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 for (unsigned OtherMulIdx = Idx+1;
1593 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1595 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1596 // If MulOp occurs in OtherMul, we can fold the two multiplies
1598 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1599 OMulOp != e; ++OMulOp)
1600 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1601 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1602 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1603 if (Mul->getNumOperands() != 2) {
1604 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1605 Mul->op_begin()+MulOp);
1606 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1607 InnerMul1 = getMulExpr(MulOps);
1609 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1610 if (OtherMul->getNumOperands() != 2) {
1611 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1612 OtherMul->op_begin()+OMulOp);
1613 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1614 InnerMul2 = getMulExpr(MulOps);
1616 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1617 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1618 if (Ops.size() == 2) return OuterMul;
1619 Ops.erase(Ops.begin()+Idx);
1620 Ops.erase(Ops.begin()+OtherMulIdx-1);
1621 Ops.push_back(OuterMul);
1622 return getAddExpr(Ops);
1628 // If there are any add recurrences in the operands list, see if any other
1629 // added values are loop invariant. If so, we can fold them into the
1631 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1634 // Scan over all recurrences, trying to fold loop invariants into them.
1635 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1636 // Scan all of the other operands to this add and add them to the vector if
1637 // they are loop invariant w.r.t. the recurrence.
1638 SmallVector<const SCEV *, 8> LIOps;
1639 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1640 const Loop *AddRecLoop = AddRec->getLoop();
1641 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1642 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1643 LIOps.push_back(Ops[i]);
1644 Ops.erase(Ops.begin()+i);
1648 // If we found some loop invariants, fold them into the recurrence.
1649 if (!LIOps.empty()) {
1650 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1651 LIOps.push_back(AddRec->getStart());
1653 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1655 AddRecOps[0] = getAddExpr(LIOps);
1657 // Build the new addrec. Propagate the NUW and NSW flags if both the
1658 // outer add and the inner addrec are guaranteed to have no overflow.
1659 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1660 HasNUW && AddRec->hasNoUnsignedWrap(),
1661 HasNSW && AddRec->hasNoSignedWrap());
1663 // If all of the other operands were loop invariant, we are done.
1664 if (Ops.size() == 1) return NewRec;
1666 // Otherwise, add the folded AddRec by the non-liv parts.
1667 for (unsigned i = 0;; ++i)
1668 if (Ops[i] == AddRec) {
1672 return getAddExpr(Ops);
1675 // Okay, if there weren't any loop invariants to be folded, check to see if
1676 // there are multiple AddRec's with the same loop induction variable being
1677 // added together. If so, we can fold them.
1678 for (unsigned OtherIdx = Idx+1;
1679 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1681 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1682 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1683 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1685 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1687 if (const SCEVAddRecExpr *OtherAddRec =
1688 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1689 if (OtherAddRec->getLoop() == AddRecLoop) {
1690 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1692 if (i >= AddRecOps.size()) {
1693 AddRecOps.append(OtherAddRec->op_begin()+i,
1694 OtherAddRec->op_end());
1697 AddRecOps[i] = getAddExpr(AddRecOps[i],
1698 OtherAddRec->getOperand(i));
1700 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1702 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop);
1703 return getAddExpr(Ops);
1706 // Otherwise couldn't fold anything into this recurrence. Move onto the
1710 // Okay, it looks like we really DO need an add expr. Check to see if we
1711 // already have one, otherwise create a new one.
1712 FoldingSetNodeID ID;
1713 ID.AddInteger(scAddExpr);
1714 ID.AddInteger(Ops.size());
1715 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1716 ID.AddPointer(Ops[i]);
1719 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1721 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1722 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1723 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1725 UniqueSCEVs.InsertNode(S, IP);
1727 if (HasNUW) S->setHasNoUnsignedWrap(true);
1728 if (HasNSW) S->setHasNoSignedWrap(true);
1732 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1734 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1735 bool HasNUW, bool HasNSW) {
1736 assert(!Ops.empty() && "Cannot get empty mul!");
1737 if (Ops.size() == 1) return Ops[0];
1739 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1740 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1741 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1742 "SCEVMulExpr operand types don't match!");
1745 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1746 if (!HasNUW && HasNSW) {
1748 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1749 E = Ops.end(); I != E; ++I)
1750 if (!isKnownNonNegative(*I)) {
1754 if (All) HasNUW = true;
1757 // Sort by complexity, this groups all similar expression types together.
1758 GroupByComplexity(Ops, LI);
1760 // If there are any constants, fold them together.
1762 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1764 // C1*(C2+V) -> C1*C2 + C1*V
1765 if (Ops.size() == 2)
1766 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1767 if (Add->getNumOperands() == 2 &&
1768 isa<SCEVConstant>(Add->getOperand(0)))
1769 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1770 getMulExpr(LHSC, Add->getOperand(1)));
1773 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1774 // We found two constants, fold them together!
1775 ConstantInt *Fold = ConstantInt::get(getContext(),
1776 LHSC->getValue()->getValue() *
1777 RHSC->getValue()->getValue());
1778 Ops[0] = getConstant(Fold);
1779 Ops.erase(Ops.begin()+1); // Erase the folded element
1780 if (Ops.size() == 1) return Ops[0];
1781 LHSC = cast<SCEVConstant>(Ops[0]);
1784 // If we are left with a constant one being multiplied, strip it off.
1785 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1786 Ops.erase(Ops.begin());
1788 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1789 // If we have a multiply of zero, it will always be zero.
1791 } else if (Ops[0]->isAllOnesValue()) {
1792 // If we have a mul by -1 of an add, try distributing the -1 among the
1794 if (Ops.size() == 2)
1795 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1796 SmallVector<const SCEV *, 4> NewOps;
1797 bool AnyFolded = false;
1798 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1800 const SCEV *Mul = getMulExpr(Ops[0], *I);
1801 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1802 NewOps.push_back(Mul);
1805 return getAddExpr(NewOps);
1809 if (Ops.size() == 1)
1813 // Skip over the add expression until we get to a multiply.
1814 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1817 // If there are mul operands inline them all into this expression.
1818 if (Idx < Ops.size()) {
1819 bool DeletedMul = false;
1820 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1821 // If we have an mul, expand the mul operands onto the end of the operands
1823 Ops.erase(Ops.begin()+Idx);
1824 Ops.append(Mul->op_begin(), Mul->op_end());
1828 // If we deleted at least one mul, we added operands to the end of the list,
1829 // and they are not necessarily sorted. Recurse to resort and resimplify
1830 // any operands we just acquired.
1832 return getMulExpr(Ops);
1835 // If there are any add recurrences in the operands list, see if any other
1836 // added values are loop invariant. If so, we can fold them into the
1838 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1841 // Scan over all recurrences, trying to fold loop invariants into them.
1842 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1843 // Scan all of the other operands to this mul and add them to the vector if
1844 // they are loop invariant w.r.t. the recurrence.
1845 SmallVector<const SCEV *, 8> LIOps;
1846 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1847 const Loop *AddRecLoop = AddRec->getLoop();
1848 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1849 if (Ops[i]->isLoopInvariant(AddRecLoop)) {
1850 LIOps.push_back(Ops[i]);
1851 Ops.erase(Ops.begin()+i);
1855 // If we found some loop invariants, fold them into the recurrence.
1856 if (!LIOps.empty()) {
1857 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1858 SmallVector<const SCEV *, 4> NewOps;
1859 NewOps.reserve(AddRec->getNumOperands());
1860 const SCEV *Scale = getMulExpr(LIOps);
1861 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1862 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1864 // Build the new addrec. Propagate the NUW and NSW flags if both the
1865 // outer mul and the inner addrec are guaranteed to have no overflow.
1866 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop,
1867 HasNUW && AddRec->hasNoUnsignedWrap(),
1868 HasNSW && AddRec->hasNoSignedWrap());
1870 // If all of the other operands were loop invariant, we are done.
1871 if (Ops.size() == 1) return NewRec;
1873 // Otherwise, multiply the folded AddRec by the non-liv parts.
1874 for (unsigned i = 0;; ++i)
1875 if (Ops[i] == AddRec) {
1879 return getMulExpr(Ops);
1882 // Okay, if there weren't any loop invariants to be folded, check to see if
1883 // there are multiple AddRec's with the same loop induction variable being
1884 // multiplied together. If so, we can fold them.
1885 for (unsigned OtherIdx = Idx+1;
1886 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1887 if (OtherIdx != Idx) {
1888 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1889 if (AddRecLoop == OtherAddRec->getLoop()) {
1890 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1891 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1892 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1893 const SCEV *B = F->getStepRecurrence(*this);
1894 const SCEV *D = G->getStepRecurrence(*this);
1895 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1898 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1900 if (Ops.size() == 2) return NewAddRec;
1902 Ops.erase(Ops.begin()+Idx);
1903 Ops.erase(Ops.begin()+OtherIdx-1);
1904 Ops.push_back(NewAddRec);
1905 return getMulExpr(Ops);
1909 // Otherwise couldn't fold anything into this recurrence. Move onto the
1913 // Okay, it looks like we really DO need an mul expr. Check to see if we
1914 // already have one, otherwise create a new one.
1915 FoldingSetNodeID ID;
1916 ID.AddInteger(scMulExpr);
1917 ID.AddInteger(Ops.size());
1918 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1919 ID.AddPointer(Ops[i]);
1922 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1924 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1925 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1926 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1928 UniqueSCEVs.InsertNode(S, IP);
1930 if (HasNUW) S->setHasNoUnsignedWrap(true);
1931 if (HasNSW) S->setHasNoSignedWrap(true);
1935 /// getUDivExpr - Get a canonical unsigned division expression, or something
1936 /// simpler if possible.
1937 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1939 assert(getEffectiveSCEVType(LHS->getType()) ==
1940 getEffectiveSCEVType(RHS->getType()) &&
1941 "SCEVUDivExpr operand types don't match!");
1943 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1944 if (RHSC->getValue()->equalsInt(1))
1945 return LHS; // X udiv 1 --> x
1946 // If the denominator is zero, the result of the udiv is undefined. Don't
1947 // try to analyze it, because the resolution chosen here may differ from
1948 // the resolution chosen in other parts of the compiler.
1949 if (!RHSC->getValue()->isZero()) {
1950 // Determine if the division can be folded into the operands of
1952 // TODO: Generalize this to non-constants by using known-bits information.
1953 const Type *Ty = LHS->getType();
1954 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1955 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1956 // For non-power-of-two values, effectively round the value up to the
1957 // nearest power of two.
1958 if (!RHSC->getValue()->getValue().isPowerOf2())
1960 const IntegerType *ExtTy =
1961 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1962 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1963 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1964 if (const SCEVConstant *Step =
1965 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1966 if (!Step->getValue()->getValue()
1967 .urem(RHSC->getValue()->getValue()) &&
1968 getZeroExtendExpr(AR, ExtTy) ==
1969 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1970 getZeroExtendExpr(Step, ExtTy),
1972 SmallVector<const SCEV *, 4> Operands;
1973 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1974 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1975 return getAddRecExpr(Operands, AR->getLoop());
1977 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1978 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1979 SmallVector<const SCEV *, 4> Operands;
1980 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1981 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1982 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1983 // Find an operand that's safely divisible.
1984 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1985 const SCEV *Op = M->getOperand(i);
1986 const SCEV *Div = getUDivExpr(Op, RHSC);
1987 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1988 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1991 return getMulExpr(Operands);
1995 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1996 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1997 SmallVector<const SCEV *, 4> Operands;
1998 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1999 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2000 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2002 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2003 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2004 if (isa<SCEVUDivExpr>(Op) ||
2005 getMulExpr(Op, RHS) != A->getOperand(i))
2007 Operands.push_back(Op);
2009 if (Operands.size() == A->getNumOperands())
2010 return getAddExpr(Operands);
2014 // Fold if both operands are constant.
2015 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2016 Constant *LHSCV = LHSC->getValue();
2017 Constant *RHSCV = RHSC->getValue();
2018 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2024 FoldingSetNodeID ID;
2025 ID.AddInteger(scUDivExpr);
2029 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2030 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2032 UniqueSCEVs.InsertNode(S, IP);
2037 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2038 /// Simplify the expression as much as possible.
2039 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
2040 const SCEV *Step, const Loop *L,
2041 bool HasNUW, bool HasNSW) {
2042 SmallVector<const SCEV *, 4> Operands;
2043 Operands.push_back(Start);
2044 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2045 if (StepChrec->getLoop() == L) {
2046 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2047 return getAddRecExpr(Operands, L);
2050 Operands.push_back(Step);
2051 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
2054 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2055 /// Simplify the expression as much as possible.
2057 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2059 bool HasNUW, bool HasNSW) {
2060 if (Operands.size() == 1) return Operands[0];
2062 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2063 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2064 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2065 "SCEVAddRecExpr operand types don't match!");
2068 if (Operands.back()->isZero()) {
2069 Operands.pop_back();
2070 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
2073 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2074 // use that information to infer NUW and NSW flags. However, computing a
2075 // BE count requires calling getAddRecExpr, so we may not yet have a
2076 // meaningful BE count at this point (and if we don't, we'd be stuck
2077 // with a SCEVCouldNotCompute as the cached BE count).
2079 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
2080 if (!HasNUW && HasNSW) {
2082 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2083 E = Operands.end(); I != E; ++I)
2084 if (!isKnownNonNegative(*I)) {
2088 if (All) HasNUW = true;
2091 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2092 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2093 const Loop *NestedLoop = NestedAR->getLoop();
2094 if (L->contains(NestedLoop) ?
2095 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2096 (!NestedLoop->contains(L) &&
2097 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2098 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2099 NestedAR->op_end());
2100 Operands[0] = NestedAR->getStart();
2101 // AddRecs require their operands be loop-invariant with respect to their
2102 // loops. Don't perform this transformation if it would break this
2104 bool AllInvariant = true;
2105 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2106 if (!Operands[i]->isLoopInvariant(L)) {
2107 AllInvariant = false;
2111 NestedOperands[0] = getAddRecExpr(Operands, L);
2112 AllInvariant = true;
2113 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2114 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
2115 AllInvariant = false;
2119 // Ok, both add recurrences are valid after the transformation.
2120 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2122 // Reset Operands to its original state.
2123 Operands[0] = NestedAR;
2127 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2128 // already have one, otherwise create a new one.
2129 FoldingSetNodeID ID;
2130 ID.AddInteger(scAddRecExpr);
2131 ID.AddInteger(Operands.size());
2132 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2133 ID.AddPointer(Operands[i]);
2137 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2139 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2140 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2141 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2142 O, Operands.size(), L);
2143 UniqueSCEVs.InsertNode(S, IP);
2145 if (HasNUW) S->setHasNoUnsignedWrap(true);
2146 if (HasNSW) S->setHasNoSignedWrap(true);
2150 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2152 SmallVector<const SCEV *, 2> Ops;
2155 return getSMaxExpr(Ops);
2159 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2160 assert(!Ops.empty() && "Cannot get empty smax!");
2161 if (Ops.size() == 1) return Ops[0];
2163 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2164 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2165 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2166 "SCEVSMaxExpr operand types don't match!");
2169 // Sort by complexity, this groups all similar expression types together.
2170 GroupByComplexity(Ops, LI);
2172 // If there are any constants, fold them together.
2174 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2176 assert(Idx < Ops.size());
2177 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2178 // We found two constants, fold them together!
2179 ConstantInt *Fold = ConstantInt::get(getContext(),
2180 APIntOps::smax(LHSC->getValue()->getValue(),
2181 RHSC->getValue()->getValue()));
2182 Ops[0] = getConstant(Fold);
2183 Ops.erase(Ops.begin()+1); // Erase the folded element
2184 if (Ops.size() == 1) return Ops[0];
2185 LHSC = cast<SCEVConstant>(Ops[0]);
2188 // If we are left with a constant minimum-int, strip it off.
2189 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2190 Ops.erase(Ops.begin());
2192 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2193 // If we have an smax with a constant maximum-int, it will always be
2198 if (Ops.size() == 1) return Ops[0];
2201 // Find the first SMax
2202 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2205 // Check to see if one of the operands is an SMax. If so, expand its operands
2206 // onto our operand list, and recurse to simplify.
2207 if (Idx < Ops.size()) {
2208 bool DeletedSMax = false;
2209 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2210 Ops.erase(Ops.begin()+Idx);
2211 Ops.append(SMax->op_begin(), SMax->op_end());
2216 return getSMaxExpr(Ops);
2219 // Okay, check to see if the same value occurs in the operand list twice. If
2220 // so, delete one. Since we sorted the list, these values are required to
2222 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2223 // X smax Y smax Y --> X smax Y
2224 // X smax Y --> X, if X is always greater than Y
2225 if (Ops[i] == Ops[i+1] ||
2226 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2227 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2229 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2230 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2234 if (Ops.size() == 1) return Ops[0];
2236 assert(!Ops.empty() && "Reduced smax down to nothing!");
2238 // Okay, it looks like we really DO need an smax expr. Check to see if we
2239 // already have one, otherwise create a new one.
2240 FoldingSetNodeID ID;
2241 ID.AddInteger(scSMaxExpr);
2242 ID.AddInteger(Ops.size());
2243 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2244 ID.AddPointer(Ops[i]);
2246 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2247 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2248 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2249 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2251 UniqueSCEVs.InsertNode(S, IP);
2255 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2257 SmallVector<const SCEV *, 2> Ops;
2260 return getUMaxExpr(Ops);
2264 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2265 assert(!Ops.empty() && "Cannot get empty umax!");
2266 if (Ops.size() == 1) return Ops[0];
2268 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2269 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2270 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2271 "SCEVUMaxExpr operand types don't match!");
2274 // Sort by complexity, this groups all similar expression types together.
2275 GroupByComplexity(Ops, LI);
2277 // If there are any constants, fold them together.
2279 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2281 assert(Idx < Ops.size());
2282 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2283 // We found two constants, fold them together!
2284 ConstantInt *Fold = ConstantInt::get(getContext(),
2285 APIntOps::umax(LHSC->getValue()->getValue(),
2286 RHSC->getValue()->getValue()));
2287 Ops[0] = getConstant(Fold);
2288 Ops.erase(Ops.begin()+1); // Erase the folded element
2289 if (Ops.size() == 1) return Ops[0];
2290 LHSC = cast<SCEVConstant>(Ops[0]);
2293 // If we are left with a constant minimum-int, strip it off.
2294 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2295 Ops.erase(Ops.begin());
2297 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2298 // If we have an umax with a constant maximum-int, it will always be
2303 if (Ops.size() == 1) return Ops[0];
2306 // Find the first UMax
2307 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2310 // Check to see if one of the operands is a UMax. If so, expand its operands
2311 // onto our operand list, and recurse to simplify.
2312 if (Idx < Ops.size()) {
2313 bool DeletedUMax = false;
2314 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2315 Ops.erase(Ops.begin()+Idx);
2316 Ops.append(UMax->op_begin(), UMax->op_end());
2321 return getUMaxExpr(Ops);
2324 // Okay, check to see if the same value occurs in the operand list twice. If
2325 // so, delete one. Since we sorted the list, these values are required to
2327 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2328 // X umax Y umax Y --> X umax Y
2329 // X umax Y --> X, if X is always greater than Y
2330 if (Ops[i] == Ops[i+1] ||
2331 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2332 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2334 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2335 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2339 if (Ops.size() == 1) return Ops[0];
2341 assert(!Ops.empty() && "Reduced umax down to nothing!");
2343 // Okay, it looks like we really DO need a umax expr. Check to see if we
2344 // already have one, otherwise create a new one.
2345 FoldingSetNodeID ID;
2346 ID.AddInteger(scUMaxExpr);
2347 ID.AddInteger(Ops.size());
2348 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2349 ID.AddPointer(Ops[i]);
2351 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2352 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2353 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2354 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2356 UniqueSCEVs.InsertNode(S, IP);
2360 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2362 // ~smax(~x, ~y) == smin(x, y).
2363 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2366 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2368 // ~umax(~x, ~y) == umin(x, y)
2369 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2372 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2373 // If we have TargetData, we can bypass creating a target-independent
2374 // constant expression and then folding it back into a ConstantInt.
2375 // This is just a compile-time optimization.
2377 return getConstant(TD->getIntPtrType(getContext()),
2378 TD->getTypeAllocSize(AllocTy));
2380 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2381 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2382 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2384 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2385 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2388 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2389 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2390 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2391 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2393 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2394 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2397 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2399 // If we have TargetData, we can bypass creating a target-independent
2400 // constant expression and then folding it back into a ConstantInt.
2401 // This is just a compile-time optimization.
2403 return getConstant(TD->getIntPtrType(getContext()),
2404 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2406 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2407 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2408 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2410 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2411 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2414 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2415 Constant *FieldNo) {
2416 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2417 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2418 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2420 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2421 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2424 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2425 // Don't attempt to do anything other than create a SCEVUnknown object
2426 // here. createSCEV only calls getUnknown after checking for all other
2427 // interesting possibilities, and any other code that calls getUnknown
2428 // is doing so in order to hide a value from SCEV canonicalization.
2430 FoldingSetNodeID ID;
2431 ID.AddInteger(scUnknown);
2434 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2435 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2436 "Stale SCEVUnknown in uniquing map!");
2439 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2441 FirstUnknown = cast<SCEVUnknown>(S);
2442 UniqueSCEVs.InsertNode(S, IP);
2446 //===----------------------------------------------------------------------===//
2447 // Basic SCEV Analysis and PHI Idiom Recognition Code
2450 /// isSCEVable - Test if values of the given type are analyzable within
2451 /// the SCEV framework. This primarily includes integer types, and it
2452 /// can optionally include pointer types if the ScalarEvolution class
2453 /// has access to target-specific information.
2454 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2455 // Integers and pointers are always SCEVable.
2456 return Ty->isIntegerTy() || Ty->isPointerTy();
2459 /// getTypeSizeInBits - Return the size in bits of the specified type,
2460 /// for which isSCEVable must return true.
2461 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2462 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2464 // If we have a TargetData, use it!
2466 return TD->getTypeSizeInBits(Ty);
2468 // Integer types have fixed sizes.
2469 if (Ty->isIntegerTy())
2470 return Ty->getPrimitiveSizeInBits();
2472 // The only other support type is pointer. Without TargetData, conservatively
2473 // assume pointers are 64-bit.
2474 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2478 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2479 /// the given type and which represents how SCEV will treat the given
2480 /// type, for which isSCEVable must return true. For pointer types,
2481 /// this is the pointer-sized integer type.
2482 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2483 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2485 if (Ty->isIntegerTy())
2488 // The only other support type is pointer.
2489 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2490 if (TD) return TD->getIntPtrType(getContext());
2492 // Without TargetData, conservatively assume pointers are 64-bit.
2493 return Type::getInt64Ty(getContext());
2496 const SCEV *ScalarEvolution::getCouldNotCompute() {
2497 return &CouldNotCompute;
2500 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2501 /// expression and create a new one.
2502 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2503 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2505 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2506 if (I != ValueExprMap.end()) return I->second;
2507 const SCEV *S = createSCEV(V);
2509 // The process of creating a SCEV for V may have caused other SCEVs
2510 // to have been created, so it's necessary to insert the new entry
2511 // from scratch, rather than trying to remember the insert position
2513 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2517 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2519 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2520 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2522 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2524 const Type *Ty = V->getType();
2525 Ty = getEffectiveSCEVType(Ty);
2526 return getMulExpr(V,
2527 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2530 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2531 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2532 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2534 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2536 const Type *Ty = V->getType();
2537 Ty = getEffectiveSCEVType(Ty);
2538 const SCEV *AllOnes =
2539 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2540 return getMinusSCEV(AllOnes, V);
2543 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2545 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2547 // Fast path: X - X --> 0.
2549 return getConstant(LHS->getType(), 0);
2552 return getAddExpr(LHS, getNegativeSCEV(RHS));
2555 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2556 /// input value to the specified type. If the type must be extended, it is zero
2559 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2561 const Type *SrcTy = V->getType();
2562 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2563 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2564 "Cannot truncate or zero extend with non-integer arguments!");
2565 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2566 return V; // No conversion
2567 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2568 return getTruncateExpr(V, Ty);
2569 return getZeroExtendExpr(V, Ty);
2572 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2573 /// input value to the specified type. If the type must be extended, it is sign
2576 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2578 const Type *SrcTy = V->getType();
2579 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2580 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2581 "Cannot truncate or zero extend with non-integer arguments!");
2582 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2583 return V; // No conversion
2584 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2585 return getTruncateExpr(V, Ty);
2586 return getSignExtendExpr(V, Ty);
2589 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2590 /// input value to the specified type. If the type must be extended, it is zero
2591 /// extended. The conversion must not be narrowing.
2593 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2594 const Type *SrcTy = V->getType();
2595 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2596 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2597 "Cannot noop or zero extend with non-integer arguments!");
2598 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2599 "getNoopOrZeroExtend cannot truncate!");
2600 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2601 return V; // No conversion
2602 return getZeroExtendExpr(V, Ty);
2605 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2606 /// input value to the specified type. If the type must be extended, it is sign
2607 /// extended. The conversion must not be narrowing.
2609 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2610 const Type *SrcTy = V->getType();
2611 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2612 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2613 "Cannot noop or sign extend with non-integer arguments!");
2614 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2615 "getNoopOrSignExtend cannot truncate!");
2616 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2617 return V; // No conversion
2618 return getSignExtendExpr(V, Ty);
2621 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2622 /// the input value to the specified type. If the type must be extended,
2623 /// it is extended with unspecified bits. The conversion must not be
2626 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2627 const Type *SrcTy = V->getType();
2628 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2629 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2630 "Cannot noop or any extend with non-integer arguments!");
2631 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2632 "getNoopOrAnyExtend cannot truncate!");
2633 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2634 return V; // No conversion
2635 return getAnyExtendExpr(V, Ty);
2638 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2639 /// input value to the specified type. The conversion must not be widening.
2641 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2642 const Type *SrcTy = V->getType();
2643 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2644 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2645 "Cannot truncate or noop with non-integer arguments!");
2646 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2647 "getTruncateOrNoop cannot extend!");
2648 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2649 return V; // No conversion
2650 return getTruncateExpr(V, Ty);
2653 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2654 /// the types using zero-extension, and then perform a umax operation
2656 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2658 const SCEV *PromotedLHS = LHS;
2659 const SCEV *PromotedRHS = RHS;
2661 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2662 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2664 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2666 return getUMaxExpr(PromotedLHS, PromotedRHS);
2669 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2670 /// the types using zero-extension, and then perform a umin operation
2672 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2674 const SCEV *PromotedLHS = LHS;
2675 const SCEV *PromotedRHS = RHS;
2677 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2678 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2680 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2682 return getUMinExpr(PromotedLHS, PromotedRHS);
2685 /// PushDefUseChildren - Push users of the given Instruction
2686 /// onto the given Worklist.
2688 PushDefUseChildren(Instruction *I,
2689 SmallVectorImpl<Instruction *> &Worklist) {
2690 // Push the def-use children onto the Worklist stack.
2691 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2693 Worklist.push_back(cast<Instruction>(*UI));
2696 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2697 /// instructions that depend on the given instruction and removes them from
2698 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2701 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2702 SmallVector<Instruction *, 16> Worklist;
2703 PushDefUseChildren(PN, Worklist);
2705 SmallPtrSet<Instruction *, 8> Visited;
2707 while (!Worklist.empty()) {
2708 Instruction *I = Worklist.pop_back_val();
2709 if (!Visited.insert(I)) continue;
2711 ValueExprMapType::iterator It =
2712 ValueExprMap.find(static_cast<Value *>(I));
2713 if (It != ValueExprMap.end()) {
2714 // Short-circuit the def-use traversal if the symbolic name
2715 // ceases to appear in expressions.
2716 if (It->second != SymName && !It->second->hasOperand(SymName))
2719 // SCEVUnknown for a PHI either means that it has an unrecognized
2720 // structure, it's a PHI that's in the progress of being computed
2721 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2722 // additional loop trip count information isn't going to change anything.
2723 // In the second case, createNodeForPHI will perform the necessary
2724 // updates on its own when it gets to that point. In the third, we do
2725 // want to forget the SCEVUnknown.
2726 if (!isa<PHINode>(I) ||
2727 !isa<SCEVUnknown>(It->second) ||
2728 (I != PN && It->second == SymName)) {
2729 ValuesAtScopes.erase(It->second);
2730 ValueExprMap.erase(It);
2734 PushDefUseChildren(I, Worklist);
2738 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2739 /// a loop header, making it a potential recurrence, or it doesn't.
2741 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2742 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2743 if (L->getHeader() == PN->getParent()) {
2744 // The loop may have multiple entrances or multiple exits; we can analyze
2745 // this phi as an addrec if it has a unique entry value and a unique
2747 Value *BEValueV = 0, *StartValueV = 0;
2748 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2749 Value *V = PN->getIncomingValue(i);
2750 if (L->contains(PN->getIncomingBlock(i))) {
2753 } else if (BEValueV != V) {
2757 } else if (!StartValueV) {
2759 } else if (StartValueV != V) {
2764 if (BEValueV && StartValueV) {
2765 // While we are analyzing this PHI node, handle its value symbolically.
2766 const SCEV *SymbolicName = getUnknown(PN);
2767 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2768 "PHI node already processed?");
2769 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2771 // Using this symbolic name for the PHI, analyze the value coming around
2773 const SCEV *BEValue = getSCEV(BEValueV);
2775 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2776 // has a special value for the first iteration of the loop.
2778 // If the value coming around the backedge is an add with the symbolic
2779 // value we just inserted, then we found a simple induction variable!
2780 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2781 // If there is a single occurrence of the symbolic value, replace it
2782 // with a recurrence.
2783 unsigned FoundIndex = Add->getNumOperands();
2784 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2785 if (Add->getOperand(i) == SymbolicName)
2786 if (FoundIndex == e) {
2791 if (FoundIndex != Add->getNumOperands()) {
2792 // Create an add with everything but the specified operand.
2793 SmallVector<const SCEV *, 8> Ops;
2794 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2795 if (i != FoundIndex)
2796 Ops.push_back(Add->getOperand(i));
2797 const SCEV *Accum = getAddExpr(Ops);
2799 // This is not a valid addrec if the step amount is varying each
2800 // loop iteration, but is not itself an addrec in this loop.
2801 if (Accum->isLoopInvariant(L) ||
2802 (isa<SCEVAddRecExpr>(Accum) &&
2803 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2804 bool HasNUW = false;
2805 bool HasNSW = false;
2807 // If the increment doesn't overflow, then neither the addrec nor
2808 // the post-increment will overflow.
2809 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2810 if (OBO->hasNoUnsignedWrap())
2812 if (OBO->hasNoSignedWrap())
2816 const SCEV *StartVal = getSCEV(StartValueV);
2817 const SCEV *PHISCEV =
2818 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2820 // Since the no-wrap flags are on the increment, they apply to the
2821 // post-incremented value as well.
2822 if (Accum->isLoopInvariant(L))
2823 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2824 Accum, L, HasNUW, HasNSW);
2826 // Okay, for the entire analysis of this edge we assumed the PHI
2827 // to be symbolic. We now need to go back and purge all of the
2828 // entries for the scalars that use the symbolic expression.
2829 ForgetSymbolicName(PN, SymbolicName);
2830 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2834 } else if (const SCEVAddRecExpr *AddRec =
2835 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2836 // Otherwise, this could be a loop like this:
2837 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2838 // In this case, j = {1,+,1} and BEValue is j.
2839 // Because the other in-value of i (0) fits the evolution of BEValue
2840 // i really is an addrec evolution.
2841 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2842 const SCEV *StartVal = getSCEV(StartValueV);
2844 // If StartVal = j.start - j.stride, we can use StartVal as the
2845 // initial step of the addrec evolution.
2846 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2847 AddRec->getOperand(1))) {
2848 const SCEV *PHISCEV =
2849 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2851 // Okay, for the entire analysis of this edge we assumed the PHI
2852 // to be symbolic. We now need to go back and purge all of the
2853 // entries for the scalars that use the symbolic expression.
2854 ForgetSymbolicName(PN, SymbolicName);
2855 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2863 // If the PHI has a single incoming value, follow that value, unless the
2864 // PHI's incoming blocks are in a different loop, in which case doing so
2865 // risks breaking LCSSA form. Instcombine would normally zap these, but
2866 // it doesn't have DominatorTree information, so it may miss cases.
2867 if (Value *V = PN->hasConstantValue(DT)) {
2868 bool AllSameLoop = true;
2869 Loop *PNLoop = LI->getLoopFor(PN->getParent());
2870 for (size_t i = 0, e = PN->getNumIncomingValues(); i != e; ++i)
2871 if (LI->getLoopFor(PN->getIncomingBlock(i)) != PNLoop) {
2872 AllSameLoop = false;
2879 // If it's not a loop phi, we can't handle it yet.
2880 return getUnknown(PN);
2883 /// createNodeForGEP - Expand GEP instructions into add and multiply
2884 /// operations. This allows them to be analyzed by regular SCEV code.
2886 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2888 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2889 // Add expression, because the Instruction may be guarded by control flow
2890 // and the no-overflow bits may not be valid for the expression in any
2893 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2894 Value *Base = GEP->getOperand(0);
2895 // Don't attempt to analyze GEPs over unsized objects.
2896 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2897 return getUnknown(GEP);
2898 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2899 gep_type_iterator GTI = gep_type_begin(GEP);
2900 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2904 // Compute the (potentially symbolic) offset in bytes for this index.
2905 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2906 // For a struct, add the member offset.
2907 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2908 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2910 // Add the field offset to the running total offset.
2911 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2913 // For an array, add the element offset, explicitly scaled.
2914 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2915 const SCEV *IndexS = getSCEV(Index);
2916 // Getelementptr indices are signed.
2917 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2919 // Multiply the index by the element size to compute the element offset.
2920 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2922 // Add the element offset to the running total offset.
2923 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2927 // Get the SCEV for the GEP base.
2928 const SCEV *BaseS = getSCEV(Base);
2930 // Add the total offset from all the GEP indices to the base.
2931 return getAddExpr(BaseS, TotalOffset);
2934 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2935 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2936 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2937 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2939 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2940 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2941 return C->getValue()->getValue().countTrailingZeros();
2943 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2944 return std::min(GetMinTrailingZeros(T->getOperand()),
2945 (uint32_t)getTypeSizeInBits(T->getType()));
2947 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2948 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2949 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2950 getTypeSizeInBits(E->getType()) : OpRes;
2953 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2954 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2955 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2956 getTypeSizeInBits(E->getType()) : OpRes;
2959 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2960 // The result is the min of all operands results.
2961 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2962 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2963 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2967 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2968 // The result is the sum of all operands results.
2969 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2970 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2971 for (unsigned i = 1, e = M->getNumOperands();
2972 SumOpRes != BitWidth && i != e; ++i)
2973 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2978 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2979 // The result is the min of all operands results.
2980 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2981 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2982 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2986 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2987 // The result is the min of all operands results.
2988 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2989 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2990 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2994 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2995 // The result is the min of all operands results.
2996 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2997 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2998 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3002 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3003 // For a SCEVUnknown, ask ValueTracking.
3004 unsigned BitWidth = getTypeSizeInBits(U->getType());
3005 APInt Mask = APInt::getAllOnesValue(BitWidth);
3006 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3007 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3008 return Zeros.countTrailingOnes();
3015 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3018 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3020 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3021 return ConstantRange(C->getValue()->getValue());
3023 unsigned BitWidth = getTypeSizeInBits(S->getType());
3024 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3026 // If the value has known zeros, the maximum unsigned value will have those
3027 // known zeros as well.
3028 uint32_t TZ = GetMinTrailingZeros(S);
3030 ConservativeResult =
3031 ConstantRange(APInt::getMinValue(BitWidth),
3032 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3034 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3035 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3036 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3037 X = X.add(getUnsignedRange(Add->getOperand(i)));
3038 return ConservativeResult.intersectWith(X);
3041 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3042 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3043 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3044 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3045 return ConservativeResult.intersectWith(X);
3048 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3049 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3050 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3051 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3052 return ConservativeResult.intersectWith(X);
3055 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3056 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3057 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3058 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3059 return ConservativeResult.intersectWith(X);
3062 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3063 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3064 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3065 return ConservativeResult.intersectWith(X.udiv(Y));
3068 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3069 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3070 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3073 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3074 ConstantRange X = getUnsignedRange(SExt->getOperand());
3075 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3078 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3079 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3080 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3083 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3084 // If there's no unsigned wrap, the value will never be less than its
3086 if (AddRec->hasNoUnsignedWrap())
3087 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3088 if (!C->getValue()->isZero())
3089 ConservativeResult =
3090 ConservativeResult.intersectWith(
3091 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3093 // TODO: non-affine addrec
3094 if (AddRec->isAffine()) {
3095 const Type *Ty = AddRec->getType();
3096 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3097 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3098 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3099 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3101 const SCEV *Start = AddRec->getStart();
3102 const SCEV *Step = AddRec->getStepRecurrence(*this);
3104 ConstantRange StartRange = getUnsignedRange(Start);
3105 ConstantRange StepRange = getSignedRange(Step);
3106 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3107 ConstantRange EndRange =
3108 StartRange.add(MaxBECountRange.multiply(StepRange));
3110 // Check for overflow. This must be done with ConstantRange arithmetic
3111 // because we could be called from within the ScalarEvolution overflow
3113 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3114 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3115 ConstantRange ExtMaxBECountRange =
3116 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3117 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3118 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3120 return ConservativeResult;
3122 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3123 EndRange.getUnsignedMin());
3124 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3125 EndRange.getUnsignedMax());
3126 if (Min.isMinValue() && Max.isMaxValue())
3127 return ConservativeResult;
3128 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3132 return ConservativeResult;
3135 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3136 // For a SCEVUnknown, ask ValueTracking.
3137 APInt Mask = APInt::getAllOnesValue(BitWidth);
3138 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3139 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3140 if (Ones == ~Zeros + 1)
3141 return ConservativeResult;
3142 return ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1));
3145 return ConservativeResult;
3148 /// getSignedRange - Determine the signed range for a particular SCEV.
3151 ScalarEvolution::getSignedRange(const SCEV *S) {
3153 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3154 return ConstantRange(C->getValue()->getValue());
3156 unsigned BitWidth = getTypeSizeInBits(S->getType());
3157 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3159 // If the value has known zeros, the maximum signed value will have those
3160 // known zeros as well.
3161 uint32_t TZ = GetMinTrailingZeros(S);
3163 ConservativeResult =
3164 ConstantRange(APInt::getSignedMinValue(BitWidth),
3165 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3167 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3168 ConstantRange X = getSignedRange(Add->getOperand(0));
3169 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3170 X = X.add(getSignedRange(Add->getOperand(i)));
3171 return ConservativeResult.intersectWith(X);
3174 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3175 ConstantRange X = getSignedRange(Mul->getOperand(0));
3176 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3177 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3178 return ConservativeResult.intersectWith(X);
3181 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3182 ConstantRange X = getSignedRange(SMax->getOperand(0));
3183 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3184 X = X.smax(getSignedRange(SMax->getOperand(i)));
3185 return ConservativeResult.intersectWith(X);
3188 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3189 ConstantRange X = getSignedRange(UMax->getOperand(0));
3190 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3191 X = X.umax(getSignedRange(UMax->getOperand(i)));
3192 return ConservativeResult.intersectWith(X);
3195 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3196 ConstantRange X = getSignedRange(UDiv->getLHS());
3197 ConstantRange Y = getSignedRange(UDiv->getRHS());
3198 return ConservativeResult.intersectWith(X.udiv(Y));
3201 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3202 ConstantRange X = getSignedRange(ZExt->getOperand());
3203 return ConservativeResult.intersectWith(X.zeroExtend(BitWidth));
3206 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3207 ConstantRange X = getSignedRange(SExt->getOperand());
3208 return ConservativeResult.intersectWith(X.signExtend(BitWidth));
3211 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3212 ConstantRange X = getSignedRange(Trunc->getOperand());
3213 return ConservativeResult.intersectWith(X.truncate(BitWidth));
3216 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3217 // If there's no signed wrap, and all the operands have the same sign or
3218 // zero, the value won't ever change sign.
3219 if (AddRec->hasNoSignedWrap()) {
3220 bool AllNonNeg = true;
3221 bool AllNonPos = true;
3222 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3223 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3224 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3227 ConservativeResult = ConservativeResult.intersectWith(
3228 ConstantRange(APInt(BitWidth, 0),
3229 APInt::getSignedMinValue(BitWidth)));
3231 ConservativeResult = ConservativeResult.intersectWith(
3232 ConstantRange(APInt::getSignedMinValue(BitWidth),
3233 APInt(BitWidth, 1)));
3236 // TODO: non-affine addrec
3237 if (AddRec->isAffine()) {
3238 const Type *Ty = AddRec->getType();
3239 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3240 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3241 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3242 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3244 const SCEV *Start = AddRec->getStart();
3245 const SCEV *Step = AddRec->getStepRecurrence(*this);
3247 ConstantRange StartRange = getSignedRange(Start);
3248 ConstantRange StepRange = getSignedRange(Step);
3249 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3250 ConstantRange EndRange =
3251 StartRange.add(MaxBECountRange.multiply(StepRange));
3253 // Check for overflow. This must be done with ConstantRange arithmetic
3254 // because we could be called from within the ScalarEvolution overflow
3256 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3257 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3258 ConstantRange ExtMaxBECountRange =
3259 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3260 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3261 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3263 return ConservativeResult;
3265 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3266 EndRange.getSignedMin());
3267 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3268 EndRange.getSignedMax());
3269 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3270 return ConservativeResult;
3271 return ConservativeResult.intersectWith(ConstantRange(Min, Max+1));
3275 return ConservativeResult;
3278 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3279 // For a SCEVUnknown, ask ValueTracking.
3280 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3281 return ConservativeResult;
3282 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3284 return ConservativeResult;
3285 return ConservativeResult.intersectWith(
3286 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3287 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1));
3290 return ConservativeResult;
3293 /// createSCEV - We know that there is no SCEV for the specified value.
3294 /// Analyze the expression.
3296 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3297 if (!isSCEVable(V->getType()))
3298 return getUnknown(V);
3300 unsigned Opcode = Instruction::UserOp1;
3301 if (Instruction *I = dyn_cast<Instruction>(V)) {
3302 Opcode = I->getOpcode();
3304 // Don't attempt to analyze instructions in blocks that aren't
3305 // reachable. Such instructions don't matter, and they aren't required
3306 // to obey basic rules for definitions dominating uses which this
3307 // analysis depends on.
3308 if (!DT->isReachableFromEntry(I->getParent()))
3309 return getUnknown(V);
3310 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3311 Opcode = CE->getOpcode();
3312 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3313 return getConstant(CI);
3314 else if (isa<ConstantPointerNull>(V))
3315 return getConstant(V->getType(), 0);
3316 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3317 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3319 return getUnknown(V);
3321 Operator *U = cast<Operator>(V);
3323 case Instruction::Add: {
3324 // The simple thing to do would be to just call getSCEV on both operands
3325 // and call getAddExpr with the result. However if we're looking at a
3326 // bunch of things all added together, this can be quite inefficient,
3327 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3328 // Instead, gather up all the operands and make a single getAddExpr call.
3329 // LLVM IR canonical form means we need only traverse the left operands.
3330 SmallVector<const SCEV *, 4> AddOps;
3331 AddOps.push_back(getSCEV(U->getOperand(1)));
3332 for (Value *Op = U->getOperand(0);
3333 Op->getValueID() == Instruction::Add + Value::InstructionVal;
3334 Op = U->getOperand(0)) {
3335 U = cast<Operator>(Op);
3336 AddOps.push_back(getSCEV(U->getOperand(1)));
3338 AddOps.push_back(getSCEV(U->getOperand(0)));
3339 return getAddExpr(AddOps);
3341 case Instruction::Mul: {
3342 // See the Add code above.
3343 SmallVector<const SCEV *, 4> MulOps;
3344 MulOps.push_back(getSCEV(U->getOperand(1)));
3345 for (Value *Op = U->getOperand(0);
3346 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3347 Op = U->getOperand(0)) {
3348 U = cast<Operator>(Op);
3349 MulOps.push_back(getSCEV(U->getOperand(1)));
3351 MulOps.push_back(getSCEV(U->getOperand(0)));
3352 return getMulExpr(MulOps);
3354 case Instruction::UDiv:
3355 return getUDivExpr(getSCEV(U->getOperand(0)),
3356 getSCEV(U->getOperand(1)));
3357 case Instruction::Sub:
3358 return getMinusSCEV(getSCEV(U->getOperand(0)),
3359 getSCEV(U->getOperand(1)));
3360 case Instruction::And:
3361 // For an expression like x&255 that merely masks off the high bits,
3362 // use zext(trunc(x)) as the SCEV expression.
3363 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3364 if (CI->isNullValue())
3365 return getSCEV(U->getOperand(1));
3366 if (CI->isAllOnesValue())
3367 return getSCEV(U->getOperand(0));
3368 const APInt &A = CI->getValue();
3370 // Instcombine's ShrinkDemandedConstant may strip bits out of
3371 // constants, obscuring what would otherwise be a low-bits mask.
3372 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3373 // knew about to reconstruct a low-bits mask value.
3374 unsigned LZ = A.countLeadingZeros();
3375 unsigned BitWidth = A.getBitWidth();
3376 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3377 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3378 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3380 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3382 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3384 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3385 IntegerType::get(getContext(), BitWidth - LZ)),
3390 case Instruction::Or:
3391 // If the RHS of the Or is a constant, we may have something like:
3392 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3393 // optimizations will transparently handle this case.
3395 // In order for this transformation to be safe, the LHS must be of the
3396 // form X*(2^n) and the Or constant must be less than 2^n.
3397 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3398 const SCEV *LHS = getSCEV(U->getOperand(0));
3399 const APInt &CIVal = CI->getValue();
3400 if (GetMinTrailingZeros(LHS) >=
3401 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3402 // Build a plain add SCEV.
3403 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3404 // If the LHS of the add was an addrec and it has no-wrap flags,
3405 // transfer the no-wrap flags, since an or won't introduce a wrap.
3406 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3407 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3408 if (OldAR->hasNoUnsignedWrap())
3409 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3410 if (OldAR->hasNoSignedWrap())
3411 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3417 case Instruction::Xor:
3418 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3419 // If the RHS of the xor is a signbit, then this is just an add.
3420 // Instcombine turns add of signbit into xor as a strength reduction step.
3421 if (CI->getValue().isSignBit())
3422 return getAddExpr(getSCEV(U->getOperand(0)),
3423 getSCEV(U->getOperand(1)));
3425 // If the RHS of xor is -1, then this is a not operation.
3426 if (CI->isAllOnesValue())
3427 return getNotSCEV(getSCEV(U->getOperand(0)));
3429 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3430 // This is a variant of the check for xor with -1, and it handles
3431 // the case where instcombine has trimmed non-demanded bits out
3432 // of an xor with -1.
3433 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3434 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3435 if (BO->getOpcode() == Instruction::And &&
3436 LCI->getValue() == CI->getValue())
3437 if (const SCEVZeroExtendExpr *Z =
3438 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3439 const Type *UTy = U->getType();
3440 const SCEV *Z0 = Z->getOperand();
3441 const Type *Z0Ty = Z0->getType();
3442 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3444 // If C is a low-bits mask, the zero extend is serving to
3445 // mask off the high bits. Complement the operand and
3446 // re-apply the zext.
3447 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3448 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3450 // If C is a single bit, it may be in the sign-bit position
3451 // before the zero-extend. In this case, represent the xor
3452 // using an add, which is equivalent, and re-apply the zext.
3453 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
3454 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3456 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3462 case Instruction::Shl:
3463 // Turn shift left of a constant amount into a multiply.
3464 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3465 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3467 // If the shift count is not less than the bitwidth, the result of
3468 // the shift is undefined. Don't try to analyze it, because the
3469 // resolution chosen here may differ from the resolution chosen in
3470 // other parts of the compiler.
3471 if (SA->getValue().uge(BitWidth))
3474 Constant *X = ConstantInt::get(getContext(),
3475 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3476 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3480 case Instruction::LShr:
3481 // Turn logical shift right of a constant into a unsigned divide.
3482 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3483 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3485 // If the shift count is not less than the bitwidth, the result of
3486 // the shift is undefined. Don't try to analyze it, because the
3487 // resolution chosen here may differ from the resolution chosen in
3488 // other parts of the compiler.
3489 if (SA->getValue().uge(BitWidth))
3492 Constant *X = ConstantInt::get(getContext(),
3493 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3494 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3498 case Instruction::AShr:
3499 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3500 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3501 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3502 if (L->getOpcode() == Instruction::Shl &&
3503 L->getOperand(1) == U->getOperand(1)) {
3504 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3506 // If the shift count is not less than the bitwidth, the result of
3507 // the shift is undefined. Don't try to analyze it, because the
3508 // resolution chosen here may differ from the resolution chosen in
3509 // other parts of the compiler.
3510 if (CI->getValue().uge(BitWidth))
3513 uint64_t Amt = BitWidth - CI->getZExtValue();
3514 if (Amt == BitWidth)
3515 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3517 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3518 IntegerType::get(getContext(),
3524 case Instruction::Trunc:
3525 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3527 case Instruction::ZExt:
3528 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3530 case Instruction::SExt:
3531 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3533 case Instruction::BitCast:
3534 // BitCasts are no-op casts so we just eliminate the cast.
3535 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3536 return getSCEV(U->getOperand(0));
3539 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3540 // lead to pointer expressions which cannot safely be expanded to GEPs,
3541 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3542 // simplifying integer expressions.
3544 case Instruction::GetElementPtr:
3545 return createNodeForGEP(cast<GEPOperator>(U));
3547 case Instruction::PHI:
3548 return createNodeForPHI(cast<PHINode>(U));
3550 case Instruction::Select:
3551 // This could be a smax or umax that was lowered earlier.
3552 // Try to recover it.
3553 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3554 Value *LHS = ICI->getOperand(0);
3555 Value *RHS = ICI->getOperand(1);
3556 switch (ICI->getPredicate()) {
3557 case ICmpInst::ICMP_SLT:
3558 case ICmpInst::ICMP_SLE:
3559 std::swap(LHS, RHS);
3561 case ICmpInst::ICMP_SGT:
3562 case ICmpInst::ICMP_SGE:
3563 // a >s b ? a+x : b+x -> smax(a, b)+x
3564 // a >s b ? b+x : a+x -> smin(a, b)+x
3565 if (LHS->getType() == U->getType()) {
3566 const SCEV *LS = getSCEV(LHS);
3567 const SCEV *RS = getSCEV(RHS);
3568 const SCEV *LA = getSCEV(U->getOperand(1));
3569 const SCEV *RA = getSCEV(U->getOperand(2));
3570 const SCEV *LDiff = getMinusSCEV(LA, LS);
3571 const SCEV *RDiff = getMinusSCEV(RA, RS);
3573 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3574 LDiff = getMinusSCEV(LA, RS);
3575 RDiff = getMinusSCEV(RA, LS);
3577 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3580 case ICmpInst::ICMP_ULT:
3581 case ICmpInst::ICMP_ULE:
3582 std::swap(LHS, RHS);
3584 case ICmpInst::ICMP_UGT:
3585 case ICmpInst::ICMP_UGE:
3586 // a >u b ? a+x : b+x -> umax(a, b)+x
3587 // a >u b ? b+x : a+x -> umin(a, b)+x
3588 if (LHS->getType() == U->getType()) {
3589 const SCEV *LS = getSCEV(LHS);
3590 const SCEV *RS = getSCEV(RHS);
3591 const SCEV *LA = getSCEV(U->getOperand(1));
3592 const SCEV *RA = getSCEV(U->getOperand(2));
3593 const SCEV *LDiff = getMinusSCEV(LA, LS);
3594 const SCEV *RDiff = getMinusSCEV(RA, RS);
3596 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3597 LDiff = getMinusSCEV(LA, RS);
3598 RDiff = getMinusSCEV(RA, LS);
3600 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3603 case ICmpInst::ICMP_NE:
3604 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3605 if (LHS->getType() == U->getType() &&
3606 isa<ConstantInt>(RHS) &&
3607 cast<ConstantInt>(RHS)->isZero()) {
3608 const SCEV *One = getConstant(LHS->getType(), 1);
3609 const SCEV *LS = getSCEV(LHS);
3610 const SCEV *LA = getSCEV(U->getOperand(1));
3611 const SCEV *RA = getSCEV(U->getOperand(2));
3612 const SCEV *LDiff = getMinusSCEV(LA, LS);
3613 const SCEV *RDiff = getMinusSCEV(RA, One);
3615 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3618 case ICmpInst::ICMP_EQ:
3619 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3620 if (LHS->getType() == U->getType() &&
3621 isa<ConstantInt>(RHS) &&
3622 cast<ConstantInt>(RHS)->isZero()) {
3623 const SCEV *One = getConstant(LHS->getType(), 1);
3624 const SCEV *LS = getSCEV(LHS);
3625 const SCEV *LA = getSCEV(U->getOperand(1));
3626 const SCEV *RA = getSCEV(U->getOperand(2));
3627 const SCEV *LDiff = getMinusSCEV(LA, One);
3628 const SCEV *RDiff = getMinusSCEV(RA, LS);
3630 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3638 default: // We cannot analyze this expression.
3642 return getUnknown(V);
3647 //===----------------------------------------------------------------------===//
3648 // Iteration Count Computation Code
3651 /// getBackedgeTakenCount - If the specified loop has a predictable
3652 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3653 /// object. The backedge-taken count is the number of times the loop header
3654 /// will be branched to from within the loop. This is one less than the
3655 /// trip count of the loop, since it doesn't count the first iteration,
3656 /// when the header is branched to from outside the loop.
3658 /// Note that it is not valid to call this method on a loop without a
3659 /// loop-invariant backedge-taken count (see
3660 /// hasLoopInvariantBackedgeTakenCount).
3662 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3663 return getBackedgeTakenInfo(L).Exact;
3666 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3667 /// return the least SCEV value that is known never to be less than the
3668 /// actual backedge taken count.
3669 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3670 return getBackedgeTakenInfo(L).Max;
3673 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3674 /// onto the given Worklist.
3676 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3677 BasicBlock *Header = L->getHeader();
3679 // Push all Loop-header PHIs onto the Worklist stack.
3680 for (BasicBlock::iterator I = Header->begin();
3681 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3682 Worklist.push_back(PN);
3685 const ScalarEvolution::BackedgeTakenInfo &
3686 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3687 // Initially insert a CouldNotCompute for this loop. If the insertion
3688 // succeeds, proceed to actually compute a backedge-taken count and
3689 // update the value. The temporary CouldNotCompute value tells SCEV
3690 // code elsewhere that it shouldn't attempt to request a new
3691 // backedge-taken count, which could result in infinite recursion.
3692 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3693 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3695 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3696 if (BECount.Exact != getCouldNotCompute()) {
3697 assert(BECount.Exact->isLoopInvariant(L) &&
3698 BECount.Max->isLoopInvariant(L) &&
3699 "Computed backedge-taken count isn't loop invariant for loop!");
3700 ++NumTripCountsComputed;
3702 // Update the value in the map.
3703 Pair.first->second = BECount;
3705 if (BECount.Max != getCouldNotCompute())
3706 // Update the value in the map.
3707 Pair.first->second = BECount;
3708 if (isa<PHINode>(L->getHeader()->begin()))
3709 // Only count loops that have phi nodes as not being computable.
3710 ++NumTripCountsNotComputed;
3713 // Now that we know more about the trip count for this loop, forget any
3714 // existing SCEV values for PHI nodes in this loop since they are only
3715 // conservative estimates made without the benefit of trip count
3716 // information. This is similar to the code in forgetLoop, except that
3717 // it handles SCEVUnknown PHI nodes specially.
3718 if (BECount.hasAnyInfo()) {
3719 SmallVector<Instruction *, 16> Worklist;
3720 PushLoopPHIs(L, Worklist);
3722 SmallPtrSet<Instruction *, 8> Visited;
3723 while (!Worklist.empty()) {
3724 Instruction *I = Worklist.pop_back_val();
3725 if (!Visited.insert(I)) continue;
3727 ValueExprMapType::iterator It =
3728 ValueExprMap.find(static_cast<Value *>(I));
3729 if (It != ValueExprMap.end()) {
3730 // SCEVUnknown for a PHI either means that it has an unrecognized
3731 // structure, or it's a PHI that's in the progress of being computed
3732 // by createNodeForPHI. In the former case, additional loop trip
3733 // count information isn't going to change anything. In the later
3734 // case, createNodeForPHI will perform the necessary updates on its
3735 // own when it gets to that point.
3736 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second)) {
3737 ValuesAtScopes.erase(It->second);
3738 ValueExprMap.erase(It);
3740 if (PHINode *PN = dyn_cast<PHINode>(I))
3741 ConstantEvolutionLoopExitValue.erase(PN);
3744 PushDefUseChildren(I, Worklist);
3748 return Pair.first->second;
3751 /// forgetLoop - This method should be called by the client when it has
3752 /// changed a loop in a way that may effect ScalarEvolution's ability to
3753 /// compute a trip count, or if the loop is deleted.
3754 void ScalarEvolution::forgetLoop(const Loop *L) {
3755 // Drop any stored trip count value.
3756 BackedgeTakenCounts.erase(L);
3758 // Drop information about expressions based on loop-header PHIs.
3759 SmallVector<Instruction *, 16> Worklist;
3760 PushLoopPHIs(L, Worklist);
3762 SmallPtrSet<Instruction *, 8> Visited;
3763 while (!Worklist.empty()) {
3764 Instruction *I = Worklist.pop_back_val();
3765 if (!Visited.insert(I)) continue;
3767 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3768 if (It != ValueExprMap.end()) {
3769 ValuesAtScopes.erase(It->second);
3770 ValueExprMap.erase(It);
3771 if (PHINode *PN = dyn_cast<PHINode>(I))
3772 ConstantEvolutionLoopExitValue.erase(PN);
3775 PushDefUseChildren(I, Worklist);
3779 /// forgetValue - This method should be called by the client when it has
3780 /// changed a value in a way that may effect its value, or which may
3781 /// disconnect it from a def-use chain linking it to a loop.
3782 void ScalarEvolution::forgetValue(Value *V) {
3783 Instruction *I = dyn_cast<Instruction>(V);
3786 // Drop information about expressions based on loop-header PHIs.
3787 SmallVector<Instruction *, 16> Worklist;
3788 Worklist.push_back(I);
3790 SmallPtrSet<Instruction *, 8> Visited;
3791 while (!Worklist.empty()) {
3792 I = Worklist.pop_back_val();
3793 if (!Visited.insert(I)) continue;
3795 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3796 if (It != ValueExprMap.end()) {
3797 ValuesAtScopes.erase(It->second);
3798 ValueExprMap.erase(It);
3799 if (PHINode *PN = dyn_cast<PHINode>(I))
3800 ConstantEvolutionLoopExitValue.erase(PN);
3803 PushDefUseChildren(I, Worklist);
3807 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3808 /// of the specified loop will execute.
3809 ScalarEvolution::BackedgeTakenInfo
3810 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3811 SmallVector<BasicBlock *, 8> ExitingBlocks;
3812 L->getExitingBlocks(ExitingBlocks);
3814 // Examine all exits and pick the most conservative values.
3815 const SCEV *BECount = getCouldNotCompute();
3816 const SCEV *MaxBECount = getCouldNotCompute();
3817 bool CouldNotComputeBECount = false;
3818 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3819 BackedgeTakenInfo NewBTI =
3820 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3822 if (NewBTI.Exact == getCouldNotCompute()) {
3823 // We couldn't compute an exact value for this exit, so
3824 // we won't be able to compute an exact value for the loop.
3825 CouldNotComputeBECount = true;
3826 BECount = getCouldNotCompute();
3827 } else if (!CouldNotComputeBECount) {
3828 if (BECount == getCouldNotCompute())
3829 BECount = NewBTI.Exact;
3831 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3833 if (MaxBECount == getCouldNotCompute())
3834 MaxBECount = NewBTI.Max;
3835 else if (NewBTI.Max != getCouldNotCompute())
3836 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3839 return BackedgeTakenInfo(BECount, MaxBECount);
3842 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3843 /// of the specified loop will execute if it exits via the specified block.
3844 ScalarEvolution::BackedgeTakenInfo
3845 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3846 BasicBlock *ExitingBlock) {
3848 // Okay, we've chosen an exiting block. See what condition causes us to
3849 // exit at this block.
3851 // FIXME: we should be able to handle switch instructions (with a single exit)
3852 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3853 if (ExitBr == 0) return getCouldNotCompute();
3854 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3856 // At this point, we know we have a conditional branch that determines whether
3857 // the loop is exited. However, we don't know if the branch is executed each
3858 // time through the loop. If not, then the execution count of the branch will
3859 // not be equal to the trip count of the loop.
3861 // Currently we check for this by checking to see if the Exit branch goes to
3862 // the loop header. If so, we know it will always execute the same number of
3863 // times as the loop. We also handle the case where the exit block *is* the
3864 // loop header. This is common for un-rotated loops.
3866 // If both of those tests fail, walk up the unique predecessor chain to the
3867 // header, stopping if there is an edge that doesn't exit the loop. If the
3868 // header is reached, the execution count of the branch will be equal to the
3869 // trip count of the loop.
3871 // More extensive analysis could be done to handle more cases here.
3873 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3874 ExitBr->getSuccessor(1) != L->getHeader() &&
3875 ExitBr->getParent() != L->getHeader()) {
3876 // The simple checks failed, try climbing the unique predecessor chain
3877 // up to the header.
3879 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3880 BasicBlock *Pred = BB->getUniquePredecessor();
3882 return getCouldNotCompute();
3883 TerminatorInst *PredTerm = Pred->getTerminator();
3884 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3885 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3888 // If the predecessor has a successor that isn't BB and isn't
3889 // outside the loop, assume the worst.
3890 if (L->contains(PredSucc))
3891 return getCouldNotCompute();
3893 if (Pred == L->getHeader()) {
3900 return getCouldNotCompute();
3903 // Proceed to the next level to examine the exit condition expression.
3904 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3905 ExitBr->getSuccessor(0),
3906 ExitBr->getSuccessor(1));
3909 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3910 /// backedge of the specified loop will execute if its exit condition
3911 /// were a conditional branch of ExitCond, TBB, and FBB.
3912 ScalarEvolution::BackedgeTakenInfo
3913 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3917 // Check if the controlling expression for this loop is an And or Or.
3918 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3919 if (BO->getOpcode() == Instruction::And) {
3920 // Recurse on the operands of the and.
3921 BackedgeTakenInfo BTI0 =
3922 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3923 BackedgeTakenInfo BTI1 =
3924 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3925 const SCEV *BECount = getCouldNotCompute();
3926 const SCEV *MaxBECount = getCouldNotCompute();
3927 if (L->contains(TBB)) {
3928 // Both conditions must be true for the loop to continue executing.
3929 // Choose the less conservative count.
3930 if (BTI0.Exact == getCouldNotCompute() ||
3931 BTI1.Exact == getCouldNotCompute())
3932 BECount = getCouldNotCompute();
3934 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3935 if (BTI0.Max == getCouldNotCompute())
3936 MaxBECount = BTI1.Max;
3937 else if (BTI1.Max == getCouldNotCompute())
3938 MaxBECount = BTI0.Max;
3940 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3942 // Both conditions must be true at the same time for the loop to exit.
3943 // For now, be conservative.
3944 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3945 if (BTI0.Max == BTI1.Max)
3946 MaxBECount = BTI0.Max;
3947 if (BTI0.Exact == BTI1.Exact)
3948 BECount = BTI0.Exact;
3951 return BackedgeTakenInfo(BECount, MaxBECount);
3953 if (BO->getOpcode() == Instruction::Or) {
3954 // Recurse on the operands of the or.
3955 BackedgeTakenInfo BTI0 =
3956 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3957 BackedgeTakenInfo BTI1 =
3958 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3959 const SCEV *BECount = getCouldNotCompute();
3960 const SCEV *MaxBECount = getCouldNotCompute();
3961 if (L->contains(FBB)) {
3962 // Both conditions must be false for the loop to continue executing.
3963 // Choose the less conservative count.
3964 if (BTI0.Exact == getCouldNotCompute() ||
3965 BTI1.Exact == getCouldNotCompute())
3966 BECount = getCouldNotCompute();
3968 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3969 if (BTI0.Max == getCouldNotCompute())
3970 MaxBECount = BTI1.Max;
3971 else if (BTI1.Max == getCouldNotCompute())
3972 MaxBECount = BTI0.Max;
3974 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3976 // Both conditions must be false at the same time for the loop to exit.
3977 // For now, be conservative.
3978 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3979 if (BTI0.Max == BTI1.Max)
3980 MaxBECount = BTI0.Max;
3981 if (BTI0.Exact == BTI1.Exact)
3982 BECount = BTI0.Exact;
3985 return BackedgeTakenInfo(BECount, MaxBECount);
3989 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3990 // Proceed to the next level to examine the icmp.
3991 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3992 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3994 // Check for a constant condition. These are normally stripped out by
3995 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3996 // preserve the CFG and is temporarily leaving constant conditions
3998 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3999 if (L->contains(FBB) == !CI->getZExtValue())
4000 // The backedge is always taken.
4001 return getCouldNotCompute();
4003 // The backedge is never taken.
4004 return getConstant(CI->getType(), 0);
4007 // If it's not an integer or pointer comparison then compute it the hard way.
4008 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4011 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4012 /// backedge of the specified loop will execute if its exit condition
4013 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4014 ScalarEvolution::BackedgeTakenInfo
4015 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4020 // If the condition was exit on true, convert the condition to exit on false
4021 ICmpInst::Predicate Cond;
4022 if (!L->contains(FBB))
4023 Cond = ExitCond->getPredicate();
4025 Cond = ExitCond->getInversePredicate();
4027 // Handle common loops like: for (X = "string"; *X; ++X)
4028 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4029 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4030 BackedgeTakenInfo ItCnt =
4031 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4032 if (ItCnt.hasAnyInfo())
4036 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4037 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4039 // Try to evaluate any dependencies out of the loop.
4040 LHS = getSCEVAtScope(LHS, L);
4041 RHS = getSCEVAtScope(RHS, L);
4043 // At this point, we would like to compute how many iterations of the
4044 // loop the predicate will return true for these inputs.
4045 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
4046 // If there is a loop-invariant, force it into the RHS.
4047 std::swap(LHS, RHS);
4048 Cond = ICmpInst::getSwappedPredicate(Cond);
4051 // Simplify the operands before analyzing them.
4052 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4054 // If we have a comparison of a chrec against a constant, try to use value
4055 // ranges to answer this query.
4056 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4057 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4058 if (AddRec->getLoop() == L) {
4059 // Form the constant range.
4060 ConstantRange CompRange(
4061 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4063 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4064 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4068 case ICmpInst::ICMP_NE: { // while (X != Y)
4069 // Convert to: while (X-Y != 0)
4070 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4071 if (BTI.hasAnyInfo()) return BTI;
4074 case ICmpInst::ICMP_EQ: { // while (X == Y)
4075 // Convert to: while (X-Y == 0)
4076 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4077 if (BTI.hasAnyInfo()) return BTI;
4080 case ICmpInst::ICMP_SLT: {
4081 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4082 if (BTI.hasAnyInfo()) return BTI;
4085 case ICmpInst::ICMP_SGT: {
4086 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4087 getNotSCEV(RHS), L, true);
4088 if (BTI.hasAnyInfo()) return BTI;
4091 case ICmpInst::ICMP_ULT: {
4092 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4093 if (BTI.hasAnyInfo()) return BTI;
4096 case ICmpInst::ICMP_UGT: {
4097 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4098 getNotSCEV(RHS), L, false);
4099 if (BTI.hasAnyInfo()) return BTI;
4104 dbgs() << "ComputeBackedgeTakenCount ";
4105 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4106 dbgs() << "[unsigned] ";
4107 dbgs() << *LHS << " "
4108 << Instruction::getOpcodeName(Instruction::ICmp)
4109 << " " << *RHS << "\n";
4114 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4117 static ConstantInt *
4118 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4119 ScalarEvolution &SE) {
4120 const SCEV *InVal = SE.getConstant(C);
4121 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4122 assert(isa<SCEVConstant>(Val) &&
4123 "Evaluation of SCEV at constant didn't fold correctly?");
4124 return cast<SCEVConstant>(Val)->getValue();
4127 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4128 /// and a GEP expression (missing the pointer index) indexing into it, return
4129 /// the addressed element of the initializer or null if the index expression is
4132 GetAddressedElementFromGlobal(GlobalVariable *GV,
4133 const std::vector<ConstantInt*> &Indices) {
4134 Constant *Init = GV->getInitializer();
4135 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4136 uint64_t Idx = Indices[i]->getZExtValue();
4137 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4138 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4139 Init = cast<Constant>(CS->getOperand(Idx));
4140 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4141 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4142 Init = cast<Constant>(CA->getOperand(Idx));
4143 } else if (isa<ConstantAggregateZero>(Init)) {
4144 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4145 assert(Idx < STy->getNumElements() && "Bad struct index!");
4146 Init = Constant::getNullValue(STy->getElementType(Idx));
4147 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4148 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4149 Init = Constant::getNullValue(ATy->getElementType());
4151 llvm_unreachable("Unknown constant aggregate type!");
4155 return 0; // Unknown initializer type
4161 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4162 /// 'icmp op load X, cst', try to see if we can compute the backedge
4163 /// execution count.
4164 ScalarEvolution::BackedgeTakenInfo
4165 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4169 ICmpInst::Predicate predicate) {
4170 if (LI->isVolatile()) return getCouldNotCompute();
4172 // Check to see if the loaded pointer is a getelementptr of a global.
4173 // TODO: Use SCEV instead of manually grubbing with GEPs.
4174 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4175 if (!GEP) return getCouldNotCompute();
4177 // Make sure that it is really a constant global we are gepping, with an
4178 // initializer, and make sure the first IDX is really 0.
4179 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4180 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4181 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4182 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4183 return getCouldNotCompute();
4185 // Okay, we allow one non-constant index into the GEP instruction.
4187 std::vector<ConstantInt*> Indexes;
4188 unsigned VarIdxNum = 0;
4189 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4190 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4191 Indexes.push_back(CI);
4192 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4193 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4194 VarIdx = GEP->getOperand(i);
4196 Indexes.push_back(0);
4199 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4200 // Check to see if X is a loop variant variable value now.
4201 const SCEV *Idx = getSCEV(VarIdx);
4202 Idx = getSCEVAtScope(Idx, L);
4204 // We can only recognize very limited forms of loop index expressions, in
4205 // particular, only affine AddRec's like {C1,+,C2}.
4206 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4207 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
4208 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4209 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4210 return getCouldNotCompute();
4212 unsigned MaxSteps = MaxBruteForceIterations;
4213 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4214 ConstantInt *ItCst = ConstantInt::get(
4215 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4216 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4218 // Form the GEP offset.
4219 Indexes[VarIdxNum] = Val;
4221 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4222 if (Result == 0) break; // Cannot compute!
4224 // Evaluate the condition for this iteration.
4225 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4226 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4227 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4229 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4230 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4233 ++NumArrayLenItCounts;
4234 return getConstant(ItCst); // Found terminating iteration!
4237 return getCouldNotCompute();
4241 /// CanConstantFold - Return true if we can constant fold an instruction of the
4242 /// specified type, assuming that all operands were constants.
4243 static bool CanConstantFold(const Instruction *I) {
4244 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4245 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4248 if (const CallInst *CI = dyn_cast<CallInst>(I))
4249 if (const Function *F = CI->getCalledFunction())
4250 return canConstantFoldCallTo(F);
4254 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4255 /// in the loop that V is derived from. We allow arbitrary operations along the
4256 /// way, but the operands of an operation must either be constants or a value
4257 /// derived from a constant PHI. If this expression does not fit with these
4258 /// constraints, return null.
4259 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4260 // If this is not an instruction, or if this is an instruction outside of the
4261 // loop, it can't be derived from a loop PHI.
4262 Instruction *I = dyn_cast<Instruction>(V);
4263 if (I == 0 || !L->contains(I)) return 0;
4265 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4266 if (L->getHeader() == I->getParent())
4269 // We don't currently keep track of the control flow needed to evaluate
4270 // PHIs, so we cannot handle PHIs inside of loops.
4274 // If we won't be able to constant fold this expression even if the operands
4275 // are constants, return early.
4276 if (!CanConstantFold(I)) return 0;
4278 // Otherwise, we can evaluate this instruction if all of its operands are
4279 // constant or derived from a PHI node themselves.
4281 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4282 if (!isa<Constant>(I->getOperand(Op))) {
4283 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4284 if (P == 0) return 0; // Not evolving from PHI
4288 return 0; // Evolving from multiple different PHIs.
4291 // This is a expression evolving from a constant PHI!
4295 /// EvaluateExpression - Given an expression that passes the
4296 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4297 /// in the loop has the value PHIVal. If we can't fold this expression for some
4298 /// reason, return null.
4299 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4300 const TargetData *TD) {
4301 if (isa<PHINode>(V)) return PHIVal;
4302 if (Constant *C = dyn_cast<Constant>(V)) return C;
4303 Instruction *I = cast<Instruction>(V);
4305 std::vector<Constant*> Operands(I->getNumOperands());
4307 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4308 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4309 if (Operands[i] == 0) return 0;
4312 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4313 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4315 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4316 &Operands[0], Operands.size(), TD);
4319 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4320 /// in the header of its containing loop, we know the loop executes a
4321 /// constant number of times, and the PHI node is just a recurrence
4322 /// involving constants, fold it.
4324 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4327 std::map<PHINode*, Constant*>::const_iterator I =
4328 ConstantEvolutionLoopExitValue.find(PN);
4329 if (I != ConstantEvolutionLoopExitValue.end())
4332 if (BEs.ugt(MaxBruteForceIterations))
4333 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4335 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4337 // Since the loop is canonicalized, the PHI node must have two entries. One
4338 // entry must be a constant (coming in from outside of the loop), and the
4339 // second must be derived from the same PHI.
4340 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4341 Constant *StartCST =
4342 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4344 return RetVal = 0; // Must be a constant.
4346 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4347 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4348 !isa<Constant>(BEValue))
4349 return RetVal = 0; // Not derived from same PHI.
4351 // Execute the loop symbolically to determine the exit value.
4352 if (BEs.getActiveBits() >= 32)
4353 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4355 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4356 unsigned IterationNum = 0;
4357 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4358 if (IterationNum == NumIterations)
4359 return RetVal = PHIVal; // Got exit value!
4361 // Compute the value of the PHI node for the next iteration.
4362 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4363 if (NextPHI == PHIVal)
4364 return RetVal = NextPHI; // Stopped evolving!
4366 return 0; // Couldn't evaluate!
4371 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4372 /// constant number of times (the condition evolves only from constants),
4373 /// try to evaluate a few iterations of the loop until we get the exit
4374 /// condition gets a value of ExitWhen (true or false). If we cannot
4375 /// evaluate the trip count of the loop, return getCouldNotCompute().
4377 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4380 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4381 if (PN == 0) return getCouldNotCompute();
4383 // If the loop is canonicalized, the PHI will have exactly two entries.
4384 // That's the only form we support here.
4385 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4387 // One entry must be a constant (coming in from outside of the loop), and the
4388 // second must be derived from the same PHI.
4389 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4390 Constant *StartCST =
4391 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4392 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4394 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4395 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4396 !isa<Constant>(BEValue))
4397 return getCouldNotCompute(); // Not derived from same PHI.
4399 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4400 // the loop symbolically to determine when the condition gets a value of
4402 unsigned IterationNum = 0;
4403 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4404 for (Constant *PHIVal = StartCST;
4405 IterationNum != MaxIterations; ++IterationNum) {
4406 ConstantInt *CondVal =
4407 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4409 // Couldn't symbolically evaluate.
4410 if (!CondVal) return getCouldNotCompute();
4412 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4413 ++NumBruteForceTripCountsComputed;
4414 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4417 // Compute the value of the PHI node for the next iteration.
4418 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4419 if (NextPHI == 0 || NextPHI == PHIVal)
4420 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4424 // Too many iterations were needed to evaluate.
4425 return getCouldNotCompute();
4428 /// getSCEVAtScope - Return a SCEV expression for the specified value
4429 /// at the specified scope in the program. The L value specifies a loop
4430 /// nest to evaluate the expression at, where null is the top-level or a
4431 /// specified loop is immediately inside of the loop.
4433 /// This method can be used to compute the exit value for a variable defined
4434 /// in a loop by querying what the value will hold in the parent loop.
4436 /// In the case that a relevant loop exit value cannot be computed, the
4437 /// original value V is returned.
4438 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4439 // Check to see if we've folded this expression at this loop before.
4440 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4441 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4442 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4444 return Pair.first->second ? Pair.first->second : V;
4446 // Otherwise compute it.
4447 const SCEV *C = computeSCEVAtScope(V, L);
4448 ValuesAtScopes[V][L] = C;
4452 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4453 if (isa<SCEVConstant>(V)) return V;
4455 // If this instruction is evolved from a constant-evolving PHI, compute the
4456 // exit value from the loop without using SCEVs.
4457 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4458 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4459 const Loop *LI = (*this->LI)[I->getParent()];
4460 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4461 if (PHINode *PN = dyn_cast<PHINode>(I))
4462 if (PN->getParent() == LI->getHeader()) {
4463 // Okay, there is no closed form solution for the PHI node. Check
4464 // to see if the loop that contains it has a known backedge-taken
4465 // count. If so, we may be able to force computation of the exit
4467 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4468 if (const SCEVConstant *BTCC =
4469 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4470 // Okay, we know how many times the containing loop executes. If
4471 // this is a constant evolving PHI node, get the final value at
4472 // the specified iteration number.
4473 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4474 BTCC->getValue()->getValue(),
4476 if (RV) return getSCEV(RV);
4480 // Okay, this is an expression that we cannot symbolically evaluate
4481 // into a SCEV. Check to see if it's possible to symbolically evaluate
4482 // the arguments into constants, and if so, try to constant propagate the
4483 // result. This is particularly useful for computing loop exit values.
4484 if (CanConstantFold(I)) {
4485 SmallVector<Constant *, 4> Operands;
4486 bool MadeImprovement = false;
4487 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4488 Value *Op = I->getOperand(i);
4489 if (Constant *C = dyn_cast<Constant>(Op)) {
4490 Operands.push_back(C);
4494 // If any of the operands is non-constant and if they are
4495 // non-integer and non-pointer, don't even try to analyze them
4496 // with scev techniques.
4497 if (!isSCEVable(Op->getType()))
4500 const SCEV *OrigV = getSCEV(Op);
4501 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4502 MadeImprovement |= OrigV != OpV;
4505 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4507 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4508 C = dyn_cast<Constant>(SU->getValue());
4510 if (C->getType() != Op->getType())
4511 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4515 Operands.push_back(C);
4518 // Check to see if getSCEVAtScope actually made an improvement.
4519 if (MadeImprovement) {
4521 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4522 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4523 Operands[0], Operands[1], TD);
4525 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4526 &Operands[0], Operands.size(), TD);
4533 // This is some other type of SCEVUnknown, just return it.
4537 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4538 // Avoid performing the look-up in the common case where the specified
4539 // expression has no loop-variant portions.
4540 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4541 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4542 if (OpAtScope != Comm->getOperand(i)) {
4543 // Okay, at least one of these operands is loop variant but might be
4544 // foldable. Build a new instance of the folded commutative expression.
4545 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4546 Comm->op_begin()+i);
4547 NewOps.push_back(OpAtScope);
4549 for (++i; i != e; ++i) {
4550 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4551 NewOps.push_back(OpAtScope);
4553 if (isa<SCEVAddExpr>(Comm))
4554 return getAddExpr(NewOps);
4555 if (isa<SCEVMulExpr>(Comm))
4556 return getMulExpr(NewOps);
4557 if (isa<SCEVSMaxExpr>(Comm))
4558 return getSMaxExpr(NewOps);
4559 if (isa<SCEVUMaxExpr>(Comm))
4560 return getUMaxExpr(NewOps);
4561 llvm_unreachable("Unknown commutative SCEV type!");
4564 // If we got here, all operands are loop invariant.
4568 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4569 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4570 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4571 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4572 return Div; // must be loop invariant
4573 return getUDivExpr(LHS, RHS);
4576 // If this is a loop recurrence for a loop that does not contain L, then we
4577 // are dealing with the final value computed by the loop.
4578 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4579 // First, attempt to evaluate each operand.
4580 // Avoid performing the look-up in the common case where the specified
4581 // expression has no loop-variant portions.
4582 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4583 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4584 if (OpAtScope == AddRec->getOperand(i))
4587 // Okay, at least one of these operands is loop variant but might be
4588 // foldable. Build a new instance of the folded commutative expression.
4589 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4590 AddRec->op_begin()+i);
4591 NewOps.push_back(OpAtScope);
4592 for (++i; i != e; ++i)
4593 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4595 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4599 // If the scope is outside the addrec's loop, evaluate it by using the
4600 // loop exit value of the addrec.
4601 if (!AddRec->getLoop()->contains(L)) {
4602 // To evaluate this recurrence, we need to know how many times the AddRec
4603 // loop iterates. Compute this now.
4604 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4605 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4607 // Then, evaluate the AddRec.
4608 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4614 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4615 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4616 if (Op == Cast->getOperand())
4617 return Cast; // must be loop invariant
4618 return getZeroExtendExpr(Op, Cast->getType());
4621 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4622 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4623 if (Op == Cast->getOperand())
4624 return Cast; // must be loop invariant
4625 return getSignExtendExpr(Op, Cast->getType());
4628 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4629 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4630 if (Op == Cast->getOperand())
4631 return Cast; // must be loop invariant
4632 return getTruncateExpr(Op, Cast->getType());
4635 llvm_unreachable("Unknown SCEV type!");
4639 /// getSCEVAtScope - This is a convenience function which does
4640 /// getSCEVAtScope(getSCEV(V), L).
4641 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4642 return getSCEVAtScope(getSCEV(V), L);
4645 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4646 /// following equation:
4648 /// A * X = B (mod N)
4650 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4651 /// A and B isn't important.
4653 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4654 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4655 ScalarEvolution &SE) {
4656 uint32_t BW = A.getBitWidth();
4657 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4658 assert(A != 0 && "A must be non-zero.");
4662 // The gcd of A and N may have only one prime factor: 2. The number of
4663 // trailing zeros in A is its multiplicity
4664 uint32_t Mult2 = A.countTrailingZeros();
4667 // 2. Check if B is divisible by D.
4669 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4670 // is not less than multiplicity of this prime factor for D.
4671 if (B.countTrailingZeros() < Mult2)
4672 return SE.getCouldNotCompute();
4674 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4677 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4678 // bit width during computations.
4679 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4680 APInt Mod(BW + 1, 0);
4681 Mod.set(BW - Mult2); // Mod = N / D
4682 APInt I = AD.multiplicativeInverse(Mod);
4684 // 4. Compute the minimum unsigned root of the equation:
4685 // I * (B / D) mod (N / D)
4686 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4688 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4690 return SE.getConstant(Result.trunc(BW));
4693 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4694 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4695 /// might be the same) or two SCEVCouldNotCompute objects.
4697 static std::pair<const SCEV *,const SCEV *>
4698 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4699 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4700 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4701 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4702 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4704 // We currently can only solve this if the coefficients are constants.
4705 if (!LC || !MC || !NC) {
4706 const SCEV *CNC = SE.getCouldNotCompute();
4707 return std::make_pair(CNC, CNC);
4710 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4711 const APInt &L = LC->getValue()->getValue();
4712 const APInt &M = MC->getValue()->getValue();
4713 const APInt &N = NC->getValue()->getValue();
4714 APInt Two(BitWidth, 2);
4715 APInt Four(BitWidth, 4);
4718 using namespace APIntOps;
4720 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4721 // The B coefficient is M-N/2
4725 // The A coefficient is N/2
4726 APInt A(N.sdiv(Two));
4728 // Compute the B^2-4ac term.
4731 SqrtTerm -= Four * (A * C);
4733 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4734 // integer value or else APInt::sqrt() will assert.
4735 APInt SqrtVal(SqrtTerm.sqrt());
4737 // Compute the two solutions for the quadratic formula.
4738 // The divisions must be performed as signed divisions.
4740 APInt TwoA( A << 1 );
4741 if (TwoA.isMinValue()) {
4742 const SCEV *CNC = SE.getCouldNotCompute();
4743 return std::make_pair(CNC, CNC);
4746 LLVMContext &Context = SE.getContext();
4748 ConstantInt *Solution1 =
4749 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4750 ConstantInt *Solution2 =
4751 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4753 return std::make_pair(SE.getConstant(Solution1),
4754 SE.getConstant(Solution2));
4755 } // end APIntOps namespace
4758 /// HowFarToZero - Return the number of times a backedge comparing the specified
4759 /// value to zero will execute. If not computable, return CouldNotCompute.
4760 ScalarEvolution::BackedgeTakenInfo
4761 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4762 // If the value is a constant
4763 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4764 // If the value is already zero, the branch will execute zero times.
4765 if (C->getValue()->isZero()) return C;
4766 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4769 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4770 if (!AddRec || AddRec->getLoop() != L)
4771 return getCouldNotCompute();
4773 if (AddRec->isAffine()) {
4774 // If this is an affine expression, the execution count of this branch is
4775 // the minimum unsigned root of the following equation:
4777 // Start + Step*N = 0 (mod 2^BW)
4781 // Step*N = -Start (mod 2^BW)
4783 // where BW is the common bit width of Start and Step.
4785 // Get the initial value for the loop.
4786 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4787 L->getParentLoop());
4788 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4789 L->getParentLoop());
4791 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4792 // For now we handle only constant steps.
4794 // First, handle unitary steps.
4795 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4796 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4797 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4798 return Start; // N = Start (as unsigned)
4800 // Then, try to solve the above equation provided that Start is constant.
4801 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4802 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4803 -StartC->getValue()->getValue(),
4806 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4807 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4808 // the quadratic equation to solve it.
4809 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4811 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4812 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4815 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4816 << " sol#2: " << *R2 << "\n";
4818 // Pick the smallest positive root value.
4819 if (ConstantInt *CB =
4820 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4821 R1->getValue(), R2->getValue()))) {
4822 if (CB->getZExtValue() == false)
4823 std::swap(R1, R2); // R1 is the minimum root now.
4825 // We can only use this value if the chrec ends up with an exact zero
4826 // value at this index. When solving for "X*X != 5", for example, we
4827 // should not accept a root of 2.
4828 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4830 return R1; // We found a quadratic root!
4835 return getCouldNotCompute();
4838 /// HowFarToNonZero - Return the number of times a backedge checking the
4839 /// specified value for nonzero will execute. If not computable, return
4841 ScalarEvolution::BackedgeTakenInfo
4842 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4843 // Loops that look like: while (X == 0) are very strange indeed. We don't
4844 // handle them yet except for the trivial case. This could be expanded in the
4845 // future as needed.
4847 // If the value is a constant, check to see if it is known to be non-zero
4848 // already. If so, the backedge will execute zero times.
4849 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4850 if (!C->getValue()->isNullValue())
4851 return getConstant(C->getType(), 0);
4852 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4855 // We could implement others, but I really doubt anyone writes loops like
4856 // this, and if they did, they would already be constant folded.
4857 return getCouldNotCompute();
4860 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4861 /// (which may not be an immediate predecessor) which has exactly one
4862 /// successor from which BB is reachable, or null if no such block is
4865 std::pair<BasicBlock *, BasicBlock *>
4866 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4867 // If the block has a unique predecessor, then there is no path from the
4868 // predecessor to the block that does not go through the direct edge
4869 // from the predecessor to the block.
4870 if (BasicBlock *Pred = BB->getSinglePredecessor())
4871 return std::make_pair(Pred, BB);
4873 // A loop's header is defined to be a block that dominates the loop.
4874 // If the header has a unique predecessor outside the loop, it must be
4875 // a block that has exactly one successor that can reach the loop.
4876 if (Loop *L = LI->getLoopFor(BB))
4877 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4879 return std::pair<BasicBlock *, BasicBlock *>();
4882 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4883 /// testing whether two expressions are equal, however for the purposes of
4884 /// looking for a condition guarding a loop, it can be useful to be a little
4885 /// more general, since a front-end may have replicated the controlling
4888 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4889 // Quick check to see if they are the same SCEV.
4890 if (A == B) return true;
4892 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4893 // two different instructions with the same value. Check for this case.
4894 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4895 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4896 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4897 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4898 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4901 // Otherwise assume they may have a different value.
4905 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4906 /// predicate Pred. Return true iff any changes were made.
4908 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4909 const SCEV *&LHS, const SCEV *&RHS) {
4910 bool Changed = false;
4912 // Canonicalize a constant to the right side.
4913 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4914 // Check for both operands constant.
4915 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4916 if (ConstantExpr::getICmp(Pred,
4918 RHSC->getValue())->isNullValue())
4919 goto trivially_false;
4921 goto trivially_true;
4923 // Otherwise swap the operands to put the constant on the right.
4924 std::swap(LHS, RHS);
4925 Pred = ICmpInst::getSwappedPredicate(Pred);
4929 // If we're comparing an addrec with a value which is loop-invariant in the
4930 // addrec's loop, put the addrec on the left. Also make a dominance check,
4931 // as both operands could be addrecs loop-invariant in each other's loop.
4932 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4933 const Loop *L = AR->getLoop();
4934 if (LHS->isLoopInvariant(L) && LHS->properlyDominates(L->getHeader(), DT)) {
4935 std::swap(LHS, RHS);
4936 Pred = ICmpInst::getSwappedPredicate(Pred);
4941 // If there's a constant operand, canonicalize comparisons with boundary
4942 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4943 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4944 const APInt &RA = RC->getValue()->getValue();
4946 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4947 case ICmpInst::ICMP_EQ:
4948 case ICmpInst::ICMP_NE:
4950 case ICmpInst::ICMP_UGE:
4951 if ((RA - 1).isMinValue()) {
4952 Pred = ICmpInst::ICMP_NE;
4953 RHS = getConstant(RA - 1);
4957 if (RA.isMaxValue()) {
4958 Pred = ICmpInst::ICMP_EQ;
4962 if (RA.isMinValue()) goto trivially_true;
4964 Pred = ICmpInst::ICMP_UGT;
4965 RHS = getConstant(RA - 1);
4968 case ICmpInst::ICMP_ULE:
4969 if ((RA + 1).isMaxValue()) {
4970 Pred = ICmpInst::ICMP_NE;
4971 RHS = getConstant(RA + 1);
4975 if (RA.isMinValue()) {
4976 Pred = ICmpInst::ICMP_EQ;
4980 if (RA.isMaxValue()) goto trivially_true;
4982 Pred = ICmpInst::ICMP_ULT;
4983 RHS = getConstant(RA + 1);
4986 case ICmpInst::ICMP_SGE:
4987 if ((RA - 1).isMinSignedValue()) {
4988 Pred = ICmpInst::ICMP_NE;
4989 RHS = getConstant(RA - 1);
4993 if (RA.isMaxSignedValue()) {
4994 Pred = ICmpInst::ICMP_EQ;
4998 if (RA.isMinSignedValue()) goto trivially_true;
5000 Pred = ICmpInst::ICMP_SGT;
5001 RHS = getConstant(RA - 1);
5004 case ICmpInst::ICMP_SLE:
5005 if ((RA + 1).isMaxSignedValue()) {
5006 Pred = ICmpInst::ICMP_NE;
5007 RHS = getConstant(RA + 1);
5011 if (RA.isMinSignedValue()) {
5012 Pred = ICmpInst::ICMP_EQ;
5016 if (RA.isMaxSignedValue()) goto trivially_true;
5018 Pred = ICmpInst::ICMP_SLT;
5019 RHS = getConstant(RA + 1);
5022 case ICmpInst::ICMP_UGT:
5023 if (RA.isMinValue()) {
5024 Pred = ICmpInst::ICMP_NE;
5028 if ((RA + 1).isMaxValue()) {
5029 Pred = ICmpInst::ICMP_EQ;
5030 RHS = getConstant(RA + 1);
5034 if (RA.isMaxValue()) goto trivially_false;
5036 case ICmpInst::ICMP_ULT:
5037 if (RA.isMaxValue()) {
5038 Pred = ICmpInst::ICMP_NE;
5042 if ((RA - 1).isMinValue()) {
5043 Pred = ICmpInst::ICMP_EQ;
5044 RHS = getConstant(RA - 1);
5048 if (RA.isMinValue()) goto trivially_false;
5050 case ICmpInst::ICMP_SGT:
5051 if (RA.isMinSignedValue()) {
5052 Pred = ICmpInst::ICMP_NE;
5056 if ((RA + 1).isMaxSignedValue()) {
5057 Pred = ICmpInst::ICMP_EQ;
5058 RHS = getConstant(RA + 1);
5062 if (RA.isMaxSignedValue()) goto trivially_false;
5064 case ICmpInst::ICMP_SLT:
5065 if (RA.isMaxSignedValue()) {
5066 Pred = ICmpInst::ICMP_NE;
5070 if ((RA - 1).isMinSignedValue()) {
5071 Pred = ICmpInst::ICMP_EQ;
5072 RHS = getConstant(RA - 1);
5076 if (RA.isMinSignedValue()) goto trivially_false;
5081 // Check for obvious equality.
5082 if (HasSameValue(LHS, RHS)) {
5083 if (ICmpInst::isTrueWhenEqual(Pred))
5084 goto trivially_true;
5085 if (ICmpInst::isFalseWhenEqual(Pred))
5086 goto trivially_false;
5089 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5090 // adding or subtracting 1 from one of the operands.
5092 case ICmpInst::ICMP_SLE:
5093 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5094 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5095 /*HasNUW=*/false, /*HasNSW=*/true);
5096 Pred = ICmpInst::ICMP_SLT;
5098 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5099 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5100 /*HasNUW=*/false, /*HasNSW=*/true);
5101 Pred = ICmpInst::ICMP_SLT;
5105 case ICmpInst::ICMP_SGE:
5106 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5107 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5108 /*HasNUW=*/false, /*HasNSW=*/true);
5109 Pred = ICmpInst::ICMP_SGT;
5111 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5112 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5113 /*HasNUW=*/false, /*HasNSW=*/true);
5114 Pred = ICmpInst::ICMP_SGT;
5118 case ICmpInst::ICMP_ULE:
5119 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5120 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5121 /*HasNUW=*/true, /*HasNSW=*/false);
5122 Pred = ICmpInst::ICMP_ULT;
5124 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5125 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5126 /*HasNUW=*/true, /*HasNSW=*/false);
5127 Pred = ICmpInst::ICMP_ULT;
5131 case ICmpInst::ICMP_UGE:
5132 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5133 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5134 /*HasNUW=*/true, /*HasNSW=*/false);
5135 Pred = ICmpInst::ICMP_UGT;
5137 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5138 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5139 /*HasNUW=*/true, /*HasNSW=*/false);
5140 Pred = ICmpInst::ICMP_UGT;
5148 // TODO: More simplifications are possible here.
5154 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5155 Pred = ICmpInst::ICMP_EQ;
5160 LHS = RHS = getConstant(Type::getInt1Ty(getContext()), 0);
5161 Pred = ICmpInst::ICMP_NE;
5165 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5166 return getSignedRange(S).getSignedMax().isNegative();
5169 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5170 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5173 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5174 return !getSignedRange(S).getSignedMin().isNegative();
5177 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5178 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5181 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5182 return isKnownNegative(S) || isKnownPositive(S);
5185 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5186 const SCEV *LHS, const SCEV *RHS) {
5187 // Canonicalize the inputs first.
5188 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5190 // If LHS or RHS is an addrec, check to see if the condition is true in
5191 // every iteration of the loop.
5192 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5193 if (isLoopEntryGuardedByCond(
5194 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5195 isLoopBackedgeGuardedByCond(
5196 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5198 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5199 if (isLoopEntryGuardedByCond(
5200 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5201 isLoopBackedgeGuardedByCond(
5202 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5205 // Otherwise see what can be done with known constant ranges.
5206 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5210 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5211 const SCEV *LHS, const SCEV *RHS) {
5212 if (HasSameValue(LHS, RHS))
5213 return ICmpInst::isTrueWhenEqual(Pred);
5215 // This code is split out from isKnownPredicate because it is called from
5216 // within isLoopEntryGuardedByCond.
5219 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5221 case ICmpInst::ICMP_SGT:
5222 Pred = ICmpInst::ICMP_SLT;
5223 std::swap(LHS, RHS);
5224 case ICmpInst::ICMP_SLT: {
5225 ConstantRange LHSRange = getSignedRange(LHS);
5226 ConstantRange RHSRange = getSignedRange(RHS);
5227 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5229 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5233 case ICmpInst::ICMP_SGE:
5234 Pred = ICmpInst::ICMP_SLE;
5235 std::swap(LHS, RHS);
5236 case ICmpInst::ICMP_SLE: {
5237 ConstantRange LHSRange = getSignedRange(LHS);
5238 ConstantRange RHSRange = getSignedRange(RHS);
5239 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5241 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5245 case ICmpInst::ICMP_UGT:
5246 Pred = ICmpInst::ICMP_ULT;
5247 std::swap(LHS, RHS);
5248 case ICmpInst::ICMP_ULT: {
5249 ConstantRange LHSRange = getUnsignedRange(LHS);
5250 ConstantRange RHSRange = getUnsignedRange(RHS);
5251 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5253 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5257 case ICmpInst::ICMP_UGE:
5258 Pred = ICmpInst::ICMP_ULE;
5259 std::swap(LHS, RHS);
5260 case ICmpInst::ICMP_ULE: {
5261 ConstantRange LHSRange = getUnsignedRange(LHS);
5262 ConstantRange RHSRange = getUnsignedRange(RHS);
5263 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5265 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5269 case ICmpInst::ICMP_NE: {
5270 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5272 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5275 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5276 if (isKnownNonZero(Diff))
5280 case ICmpInst::ICMP_EQ:
5281 // The check at the top of the function catches the case where
5282 // the values are known to be equal.
5288 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5289 /// protected by a conditional between LHS and RHS. This is used to
5290 /// to eliminate casts.
5292 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5293 ICmpInst::Predicate Pred,
5294 const SCEV *LHS, const SCEV *RHS) {
5295 // Interpret a null as meaning no loop, where there is obviously no guard
5296 // (interprocedural conditions notwithstanding).
5297 if (!L) return true;
5299 BasicBlock *Latch = L->getLoopLatch();
5303 BranchInst *LoopContinuePredicate =
5304 dyn_cast<BranchInst>(Latch->getTerminator());
5305 if (!LoopContinuePredicate ||
5306 LoopContinuePredicate->isUnconditional())
5309 return isImpliedCond(Pred, LHS, RHS,
5310 LoopContinuePredicate->getCondition(),
5311 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5314 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5315 /// by a conditional between LHS and RHS. This is used to help avoid max
5316 /// expressions in loop trip counts, and to eliminate casts.
5318 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5319 ICmpInst::Predicate Pred,
5320 const SCEV *LHS, const SCEV *RHS) {
5321 // Interpret a null as meaning no loop, where there is obviously no guard
5322 // (interprocedural conditions notwithstanding).
5323 if (!L) return false;
5325 // Starting at the loop predecessor, climb up the predecessor chain, as long
5326 // as there are predecessors that can be found that have unique successors
5327 // leading to the original header.
5328 for (std::pair<BasicBlock *, BasicBlock *>
5329 Pair(L->getLoopPredecessor(), L->getHeader());
5331 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5333 BranchInst *LoopEntryPredicate =
5334 dyn_cast<BranchInst>(Pair.first->getTerminator());
5335 if (!LoopEntryPredicate ||
5336 LoopEntryPredicate->isUnconditional())
5339 if (isImpliedCond(Pred, LHS, RHS,
5340 LoopEntryPredicate->getCondition(),
5341 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5348 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5349 /// and RHS is true whenever the given Cond value evaluates to true.
5350 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5351 const SCEV *LHS, const SCEV *RHS,
5352 Value *FoundCondValue,
5354 // Recursively handle And and Or conditions.
5355 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5356 if (BO->getOpcode() == Instruction::And) {
5358 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5359 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5360 } else if (BO->getOpcode() == Instruction::Or) {
5362 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5363 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5367 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5368 if (!ICI) return false;
5370 // Bail if the ICmp's operands' types are wider than the needed type
5371 // before attempting to call getSCEV on them. This avoids infinite
5372 // recursion, since the analysis of widening casts can require loop
5373 // exit condition information for overflow checking, which would
5375 if (getTypeSizeInBits(LHS->getType()) <
5376 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5379 // Now that we found a conditional branch that dominates the loop, check to
5380 // see if it is the comparison we are looking for.
5381 ICmpInst::Predicate FoundPred;
5383 FoundPred = ICI->getInversePredicate();
5385 FoundPred = ICI->getPredicate();
5387 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5388 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5390 // Balance the types. The case where FoundLHS' type is wider than
5391 // LHS' type is checked for above.
5392 if (getTypeSizeInBits(LHS->getType()) >
5393 getTypeSizeInBits(FoundLHS->getType())) {
5394 if (CmpInst::isSigned(Pred)) {
5395 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5396 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5398 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5399 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5403 // Canonicalize the query to match the way instcombine will have
5404 // canonicalized the comparison.
5405 if (SimplifyICmpOperands(Pred, LHS, RHS))
5407 return CmpInst::isTrueWhenEqual(Pred);
5408 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5409 if (FoundLHS == FoundRHS)
5410 return CmpInst::isFalseWhenEqual(Pred);
5412 // Check to see if we can make the LHS or RHS match.
5413 if (LHS == FoundRHS || RHS == FoundLHS) {
5414 if (isa<SCEVConstant>(RHS)) {
5415 std::swap(FoundLHS, FoundRHS);
5416 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5418 std::swap(LHS, RHS);
5419 Pred = ICmpInst::getSwappedPredicate(Pred);
5423 // Check whether the found predicate is the same as the desired predicate.
5424 if (FoundPred == Pred)
5425 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5427 // Check whether swapping the found predicate makes it the same as the
5428 // desired predicate.
5429 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5430 if (isa<SCEVConstant>(RHS))
5431 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5433 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5434 RHS, LHS, FoundLHS, FoundRHS);
5437 // Check whether the actual condition is beyond sufficient.
5438 if (FoundPred == ICmpInst::ICMP_EQ)
5439 if (ICmpInst::isTrueWhenEqual(Pred))
5440 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5442 if (Pred == ICmpInst::ICMP_NE)
5443 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5444 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5447 // Otherwise assume the worst.
5451 /// isImpliedCondOperands - Test whether the condition described by Pred,
5452 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5453 /// and FoundRHS is true.
5454 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5455 const SCEV *LHS, const SCEV *RHS,
5456 const SCEV *FoundLHS,
5457 const SCEV *FoundRHS) {
5458 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5459 FoundLHS, FoundRHS) ||
5460 // ~x < ~y --> x > y
5461 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5462 getNotSCEV(FoundRHS),
5463 getNotSCEV(FoundLHS));
5466 /// isImpliedCondOperandsHelper - Test whether the condition described by
5467 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5468 /// FoundLHS, and FoundRHS is true.
5470 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5471 const SCEV *LHS, const SCEV *RHS,
5472 const SCEV *FoundLHS,
5473 const SCEV *FoundRHS) {
5475 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5476 case ICmpInst::ICMP_EQ:
5477 case ICmpInst::ICMP_NE:
5478 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5481 case ICmpInst::ICMP_SLT:
5482 case ICmpInst::ICMP_SLE:
5483 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5484 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5487 case ICmpInst::ICMP_SGT:
5488 case ICmpInst::ICMP_SGE:
5489 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5490 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5493 case ICmpInst::ICMP_ULT:
5494 case ICmpInst::ICMP_ULE:
5495 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5496 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5499 case ICmpInst::ICMP_UGT:
5500 case ICmpInst::ICMP_UGE:
5501 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5502 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5510 /// getBECount - Subtract the end and start values and divide by the step,
5511 /// rounding up, to get the number of times the backedge is executed. Return
5512 /// CouldNotCompute if an intermediate computation overflows.
5513 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5517 assert(!isKnownNegative(Step) &&
5518 "This code doesn't handle negative strides yet!");
5520 const Type *Ty = Start->getType();
5521 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5522 const SCEV *Diff = getMinusSCEV(End, Start);
5523 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5525 // Add an adjustment to the difference between End and Start so that
5526 // the division will effectively round up.
5527 const SCEV *Add = getAddExpr(Diff, RoundUp);
5530 // Check Add for unsigned overflow.
5531 // TODO: More sophisticated things could be done here.
5532 const Type *WideTy = IntegerType::get(getContext(),
5533 getTypeSizeInBits(Ty) + 1);
5534 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5535 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5536 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5537 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5538 return getCouldNotCompute();
5541 return getUDivExpr(Add, Step);
5544 /// HowManyLessThans - Return the number of times a backedge containing the
5545 /// specified less-than comparison will execute. If not computable, return
5546 /// CouldNotCompute.
5547 ScalarEvolution::BackedgeTakenInfo
5548 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5549 const Loop *L, bool isSigned) {
5550 // Only handle: "ADDREC < LoopInvariant".
5551 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
5553 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5554 if (!AddRec || AddRec->getLoop() != L)
5555 return getCouldNotCompute();
5557 // Check to see if we have a flag which makes analysis easy.
5558 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5559 AddRec->hasNoUnsignedWrap();
5561 if (AddRec->isAffine()) {
5562 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5563 const SCEV *Step = AddRec->getStepRecurrence(*this);
5566 return getCouldNotCompute();
5567 if (Step->isOne()) {
5568 // With unit stride, the iteration never steps past the limit value.
5569 } else if (isKnownPositive(Step)) {
5570 // Test whether a positive iteration can step past the limit
5571 // value and past the maximum value for its type in a single step.
5572 // Note that it's not sufficient to check NoWrap here, because even
5573 // though the value after a wrap is undefined, it's not undefined
5574 // behavior, so if wrap does occur, the loop could either terminate or
5575 // loop infinitely, but in either case, the loop is guaranteed to
5576 // iterate at least until the iteration where the wrapping occurs.
5577 const SCEV *One = getConstant(Step->getType(), 1);
5579 APInt Max = APInt::getSignedMaxValue(BitWidth);
5580 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5581 .slt(getSignedRange(RHS).getSignedMax()))
5582 return getCouldNotCompute();
5584 APInt Max = APInt::getMaxValue(BitWidth);
5585 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5586 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5587 return getCouldNotCompute();
5590 // TODO: Handle negative strides here and below.
5591 return getCouldNotCompute();
5593 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5594 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5595 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5596 // treat m-n as signed nor unsigned due to overflow possibility.
5598 // First, we get the value of the LHS in the first iteration: n
5599 const SCEV *Start = AddRec->getOperand(0);
5601 // Determine the minimum constant start value.
5602 const SCEV *MinStart = getConstant(isSigned ?
5603 getSignedRange(Start).getSignedMin() :
5604 getUnsignedRange(Start).getUnsignedMin());
5606 // If we know that the condition is true in order to enter the loop,
5607 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5608 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5609 // the division must round up.
5610 const SCEV *End = RHS;
5611 if (!isLoopEntryGuardedByCond(L,
5612 isSigned ? ICmpInst::ICMP_SLT :
5614 getMinusSCEV(Start, Step), RHS))
5615 End = isSigned ? getSMaxExpr(RHS, Start)
5616 : getUMaxExpr(RHS, Start);
5618 // Determine the maximum constant end value.
5619 const SCEV *MaxEnd = getConstant(isSigned ?
5620 getSignedRange(End).getSignedMax() :
5621 getUnsignedRange(End).getUnsignedMax());
5623 // If MaxEnd is within a step of the maximum integer value in its type,
5624 // adjust it down to the minimum value which would produce the same effect.
5625 // This allows the subsequent ceiling division of (N+(step-1))/step to
5626 // compute the correct value.
5627 const SCEV *StepMinusOne = getMinusSCEV(Step,
5628 getConstant(Step->getType(), 1));
5631 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5634 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5637 // Finally, we subtract these two values and divide, rounding up, to get
5638 // the number of times the backedge is executed.
5639 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5641 // The maximum backedge count is similar, except using the minimum start
5642 // value and the maximum end value.
5643 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5645 return BackedgeTakenInfo(BECount, MaxBECount);
5648 return getCouldNotCompute();
5651 /// getNumIterationsInRange - Return the number of iterations of this loop that
5652 /// produce values in the specified constant range. Another way of looking at
5653 /// this is that it returns the first iteration number where the value is not in
5654 /// the condition, thus computing the exit count. If the iteration count can't
5655 /// be computed, an instance of SCEVCouldNotCompute is returned.
5656 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5657 ScalarEvolution &SE) const {
5658 if (Range.isFullSet()) // Infinite loop.
5659 return SE.getCouldNotCompute();
5661 // If the start is a non-zero constant, shift the range to simplify things.
5662 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5663 if (!SC->getValue()->isZero()) {
5664 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5665 Operands[0] = SE.getConstant(SC->getType(), 0);
5666 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5667 if (const SCEVAddRecExpr *ShiftedAddRec =
5668 dyn_cast<SCEVAddRecExpr>(Shifted))
5669 return ShiftedAddRec->getNumIterationsInRange(
5670 Range.subtract(SC->getValue()->getValue()), SE);
5671 // This is strange and shouldn't happen.
5672 return SE.getCouldNotCompute();
5675 // The only time we can solve this is when we have all constant indices.
5676 // Otherwise, we cannot determine the overflow conditions.
5677 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5678 if (!isa<SCEVConstant>(getOperand(i)))
5679 return SE.getCouldNotCompute();
5682 // Okay at this point we know that all elements of the chrec are constants and
5683 // that the start element is zero.
5685 // First check to see if the range contains zero. If not, the first
5687 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5688 if (!Range.contains(APInt(BitWidth, 0)))
5689 return SE.getConstant(getType(), 0);
5692 // If this is an affine expression then we have this situation:
5693 // Solve {0,+,A} in Range === Ax in Range
5695 // We know that zero is in the range. If A is positive then we know that
5696 // the upper value of the range must be the first possible exit value.
5697 // If A is negative then the lower of the range is the last possible loop
5698 // value. Also note that we already checked for a full range.
5699 APInt One(BitWidth,1);
5700 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5701 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5703 // The exit value should be (End+A)/A.
5704 APInt ExitVal = (End + A).udiv(A);
5705 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5707 // Evaluate at the exit value. If we really did fall out of the valid
5708 // range, then we computed our trip count, otherwise wrap around or other
5709 // things must have happened.
5710 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5711 if (Range.contains(Val->getValue()))
5712 return SE.getCouldNotCompute(); // Something strange happened
5714 // Ensure that the previous value is in the range. This is a sanity check.
5715 assert(Range.contains(
5716 EvaluateConstantChrecAtConstant(this,
5717 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5718 "Linear scev computation is off in a bad way!");
5719 return SE.getConstant(ExitValue);
5720 } else if (isQuadratic()) {
5721 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5722 // quadratic equation to solve it. To do this, we must frame our problem in
5723 // terms of figuring out when zero is crossed, instead of when
5724 // Range.getUpper() is crossed.
5725 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5726 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5727 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5729 // Next, solve the constructed addrec
5730 std::pair<const SCEV *,const SCEV *> Roots =
5731 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5732 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5733 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5735 // Pick the smallest positive root value.
5736 if (ConstantInt *CB =
5737 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5738 R1->getValue(), R2->getValue()))) {
5739 if (CB->getZExtValue() == false)
5740 std::swap(R1, R2); // R1 is the minimum root now.
5742 // Make sure the root is not off by one. The returned iteration should
5743 // not be in the range, but the previous one should be. When solving
5744 // for "X*X < 5", for example, we should not return a root of 2.
5745 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5748 if (Range.contains(R1Val->getValue())) {
5749 // The next iteration must be out of the range...
5750 ConstantInt *NextVal =
5751 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5753 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5754 if (!Range.contains(R1Val->getValue()))
5755 return SE.getConstant(NextVal);
5756 return SE.getCouldNotCompute(); // Something strange happened
5759 // If R1 was not in the range, then it is a good return value. Make
5760 // sure that R1-1 WAS in the range though, just in case.
5761 ConstantInt *NextVal =
5762 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5763 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5764 if (Range.contains(R1Val->getValue()))
5766 return SE.getCouldNotCompute(); // Something strange happened
5771 return SE.getCouldNotCompute();
5776 //===----------------------------------------------------------------------===//
5777 // SCEVCallbackVH Class Implementation
5778 //===----------------------------------------------------------------------===//
5780 void ScalarEvolution::SCEVCallbackVH::deleted() {
5781 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5782 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5783 SE->ConstantEvolutionLoopExitValue.erase(PN);
5784 SE->ValueExprMap.erase(getValPtr());
5785 // this now dangles!
5788 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5789 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5791 // Forget all the expressions associated with users of the old value,
5792 // so that future queries will recompute the expressions using the new
5794 Value *Old = getValPtr();
5795 SmallVector<User *, 16> Worklist;
5796 SmallPtrSet<User *, 8> Visited;
5797 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5799 Worklist.push_back(*UI);
5800 while (!Worklist.empty()) {
5801 User *U = Worklist.pop_back_val();
5802 // Deleting the Old value will cause this to dangle. Postpone
5803 // that until everything else is done.
5806 if (!Visited.insert(U))
5808 if (PHINode *PN = dyn_cast<PHINode>(U))
5809 SE->ConstantEvolutionLoopExitValue.erase(PN);
5810 SE->ValueExprMap.erase(U);
5811 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5813 Worklist.push_back(*UI);
5815 // Delete the Old value.
5816 if (PHINode *PN = dyn_cast<PHINode>(Old))
5817 SE->ConstantEvolutionLoopExitValue.erase(PN);
5818 SE->ValueExprMap.erase(Old);
5819 // this now dangles!
5822 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5823 : CallbackVH(V), SE(se) {}
5825 //===----------------------------------------------------------------------===//
5826 // ScalarEvolution Class Implementation
5827 //===----------------------------------------------------------------------===//
5829 ScalarEvolution::ScalarEvolution()
5830 : FunctionPass(ID), FirstUnknown(0) {
5833 bool ScalarEvolution::runOnFunction(Function &F) {
5835 LI = &getAnalysis<LoopInfo>();
5836 TD = getAnalysisIfAvailable<TargetData>();
5837 DT = &getAnalysis<DominatorTree>();
5841 void ScalarEvolution::releaseMemory() {
5842 // Iterate through all the SCEVUnknown instances and call their
5843 // destructors, so that they release their references to their values.
5844 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
5848 ValueExprMap.clear();
5849 BackedgeTakenCounts.clear();
5850 ConstantEvolutionLoopExitValue.clear();
5851 ValuesAtScopes.clear();
5852 UniqueSCEVs.clear();
5853 SCEVAllocator.Reset();
5856 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5857 AU.setPreservesAll();
5858 AU.addRequiredTransitive<LoopInfo>();
5859 AU.addRequiredTransitive<DominatorTree>();
5862 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5863 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5866 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5868 // Print all inner loops first
5869 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5870 PrintLoopInfo(OS, SE, *I);
5873 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5876 SmallVector<BasicBlock *, 8> ExitBlocks;
5877 L->getExitBlocks(ExitBlocks);
5878 if (ExitBlocks.size() != 1)
5879 OS << "<multiple exits> ";
5881 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5882 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5884 OS << "Unpredictable backedge-taken count. ";
5889 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5892 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5893 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5895 OS << "Unpredictable max backedge-taken count. ";
5901 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5902 // ScalarEvolution's implementation of the print method is to print
5903 // out SCEV values of all instructions that are interesting. Doing
5904 // this potentially causes it to create new SCEV objects though,
5905 // which technically conflicts with the const qualifier. This isn't
5906 // observable from outside the class though, so casting away the
5907 // const isn't dangerous.
5908 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5910 OS << "Classifying expressions for: ";
5911 WriteAsOperand(OS, F, /*PrintType=*/false);
5913 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5914 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5917 const SCEV *SV = SE.getSCEV(&*I);
5920 const Loop *L = LI->getLoopFor((*I).getParent());
5922 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5929 OS << "\t\t" "Exits: ";
5930 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5931 if (!ExitValue->isLoopInvariant(L)) {
5932 OS << "<<Unknown>>";
5941 OS << "Determining loop execution counts for: ";
5942 WriteAsOperand(OS, F, /*PrintType=*/false);
5944 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5945 PrintLoopInfo(OS, &SE, *I);