150 Init = cast<Constant>(CS->getOperand(Idx));
4151 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4152 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4153 Init = cast<Constant>(CA->getOperand(Idx));
4154 } else if (isa<ConstantAggregateZero>(Init)) {
4155 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4156 assert(Idx < STy->getNumElements() && "Bad struct index!");
4157 Init = Constant::getNullValue(STy->getElementType(Idx));
4158 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4159 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4160 Init = Constant::getNullValue(ATy->getElementType());
4162 llvm_unreachable("Unknown constant aggregate type!");
4166 return 0; // Unknown initializer type
4172 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4173 /// 'icmp op load X, cst', try to see if we can compute the backedge
4174 /// execution count.
4175 ScalarEvolution::BackedgeTakenInfo
4176 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4180 ICmpInst::Predicate predicate) {
4181 if (LI->isVolatile()) return getCouldNotCompute();
4183 // Check to see if the loaded pointer is a getelementptr of a global.
4184 // TODO: Use SCEV instead of manually grubbing with GEPs.
4185 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4186 if (!GEP) return getCouldNotCompute();
4188 // Make sure that it is really a constant global we are gepping, with an
4189 // initializer, and make sure the first IDX is really 0.
4190 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4191 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4192 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4193 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4194 return getCouldNotCompute();
4196 // Okay, we allow one non-constant index into the GEP instruction.
4198 std::vector<ConstantInt*> Indexes;
4199 unsigned VarIdxNum = 0;
4200 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4201 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4202 Indexes.push_back(CI);
4203 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4204 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4205 VarIdx = GEP->getOperand(i);
4207 Indexes.push_back(0);
4210 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4211 // Check to see if X is a loop variant variable value now.
4212 const SCEV *Idx = getSCEV(VarIdx);
4213 Idx = getSCEVAtScope(Idx, L);
4215 // We can only recognize very limited forms of loop index expressions, in
4216 // particular, only affine AddRec's like {C1,+,C2}.
4217 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4218 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4219 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4220 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4221 return getCouldNotCompute();
4223 unsigned MaxSteps = MaxBruteForceIterations;
4224 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4225 ConstantInt *ItCst = ConstantInt::get(
4226 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4227 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4229 // Form the GEP offset.
4230 Indexes[VarIdxNum] = Val;
4232 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4233 if (Result == 0) break; // Cannot compute!
4235 // Evaluate the condition for this iteration.
4236 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4237 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4238 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4240 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4241 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4244 ++NumArrayLenItCounts;
4245 return getConstant(ItCst); // Found terminating iteration!
4248 return getCouldNotCompute();
4252 /// CanConstantFold - Return true if we can constant fold an instruction of the
4253 /// specified type, assuming that all operands were constants.
4254 static bool CanConstantFold(const Instruction *I) {
4255 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4256 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4259 if (const CallInst *CI = dyn_cast<CallInst>(I))
4260 if (const Function *F = CI->getCalledFunction())
4261 return canConstantFoldCallTo(F);
4265 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4266 /// in the loop that V is derived from. We allow arbitrary operations along the
4267 /// way, but the operands of an operation must either be constants or a value
4268 /// derived from a constant PHI. If this expression does not fit with these
4269 /// constraints, return null.
4270 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4271 // If this is not an instruction, or if this is an instruction outside of the
4272 // loop, it can't be derived from a loop PHI.
4273 Instruction *I = dyn_cast<Instruction>(V);
4274 if (I == 0 || !L->contains(I)) return 0;
4276 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4277 if (L->getHeader() == I->getParent())
4280 // We don't currently keep track of the control flow needed to evaluate
4281 // PHIs, so we cannot handle PHIs inside of loops.
4285 // If we won't be able to constant fold this expression even if the operands
4286 // are constants, return early.
4287 if (!CanConstantFold(I)) return 0;
4289 // Otherwise, we can evaluate this instruction if all of its operands are
4290 // constant or derived from a PHI node themselves.
4292 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4293 if (!isa<Constant>(I->getOperand(Op))) {
4294 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4295 if (P == 0) return 0; // Not evolving from PHI
4299 return 0; // Evolving from multiple different PHIs.
4302 // This is a expression evolving from a constant PHI!
4306 /// EvaluateExpression - Given an expression that passes the
4307 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4308 /// in the loop has the value PHIVal. If we can't fold this expression for some
4309 /// reason, return null.
4310 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4311 const TargetData *TD) {
4312 if (isa<PHINode>(V)) return PHIVal;
4313 if (Constant *C = dyn_cast<Constant>(V)) return C;
4314 Instruction *I = cast<Instruction>(V);
4316 std::vector<Constant*> Operands(I->getNumOperands());
4318 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4319 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4320 if (Operands[i] == 0) return 0;
4323 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4324 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4326 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4327 &Operands[0], Operands.size(), TD);
4330 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4331 /// in the header of its containing loop, we know the loop executes a
4332 /// constant number of times, and the PHI node is just a recurrence
4333 /// involving constants, fold it.
4335 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4338 std::map<PHINode*, Constant*>::const_iterator I =
4339 ConstantEvolutionLoopExitValue.find(PN);
4340 if (I != ConstantEvolutionLoopExitValue.end())
4343 if (BEs.ugt(MaxBruteForceIterations))
4344 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4346 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4348 // Since the loop is canonicalized, the PHI node must have two entries. One
4349 // entry must be a constant (coming in from outside of the loop), and the
4350 // second must be derived from the same PHI.
4351 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4352 Constant *StartCST =
4353 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4355 return RetVal = 0; // Must be a constant.
4357 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4358 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4359 !isa<Constant>(BEValue))
4360 return RetVal = 0; // Not derived from same PHI.
4362 // Execute the loop symbolically to determine the exit value.
4363 if (BEs.getActiveBits() >= 32)
4364 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4366 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4367 unsigned IterationNum = 0;
4368 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4369 if (IterationNum == NumIterations)
4370 return RetVal = PHIVal; // Got exit value!
4372 // Compute the value of the PHI node for the next iteration.
4373 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4374 if (NextPHI == PHIVal)
4375 return RetVal = NextPHI; // Stopped evolving!
4377 return 0; // Couldn't evaluate!
4382 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4383 /// constant number of times (the condition evolves only from constants),
4384 /// try to evaluate a few iterations of the loop until we get the exit
4385 /// condition gets a value of ExitWhen (true or false). If we cannot
4386 /// evaluate the trip count of the loop, return getCouldNotCompute().
4388 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4391 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4392 if (PN == 0) return getCouldNotCompute();
4394 // If the loop is canonicalized, the PHI will have exactly two entries.
4395 // That's the only form we support here.
4396 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4398 // One entry must be a constant (coming in from outside of the loop), and the
4399 // second must be derived from the same PHI.
4400 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4401 Constant *StartCST =
4402 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4403 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4405 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4406 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4407 !isa<Constant>(BEValue))
4408 return getCouldNotCompute(); // Not derived from same PHI.
4410 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4411 // the loop symbolically to determine when the condition gets a value of
4413 unsigned IterationNum = 0;
4414 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4415 for (Constant *PHIVal = StartCST;
4416 IterationNum != MaxIterations; ++IterationNum) {
4417 ConstantInt *CondVal =
4418 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4420 // Couldn't symbolically evaluate.
4421 if (!CondVal) return getCouldNotCompute();
4423 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4424 ++NumBruteForceTripCountsComputed;
4425 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4428 // Compute the value of the PHI node for the next iteration.
4429 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4430 if (NextPHI == 0 || NextPHI == PHIVal)
4431 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4435 // Too many iterations were needed to evaluate.
4436 return getCouldNotCompute();
4439 /// getSCEVAtScope - Return a SCEV expression for the specified value
4440 /// at the specified scope in the program. The L value specifies a loop
4441 /// nest to evaluate the expression at, where null is the top-level or a
4442 /// specified loop is immediately inside of the loop.
4444 /// This method can be used to compute the exit value for a variable defined
4445 /// in a loop by querying what the value will hold in the parent loop.
4447 /// In the case that a relevant loop exit value cannot be computed, the
4448 /// original value V is returned.
4449 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4450 // Check to see if we've folded this expression at this loop before.
4451 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4452 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4453 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4455 return Pair.first->second ? Pair.first->second : V;
4457 // Otherwise compute it.
4458 const SCEV *C = computeSCEVAtScope(V, L);
4459 ValuesAtScopes[V][L] = C;
4463 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4464 if (isa<SCEVConstant>(V)) return V;
4466 // If this instruction is evolved from a constant-evolving PHI, compute the
4467 // exit value from the loop without using SCEVs.
4468 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4469 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4470 const Loop *LI = (*this->LI)[I->getParent()];
4471 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4472 if (PHINode *PN = dyn_cast<PHINode>(I))
4473 if (PN->getParent() == LI->getHeader()) {
4474 // Okay, there is no closed form solution for the PHI node. Check
4475 // to see if the loop that contains it has a known backedge-taken
4476 // count. If so, we may be able to force computation of the exit
4478 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4479 if (const SCEVConstant *BTCC =
4480 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4481 // Okay, we know how many times the containing loop executes. If
4482 // this is a constant evolving PHI node, get the final value at
4483 // the specified iteration number.
4484 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4485 BTCC->getValue()->getValue(),
4487 if (RV) return getSCEV(RV);
4491 // Okay, this is an expression that we cannot symbolically evaluate
4492 // into a SCEV. Check to see if it's possible to symbolically evaluate
4493 // the arguments into constants, and if so, try to constant propagate the
4494 // result. This is particularly useful for computing loop exit values.
4495 if (CanConstantFold(I)) {
4496 SmallVector<Constant *, 4> Operands;
4497 bool MadeImprovement = false;
4498 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4499 Value *Op = I->getOperand(i);
4500 if (Constant *C = dyn_cast<Constant>(Op)) {
4501 Operands.push_back(C);
4505 // If any of the operands is non-constant and if they are
4506 // non-integer and non-pointer, don't even try to analyze them
4507 // with scev techniques.
4508 if (!isSCEVable(Op->getType()))
4511 const SCEV *OrigV = getSCEV(Op);
4512 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4513 MadeImprovement |= OrigV != OpV;
4516 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4518 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4519 C = dyn_cast<Constant>(SU->getValue());
4521 if (C->getType() != Op->getType())
4522 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4526 Operands.push_back(C);
4529 // Check to see if getSCEVAtScope actually made an improvement.
4530 if (MadeImprovement) {
4532 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4533 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4534 Operands[0], Operands[1], TD);
4536 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4537 &Operands[0], Operands.size(), TD);
4544 // This is some other type of SCEVUnknown, just return it.
4548 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4549 // Avoid performing the look-up in the common case where the specified
4550 // expression has no loop-variant portions.
4551 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4552 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4553 if (OpAtScope != Comm->getOperand(i)) {
4554 // Okay, at least one of these operands is loop variant but might be
4555 // foldable. Build a new instance of the folded commutative expression.
4556 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4557 Comm->op_begin()+i);
4558 NewOps.push_back(OpAtScope);
4560 for (++i; i != e; ++i) {
4561 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4562 NewOps.push_back(OpAtScope);
4564 if (isa<SCEVAddExpr>(Comm))
4565 return getAddExpr(NewOps);
4566 if (isa<SCEVMulExpr>(Comm))
4567 return getMulExpr(NewOps);
4568 if (isa<SCEVSMaxExpr>(Comm))
4569 return getSMaxExpr(NewOps);
4570 if (isa<SCEVUMaxExpr>(Comm))
4571 return getUMaxExpr(NewOps);
4572 llvm_unreachable("Unknown commutative SCEV type!");
4575 // If we got here, all operands are loop invariant.
4579 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4580 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4581 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4582 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4583 return Div; // must be loop invariant
4584 return getUDivExpr(LHS, RHS);
4587 // If this is a loop recurrence for a loop that does not contain L, then we
4588 // are dealing with the final value computed by the loop.
4589 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4590 // First, attempt to evaluate each operand.
4591 // Avoid performing the look-up in the common case where the specified
4592 // expression has no loop-variant portions.
4593 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4594 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4595 if (OpAtScope == AddRec->getOperand(i))
4598 // Okay, at least one of these operands is loop variant but might be
4599 // foldable. Build a new instance of the folded commutative expression.
4600 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4601 AddRec->op_begin()+i);
4602 NewOps.push_back(OpAtScope);
4603 for (++i; i != e; ++i)
4604 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4606 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4610 // If the scope is outside the addrec's loop, evaluate it by using the
4611 // loop exit value of the addrec.
4612 if (!AddRec->getLoop()->contains(L)) {
4613 // To evaluate this recurrence, we need to know how many times the AddRec
4614 // loop iterates. Compute this now.
4615 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4616 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4618 // Then, evaluate the AddRec.
4619 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4625 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4626 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4627 if (Op == Cast->getOperand())
4628 return Cast; // must be loop invariant
4629 return getZeroExtendExpr(Op, Cast->getType());
4632 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4633 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4634 if (Op == Cast->getOperand())
4635 return Cast; // must be loop invariant
4636 return getSignExtendExpr(Op, Cast->getType());
4639 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4640 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4641 if (Op == Cast->getOperand())
4642 return Cast; // must be loop invariant
4643 return getTruncateExpr(Op, Cast->getType());
4646 llvm_unreachable("Unknown SCEV type!");
4650 /// getSCEVAtScope - This is a convenience function which does
4651 /// getSCEVAtScope(getSCEV(V), L).
4652 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4653 return getSCEVAtScope(getSCEV(V), L);
4656 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4657 /// following equation:
4659 /// A * X = B (mod N)
4661 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4662 /// A and B isn't important.
4664 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4665 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4666 ScalarEvolution &SE) {
4667 uint32_t BW = A.getBitWidth();
4668 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4669 assert(A != 0 && "A must be non-zero.");
4673 // The gcd of A and N may have only one prime factor: 2. The number of
4674 // trailing zeros in A is its multiplicity
4675 uint32_t Mult2 = A.countTrailingZeros();
4678 // 2. Check if B is divisible by D.
4680 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4681 // is not less than multiplicity of this prime factor for D.
4682 if (B.countTrailingZeros() < Mult2)
4683 return SE.getCouldNotCompute();
4685 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4688 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4689 // bit width during computations.
4690 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4691 APInt Mod(BW + 1, 0);
4692 Mod.set(BW - Mult2); // Mod = N / D
4693 APInt I = AD.multiplicativeInverse(Mod);
4695 // 4. Compute the minimum unsigned root of the equation:
4696 // I * (B / D) mod (N / D)
4697 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4699 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4701 return SE.getConstant(Result.trunc(BW));
4704 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4705 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4706 /// might be the same) or two SCEVCouldNotCompute objects.
4708 static std::pair<const SCEV *,const SCEV *>
4709 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4710 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4711 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4712 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4713 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4715 // We currently can only solve this if the coefficients are constants.
4716 if (!LC || !MC || !NC) {
4717 const SCEV *CNC = SE.getCouldNotCompute();
4718 return std::make_pair(CNC, CNC);
4721 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4722 const APInt &L = LC->getValue()->getValue();
4723 const APInt &M = MC->getValue()->getValue();
4724 const APInt &N = NC->getValue()->getValue();
4725 APInt Two(BitWidth, 2);
4726 APInt Four(BitWidth, 4);
4729 using namespace APIntOps;
4731 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4732 // The B coefficient is M-N/2
4736 // The A coefficient is N/2
4737 APInt A(N.sdiv(Two));
4739 // Compute the B^2-4ac term.
4742 SqrtTerm -= Four * (A * C);
4744 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4745 // integer value or else APInt::sqrt() will assert.
4746 APInt SqrtVal(SqrtTerm.sqrt());
4748 // Compute the two solutions for the quadratic formula.
4749 // The divisions must be performed as signed divisions.
4751 APInt TwoA( A << 1 );
4752 if (TwoA.isMinValue()) {
4753 const SCEV *CNC = SE.getCouldNotCompute();
4754 return std::make_pair(CNC, CNC);
4757 LLVMContext &Context = SE.getContext();
4759 ConstantInt *Solution1 =
4760 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4761 ConstantInt *Solution2 =
4762 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4764 return std::make_pair(SE.getConstant(Solution1),
4765 SE.getConstant(Solution2));
4766 } // end APIntOps namespace
4769 /// HowFarToZero - Return the number of times a backedge comparing the specified
4770 /// value to zero will execute. If not computable, return CouldNotCompute.
4771 ScalarEvolution::BackedgeTakenInfo
4772 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4773 // If the value is a constant
4774 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4775 // If the value is already zero, the branch will execute zero times.
4776 if (C->getValue()->isZero()) return C;
4777 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4780 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4781 if (!AddRec || AddRec->getLoop() != L)
4782 return getCouldNotCompute();
4784 if (AddRec->isAffine()) {
4785 // If this is an affine expression, the execution count of this branch is
4786 // the minimum unsigned root of the following equation:
4788 // Start + Step*N = 0 (mod 2^BW)
4792 // Step*N = -Start (mod 2^BW)
4794 // where BW is the common bit width of Start and Step.
4796 // Get the initial value for the loop.
4797 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4798 L->getParentLoop());
4799 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4800 L->getParentLoop());
4802 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4803 // For now we handle only constant steps.
4805 // First, handle unitary steps.
4806 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4807 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4808 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4809 return Start; // N = Start (as unsigned)
4811 // Then, try to solve the above equation provided that Start is constant.
4812 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4813 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4814 -StartC->getValue()->getValue(),
4817 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4818 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4819 // the quadratic equation to solve it.
4820 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4822 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4823 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4826 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4827 << " sol#2: " << *R2 << "\n";
4829 // Pick the smallest positive root value.
4830 if (ConstantInt *CB =
4831 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4832 R1->getValue(), R2->getValue()))) {
4833 if (CB->getZExtValue() == false)
4834 std::swap(R1, R2); // R1 is the minimum root now.
4836 // We can only use this value if the chrec ends up with an exact zero
4837 // value at this index. When solving for "X*X != 5", for example, we
4838 // should not accept a root of 2.
4839 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4841 return R1; // We found a quadratic root!
4846 return getCouldNotCompute();
4849 /// HowFarToNonZero - Return the number of times a backedge checking the
4850 /// specified value for nonzero will execute. If not computable, return
4852 ScalarEvolution::BackedgeTakenInfo
4853 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4854 // Loops that look like: while (X == 0) are very strange indeed. We don't
4855 // handle them yet except for the trivial case. This could be expanded in the
4856 // future as needed.
4858 // If the value is a constant, check to see if it is known to be non-zero
4859 // already. If so, the backedge will execute zero times.
4860 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4861 if (!C->getValue()->isNullValue())
4862 return getConstant(C->getType(), 0);
4863 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4866 // We could implement others, but I really doubt anyone writes loops like
4867 // this, and if they did, they would already be constant folded.
4868 return getCouldNotCompute();
4871 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4872 /// (which may not be an immediate predecessor) which has exactly one
4873 /// successor from which BB is reachable, or null if no such block is
4876 std::pair<BasicBlock *, BasicBlock *>
4877 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4878 // If the block has a unique predecessor, then there is no path from the
4879 // predecessor to the block that does not go through the direct edge
4880 // from the predecessor to the block.
4881 if (BasicBlock *Pred = BB->getSinglePredecessor())
4882 return std::make_pair(Pred, BB);
4884 // A loop's header is defined to be a block that dominates the loop.
4885 // If the header has a unique predecessor outside the loop, it must be
4886 // a block that has exactly one successor that can reach the loop.
4887 if (Loop *L = LI->getLoopFor(BB))
4888 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4890 return std::pair<BasicBlock *, BasicBlock *>();
4893 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4894 /// testing whether two expressions are equal, however for the purposes of
4895 /// looking for a condition guarding a loop, it can be useful to be a little
4896 /// more general, since a front-end may have replicated the controlling
4899 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4900 // Quick check to see if they are the same SCEV.
4901 if (A == B) return true;
4903 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4904 // two different instructions with the same value. Check for this case.
4905 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4906 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4907 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4908 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4909 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4912 // Otherwise assume they may have a different value.
4916 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4917 /// predicate Pred. Return true iff any changes were made.
4919 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4920 const SCEV *&LHS, const SCEV *&RHS) {
4921 bool Changed = false;
4923 // Canonicalize a constant to the right side.
4924 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4925 // Check for both operands constant.
4926 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4927 if (ConstantExpr::getICmp(Pred,
4929 RHSC->getValue())->isNullValue())
4930 goto trivially_false;
4932 goto trivially_true;
4934 // Otherwise swap the operands to put the constant on the right.
4935 std::swap(LHS, RHS);
4936 Pred = ICmpInst::getSwappedPredicate(Pred);
4940 // If we're comparing an addrec with a value which is loop-invariant in the
4941 // addrec's loop, put the addrec on the left. Also make a dominance check,
4942 // as both operands could be addrecs loop-invariant in each other's loop.
4943 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4944 const Loop *L = AR->getLoop();
4945 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4946 std::swap(LHS, RHS);
4947 Pred = ICmpInst::getSwappedPredicate(Pred);
4952 // If there's a constant operand, canonicalize comparisons with boundary
4953 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4954 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4955 const APInt &RA = RC->getValue()->getValue();
4957 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4958 case ICmpInst::ICMP_EQ:
4959 case ICmpInst::ICMP_NE:
4961 case ICmpInst::ICMP_UGE:
4962 if ((RA - 1).isMinValue()) {
4963 Pred = ICmpInst::ICMP_NE;
4964 RHS = getConstant(RA - 1);
4968 if (RA.isMaxValue()) {
4969 Pred = ICmpInst::ICMP_EQ;
4973 if (RA.isMinValue()) goto trivially_true;
4975 Pred = ICmpInst::ICMP_UGT;
4976 RHS = getConstant(RA - 1);
4979 case ICmpInst::ICMP_ULE:
4980 if ((RA + 1).isMaxValue()) {
4981 Pred = ICmpInst::ICMP_NE;
4982 RHS = getConstant(RA + 1);
4986 if (RA.isMinValue()) {
4987 Pred = ICmpInst::ICMP_EQ;
4991 if (RA.isMaxValue()) goto trivially_true;
4993 Pred = ICmpInst::ICMP_ULT;
4994 RHS = getConstant(RA + 1);
4997 case ICmpInst::ICMP_SGE:
4998 if ((RA - 1).isMinSignedValue()) {
4999 Pred = ICmpInst::ICMP_NE;
5000 RHS = getConstant(RA - 1);
5004 if (RA.isMaxSignedValue()) {
5005 Pred = ICmpInst::ICMP_EQ;
5009 if (RA.isMinSignedValue()) goto trivially_true;
5011 Pred = ICmpInst::ICMP_SGT;
5012 RHS = getConstant(RA - 1);
5015 case ICmpInst::ICMP_SLE:
5016 if ((RA + 1).isMaxSignedValue()) {
5017 Pred = ICmpInst::ICMP_NE;
5018 RHS = getConstant(RA + 1);
5022 if (RA.isMinSignedValue()) {
5023 Pred = ICmpInst::ICMP_EQ;
5027 if (RA.isMaxSignedValue()) goto trivially_true;
5029 Pred = ICmpInst::ICMP_SLT;
5030 RHS = getConstant(RA + 1);
5033 case ICmpInst::ICMP_UGT:
5034 if (RA.isMinValue()) {
5035 Pred = ICmpInst::ICMP_NE;
5039 if ((RA + 1).isMaxValue()) {
5040 Pred = ICmpInst::ICMP_EQ;
5041 RHS = getConstant(RA + 1);
5045 if (RA.isMaxValue()) goto trivially_false;
5047 case ICmpInst::ICMP_ULT:
5048 if (RA.isMaxValue()) {
5049 Pred = ICmpInst::ICMP_NE;
5053 if ((RA - 1).isMinValue()) {
5054 Pred = ICmpInst::ICMP_EQ;
5055 RHS = getConstant(RA - 1);
5059 if (RA.isMinValue()) goto trivially_false;
5061 case ICmpInst::ICMP_SGT:
5062 if (RA.isMinSignedValue()) {
5063 Pred = ICmpInst::ICMP_NE;
5067 if ((RA + 1).isMaxSignedValue()) {
5068 Pred = ICmpInst::ICMP_EQ;
5069 RHS = getConstant(RA + 1);
5073 if (RA.isMaxSignedValue()) goto trivially_false;
5075 case ICmpInst::ICMP_SLT:
5076 if (RA.isMaxSignedValue()) {
5077 Pred = ICmpInst::ICMP_NE;
5081 if ((RA - 1).isMinSignedValue()) {
5082 Pred = ICmpInst::ICMP_EQ;
5083 RHS = getConstant(RA - 1);
5087 if (RA.isMinSignedValue()) goto trivially_false;
5092 // Check for obvious equality.
5093 if (HasSameValue(LHS, RHS)) {
5094 if (ICmpInst::isTrueWhenEqual(Pred))
5095 goto trivially_true;
5096 if (ICmpInst::isFalseWhenEqual(Pred))
5097 goto trivially_false;
5100 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5101 // adding or subtracting 1 from one of the operands.
5103 case ICmpInst::ICMP_SLE:
5104 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5105 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5106 /*HasNUW=*/false, /*HasNSW=*/true);
5107 Pred = ICmpInst::ICMP_SLT;
5109 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5110 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5111 /*HasNUW=*/false, /*HasNSW=*/true);
5112 Pred = ICmpInst::ICMP_SLT;
5116 case ICmpInst::ICMP_SGE:
5117 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5118 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5119 /*HasNUW=*/false, /*HasNSW=*/true);
5120 Pred = ICmpInst::ICMP_SGT;
5122 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5123 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5124 /*HasNUW=*/false, /*HasNSW=*/true);
5125 Pred = ICmpInst::ICMP_SGT;
5129 case ICmpInst::ICMP_ULE:
5130 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5131 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5132 /*HasNUW=*/true, /*HasNSW=*/false);
5133 Pred = ICmpInst::ICMP_ULT;
5135 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5136 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5137 /*HasNUW=*/true, /*HasNSW=*/false);
5138 Pred = ICmpInst::ICMP_ULT;
5142 case ICmpInst::ICMP_UGE:
5143 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5144 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5145 /*HasNUW=*/true, /*HasNSW=*/false);
5146 Pred = ICmpInst::ICMP_UGT;
5148 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5149 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5150 /*HasNUW=*/true, /*HasNSW=*/false);
5151 Pred = ICmpInst::ICMP_UGT;
5159 // TODO: More simplifications are possible here.
5165 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5166 Pred = ICmpInst::ICMP_EQ;
5171 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5172 Pred = ICmpInst::ICMP_NE;
5176 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5177 return getSignedRange(S).getSignedMax().isNegative();
5180 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5181 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5184 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5185 return !getSignedRange(S).getSignedMin().isNegative();
5188 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5189 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5192 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5193 return isKnownNegative(S) || isKnownPositive(S);
5196 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5197 const SCEV *LHS, const SCEV *RHS) {
5198 // Canonicalize the inputs first.
5199 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5201 // If LHS or RHS is an addrec, check to see if the condition is true in
5202 // every iteration of the loop.
5203 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5204 if (isLoopEntryGuardedByCond(
5205 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5206 isLoopBackedgeGuardedByCond(
5207 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5209 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5210 if (isLoopEntryGuardedByCond(
5211 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5212 isLoopBackedgeGuardedByCond(
5213 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5216 // Otherwise see what can be done with known constant ranges.
5217 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5221 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5222 const SCEV *LHS, const SCEV *RHS) {
5223 if (HasSameValue(LHS, RHS))
5224 return ICmpInst::isTrueWhenEqual(Pred);
5226 // This code is split out from isKnownPredicate because it is called from
5227 // within isLoopEntryGuardedByCond.
5230 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5232 case ICmpInst::ICMP_SGT:
5233 Pred = ICmpInst::ICMP_SLT;
5234 std::swap(LHS, RHS);
5235 case ICmpInst::ICMP_SLT: {
5236 ConstantRange LHSRange = getSignedRange(LHS);
5237 ConstantRange RHSRange = getSignedRange(RHS);
5238 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5240 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5244 case ICmpInst::ICMP_SGE:
5245 Pred = ICmpInst::ICMP_SLE;
5246 std::swap(LHS, RHS);
5247 case ICmpInst::ICMP_SLE: {
5248 ConstantRange LHSRange = getSignedRange(LHS);
5249 ConstantRange RHSRange = getSignedRange(RHS);
5250 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5252 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5256 case ICmpInst::ICMP_UGT:
5257 Pred = ICmpInst::ICMP_ULT;
5258 std::swap(LHS, RHS);
5259 case ICmpInst::ICMP_ULT: {
5260 ConstantRange LHSRange = getUnsignedRange(LHS);
5261 ConstantRange RHSRange = getUnsignedRange(RHS);
5262 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5264 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5268 case ICmpInst::ICMP_UGE:
5269 Pred = ICmpInst::ICMP_ULE;
5270 std::swap(LHS, RHS);
5271 case ICmpInst::ICMP_ULE: {
5272 ConstantRange LHSRange = getUnsignedRange(LHS);
5273 ConstantRange RHSRange = getUnsignedRange(RHS);
5274 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5276 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5280 case ICmpInst::ICMP_NE: {
5281 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5283 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5286 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5287 if (isKnownNonZero(Diff))
5291 case ICmpInst::ICMP_EQ:
5292 // The check at the top of the function catches the case where
5293 // the values are known to be equal.
5299 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5300 /// protected by a conditional between LHS and RHS. This is used to
5301 /// to eliminate casts.
5303 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5304 ICmpInst::Predicate Pred,
5305 const SCEV *LHS, const SCEV *RHS) {
5306 // Interpret a null as meaning no loop, where there is obviously no guard
5307 // (interprocedural conditions notwithstanding).
5308 if (!L) return true;
5310 BasicBlock *Latch = L->getLoopLatch();
5314 BranchInst *LoopContinuePredicate =
5315 dyn_cast<BranchInst>(Latch->getTerminator());
5316 if (!LoopContinuePredicate ||
5317 LoopContinuePredicate->isUnconditional())
5320 return isImpliedCond(Pred, LHS, RHS,
5321 LoopContinuePredicate->getCondition(),
5322 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5325 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5326 /// by a conditional between LHS and RHS. This is used to help avoid max
5327 /// expressions in loop trip counts, and to eliminate casts.
5329 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5330 ICmpInst::Predicate Pred,
5331 const SCEV *LHS, const SCEV *RHS) {
5332 // Interpret a null as meaning no loop, where there is obviously no guard
5333 // (interprocedural conditions notwithstanding).
5334 if (!L) return false;
5336 // Starting at the loop predecessor, climb up the predecessor chain, as long
5337 // as there are predecessors that can be found that have unique successors
5338 // leading to the original header.
5339 for (std::pair<BasicBlock *, BasicBlock *>
5340 Pair(L->getLoopPredecessor(), L->getHeader());
5342 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5344 BranchInst *LoopEntryPredicate =
5345 dyn_cast<BranchInst>(Pair.first->getTerminator());
5346 if (!LoopEntryPredicate ||
5347 LoopEntryPredicate->isUnconditional())
5350 if (isImpliedCond(Pred, LHS, RHS,
5351 LoopEntryPredicate->getCondition(),
5352 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5359 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5360 /// and RHS is true whenever the given Cond value evaluates to true.
5361 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5362 const SCEV *LHS, const SCEV *RHS,
5363 Value *FoundCondValue,
5365 // Recursively handle And and Or conditions.
5366 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5367 if (BO->getOpcode() == Instruction::And) {
5369 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5370 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5371 } else if (BO->getOpcode() == Instruction::Or) {
5373 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5374 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5378 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5379 if (!ICI) return false;
5381 // Bail if the ICmp's operands' types are wider than the needed type
5382 // before attempting to call getSCEV on them. This avoids infinite
5383 // recursion, since the analysis of widening casts can require loop
5384 // exit condition information for overflow checking, which would
5386 if (getTypeSizeInBits(LHS->getType()) <
5387 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5390 // Now that we found a conditional branch that dominates the loop, check to
5391 // see if it is the comparison we are looking for.
5392 ICmpInst::Predicate FoundPred;
5394 FoundPred = ICI->getInversePredicate();
5396 FoundPred = ICI->getPredicate();
5398 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5399 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5401 // Balance the types. The case where FoundLHS' type is wider than
5402 // LHS' type is checked for above.
5403 if (getTypeSizeInBits(LHS->getType()) >
5404 getTypeSizeInBits(FoundLHS->getType())) {
5405 if (CmpInst::isSigned(Pred)) {
5406 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5407 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5409 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5410 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5414 // Canonicalize the query to match the way instcombine will have
5415 // canonicalized the comparison.
5416 if (SimplifyICmpOperands(Pred, LHS, RHS))
5418 return CmpInst::isTrueWhenEqual(Pred);
5419 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5420 if (FoundLHS == FoundRHS)
5421 return CmpInst::isFalseWhenEqual(Pred);
5423 // Check to see if we can make the LHS or RHS match.
5424 if (LHS == FoundRHS || RHS == FoundLHS) {
5425 if (isa<SCEVConstant>(RHS)) {
5426 std::swap(FoundLHS, FoundRHS);
5427 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5429 std::swap(LHS, RHS);
5430 Pred = ICmpInst::getSwappedPredicate(Pred);
5434 // Check whether the found predicate is the same as the desired predicate.
5435 if (FoundPred == Pred)
5436 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5438 // Check whether swapping the found predicate makes it the same as the
5439 // desired predicate.
5440 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5441 if (isa<SCEVConstant>(RHS))
5442 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5444 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5445 RHS, LHS, FoundLHS, FoundRHS);
5448 // Check whether the actual condition is beyond sufficient.
5449 if (FoundPred == ICmpInst::ICMP_EQ)
5450 if (ICmpInst::isTrueWhenEqual(Pred))
5451 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5453 if (Pred == ICmpInst::ICMP_NE)
5454 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5455 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5458 // Otherwise assume the worst.
5462 /// isImpliedCondOperands - Test whether the condition described by Pred,
5463 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5464 /// and FoundRHS is true.
5465 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5466 const SCEV *LHS, const SCEV *RHS,
5467 const SCEV *FoundLHS,
5468 const SCEV *FoundRHS) {
5469 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5470 FoundLHS, FoundRHS) ||
5471 // ~x < ~y --> x > y
5472 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5473 getNotSCEV(FoundRHS),
5474 getNotSCEV(FoundLHS));
5477 /// isImpliedCondOperandsHelper - Test whether the condition described by
5478 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5479 /// FoundLHS, and FoundRHS is true.
5481 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5482 const SCEV *LHS, const SCEV *RHS,
5483 const SCEV *FoundLHS,
5484 const SCEV *FoundRHS) {
5486 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5487 case ICmpInst::ICMP_EQ:
5488 case ICmpInst::ICMP_NE:
5489 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5492 case ICmpInst::ICMP_SLT:
5493 case ICmpInst::ICMP_SLE:
5494 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5495 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5498 case ICmpInst::ICMP_SGT:
5499 case ICmpInst::ICMP_SGE:
5500 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5501 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5504 case ICmpInst::ICMP_ULT:
5505 case ICmpInst::ICMP_ULE:
5506 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5507 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5510 case ICmpInst::ICMP_UGT:
5511 case ICmpInst::ICMP_UGE:
5512 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5513 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5521 /// getBECount - Subtract the end and start values and divide by the step,
5522 /// rounding up, to get the number of times the backedge is executed. Return
5523 /// CouldNotCompute if an intermediate computation overflows.
5524 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5528 assert(!isKnownNegative(Step) &&
5529 "This code doesn't handle negative strides yet!");
5531 const Type *Ty = Start->getType();
5532 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5533 const SCEV *Diff = getMinusSCEV(End, Start);
5534 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5536 // Add an adjustment to the difference between End and Start so that
5537 // the division will effectively round up.
5538 const SCEV *Add = getAddExpr(Diff, RoundUp);
5541 // Check Add for unsigned overflow.
5542 // TODO: More sophisticated things could be done here.
5543 const Type *WideTy = IntegerType::get(getContext(),
5544 getTypeSizeInBits(Ty) + 1);
5545 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5546 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5547 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5548 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5549 return getCouldNotCompute();
5552 return getUDivExpr(Add, Step);
5555 /// HowManyLessThans - Return the number of times a backedge containing the
5556 /// specified less-than comparison will execute. If not computable, return
5557 /// CouldNotCompute.
5558 ScalarEvolution::BackedgeTakenInfo
5559 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5560 const Loop *L, bool isSigned) {
5561 // Only handle: "ADDREC < LoopInvariant".
5562 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5564 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5565 if (!AddRec || AddRec->getLoop() != L)
5566 return getCouldNotCompute();
5568 // Check to see if we have a flag which makes analysis easy.
5569 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5570 AddRec->hasNoUnsignedWrap();
5572 if (AddRec->isAffine()) {
5573 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5574 const SCEV *Step = AddRec->getStepRecurrence(*this);
5577 return getCouldNotCompute();
5578 if (Step->isOne()) {
5579 // With unit stride, the iteration never steps past the limit value.
5580 } else if (isKnownPositive(Step)) {
5581 // Test whether a positive iteration can step past the limit
5582 // value and past the maximum value for its type in a single step.
5583 // Note that it's not sufficient to check NoWrap here, because even
5584 // though the value after a wrap is undefined, it's not undefined
5585 // behavior, so if wrap does occur, the loop could either terminate or
5586 // loop infinitely, but in either case, the loop is guaranteed to
5587 // iterate at least until the iteration where the wrapping occurs.
5588 const SCEV *One = getConstant(Step->getType(), 1);
5590 APInt Max = APInt::getSignedMaxValue(BitWidth);
5591 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5592 .slt(getSignedRange(RHS).getSignedMax()))
5593 return getCouldNotCompute();
5595 APInt Max = APInt::getMaxValue(BitWidth);
5596 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5597 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5598 return getCouldNotCompute();
5601 // TODO: Handle negative strides here and below.
5602 return getCouldNotCompute();
5604 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5605 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5606 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5607 // treat m-n as signed nor unsigned due to overflow possibility.
5609 // First, we get the value of the LHS in the first iteration: n
5610 const SCEV *Start = AddRec->getOperand(0);
5612 // Determine the minimum constant start value.
5613 const SCEV *MinStart = getConstant(isSigned ?
5614 getSignedRange(Start).getSignedMin() :
5615 getUnsignedRange(Start).getUnsignedMin());
5617 // If we know that the condition is true in order to enter the loop,
5618 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5619 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5620 // the division must round up.
5621 const SCEV *End = RHS;
5622 if (!isLoopEntryGuardedByCond(L,
5623 isSigned ? ICmpInst::ICMP_SLT :
5625 getMinusSCEV(Start, Step), RHS))
5626 End = isSigned ? getSMaxExpr(RHS, Start)
5627 : getUMaxExpr(RHS, Start);
5629 // Determine the maximum constant end value.
5630 const SCEV *MaxEnd = getConstant(isSigned ?
5631 getSignedRange(End).getSignedMax() :
5632 getUnsignedRange(End).getUnsignedMax());
5634 // If MaxEnd is within a step of the maximum integer value in its type,
5635 // adjust it down to the minimum value which would produce the same effect.
5636 // This allows the subsequent ceiling division of (N+(step-1))/step to
5637 // compute the correct value.
5638 const SCEV *StepMinusOne = getMinusSCEV(Step,
5639 getConstant(Step->getType(), 1));
5642 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5645 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5648 // Finally, we subtract these two values and divide, rounding up, to get
5649 // the number of times the backedge is executed.
5650 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5652 // The maximum backedge count is similar, except using the minimum start
5653 // value and the maximum end value.
5654 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5656 return BackedgeTakenInfo(BECount, MaxBECount);
5659 return getCouldNotCompute();
5662 /// getNumIterationsInRange - Return the number of iterations of this loop that
5663 /// produce values in the specified constant range. Another way of looking at
5664 /// this is that it returns the first iteration number where the value is not in
5665 /// the condition, thus computing the exit count. If the iteration count can't
5666 /// be computed, an instance of SCEVCouldNotCompute is returned.
5667 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5668 ScalarEvolution &SE) const {
5669 if (Range.isFullSet()) // Infinite loop.
5670 return SE.getCouldNotCompute();
5672 // If the start is a non-zero constant, shift the range to simplify things.
5673 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5674 if (!SC->getValue()->isZero()) {
5675 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5676 Operands[0] = SE.getConstant(SC->getType(), 0);
5677 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5678 if (const SCEVAddRecExpr *ShiftedAddRec =
5679 dyn_cast<SCEVAddRecExpr>(Shifted))
5680 return ShiftedAddRec->getNumIterationsInRange(
5681 Range.subtract(SC->getValue()->getValue()), SE);
5682 // This is strange and shouldn't happen.
5683 return SE.getCouldNotCompute();
5686 // The only time we can solve this is when we have all constant indices.
5687 // Otherwise, we cannot determine the overflow conditions.
5688 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5689 if (!isa<SCEVConstant>(getOperand(i)))
5690 return SE.getCouldNotCompute();
5693 // Okay at this point we know that all elements of the chrec are constants and
5694 // that the start element is zero.
5696 // First check to see if the range contains zero. If not, the first
5698 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5699 if (!Range.contains(APInt(BitWidth, 0)))
5700 return SE.getConstant(getType(), 0);
5703 // If this is an affine expression then we have this situation:
5704 // Solve {0,+,A} in Range === Ax in Range
5706 // We know that zero is in the range. If A is positive then we know that
5707 // the upper value of the range must be the first possible exit value.
5708 // If A is negative then the lower of the range is the last possible loop
5709 // value. Also note that we already checked for a full range.
5710 APInt One(BitWidth,1);
5711 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5712 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5714 // The exit value should be (End+A)/A.
5715 APInt ExitVal = (End + A).udiv(A);
5716 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5718 // Evaluate at the exit value. If we really did fall out of the valid
5719 // range, then we computed our trip count, otherwise wrap around or other
5720 // things must have happened.
5721 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5722 if (Range.contains(Val->getValue()))
5723 return SE.getCouldNotCompute(); // Something strange happened
5725 // Ensure that the previous value is in the range. This is a sanity check.
5726 assert(Range.contains(
5727 EvaluateConstantChrecAtConstant(this,
5728 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5729 "Linear scev computation is off in a bad way!");
5730 return SE.getConstant(ExitValue);
5731 } else if (isQuadratic()) {
5732 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5733 // quadratic equation to solve it. To do this, we must frame our problem in
5734 // terms of figuring out when zero is crossed, instead of when
5735 // Range.getUpper() is crossed.
5736 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5737 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5738 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5740 // Next, solve the constructed addrec
5741 std::pair<const SCEV *,const SCEV *> Roots =
5742 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5743 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5744 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5746 // Pick the smallest positive root value.
5747 if (ConstantInt *CB =
5748 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5749 R1->getValue(), R2->getValue()))) {
5750 if (CB->getZExtValue() == false)
5751 std::swap(R1, R2); // R1 is the minimum root now.
5753 // Make sure the root is not off by one. The returned iteration should
5754 // not be in the range, but the previous one should be. When solving
5755 // for "X*X < 5", for example, we should not return a root of 2.
5756 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5759 if (Range.contains(R1Val->getValue())) {
5760 // The next iteration must be out of the range...
5761 ConstantInt *NextVal =
5762 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5764 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5765 if (!Range.contains(R1Val->getValue()))
5766 return SE.getConstant(NextVal);
5767 return SE.getCouldNotCompute(); // Something strange happened
5770 // If R1 was not in the range, then it is a good return value. Make
5771 // sure that R1-1 WAS in the range though, just in case.
5772 ConstantInt *NextVal =
5773 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5774 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5775 if (Range.contains(R1Val->getValue()))
5777 return SE.getCouldNotCompute(); // Something strange happened
5782 return SE.getCouldNotCompute();
5787 //===----------------------------------------------------------------------===//
5788 // SCEVCallbackVH Class Implementation
5789 //===----------------------------------------------------------------------===//
5791 void ScalarEvolution::SCEVCallbackVH::deleted() {
5792 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5793 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5794 SE->ConstantEvolutionLoopExitValue.erase(PN);
5795 SE->ValueExprMap.erase(getValPtr());
5796 // this now dangles!
5799 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5800 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5802 // Forget all the expressions associated with users of the old value,
5803 // so that future queries will recompute the expressions using the new
5805 Value *Old = getValPtr();
5806 SmallVector<User *, 16> Worklist;
5807 SmallPtrSet<User *, 8> Visited;
5808 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5810 Worklist.push_back(*UI);
5811 while (!Worklist.empty()) {
5812 User *U = Worklist.pop_back_val();
5813 // Deleting the Old value will cause this to dangle. Postpone
5814 // that until everything else is done.
5817 if (!Visited.insert(U))
5819 if (PHINode *PN = dyn_cast<PHINode>(U))
5820 SE->ConstantEvolutionLoopExitValue.erase(PN);
5821 SE->ValueExprMap.erase(U);
5822 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5824 Worklist.push_back(*UI);
5826 // Delete the Old value.
5827 if (PHINode *PN = dyn_cast<PHINode>(Old))
5828 SE->ConstantEvolutionLoopExitValue.erase(PN);
5829 SE->ValueExprMap.erase(Old);
5830 // this now dangles!
5833 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5834 : CallbackVH(V), SE(se) {}
5836 //===----------------------------------------------------------------------===//
5837 // ScalarEvolution Class Implementation
5838 //===----------------------------------------------------------------------===//
5840 ScalarEvolution::ScalarEvolution()
5841 : FunctionPass(ID), FirstUnknown(0) {
5844 bool ScalarEvolution::runOnFunction(Function &F) {
5846 LI = &getAnalysis<LoopInfo>();
5847 TD = getAnalysisIfAvailable<TargetData>();
5848 DT = &getAnalysis<DominatorTree>();
5852 void ScalarEvolution::releaseMemory() {
5853 // Iterate through all the SCEVUnknown instances and call their
5854 // destructors, so that they release their references to their values.
5855 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
5859 ValueExprMap.clear();
5860 BackedgeTakenCounts.clear();
5861 ConstantEvolutionLoopExitValue.clear();
5862 ValuesAtScopes.clear();
5863 UniqueSCEVs.clear();
5864 SCEVAllocator.Reset();
5867 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5868 AU.setPreservesAll();
5869 AU.addRequiredTransitive<LoopInfo>();
5870 AU.addRequiredTransitive<DominatorTree>();
5873 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5874 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5877 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5879 // Print all inner loops first
5880 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5881 PrintLoopInfo(OS, SE, *I);
5884 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5887 SmallVector<BasicBlock *, 8> ExitBlocks;
5888 L->getExitBlocks(ExitBlocks);
5889 if (ExitBlocks.size() != 1)
5890 OS << "<multiple exits> ";
5892 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5893 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5895 OS << "Unpredictable backedge-taken count. ";
5900 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5903 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5904 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5906 OS << "Unpredictable max backedge-taken count. ";
5912 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5913 // ScalarEvolution's implementation of the print method is to print
5914 // out SCEV values of all instructions that are interesting. Doing
5915 // this potentially causes it to create new SCEV objects though,
5916 // which technically conflicts with the const qualifier. This isn't
5917 // observable from outside the class though, so casting away the
5918 // const isn't dangerous.
5919 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5921 OS << "Classifying expressions for: ";
5922 WriteAsOperand(OS, F, /*PrintType=*/false);
5924 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5925 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5928 const SCEV *SV = SE.getSCEV(&*I);
5931 const Loop *L = LI->getLoopFor((*I).getParent());
5933 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5940 OS << "\t\t" "Exits: ";
5941 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5942 if (!ExitValue->isLoopInvariant(L)) {
5943 OS << "<<Unknown>>";
5952 OS << "Determining loop execution counts for: ";
5953 WriteAsOperand(OS, F, /*PrintType=*/false);
5955 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5956 PrintLoopInfo(OS, &SE, *I);