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/InstructionSimplify.h"
73 #include "llvm/Analysis/LoopInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/Assembly/Writer.h"
76 #include "llvm/Target/TargetData.h"
77 #include "llvm/Support/CommandLine.h"
78 #include "llvm/Support/ConstantRange.h"
79 #include "llvm/Support/Debug.h"
80 #include "llvm/Support/ErrorHandling.h"
81 #include "llvm/Support/GetElementPtrTypeIterator.h"
82 #include "llvm/Support/InstIterator.h"
83 #include "llvm/Support/MathExtras.h"
84 #include "llvm/Support/raw_ostream.h"
85 #include "llvm/ADT/Statistic.h"
86 #include "llvm/ADT/STLExtras.h"
87 #include "llvm/ADT/SmallPtrSet.h"
91 STATISTIC(NumArrayLenItCounts,
92 "Number of trip counts computed with array length");
93 STATISTIC(NumTripCountsComputed,
94 "Number of loops with predictable loop counts");
95 STATISTIC(NumTripCountsNotComputed,
96 "Number of loops without predictable loop counts");
97 STATISTIC(NumBruteForceTripCountsComputed,
98 "Number of loops with trip counts computed by force");
100 static cl::opt<unsigned>
101 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
102 cl::desc("Maximum number of iterations SCEV will "
103 "symbolically execute a constant "
107 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
108 "Scalar Evolution Analysis", false, true)
109 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
110 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
111 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
112 "Scalar Evolution Analysis", false, true)
113 char ScalarEvolution::ID = 0;
115 //===----------------------------------------------------------------------===//
116 // SCEV class definitions
117 //===----------------------------------------------------------------------===//
119 //===----------------------------------------------------------------------===//
120 // Implementation of the SCEV class.
123 void SCEV::dump() const {
128 void SCEV::print(raw_ostream &OS) const {
129 switch (getSCEVType()) {
131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
135 const SCEV *Op = Trunc->getOperand();
136 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
137 << *Trunc->getType() << ")";
141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
142 const SCEV *Op = ZExt->getOperand();
143 OS << "(zext " << *Op->getType() << " " << *Op << " to "
144 << *ZExt->getType() << ")";
148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
149 const SCEV *Op = SExt->getOperand();
150 OS << "(sext " << *Op->getType() << " " << *Op << " to "
151 << *SExt->getType() << ")";
155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
156 OS << "{" << *AR->getOperand(0);
157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
158 OS << ",+," << *AR->getOperand(i);
160 if (AR->hasNoUnsignedWrap())
162 if (AR->hasNoSignedWrap())
164 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
172 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
173 const char *OpStr = 0;
174 switch (NAry->getSCEVType()) {
175 case scAddExpr: OpStr = " + "; break;
176 case scMulExpr: OpStr = " * "; break;
177 case scUMaxExpr: OpStr = " umax "; break;
178 case scSMaxExpr: OpStr = " smax "; break;
181 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
184 if (llvm::next(I) != E)
191 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
192 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
196 const SCEVUnknown *U = cast<SCEVUnknown>(this);
198 if (U->isSizeOf(AllocTy)) {
199 OS << "sizeof(" << *AllocTy << ")";
202 if (U->isAlignOf(AllocTy)) {
203 OS << "alignof(" << *AllocTy << ")";
209 if (U->isOffsetOf(CTy, FieldNo)) {
210 OS << "offsetof(" << *CTy << ", ";
211 WriteAsOperand(OS, FieldNo, false);
216 // Otherwise just print it normally.
217 WriteAsOperand(OS, U->getValue(), false);
220 case scCouldNotCompute:
221 OS << "***COULDNOTCOMPUTE***";
225 llvm_unreachable("Unknown SCEV kind!");
228 const Type *SCEV::getType() const {
229 switch (getSCEVType()) {
231 return cast<SCEVConstant>(this)->getType();
235 return cast<SCEVCastExpr>(this)->getType();
240 return cast<SCEVNAryExpr>(this)->getType();
242 return cast<SCEVAddExpr>(this)->getType();
244 return cast<SCEVUDivExpr>(this)->getType();
246 return cast<SCEVUnknown>(this)->getType();
247 case scCouldNotCompute:
248 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
252 llvm_unreachable("Unknown SCEV kind!");
256 bool SCEV::isZero() const {
257 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
258 return SC->getValue()->isZero();
262 bool SCEV::isOne() const {
263 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
264 return SC->getValue()->isOne();
268 bool SCEV::isAllOnesValue() const {
269 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
270 return SC->getValue()->isAllOnesValue();
274 SCEVCouldNotCompute::SCEVCouldNotCompute() :
275 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
277 bool SCEVCouldNotCompute::classof(const SCEV *S) {
278 return S->getSCEVType() == scCouldNotCompute;
281 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
283 ID.AddInteger(scConstant);
286 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
287 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
288 UniqueSCEVs.InsertNode(S, IP);
292 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
293 return getConstant(ConstantInt::get(getContext(), Val));
297 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
298 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
299 return getConstant(ConstantInt::get(ITy, V, isSigned));
302 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
303 unsigned SCEVTy, const SCEV *op, const Type *ty)
304 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
306 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
307 const SCEV *op, const Type *ty)
308 : SCEVCastExpr(ID, scTruncate, op, ty) {
309 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
310 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
311 "Cannot truncate non-integer value!");
314 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
315 const SCEV *op, const Type *ty)
316 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
317 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
318 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
319 "Cannot zero extend non-integer value!");
322 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
323 const SCEV *op, const Type *ty)
324 : SCEVCastExpr(ID, scSignExtend, op, ty) {
325 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
326 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
327 "Cannot sign extend non-integer value!");
330 void SCEVUnknown::deleted() {
331 // Clear this SCEVUnknown from various maps.
332 SE->forgetMemoizedResults(this);
334 // Remove this SCEVUnknown from the uniquing map.
335 SE->UniqueSCEVs.RemoveNode(this);
337 // Release the value.
341 void SCEVUnknown::allUsesReplacedWith(Value *New) {
342 // Clear this SCEVUnknown from various maps.
343 SE->forgetMemoizedResults(this);
345 // Remove this SCEVUnknown from the uniquing map.
346 SE->UniqueSCEVs.RemoveNode(this);
348 // Update this SCEVUnknown to point to the new value. This is needed
349 // because there may still be outstanding SCEVs which still point to
354 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
355 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
356 if (VCE->getOpcode() == Instruction::PtrToInt)
357 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
358 if (CE->getOpcode() == Instruction::GetElementPtr &&
359 CE->getOperand(0)->isNullValue() &&
360 CE->getNumOperands() == 2)
361 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
363 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
371 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
372 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
373 if (VCE->getOpcode() == Instruction::PtrToInt)
374 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
375 if (CE->getOpcode() == Instruction::GetElementPtr &&
376 CE->getOperand(0)->isNullValue()) {
378 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
379 if (const StructType *STy = dyn_cast<StructType>(Ty))
380 if (!STy->isPacked() &&
381 CE->getNumOperands() == 3 &&
382 CE->getOperand(1)->isNullValue()) {
383 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
385 STy->getNumElements() == 2 &&
386 STy->getElementType(0)->isIntegerTy(1)) {
387 AllocTy = STy->getElementType(1);
396 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
397 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
398 if (VCE->getOpcode() == Instruction::PtrToInt)
399 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
400 if (CE->getOpcode() == Instruction::GetElementPtr &&
401 CE->getNumOperands() == 3 &&
402 CE->getOperand(0)->isNullValue() &&
403 CE->getOperand(1)->isNullValue()) {
405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
406 // Ignore vector types here so that ScalarEvolutionExpander doesn't
407 // emit getelementptrs that index into vectors.
408 if (Ty->isStructTy() || Ty->isArrayTy()) {
410 FieldNo = CE->getOperand(2);
418 //===----------------------------------------------------------------------===//
420 //===----------------------------------------------------------------------===//
423 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
424 /// than the complexity of the RHS. This comparator is used to canonicalize
426 class SCEVComplexityCompare {
427 const LoopInfo *const LI;
429 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
431 // Return true or false if LHS is less than, or at least RHS, respectively.
432 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
433 return compare(LHS, RHS) < 0;
436 // Return negative, zero, or positive, if LHS is less than, equal to, or
437 // greater than RHS, respectively. A three-way result allows recursive
438 // comparisons to be more efficient.
439 int compare(const SCEV *LHS, const SCEV *RHS) const {
440 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
444 // Primarily, sort the SCEVs by their getSCEVType().
445 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
447 return (int)LType - (int)RType;
449 // Aside from the getSCEVType() ordering, the particular ordering
450 // isn't very important except that it's beneficial to be consistent,
451 // so that (a + b) and (b + a) don't end up as different expressions.
454 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
455 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
457 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
458 // not as complete as it could be.
459 const Value *LV = LU->getValue(), *RV = RU->getValue();
461 // Order pointer values after integer values. This helps SCEVExpander
463 bool LIsPointer = LV->getType()->isPointerTy(),
464 RIsPointer = RV->getType()->isPointerTy();
465 if (LIsPointer != RIsPointer)
466 return (int)LIsPointer - (int)RIsPointer;
468 // Compare getValueID values.
469 unsigned LID = LV->getValueID(),
470 RID = RV->getValueID();
472 return (int)LID - (int)RID;
474 // Sort arguments by their position.
475 if (const Argument *LA = dyn_cast<Argument>(LV)) {
476 const Argument *RA = cast<Argument>(RV);
477 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
478 return (int)LArgNo - (int)RArgNo;
481 // For instructions, compare their loop depth, and their operand
482 // count. This is pretty loose.
483 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
484 const Instruction *RInst = cast<Instruction>(RV);
486 // Compare loop depths.
487 const BasicBlock *LParent = LInst->getParent(),
488 *RParent = RInst->getParent();
489 if (LParent != RParent) {
490 unsigned LDepth = LI->getLoopDepth(LParent),
491 RDepth = LI->getLoopDepth(RParent);
492 if (LDepth != RDepth)
493 return (int)LDepth - (int)RDepth;
496 // Compare the number of operands.
497 unsigned LNumOps = LInst->getNumOperands(),
498 RNumOps = RInst->getNumOperands();
499 return (int)LNumOps - (int)RNumOps;
506 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
507 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
509 // Compare constant values.
510 const APInt &LA = LC->getValue()->getValue();
511 const APInt &RA = RC->getValue()->getValue();
512 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
513 if (LBitWidth != RBitWidth)
514 return (int)LBitWidth - (int)RBitWidth;
515 return LA.ult(RA) ? -1 : 1;
519 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
520 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
522 // Compare addrec loop depths.
523 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
524 if (LLoop != RLoop) {
525 unsigned LDepth = LLoop->getLoopDepth(),
526 RDepth = RLoop->getLoopDepth();
527 if (LDepth != RDepth)
528 return (int)LDepth - (int)RDepth;
531 // Addrec complexity grows with operand count.
532 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
533 if (LNumOps != RNumOps)
534 return (int)LNumOps - (int)RNumOps;
536 // Lexicographically compare.
537 for (unsigned i = 0; i != LNumOps; ++i) {
538 long X = compare(LA->getOperand(i), RA->getOperand(i));
550 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
551 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
553 // Lexicographically compare n-ary expressions.
554 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
555 for (unsigned i = 0; i != LNumOps; ++i) {
558 long X = compare(LC->getOperand(i), RC->getOperand(i));
562 return (int)LNumOps - (int)RNumOps;
566 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
567 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
569 // Lexicographically compare udiv expressions.
570 long X = compare(LC->getLHS(), RC->getLHS());
573 return compare(LC->getRHS(), RC->getRHS());
579 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
580 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
582 // Compare cast expressions by operand.
583 return compare(LC->getOperand(), RC->getOperand());
590 llvm_unreachable("Unknown SCEV kind!");
596 /// GroupByComplexity - Given a list of SCEV objects, order them by their
597 /// complexity, and group objects of the same complexity together by value.
598 /// When this routine is finished, we know that any duplicates in the vector are
599 /// consecutive and that complexity is monotonically increasing.
601 /// Note that we go take special precautions to ensure that we get deterministic
602 /// results from this routine. In other words, we don't want the results of
603 /// this to depend on where the addresses of various SCEV objects happened to
606 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
608 if (Ops.size() < 2) return; // Noop
609 if (Ops.size() == 2) {
610 // This is the common case, which also happens to be trivially simple.
612 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
613 if (SCEVComplexityCompare(LI)(RHS, LHS))
618 // Do the rough sort by complexity.
619 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
621 // Now that we are sorted by complexity, group elements of the same
622 // complexity. Note that this is, at worst, N^2, but the vector is likely to
623 // be extremely short in practice. Note that we take this approach because we
624 // do not want to depend on the addresses of the objects we are grouping.
625 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
626 const SCEV *S = Ops[i];
627 unsigned Complexity = S->getSCEVType();
629 // If there are any objects of the same complexity and same value as this
631 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
632 if (Ops[j] == S) { // Found a duplicate.
633 // Move it to immediately after i'th element.
634 std::swap(Ops[i+1], Ops[j]);
635 ++i; // no need to rescan it.
636 if (i == e-2) return; // Done!
644 //===----------------------------------------------------------------------===//
645 // Simple SCEV method implementations
646 //===----------------------------------------------------------------------===//
648 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
650 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
652 const Type* ResultTy) {
653 // Handle the simplest case efficiently.
655 return SE.getTruncateOrZeroExtend(It, ResultTy);
657 // We are using the following formula for BC(It, K):
659 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
661 // Suppose, W is the bitwidth of the return value. We must be prepared for
662 // overflow. Hence, we must assure that the result of our computation is
663 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
664 // safe in modular arithmetic.
666 // However, this code doesn't use exactly that formula; the formula it uses
667 // is something like the following, where T is the number of factors of 2 in
668 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
671 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
673 // This formula is trivially equivalent to the previous formula. However,
674 // this formula can be implemented much more efficiently. The trick is that
675 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
676 // arithmetic. To do exact division in modular arithmetic, all we have
677 // to do is multiply by the inverse. Therefore, this step can be done at
680 // The next issue is how to safely do the division by 2^T. The way this
681 // is done is by doing the multiplication step at a width of at least W + T
682 // bits. This way, the bottom W+T bits of the product are accurate. Then,
683 // when we perform the division by 2^T (which is equivalent to a right shift
684 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
685 // truncated out after the division by 2^T.
687 // In comparison to just directly using the first formula, this technique
688 // is much more efficient; using the first formula requires W * K bits,
689 // but this formula less than W + K bits. Also, the first formula requires
690 // a division step, whereas this formula only requires multiplies and shifts.
692 // It doesn't matter whether the subtraction step is done in the calculation
693 // width or the input iteration count's width; if the subtraction overflows,
694 // the result must be zero anyway. We prefer here to do it in the width of
695 // the induction variable because it helps a lot for certain cases; CodeGen
696 // isn't smart enough to ignore the overflow, which leads to much less
697 // efficient code if the width of the subtraction is wider than the native
700 // (It's possible to not widen at all by pulling out factors of 2 before
701 // the multiplication; for example, K=2 can be calculated as
702 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
703 // extra arithmetic, so it's not an obvious win, and it gets
704 // much more complicated for K > 3.)
706 // Protection from insane SCEVs; this bound is conservative,
707 // but it probably doesn't matter.
709 return SE.getCouldNotCompute();
711 unsigned W = SE.getTypeSizeInBits(ResultTy);
713 // Calculate K! / 2^T and T; we divide out the factors of two before
714 // multiplying for calculating K! / 2^T to avoid overflow.
715 // Other overflow doesn't matter because we only care about the bottom
716 // W bits of the result.
717 APInt OddFactorial(W, 1);
719 for (unsigned i = 3; i <= K; ++i) {
721 unsigned TwoFactors = Mult.countTrailingZeros();
723 Mult = Mult.lshr(TwoFactors);
724 OddFactorial *= Mult;
727 // We need at least W + T bits for the multiplication step
728 unsigned CalculationBits = W + T;
730 // Calculate 2^T, at width T+W.
731 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
733 // Calculate the multiplicative inverse of K! / 2^T;
734 // this multiplication factor will perform the exact division by
736 APInt Mod = APInt::getSignedMinValue(W+1);
737 APInt MultiplyFactor = OddFactorial.zext(W+1);
738 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
739 MultiplyFactor = MultiplyFactor.trunc(W);
741 // Calculate the product, at width T+W
742 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
744 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
745 for (unsigned i = 1; i != K; ++i) {
746 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
747 Dividend = SE.getMulExpr(Dividend,
748 SE.getTruncateOrZeroExtend(S, CalculationTy));
752 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
754 // Truncate the result, and divide by K! / 2^T.
756 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
757 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
760 /// evaluateAtIteration - Return the value of this chain of recurrences at
761 /// the specified iteration number. We can evaluate this recurrence by
762 /// multiplying each element in the chain by the binomial coefficient
763 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
765 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
767 /// where BC(It, k) stands for binomial coefficient.
769 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
770 ScalarEvolution &SE) const {
771 const SCEV *Result = getStart();
772 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
773 // The computation is correct in the face of overflow provided that the
774 // multiplication is performed _after_ the evaluation of the binomial
776 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
777 if (isa<SCEVCouldNotCompute>(Coeff))
780 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
785 //===----------------------------------------------------------------------===//
786 // SCEV Expression folder implementations
787 //===----------------------------------------------------------------------===//
789 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
791 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
792 "This is not a truncating conversion!");
793 assert(isSCEVable(Ty) &&
794 "This is not a conversion to a SCEVable type!");
795 Ty = getEffectiveSCEVType(Ty);
798 ID.AddInteger(scTruncate);
802 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
804 // Fold if the operand is constant.
805 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
807 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
808 getEffectiveSCEVType(Ty))));
810 // trunc(trunc(x)) --> trunc(x)
811 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
812 return getTruncateExpr(ST->getOperand(), Ty);
814 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
815 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
816 return getTruncateOrSignExtend(SS->getOperand(), Ty);
818 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
819 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
820 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
822 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
823 // eliminate all the truncates.
824 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
825 SmallVector<const SCEV *, 4> Operands;
826 bool hasTrunc = false;
827 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
828 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
829 hasTrunc = isa<SCEVTruncateExpr>(S);
830 Operands.push_back(S);
833 return getAddExpr(Operands, false, false);
834 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
837 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
838 // eliminate all the truncates.
839 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
840 SmallVector<const SCEV *, 4> Operands;
841 bool hasTrunc = false;
842 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
843 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
844 hasTrunc = isa<SCEVTruncateExpr>(S);
845 Operands.push_back(S);
848 return getMulExpr(Operands, false, false);
849 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
852 // If the input value is a chrec scev, truncate the chrec's operands.
853 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
854 SmallVector<const SCEV *, 4> Operands;
855 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
856 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
857 return getAddRecExpr(Operands, AddRec->getLoop());
860 // As a special case, fold trunc(undef) to undef. We don't want to
861 // know too much about SCEVUnknowns, but this special case is handy
863 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
864 if (isa<UndefValue>(U->getValue()))
865 return getSCEV(UndefValue::get(Ty));
867 // The cast wasn't folded; create an explicit cast node. We can reuse
868 // the existing insert position since if we get here, we won't have
869 // made any changes which would invalidate it.
870 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
872 UniqueSCEVs.InsertNode(S, IP);
876 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
878 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
879 "This is not an extending conversion!");
880 assert(isSCEVable(Ty) &&
881 "This is not a conversion to a SCEVable type!");
882 Ty = getEffectiveSCEVType(Ty);
884 // Fold if the operand is constant.
885 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
887 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
888 getEffectiveSCEVType(Ty))));
890 // zext(zext(x)) --> zext(x)
891 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
892 return getZeroExtendExpr(SZ->getOperand(), Ty);
894 // Before doing any expensive analysis, check to see if we've already
895 // computed a SCEV for this Op and Ty.
897 ID.AddInteger(scZeroExtend);
901 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
903 // zext(trunc(x)) --> zext(x) or x or trunc(x)
904 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
905 // It's possible the bits taken off by the truncate were all zero bits. If
906 // so, we should be able to simplify this further.
907 const SCEV *X = ST->getOperand();
908 ConstantRange CR = getUnsignedRange(X);
909 unsigned TruncBits = getTypeSizeInBits(ST->getType());
910 unsigned NewBits = getTypeSizeInBits(Ty);
911 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
912 CR.zextOrTrunc(NewBits)))
913 return getTruncateOrZeroExtend(X, Ty);
916 // If the input value is a chrec scev, and we can prove that the value
917 // did not overflow the old, smaller, value, we can zero extend all of the
918 // operands (often constants). This allows analysis of something like
919 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
920 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
921 if (AR->isAffine()) {
922 const SCEV *Start = AR->getStart();
923 const SCEV *Step = AR->getStepRecurrence(*this);
924 unsigned BitWidth = getTypeSizeInBits(AR->getType());
925 const Loop *L = AR->getLoop();
927 // If we have special knowledge that this addrec won't overflow,
928 // we don't need to do any further analysis.
929 if (AR->hasNoUnsignedWrap())
930 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
931 getZeroExtendExpr(Step, Ty),
934 // Check whether the backedge-taken count is SCEVCouldNotCompute.
935 // Note that this serves two purposes: It filters out loops that are
936 // simply not analyzable, and it covers the case where this code is
937 // being called from within backedge-taken count analysis, such that
938 // attempting to ask for the backedge-taken count would likely result
939 // in infinite recursion. In the later case, the analysis code will
940 // cope with a conservative value, and it will take care to purge
941 // that value once it has finished.
942 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
943 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
944 // Manually compute the final value for AR, checking for
947 // Check whether the backedge-taken count can be losslessly casted to
948 // the addrec's type. The count is always unsigned.
949 const SCEV *CastedMaxBECount =
950 getTruncateOrZeroExtend(MaxBECount, Start->getType());
951 const SCEV *RecastedMaxBECount =
952 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
953 if (MaxBECount == RecastedMaxBECount) {
954 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
955 // Check whether Start+Step*MaxBECount has no unsigned overflow.
956 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
957 const SCEV *Add = getAddExpr(Start, ZMul);
958 const SCEV *OperandExtendedAdd =
959 getAddExpr(getZeroExtendExpr(Start, WideTy),
960 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
961 getZeroExtendExpr(Step, WideTy)));
962 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
963 // Return the expression with the addrec on the outside.
964 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
965 getZeroExtendExpr(Step, Ty),
968 // Similar to above, only this time treat the step value as signed.
969 // This covers loops that count down.
970 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
971 Add = getAddExpr(Start, SMul);
973 getAddExpr(getZeroExtendExpr(Start, WideTy),
974 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
975 getSignExtendExpr(Step, WideTy)));
976 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
977 // Return the expression with the addrec on the outside.
978 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
979 getSignExtendExpr(Step, Ty),
983 // If the backedge is guarded by a comparison with the pre-inc value
984 // the addrec is safe. Also, if the entry is guarded by a comparison
985 // with the start value and the backedge is guarded by a comparison
986 // with the post-inc value, the addrec is safe.
987 if (isKnownPositive(Step)) {
988 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
989 getUnsignedRange(Step).getUnsignedMax());
990 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
991 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
992 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
993 AR->getPostIncExpr(*this), N)))
994 // Return the expression with the addrec on the outside.
995 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
996 getZeroExtendExpr(Step, Ty),
998 } else if (isKnownNegative(Step)) {
999 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1000 getSignedRange(Step).getSignedMin());
1001 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1002 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1003 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1004 AR->getPostIncExpr(*this), N)))
1005 // Return the expression with the addrec on the outside.
1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1007 getSignExtendExpr(Step, Ty),
1013 // The cast wasn't folded; create an explicit cast node.
1014 // Recompute the insert position, as it may have been invalidated.
1015 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1016 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1018 UniqueSCEVs.InsertNode(S, IP);
1022 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1024 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1025 "This is not an extending conversion!");
1026 assert(isSCEVable(Ty) &&
1027 "This is not a conversion to a SCEVable type!");
1028 Ty = getEffectiveSCEVType(Ty);
1030 // Fold if the operand is constant.
1031 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1033 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1034 getEffectiveSCEVType(Ty))));
1036 // sext(sext(x)) --> sext(x)
1037 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1038 return getSignExtendExpr(SS->getOperand(), Ty);
1040 // sext(zext(x)) --> zext(x)
1041 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1042 return getZeroExtendExpr(SZ->getOperand(), Ty);
1044 // Before doing any expensive analysis, check to see if we've already
1045 // computed a SCEV for this Op and Ty.
1046 FoldingSetNodeID ID;
1047 ID.AddInteger(scSignExtend);
1051 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1053 // If the input value is provably positive, build a zext instead.
1054 if (isKnownNonNegative(Op))
1055 return getZeroExtendExpr(Op, Ty);
1057 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1058 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1059 // It's possible the bits taken off by the truncate were all sign bits. If
1060 // so, we should be able to simplify this further.
1061 const SCEV *X = ST->getOperand();
1062 ConstantRange CR = getSignedRange(X);
1063 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1064 unsigned NewBits = getTypeSizeInBits(Ty);
1065 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1066 CR.sextOrTrunc(NewBits)))
1067 return getTruncateOrSignExtend(X, Ty);
1070 // If the input value is a chrec scev, and we can prove that the value
1071 // did not overflow the old, smaller, value, we can sign extend all of the
1072 // operands (often constants). This allows analysis of something like
1073 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1074 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1075 if (AR->isAffine()) {
1076 const SCEV *Start = AR->getStart();
1077 const SCEV *Step = AR->getStepRecurrence(*this);
1078 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1079 const Loop *L = AR->getLoop();
1081 // If we have special knowledge that this addrec won't overflow,
1082 // we don't need to do any further analysis.
1083 if (AR->hasNoSignedWrap())
1084 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1085 getSignExtendExpr(Step, Ty),
1088 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1089 // Note that this serves two purposes: It filters out loops that are
1090 // simply not analyzable, and it covers the case where this code is
1091 // being called from within backedge-taken count analysis, such that
1092 // attempting to ask for the backedge-taken count would likely result
1093 // in infinite recursion. In the later case, the analysis code will
1094 // cope with a conservative value, and it will take care to purge
1095 // that value once it has finished.
1096 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1097 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1098 // Manually compute the final value for AR, checking for
1101 // Check whether the backedge-taken count can be losslessly casted to
1102 // the addrec's type. The count is always unsigned.
1103 const SCEV *CastedMaxBECount =
1104 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1105 const SCEV *RecastedMaxBECount =
1106 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1107 if (MaxBECount == RecastedMaxBECount) {
1108 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1109 // Check whether Start+Step*MaxBECount has no signed overflow.
1110 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1111 const SCEV *Add = getAddExpr(Start, SMul);
1112 const SCEV *OperandExtendedAdd =
1113 getAddExpr(getSignExtendExpr(Start, WideTy),
1114 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1115 getSignExtendExpr(Step, WideTy)));
1116 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1117 // Return the expression with the addrec on the outside.
1118 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1119 getSignExtendExpr(Step, Ty),
1122 // Similar to above, only this time treat the step value as unsigned.
1123 // This covers loops that count up with an unsigned step.
1124 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1125 Add = getAddExpr(Start, UMul);
1126 OperandExtendedAdd =
1127 getAddExpr(getSignExtendExpr(Start, WideTy),
1128 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1129 getZeroExtendExpr(Step, WideTy)));
1130 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1131 // Return the expression with the addrec on the outside.
1132 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1133 getZeroExtendExpr(Step, Ty),
1137 // If the backedge is guarded by a comparison with the pre-inc value
1138 // the addrec is safe. Also, if the entry is guarded by a comparison
1139 // with the start value and the backedge is guarded by a comparison
1140 // with the post-inc value, the addrec is safe.
1141 if (isKnownPositive(Step)) {
1142 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1143 getSignedRange(Step).getSignedMax());
1144 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1145 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1146 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1147 AR->getPostIncExpr(*this), N)))
1148 // Return the expression with the addrec on the outside.
1149 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1150 getSignExtendExpr(Step, Ty),
1152 } else if (isKnownNegative(Step)) {
1153 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1154 getSignedRange(Step).getSignedMin());
1155 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1156 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1157 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1158 AR->getPostIncExpr(*this), N)))
1159 // Return the expression with the addrec on the outside.
1160 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1161 getSignExtendExpr(Step, Ty),
1167 // The cast wasn't folded; create an explicit cast node.
1168 // Recompute the insert position, as it may have been invalidated.
1169 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1170 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1172 UniqueSCEVs.InsertNode(S, IP);
1176 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1177 /// unspecified bits out to the given type.
1179 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1181 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1182 "This is not an extending conversion!");
1183 assert(isSCEVable(Ty) &&
1184 "This is not a conversion to a SCEVable type!");
1185 Ty = getEffectiveSCEVType(Ty);
1187 // Sign-extend negative constants.
1188 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1189 if (SC->getValue()->getValue().isNegative())
1190 return getSignExtendExpr(Op, Ty);
1192 // Peel off a truncate cast.
1193 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1194 const SCEV *NewOp = T->getOperand();
1195 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1196 return getAnyExtendExpr(NewOp, Ty);
1197 return getTruncateOrNoop(NewOp, Ty);
1200 // Next try a zext cast. If the cast is folded, use it.
1201 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1202 if (!isa<SCEVZeroExtendExpr>(ZExt))
1205 // Next try a sext cast. If the cast is folded, use it.
1206 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1207 if (!isa<SCEVSignExtendExpr>(SExt))
1210 // Force the cast to be folded into the operands of an addrec.
1211 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1212 SmallVector<const SCEV *, 4> Ops;
1213 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1215 Ops.push_back(getAnyExtendExpr(*I, Ty));
1216 return getAddRecExpr(Ops, AR->getLoop());
1219 // As a special case, fold anyext(undef) to undef. We don't want to
1220 // know too much about SCEVUnknowns, but this special case is handy
1222 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1223 if (isa<UndefValue>(U->getValue()))
1224 return getSCEV(UndefValue::get(Ty));
1226 // If the expression is obviously signed, use the sext cast value.
1227 if (isa<SCEVSMaxExpr>(Op))
1230 // Absent any other information, use the zext cast value.
1234 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1235 /// a list of operands to be added under the given scale, update the given
1236 /// map. This is a helper function for getAddRecExpr. As an example of
1237 /// what it does, given a sequence of operands that would form an add
1238 /// expression like this:
1240 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1242 /// where A and B are constants, update the map with these values:
1244 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1246 /// and add 13 + A*B*29 to AccumulatedConstant.
1247 /// This will allow getAddRecExpr to produce this:
1249 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1251 /// This form often exposes folding opportunities that are hidden in
1252 /// the original operand list.
1254 /// Return true iff it appears that any interesting folding opportunities
1255 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1256 /// the common case where no interesting opportunities are present, and
1257 /// is also used as a check to avoid infinite recursion.
1260 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1261 SmallVector<const SCEV *, 8> &NewOps,
1262 APInt &AccumulatedConstant,
1263 const SCEV *const *Ops, size_t NumOperands,
1265 ScalarEvolution &SE) {
1266 bool Interesting = false;
1268 // Iterate over the add operands. They are sorted, with constants first.
1270 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1272 // Pull a buried constant out to the outside.
1273 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1275 AccumulatedConstant += Scale * C->getValue()->getValue();
1278 // Next comes everything else. We're especially interested in multiplies
1279 // here, but they're in the middle, so just visit the rest with one loop.
1280 for (; i != NumOperands; ++i) {
1281 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1282 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1284 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1285 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1286 // A multiplication of a constant with another add; recurse.
1287 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1289 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1290 Add->op_begin(), Add->getNumOperands(),
1293 // A multiplication of a constant with some other value. Update
1295 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1296 const SCEV *Key = SE.getMulExpr(MulOps);
1297 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1298 M.insert(std::make_pair(Key, NewScale));
1300 NewOps.push_back(Pair.first->first);
1302 Pair.first->second += NewScale;
1303 // The map already had an entry for this value, which may indicate
1304 // a folding opportunity.
1309 // An ordinary operand. Update the map.
1310 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1311 M.insert(std::make_pair(Ops[i], Scale));
1313 NewOps.push_back(Pair.first->first);
1315 Pair.first->second += Scale;
1316 // The map already had an entry for this value, which may indicate
1317 // a folding opportunity.
1327 struct APIntCompare {
1328 bool operator()(const APInt &LHS, const APInt &RHS) const {
1329 return LHS.ult(RHS);
1334 /// getAddExpr - Get a canonical add expression, or something simpler if
1336 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1337 bool HasNUW, bool HasNSW) {
1338 assert(!Ops.empty() && "Cannot get empty add!");
1339 if (Ops.size() == 1) return Ops[0];
1341 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1342 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1343 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1344 "SCEVAddExpr operand types don't match!");
1347 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1348 if (!HasNUW && HasNSW) {
1350 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1351 E = Ops.end(); I != E; ++I)
1352 if (!isKnownNonNegative(*I)) {
1356 if (All) HasNUW = true;
1359 // Sort by complexity, this groups all similar expression types together.
1360 GroupByComplexity(Ops, LI);
1362 // If there are any constants, fold them together.
1364 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1366 assert(Idx < Ops.size());
1367 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1368 // We found two constants, fold them together!
1369 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1370 RHSC->getValue()->getValue());
1371 if (Ops.size() == 2) return Ops[0];
1372 Ops.erase(Ops.begin()+1); // Erase the folded element
1373 LHSC = cast<SCEVConstant>(Ops[0]);
1376 // If we are left with a constant zero being added, strip it off.
1377 if (LHSC->getValue()->isZero()) {
1378 Ops.erase(Ops.begin());
1382 if (Ops.size() == 1) return Ops[0];
1385 // Okay, check to see if the same value occurs in the operand list more than
1386 // once. If so, merge them together into an multiply expression. Since we
1387 // sorted the list, these values are required to be adjacent.
1388 const Type *Ty = Ops[0]->getType();
1389 bool FoundMatch = false;
1390 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1391 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1392 // Scan ahead to count how many equal operands there are.
1394 while (i+Count != e && Ops[i+Count] == Ops[i])
1396 // Merge the values into a multiply.
1397 const SCEV *Scale = getConstant(Ty, Count);
1398 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1399 if (Ops.size() == Count)
1402 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1403 --i; e -= Count - 1;
1407 return getAddExpr(Ops, HasNUW, HasNSW);
1409 // Check for truncates. If all the operands are truncated from the same
1410 // type, see if factoring out the truncate would permit the result to be
1411 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1412 // if the contents of the resulting outer trunc fold to something simple.
1413 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1414 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1415 const Type *DstType = Trunc->getType();
1416 const Type *SrcType = Trunc->getOperand()->getType();
1417 SmallVector<const SCEV *, 8> LargeOps;
1419 // Check all the operands to see if they can be represented in the
1420 // source type of the truncate.
1421 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1422 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1423 if (T->getOperand()->getType() != SrcType) {
1427 LargeOps.push_back(T->getOperand());
1428 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1429 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1430 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1431 SmallVector<const SCEV *, 8> LargeMulOps;
1432 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1433 if (const SCEVTruncateExpr *T =
1434 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1435 if (T->getOperand()->getType() != SrcType) {
1439 LargeMulOps.push_back(T->getOperand());
1440 } else if (const SCEVConstant *C =
1441 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1442 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1449 LargeOps.push_back(getMulExpr(LargeMulOps));
1456 // Evaluate the expression in the larger type.
1457 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1458 // If it folds to something simple, use it. Otherwise, don't.
1459 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1460 return getTruncateExpr(Fold, DstType);
1464 // Skip past any other cast SCEVs.
1465 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1468 // If there are add operands they would be next.
1469 if (Idx < Ops.size()) {
1470 bool DeletedAdd = false;
1471 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1472 // If we have an add, expand the add operands onto the end of the operands
1474 Ops.erase(Ops.begin()+Idx);
1475 Ops.append(Add->op_begin(), Add->op_end());
1479 // If we deleted at least one add, we added operands to the end of the list,
1480 // and they are not necessarily sorted. Recurse to resort and resimplify
1481 // any operands we just acquired.
1483 return getAddExpr(Ops);
1486 // Skip over the add expression until we get to a multiply.
1487 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1490 // Check to see if there are any folding opportunities present with
1491 // operands multiplied by constant values.
1492 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1493 uint64_t BitWidth = getTypeSizeInBits(Ty);
1494 DenseMap<const SCEV *, APInt> M;
1495 SmallVector<const SCEV *, 8> NewOps;
1496 APInt AccumulatedConstant(BitWidth, 0);
1497 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1498 Ops.data(), Ops.size(),
1499 APInt(BitWidth, 1), *this)) {
1500 // Some interesting folding opportunity is present, so its worthwhile to
1501 // re-generate the operands list. Group the operands by constant scale,
1502 // to avoid multiplying by the same constant scale multiple times.
1503 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1504 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1505 E = NewOps.end(); I != E; ++I)
1506 MulOpLists[M.find(*I)->second].push_back(*I);
1507 // Re-generate the operands list.
1509 if (AccumulatedConstant != 0)
1510 Ops.push_back(getConstant(AccumulatedConstant));
1511 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1512 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1514 Ops.push_back(getMulExpr(getConstant(I->first),
1515 getAddExpr(I->second)));
1517 return getConstant(Ty, 0);
1518 if (Ops.size() == 1)
1520 return getAddExpr(Ops);
1524 // If we are adding something to a multiply expression, make sure the
1525 // something is not already an operand of the multiply. If so, merge it into
1527 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1528 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1529 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1530 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1531 if (isa<SCEVConstant>(MulOpSCEV))
1533 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1534 if (MulOpSCEV == Ops[AddOp]) {
1535 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1536 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1537 if (Mul->getNumOperands() != 2) {
1538 // If the multiply has more than two operands, we must get the
1540 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1541 Mul->op_begin()+MulOp);
1542 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1543 InnerMul = getMulExpr(MulOps);
1545 const SCEV *One = getConstant(Ty, 1);
1546 const SCEV *AddOne = getAddExpr(One, InnerMul);
1547 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1548 if (Ops.size() == 2) return OuterMul;
1550 Ops.erase(Ops.begin()+AddOp);
1551 Ops.erase(Ops.begin()+Idx-1);
1553 Ops.erase(Ops.begin()+Idx);
1554 Ops.erase(Ops.begin()+AddOp-1);
1556 Ops.push_back(OuterMul);
1557 return getAddExpr(Ops);
1560 // Check this multiply against other multiplies being added together.
1561 for (unsigned OtherMulIdx = Idx+1;
1562 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1564 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1565 // If MulOp occurs in OtherMul, we can fold the two multiplies
1567 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1568 OMulOp != e; ++OMulOp)
1569 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1570 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1571 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1572 if (Mul->getNumOperands() != 2) {
1573 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1574 Mul->op_begin()+MulOp);
1575 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1576 InnerMul1 = getMulExpr(MulOps);
1578 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1579 if (OtherMul->getNumOperands() != 2) {
1580 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1581 OtherMul->op_begin()+OMulOp);
1582 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1583 InnerMul2 = getMulExpr(MulOps);
1585 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1586 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1587 if (Ops.size() == 2) return OuterMul;
1588 Ops.erase(Ops.begin()+Idx);
1589 Ops.erase(Ops.begin()+OtherMulIdx-1);
1590 Ops.push_back(OuterMul);
1591 return getAddExpr(Ops);
1597 // If there are any add recurrences in the operands list, see if any other
1598 // added values are loop invariant. If so, we can fold them into the
1600 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1603 // Scan over all recurrences, trying to fold loop invariants into them.
1604 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1605 // Scan all of the other operands to this add and add them to the vector if
1606 // they are loop invariant w.r.t. the recurrence.
1607 SmallVector<const SCEV *, 8> LIOps;
1608 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1609 const Loop *AddRecLoop = AddRec->getLoop();
1610 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1611 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1612 LIOps.push_back(Ops[i]);
1613 Ops.erase(Ops.begin()+i);
1617 // If we found some loop invariants, fold them into the recurrence.
1618 if (!LIOps.empty()) {
1619 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1620 LIOps.push_back(AddRec->getStart());
1622 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1624 AddRecOps[0] = getAddExpr(LIOps);
1626 // Build the new addrec. Propagate the NUW and NSW flags if both the
1627 // outer add and the inner addrec are guaranteed to have no overflow.
1628 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1629 HasNUW && AddRec->hasNoUnsignedWrap(),
1630 HasNSW && AddRec->hasNoSignedWrap());
1632 // If all of the other operands were loop invariant, we are done.
1633 if (Ops.size() == 1) return NewRec;
1635 // Otherwise, add the folded AddRec by the non-liv parts.
1636 for (unsigned i = 0;; ++i)
1637 if (Ops[i] == AddRec) {
1641 return getAddExpr(Ops);
1644 // Okay, if there weren't any loop invariants to be folded, check to see if
1645 // there are multiple AddRec's with the same loop induction variable being
1646 // added together. If so, we can fold them.
1647 for (unsigned OtherIdx = Idx+1;
1648 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1650 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1651 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1652 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1654 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1656 if (const SCEVAddRecExpr *OtherAddRec =
1657 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1658 if (OtherAddRec->getLoop() == AddRecLoop) {
1659 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1661 if (i >= AddRecOps.size()) {
1662 AddRecOps.append(OtherAddRec->op_begin()+i,
1663 OtherAddRec->op_end());
1666 AddRecOps[i] = getAddExpr(AddRecOps[i],
1667 OtherAddRec->getOperand(i));
1669 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1671 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop);
1672 return getAddExpr(Ops);
1675 // Otherwise couldn't fold anything into this recurrence. Move onto the
1679 // Okay, it looks like we really DO need an add expr. Check to see if we
1680 // already have one, otherwise create a new one.
1681 FoldingSetNodeID ID;
1682 ID.AddInteger(scAddExpr);
1683 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1684 ID.AddPointer(Ops[i]);
1687 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1689 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1690 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1691 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1693 UniqueSCEVs.InsertNode(S, IP);
1695 if (HasNUW) S->setHasNoUnsignedWrap(true);
1696 if (HasNSW) S->setHasNoSignedWrap(true);
1700 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1702 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1703 bool HasNUW, bool HasNSW) {
1704 assert(!Ops.empty() && "Cannot get empty mul!");
1705 if (Ops.size() == 1) return Ops[0];
1707 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1708 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1709 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1710 "SCEVMulExpr operand types don't match!");
1713 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1714 if (!HasNUW && HasNSW) {
1716 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1717 E = Ops.end(); I != E; ++I)
1718 if (!isKnownNonNegative(*I)) {
1722 if (All) HasNUW = true;
1725 // Sort by complexity, this groups all similar expression types together.
1726 GroupByComplexity(Ops, LI);
1728 // If there are any constants, fold them together.
1730 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1732 // C1*(C2+V) -> C1*C2 + C1*V
1733 if (Ops.size() == 2)
1734 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1735 if (Add->getNumOperands() == 2 &&
1736 isa<SCEVConstant>(Add->getOperand(0)))
1737 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1738 getMulExpr(LHSC, Add->getOperand(1)));
1741 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1742 // We found two constants, fold them together!
1743 ConstantInt *Fold = ConstantInt::get(getContext(),
1744 LHSC->getValue()->getValue() *
1745 RHSC->getValue()->getValue());
1746 Ops[0] = getConstant(Fold);
1747 Ops.erase(Ops.begin()+1); // Erase the folded element
1748 if (Ops.size() == 1) return Ops[0];
1749 LHSC = cast<SCEVConstant>(Ops[0]);
1752 // If we are left with a constant one being multiplied, strip it off.
1753 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1754 Ops.erase(Ops.begin());
1756 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1757 // If we have a multiply of zero, it will always be zero.
1759 } else if (Ops[0]->isAllOnesValue()) {
1760 // If we have a mul by -1 of an add, try distributing the -1 among the
1762 if (Ops.size() == 2)
1763 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1764 SmallVector<const SCEV *, 4> NewOps;
1765 bool AnyFolded = false;
1766 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1768 const SCEV *Mul = getMulExpr(Ops[0], *I);
1769 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1770 NewOps.push_back(Mul);
1773 return getAddExpr(NewOps);
1777 if (Ops.size() == 1)
1781 // Skip over the add expression until we get to a multiply.
1782 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1785 // If there are mul operands inline them all into this expression.
1786 if (Idx < Ops.size()) {
1787 bool DeletedMul = false;
1788 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1789 // If we have an mul, expand the mul operands onto the end of the operands
1791 Ops.erase(Ops.begin()+Idx);
1792 Ops.append(Mul->op_begin(), Mul->op_end());
1796 // If we deleted at least one mul, we added operands to the end of the list,
1797 // and they are not necessarily sorted. Recurse to resort and resimplify
1798 // any operands we just acquired.
1800 return getMulExpr(Ops);
1803 // If there are any add recurrences in the operands list, see if any other
1804 // added values are loop invariant. If so, we can fold them into the
1806 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1809 // Scan over all recurrences, trying to fold loop invariants into them.
1810 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1811 // Scan all of the other operands to this mul and add them to the vector if
1812 // they are loop invariant w.r.t. the recurrence.
1813 SmallVector<const SCEV *, 8> LIOps;
1814 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1815 const Loop *AddRecLoop = AddRec->getLoop();
1816 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1817 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1818 LIOps.push_back(Ops[i]);
1819 Ops.erase(Ops.begin()+i);
1823 // If we found some loop invariants, fold them into the recurrence.
1824 if (!LIOps.empty()) {
1825 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1826 SmallVector<const SCEV *, 4> NewOps;
1827 NewOps.reserve(AddRec->getNumOperands());
1828 const SCEV *Scale = getMulExpr(LIOps);
1829 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1830 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1832 // Build the new addrec. Propagate the NUW and NSW flags if both the
1833 // outer mul and the inner addrec are guaranteed to have no overflow.
1834 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop,
1835 HasNUW && AddRec->hasNoUnsignedWrap(),
1836 HasNSW && AddRec->hasNoSignedWrap());
1838 // If all of the other operands were loop invariant, we are done.
1839 if (Ops.size() == 1) return NewRec;
1841 // Otherwise, multiply the folded AddRec by the non-liv parts.
1842 for (unsigned i = 0;; ++i)
1843 if (Ops[i] == AddRec) {
1847 return getMulExpr(Ops);
1850 // Okay, if there weren't any loop invariants to be folded, check to see if
1851 // there are multiple AddRec's with the same loop induction variable being
1852 // multiplied together. If so, we can fold them.
1853 for (unsigned OtherIdx = Idx+1;
1854 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1856 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1857 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> -->
1858 // {A*C,+,F*D + G*B + B*D}<L>
1859 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1861 if (const SCEVAddRecExpr *OtherAddRec =
1862 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1863 if (OtherAddRec->getLoop() == AddRecLoop) {
1864 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1865 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1866 const SCEV *B = F->getStepRecurrence(*this);
1867 const SCEV *D = G->getStepRecurrence(*this);
1868 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1871 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1873 if (Ops.size() == 2) return NewAddRec;
1874 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
1875 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1877 return getMulExpr(Ops);
1880 // Otherwise couldn't fold anything into this recurrence. Move onto the
1884 // Okay, it looks like we really DO need an mul expr. Check to see if we
1885 // already have one, otherwise create a new one.
1886 FoldingSetNodeID ID;
1887 ID.AddInteger(scMulExpr);
1888 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1889 ID.AddPointer(Ops[i]);
1892 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1894 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1895 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1896 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1898 UniqueSCEVs.InsertNode(S, IP);
1900 if (HasNUW) S->setHasNoUnsignedWrap(true);
1901 if (HasNSW) S->setHasNoSignedWrap(true);
1905 /// getUDivExpr - Get a canonical unsigned division expression, or something
1906 /// simpler if possible.
1907 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1909 assert(getEffectiveSCEVType(LHS->getType()) ==
1910 getEffectiveSCEVType(RHS->getType()) &&
1911 "SCEVUDivExpr operand types don't match!");
1913 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1914 if (RHSC->getValue()->equalsInt(1))
1915 return LHS; // X udiv 1 --> x
1916 // If the denominator is zero, the result of the udiv is undefined. Don't
1917 // try to analyze it, because the resolution chosen here may differ from
1918 // the resolution chosen in other parts of the compiler.
1919 if (!RHSC->getValue()->isZero()) {
1920 // Determine if the division can be folded into the operands of
1922 // TODO: Generalize this to non-constants by using known-bits information.
1923 const Type *Ty = LHS->getType();
1924 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1925 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1926 // For non-power-of-two values, effectively round the value up to the
1927 // nearest power of two.
1928 if (!RHSC->getValue()->getValue().isPowerOf2())
1930 const IntegerType *ExtTy =
1931 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1932 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1933 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1934 if (const SCEVConstant *Step =
1935 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1936 if (!Step->getValue()->getValue()
1937 .urem(RHSC->getValue()->getValue()) &&
1938 getZeroExtendExpr(AR, ExtTy) ==
1939 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1940 getZeroExtendExpr(Step, ExtTy),
1942 SmallVector<const SCEV *, 4> Operands;
1943 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1944 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1945 return getAddRecExpr(Operands, AR->getLoop());
1947 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1948 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1949 SmallVector<const SCEV *, 4> Operands;
1950 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1951 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1952 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1953 // Find an operand that's safely divisible.
1954 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1955 const SCEV *Op = M->getOperand(i);
1956 const SCEV *Div = getUDivExpr(Op, RHSC);
1957 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1958 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1961 return getMulExpr(Operands);
1965 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1966 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1967 SmallVector<const SCEV *, 4> Operands;
1968 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1969 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1970 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1972 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1973 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1974 if (isa<SCEVUDivExpr>(Op) ||
1975 getMulExpr(Op, RHS) != A->getOperand(i))
1977 Operands.push_back(Op);
1979 if (Operands.size() == A->getNumOperands())
1980 return getAddExpr(Operands);
1984 // Fold if both operands are constant.
1985 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1986 Constant *LHSCV = LHSC->getValue();
1987 Constant *RHSCV = RHSC->getValue();
1988 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1994 FoldingSetNodeID ID;
1995 ID.AddInteger(scUDivExpr);
1999 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2000 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2002 UniqueSCEVs.InsertNode(S, IP);
2007 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2008 /// Simplify the expression as much as possible.
2009 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
2010 const SCEV *Step, const Loop *L,
2011 bool HasNUW, bool HasNSW) {
2012 SmallVector<const SCEV *, 4> Operands;
2013 Operands.push_back(Start);
2014 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2015 if (StepChrec->getLoop() == L) {
2016 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2017 return getAddRecExpr(Operands, L);
2020 Operands.push_back(Step);
2021 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
2024 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2025 /// Simplify the expression as much as possible.
2027 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2029 bool HasNUW, bool HasNSW) {
2030 if (Operands.size() == 1) return Operands[0];
2032 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2033 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2034 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2035 "SCEVAddRecExpr operand types don't match!");
2036 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2037 assert(isLoopInvariant(Operands[i], L) &&
2038 "SCEVAddRecExpr operand is not loop-invariant!");
2041 if (Operands.back()->isZero()) {
2042 Operands.pop_back();
2043 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
2046 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2047 // use that information to infer NUW and NSW flags. However, computing a
2048 // BE count requires calling getAddRecExpr, so we may not yet have a
2049 // meaningful BE count at this point (and if we don't, we'd be stuck
2050 // with a SCEVCouldNotCompute as the cached BE count).
2052 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
2053 if (!HasNUW && HasNSW) {
2055 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2056 E = Operands.end(); I != E; ++I)
2057 if (!isKnownNonNegative(*I)) {
2061 if (All) HasNUW = true;
2064 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2065 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2066 const Loop *NestedLoop = NestedAR->getLoop();
2067 if (L->contains(NestedLoop) ?
2068 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2069 (!NestedLoop->contains(L) &&
2070 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2071 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2072 NestedAR->op_end());
2073 Operands[0] = NestedAR->getStart();
2074 // AddRecs require their operands be loop-invariant with respect to their
2075 // loops. Don't perform this transformation if it would break this
2077 bool AllInvariant = true;
2078 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2079 if (!isLoopInvariant(Operands[i], L)) {
2080 AllInvariant = false;
2084 NestedOperands[0] = getAddRecExpr(Operands, L);
2085 AllInvariant = true;
2086 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2087 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2088 AllInvariant = false;
2092 // Ok, both add recurrences are valid after the transformation.
2093 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2095 // Reset Operands to its original state.
2096 Operands[0] = NestedAR;
2100 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2101 // already have one, otherwise create a new one.
2102 FoldingSetNodeID ID;
2103 ID.AddInteger(scAddRecExpr);
2104 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2105 ID.AddPointer(Operands[i]);
2109 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2111 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2112 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2113 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2114 O, Operands.size(), L);
2115 UniqueSCEVs.InsertNode(S, IP);
2117 if (HasNUW) S->setHasNoUnsignedWrap(true);
2118 if (HasNSW) S->setHasNoSignedWrap(true);
2122 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2124 SmallVector<const SCEV *, 2> Ops;
2127 return getSMaxExpr(Ops);
2131 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2132 assert(!Ops.empty() && "Cannot get empty smax!");
2133 if (Ops.size() == 1) return Ops[0];
2135 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2136 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2137 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2138 "SCEVSMaxExpr operand types don't match!");
2141 // Sort by complexity, this groups all similar expression types together.
2142 GroupByComplexity(Ops, LI);
2144 // If there are any constants, fold them together.
2146 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2148 assert(Idx < Ops.size());
2149 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2150 // We found two constants, fold them together!
2151 ConstantInt *Fold = ConstantInt::get(getContext(),
2152 APIntOps::smax(LHSC->getValue()->getValue(),
2153 RHSC->getValue()->getValue()));
2154 Ops[0] = getConstant(Fold);
2155 Ops.erase(Ops.begin()+1); // Erase the folded element
2156 if (Ops.size() == 1) return Ops[0];
2157 LHSC = cast<SCEVConstant>(Ops[0]);
2160 // If we are left with a constant minimum-int, strip it off.
2161 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2162 Ops.erase(Ops.begin());
2164 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2165 // If we have an smax with a constant maximum-int, it will always be
2170 if (Ops.size() == 1) return Ops[0];
2173 // Find the first SMax
2174 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2177 // Check to see if one of the operands is an SMax. If so, expand its operands
2178 // onto our operand list, and recurse to simplify.
2179 if (Idx < Ops.size()) {
2180 bool DeletedSMax = false;
2181 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2182 Ops.erase(Ops.begin()+Idx);
2183 Ops.append(SMax->op_begin(), SMax->op_end());
2188 return getSMaxExpr(Ops);
2191 // Okay, check to see if the same value occurs in the operand list twice. If
2192 // so, delete one. Since we sorted the list, these values are required to
2194 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2195 // X smax Y smax Y --> X smax Y
2196 // X smax Y --> X, if X is always greater than Y
2197 if (Ops[i] == Ops[i+1] ||
2198 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2199 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2201 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2202 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2206 if (Ops.size() == 1) return Ops[0];
2208 assert(!Ops.empty() && "Reduced smax down to nothing!");
2210 // Okay, it looks like we really DO need an smax expr. Check to see if we
2211 // already have one, otherwise create a new one.
2212 FoldingSetNodeID ID;
2213 ID.AddInteger(scSMaxExpr);
2214 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2215 ID.AddPointer(Ops[i]);
2217 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2218 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2219 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2220 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2222 UniqueSCEVs.InsertNode(S, IP);
2226 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2228 SmallVector<const SCEV *, 2> Ops;
2231 return getUMaxExpr(Ops);
2235 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2236 assert(!Ops.empty() && "Cannot get empty umax!");
2237 if (Ops.size() == 1) return Ops[0];
2239 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2240 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2241 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2242 "SCEVUMaxExpr operand types don't match!");
2245 // Sort by complexity, this groups all similar expression types together.
2246 GroupByComplexity(Ops, LI);
2248 // If there are any constants, fold them together.
2250 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2252 assert(Idx < Ops.size());
2253 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2254 // We found two constants, fold them together!
2255 ConstantInt *Fold = ConstantInt::get(getContext(),
2256 APIntOps::umax(LHSC->getValue()->getValue(),
2257 RHSC->getValue()->getValue()));
2258 Ops[0] = getConstant(Fold);
2259 Ops.erase(Ops.begin()+1); // Erase the folded element
2260 if (Ops.size() == 1) return Ops[0];
2261 LHSC = cast<SCEVConstant>(Ops[0]);
2264 // If we are left with a constant minimum-int, strip it off.
2265 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2266 Ops.erase(Ops.begin());
2268 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2269 // If we have an umax with a constant maximum-int, it will always be
2274 if (Ops.size() == 1) return Ops[0];
2277 // Find the first UMax
2278 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2281 // Check to see if one of the operands is a UMax. If so, expand its operands
2282 // onto our operand list, and recurse to simplify.
2283 if (Idx < Ops.size()) {
2284 bool DeletedUMax = false;
2285 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2286 Ops.erase(Ops.begin()+Idx);
2287 Ops.append(UMax->op_begin(), UMax->op_end());
2292 return getUMaxExpr(Ops);
2295 // Okay, check to see if the same value occurs in the operand list twice. If
2296 // so, delete one. Since we sorted the list, these values are required to
2298 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2299 // X umax Y umax Y --> X umax Y
2300 // X umax Y --> X, if X is always greater than Y
2301 if (Ops[i] == Ops[i+1] ||
2302 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2303 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2305 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2306 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2310 if (Ops.size() == 1) return Ops[0];
2312 assert(!Ops.empty() && "Reduced umax down to nothing!");
2314 // Okay, it looks like we really DO need a umax expr. Check to see if we
2315 // already have one, otherwise create a new one.
2316 FoldingSetNodeID ID;
2317 ID.AddInteger(scUMaxExpr);
2318 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2319 ID.AddPointer(Ops[i]);
2321 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2322 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2323 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2324 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2326 UniqueSCEVs.InsertNode(S, IP);
2330 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2332 // ~smax(~x, ~y) == smin(x, y).
2333 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2336 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2338 // ~umax(~x, ~y) == umin(x, y)
2339 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2342 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2343 // If we have TargetData, we can bypass creating a target-independent
2344 // constant expression and then folding it back into a ConstantInt.
2345 // This is just a compile-time optimization.
2347 return getConstant(TD->getIntPtrType(getContext()),
2348 TD->getTypeAllocSize(AllocTy));
2350 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2351 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2352 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2354 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2355 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2358 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2359 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2361 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2363 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2364 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2367 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2369 // If we have TargetData, we can bypass creating a target-independent
2370 // constant expression and then folding it back into a ConstantInt.
2371 // This is just a compile-time optimization.
2373 return getConstant(TD->getIntPtrType(getContext()),
2374 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2376 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2378 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2380 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2381 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2384 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2385 Constant *FieldNo) {
2386 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2387 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2388 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2390 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2391 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2394 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2395 // Don't attempt to do anything other than create a SCEVUnknown object
2396 // here. createSCEV only calls getUnknown after checking for all other
2397 // interesting possibilities, and any other code that calls getUnknown
2398 // is doing so in order to hide a value from SCEV canonicalization.
2400 FoldingSetNodeID ID;
2401 ID.AddInteger(scUnknown);
2404 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2405 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2406 "Stale SCEVUnknown in uniquing map!");
2409 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2411 FirstUnknown = cast<SCEVUnknown>(S);
2412 UniqueSCEVs.InsertNode(S, IP);
2416 //===----------------------------------------------------------------------===//
2417 // Basic SCEV Analysis and PHI Idiom Recognition Code
2420 /// isSCEVable - Test if values of the given type are analyzable within
2421 /// the SCEV framework. This primarily includes integer types, and it
2422 /// can optionally include pointer types if the ScalarEvolution class
2423 /// has access to target-specific information.
2424 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2425 // Integers and pointers are always SCEVable.
2426 return Ty->isIntegerTy() || Ty->isPointerTy();
2429 /// getTypeSizeInBits - Return the size in bits of the specified type,
2430 /// for which isSCEVable must return true.
2431 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2432 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2434 // If we have a TargetData, use it!
2436 return TD->getTypeSizeInBits(Ty);
2438 // Integer types have fixed sizes.
2439 if (Ty->isIntegerTy())
2440 return Ty->getPrimitiveSizeInBits();
2442 // The only other support type is pointer. Without TargetData, conservatively
2443 // assume pointers are 64-bit.
2444 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2448 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2449 /// the given type and which represents how SCEV will treat the given
2450 /// type, for which isSCEVable must return true. For pointer types,
2451 /// this is the pointer-sized integer type.
2452 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2453 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2455 if (Ty->isIntegerTy())
2458 // The only other support type is pointer.
2459 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2460 if (TD) return TD->getIntPtrType(getContext());
2462 // Without TargetData, conservatively assume pointers are 64-bit.
2463 return Type::getInt64Ty(getContext());
2466 const SCEV *ScalarEvolution::getCouldNotCompute() {
2467 return &CouldNotCompute;
2470 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2471 /// expression and create a new one.
2472 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2473 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2475 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2476 if (I != ValueExprMap.end()) return I->second;
2477 const SCEV *S = createSCEV(V);
2479 // The process of creating a SCEV for V may have caused other SCEVs
2480 // to have been created, so it's necessary to insert the new entry
2481 // from scratch, rather than trying to remember the insert position
2483 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2487 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2489 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2490 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2492 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2494 const Type *Ty = V->getType();
2495 Ty = getEffectiveSCEVType(Ty);
2496 return getMulExpr(V,
2497 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2500 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2501 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2502 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2504 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2506 const Type *Ty = V->getType();
2507 Ty = getEffectiveSCEVType(Ty);
2508 const SCEV *AllOnes =
2509 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2510 return getMinusSCEV(AllOnes, V);
2513 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1,
2514 /// and thus the HasNUW and HasNSW bits apply to the resultant add, not
2515 /// whether the sub would have overflowed.
2516 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2517 bool HasNUW, bool HasNSW) {
2518 // Fast path: X - X --> 0.
2520 return getConstant(LHS->getType(), 0);
2523 return getAddExpr(LHS, getNegativeSCEV(RHS), HasNUW, HasNSW);
2526 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2527 /// input value to the specified type. If the type must be extended, it is zero
2530 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) {
2531 const Type *SrcTy = V->getType();
2532 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2533 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2534 "Cannot truncate or zero extend with non-integer arguments!");
2535 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2536 return V; // No conversion
2537 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2538 return getTruncateExpr(V, Ty);
2539 return getZeroExtendExpr(V, Ty);
2542 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2543 /// input value to the specified type. If the type must be extended, it is sign
2546 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2548 const Type *SrcTy = V->getType();
2549 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2550 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2551 "Cannot truncate or zero extend with non-integer arguments!");
2552 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2553 return V; // No conversion
2554 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2555 return getTruncateExpr(V, Ty);
2556 return getSignExtendExpr(V, Ty);
2559 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2560 /// input value to the specified type. If the type must be extended, it is zero
2561 /// extended. The conversion must not be narrowing.
2563 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2564 const Type *SrcTy = V->getType();
2565 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2566 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2567 "Cannot noop or zero extend with non-integer arguments!");
2568 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2569 "getNoopOrZeroExtend cannot truncate!");
2570 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2571 return V; // No conversion
2572 return getZeroExtendExpr(V, Ty);
2575 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2576 /// input value to the specified type. If the type must be extended, it is sign
2577 /// extended. The conversion must not be narrowing.
2579 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2580 const Type *SrcTy = V->getType();
2581 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2582 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2583 "Cannot noop or sign extend with non-integer arguments!");
2584 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2585 "getNoopOrSignExtend cannot truncate!");
2586 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2587 return V; // No conversion
2588 return getSignExtendExpr(V, Ty);
2591 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2592 /// the input value to the specified type. If the type must be extended,
2593 /// it is extended with unspecified bits. The conversion must not be
2596 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2597 const Type *SrcTy = V->getType();
2598 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2599 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2600 "Cannot noop or any extend with non-integer arguments!");
2601 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2602 "getNoopOrAnyExtend cannot truncate!");
2603 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2604 return V; // No conversion
2605 return getAnyExtendExpr(V, Ty);
2608 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2609 /// input value to the specified type. The conversion must not be widening.
2611 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2612 const Type *SrcTy = V->getType();
2613 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2614 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2615 "Cannot truncate or noop with non-integer arguments!");
2616 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2617 "getTruncateOrNoop cannot extend!");
2618 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2619 return V; // No conversion
2620 return getTruncateExpr(V, Ty);
2623 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2624 /// the types using zero-extension, and then perform a umax operation
2626 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2628 const SCEV *PromotedLHS = LHS;
2629 const SCEV *PromotedRHS = RHS;
2631 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2632 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2634 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2636 return getUMaxExpr(PromotedLHS, PromotedRHS);
2639 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2640 /// the types using zero-extension, and then perform a umin operation
2642 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2644 const SCEV *PromotedLHS = LHS;
2645 const SCEV *PromotedRHS = RHS;
2647 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2648 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2650 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2652 return getUMinExpr(PromotedLHS, PromotedRHS);
2655 /// PushDefUseChildren - Push users of the given Instruction
2656 /// onto the given Worklist.
2658 PushDefUseChildren(Instruction *I,
2659 SmallVectorImpl<Instruction *> &Worklist) {
2660 // Push the def-use children onto the Worklist stack.
2661 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2663 Worklist.push_back(cast<Instruction>(*UI));
2666 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2667 /// instructions that depend on the given instruction and removes them from
2668 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2671 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2672 SmallVector<Instruction *, 16> Worklist;
2673 PushDefUseChildren(PN, Worklist);
2675 SmallPtrSet<Instruction *, 8> Visited;
2677 while (!Worklist.empty()) {
2678 Instruction *I = Worklist.pop_back_val();
2679 if (!Visited.insert(I)) continue;
2681 ValueExprMapType::iterator It =
2682 ValueExprMap.find(static_cast<Value *>(I));
2683 if (It != ValueExprMap.end()) {
2684 const SCEV *Old = It->second;
2686 // Short-circuit the def-use traversal if the symbolic name
2687 // ceases to appear in expressions.
2688 if (Old != SymName && !hasOperand(Old, SymName))
2691 // SCEVUnknown for a PHI either means that it has an unrecognized
2692 // structure, it's a PHI that's in the progress of being computed
2693 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2694 // additional loop trip count information isn't going to change anything.
2695 // In the second case, createNodeForPHI will perform the necessary
2696 // updates on its own when it gets to that point. In the third, we do
2697 // want to forget the SCEVUnknown.
2698 if (!isa<PHINode>(I) ||
2699 !isa<SCEVUnknown>(Old) ||
2700 (I != PN && Old == SymName)) {
2701 forgetMemoizedResults(Old);
2702 ValueExprMap.erase(It);
2706 PushDefUseChildren(I, Worklist);
2710 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2711 /// a loop header, making it a potential recurrence, or it doesn't.
2713 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2714 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2715 if (L->getHeader() == PN->getParent()) {
2716 // The loop may have multiple entrances or multiple exits; we can analyze
2717 // this phi as an addrec if it has a unique entry value and a unique
2719 Value *BEValueV = 0, *StartValueV = 0;
2720 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2721 Value *V = PN->getIncomingValue(i);
2722 if (L->contains(PN->getIncomingBlock(i))) {
2725 } else if (BEValueV != V) {
2729 } else if (!StartValueV) {
2731 } else if (StartValueV != V) {
2736 if (BEValueV && StartValueV) {
2737 // While we are analyzing this PHI node, handle its value symbolically.
2738 const SCEV *SymbolicName = getUnknown(PN);
2739 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2740 "PHI node already processed?");
2741 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2743 // Using this symbolic name for the PHI, analyze the value coming around
2745 const SCEV *BEValue = getSCEV(BEValueV);
2747 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2748 // has a special value for the first iteration of the loop.
2750 // If the value coming around the backedge is an add with the symbolic
2751 // value we just inserted, then we found a simple induction variable!
2752 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2753 // If there is a single occurrence of the symbolic value, replace it
2754 // with a recurrence.
2755 unsigned FoundIndex = Add->getNumOperands();
2756 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2757 if (Add->getOperand(i) == SymbolicName)
2758 if (FoundIndex == e) {
2763 if (FoundIndex != Add->getNumOperands()) {
2764 // Create an add with everything but the specified operand.
2765 SmallVector<const SCEV *, 8> Ops;
2766 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2767 if (i != FoundIndex)
2768 Ops.push_back(Add->getOperand(i));
2769 const SCEV *Accum = getAddExpr(Ops);
2771 // This is not a valid addrec if the step amount is varying each
2772 // loop iteration, but is not itself an addrec in this loop.
2773 if (isLoopInvariant(Accum, L) ||
2774 (isa<SCEVAddRecExpr>(Accum) &&
2775 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2776 bool HasNUW = false;
2777 bool HasNSW = false;
2779 // If the increment doesn't overflow, then neither the addrec nor
2780 // the post-increment will overflow.
2781 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2782 if (OBO->hasNoUnsignedWrap())
2784 if (OBO->hasNoSignedWrap())
2786 } else if (const GEPOperator *GEP =
2787 dyn_cast<GEPOperator>(BEValueV)) {
2788 // If the increment is a GEP, then we know it won't perform a
2789 // signed overflow, because the address space cannot be
2792 // NOTE: This isn't strictly true, because you could have an
2793 // object straddling the 2G address boundary in a 32-bit address
2794 // space (for example). We really want to model this as a "has
2795 // no signed/unsigned wrap" where the base pointer is treated as
2796 // unsigned and the increment is known to not have signed
2799 // This is a highly theoretical concern though, and this is good
2800 // enough for all cases we know of at this point. :)
2802 HasNSW |= GEP->isInBounds();
2805 const SCEV *StartVal = getSCEV(StartValueV);
2806 const SCEV *PHISCEV =
2807 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2809 // Since the no-wrap flags are on the increment, they apply to the
2810 // post-incremented value as well.
2811 if (isLoopInvariant(Accum, L))
2812 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2813 Accum, L, HasNUW, HasNSW);
2815 // Okay, for the entire analysis of this edge we assumed the PHI
2816 // to be symbolic. We now need to go back and purge all of the
2817 // entries for the scalars that use the symbolic expression.
2818 ForgetSymbolicName(PN, SymbolicName);
2819 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2823 } else if (const SCEVAddRecExpr *AddRec =
2824 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2825 // Otherwise, this could be a loop like this:
2826 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2827 // In this case, j = {1,+,1} and BEValue is j.
2828 // Because the other in-value of i (0) fits the evolution of BEValue
2829 // i really is an addrec evolution.
2830 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2831 const SCEV *StartVal = getSCEV(StartValueV);
2833 // If StartVal = j.start - j.stride, we can use StartVal as the
2834 // initial step of the addrec evolution.
2835 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2836 AddRec->getOperand(1))) {
2837 const SCEV *PHISCEV =
2838 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2840 // Okay, for the entire analysis of this edge we assumed the PHI
2841 // to be symbolic. We now need to go back and purge all of the
2842 // entries for the scalars that use the symbolic expression.
2843 ForgetSymbolicName(PN, SymbolicName);
2844 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2852 // If the PHI has a single incoming value, follow that value, unless the
2853 // PHI's incoming blocks are in a different loop, in which case doing so
2854 // risks breaking LCSSA form. Instcombine would normally zap these, but
2855 // it doesn't have DominatorTree information, so it may miss cases.
2856 if (Value *V = SimplifyInstruction(PN, TD, DT))
2857 if (LI->replacementPreservesLCSSAForm(PN, V))
2860 // If it's not a loop phi, we can't handle it yet.
2861 return getUnknown(PN);
2864 /// createNodeForGEP - Expand GEP instructions into add and multiply
2865 /// operations. This allows them to be analyzed by regular SCEV code.
2867 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2869 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2870 // Add expression, because the Instruction may be guarded by control flow
2871 // and the no-overflow bits may not be valid for the expression in any
2874 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2875 Value *Base = GEP->getOperand(0);
2876 // Don't attempt to analyze GEPs over unsized objects.
2877 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2878 return getUnknown(GEP);
2879 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2880 gep_type_iterator GTI = gep_type_begin(GEP);
2881 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2885 // Compute the (potentially symbolic) offset in bytes for this index.
2886 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2887 // For a struct, add the member offset.
2888 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2889 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2891 // Add the field offset to the running total offset.
2892 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2894 // For an array, add the element offset, explicitly scaled.
2895 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2896 const SCEV *IndexS = getSCEV(Index);
2897 // Getelementptr indices are signed.
2898 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2900 // Multiply the index by the element size to compute the element offset.
2901 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2903 // Add the element offset to the running total offset.
2904 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2908 // Get the SCEV for the GEP base.
2909 const SCEV *BaseS = getSCEV(Base);
2911 // Add the total offset from all the GEP indices to the base.
2912 return getAddExpr(BaseS, TotalOffset);
2915 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2916 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2917 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2918 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2920 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2921 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2922 return C->getValue()->getValue().countTrailingZeros();
2924 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2925 return std::min(GetMinTrailingZeros(T->getOperand()),
2926 (uint32_t)getTypeSizeInBits(T->getType()));
2928 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2929 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2930 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2931 getTypeSizeInBits(E->getType()) : OpRes;
2934 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2935 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2936 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2937 getTypeSizeInBits(E->getType()) : OpRes;
2940 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2941 // The result is the min of all operands results.
2942 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2943 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2944 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2948 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2949 // The result is the sum of all operands results.
2950 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2951 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2952 for (unsigned i = 1, e = M->getNumOperands();
2953 SumOpRes != BitWidth && i != e; ++i)
2954 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2959 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(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 SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2968 // The result is the min of all operands results.
2969 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2970 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2971 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2975 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2976 // The result is the min of all operands results.
2977 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2978 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2979 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2983 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2984 // For a SCEVUnknown, ask ValueTracking.
2985 unsigned BitWidth = getTypeSizeInBits(U->getType());
2986 APInt Mask = APInt::getAllOnesValue(BitWidth);
2987 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2988 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2989 return Zeros.countTrailingOnes();
2996 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2999 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3000 // See if we've computed this range already.
3001 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3002 if (I != UnsignedRanges.end())
3005 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3006 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3008 unsigned BitWidth = getTypeSizeInBits(S->getType());
3009 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3011 // If the value has known zeros, the maximum unsigned value will have those
3012 // known zeros as well.
3013 uint32_t TZ = GetMinTrailingZeros(S);
3015 ConservativeResult =
3016 ConstantRange(APInt::getMinValue(BitWidth),
3017 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3019 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3020 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3021 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3022 X = X.add(getUnsignedRange(Add->getOperand(i)));
3023 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3026 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3027 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3028 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3029 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3030 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3033 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3034 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3035 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3036 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3037 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3040 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3041 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3042 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3043 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3044 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3047 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3048 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3049 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3050 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3053 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3054 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3055 return setUnsignedRange(ZExt,
3056 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3059 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3060 ConstantRange X = getUnsignedRange(SExt->getOperand());
3061 return setUnsignedRange(SExt,
3062 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3065 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3066 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3067 return setUnsignedRange(Trunc,
3068 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3071 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3072 // If there's no unsigned wrap, the value will never be less than its
3074 if (AddRec->hasNoUnsignedWrap())
3075 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3076 if (!C->getValue()->isZero())
3077 ConservativeResult =
3078 ConservativeResult.intersectWith(
3079 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3081 // TODO: non-affine addrec
3082 if (AddRec->isAffine()) {
3083 const Type *Ty = AddRec->getType();
3084 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3085 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3086 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3087 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3089 const SCEV *Start = AddRec->getStart();
3090 const SCEV *Step = AddRec->getStepRecurrence(*this);
3092 ConstantRange StartRange = getUnsignedRange(Start);
3093 ConstantRange StepRange = getSignedRange(Step);
3094 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3095 ConstantRange EndRange =
3096 StartRange.add(MaxBECountRange.multiply(StepRange));
3098 // Check for overflow. This must be done with ConstantRange arithmetic
3099 // because we could be called from within the ScalarEvolution overflow
3101 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3102 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3103 ConstantRange ExtMaxBECountRange =
3104 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3105 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3106 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3108 return setUnsignedRange(AddRec, ConservativeResult);
3110 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3111 EndRange.getUnsignedMin());
3112 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3113 EndRange.getUnsignedMax());
3114 if (Min.isMinValue() && Max.isMaxValue())
3115 return setUnsignedRange(AddRec, ConservativeResult);
3116 return setUnsignedRange(AddRec,
3117 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3121 return setUnsignedRange(AddRec, ConservativeResult);
3124 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3125 // For a SCEVUnknown, ask ValueTracking.
3126 APInt Mask = APInt::getAllOnesValue(BitWidth);
3127 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3128 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3129 if (Ones == ~Zeros + 1)
3130 return setUnsignedRange(U, ConservativeResult);
3131 return setUnsignedRange(U,
3132 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3135 return setUnsignedRange(S, ConservativeResult);
3138 /// getSignedRange - Determine the signed range for a particular SCEV.
3141 ScalarEvolution::getSignedRange(const SCEV *S) {
3142 // See if we've computed this range already.
3143 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3144 if (I != SignedRanges.end())
3147 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3148 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3150 unsigned BitWidth = getTypeSizeInBits(S->getType());
3151 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3153 // If the value has known zeros, the maximum signed value will have those
3154 // known zeros as well.
3155 uint32_t TZ = GetMinTrailingZeros(S);
3157 ConservativeResult =
3158 ConstantRange(APInt::getSignedMinValue(BitWidth),
3159 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3161 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3162 ConstantRange X = getSignedRange(Add->getOperand(0));
3163 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3164 X = X.add(getSignedRange(Add->getOperand(i)));
3165 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3168 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3169 ConstantRange X = getSignedRange(Mul->getOperand(0));
3170 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3171 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3172 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3175 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3176 ConstantRange X = getSignedRange(SMax->getOperand(0));
3177 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3178 X = X.smax(getSignedRange(SMax->getOperand(i)));
3179 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3182 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3183 ConstantRange X = getSignedRange(UMax->getOperand(0));
3184 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3185 X = X.umax(getSignedRange(UMax->getOperand(i)));
3186 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3189 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3190 ConstantRange X = getSignedRange(UDiv->getLHS());
3191 ConstantRange Y = getSignedRange(UDiv->getRHS());
3192 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3195 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3196 ConstantRange X = getSignedRange(ZExt->getOperand());
3197 return setSignedRange(ZExt,
3198 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3201 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3202 ConstantRange X = getSignedRange(SExt->getOperand());
3203 return setSignedRange(SExt,
3204 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3207 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3208 ConstantRange X = getSignedRange(Trunc->getOperand());
3209 return setSignedRange(Trunc,
3210 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3213 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3214 // If there's no signed wrap, and all the operands have the same sign or
3215 // zero, the value won't ever change sign.
3216 if (AddRec->hasNoSignedWrap()) {
3217 bool AllNonNeg = true;
3218 bool AllNonPos = true;
3219 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3220 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3221 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3224 ConservativeResult = ConservativeResult.intersectWith(
3225 ConstantRange(APInt(BitWidth, 0),
3226 APInt::getSignedMinValue(BitWidth)));
3228 ConservativeResult = ConservativeResult.intersectWith(
3229 ConstantRange(APInt::getSignedMinValue(BitWidth),
3230 APInt(BitWidth, 1)));
3233 // TODO: non-affine addrec
3234 if (AddRec->isAffine()) {
3235 const Type *Ty = AddRec->getType();
3236 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3237 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3238 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3239 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3241 const SCEV *Start = AddRec->getStart();
3242 const SCEV *Step = AddRec->getStepRecurrence(*this);
3244 ConstantRange StartRange = getSignedRange(Start);
3245 ConstantRange StepRange = getSignedRange(Step);
3246 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3247 ConstantRange EndRange =
3248 StartRange.add(MaxBECountRange.multiply(StepRange));
3250 // Check for overflow. This must be done with ConstantRange arithmetic
3251 // because we could be called from within the ScalarEvolution overflow
3253 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3254 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3255 ConstantRange ExtMaxBECountRange =
3256 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3257 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3258 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3260 return setSignedRange(AddRec, ConservativeResult);
3262 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3263 EndRange.getSignedMin());
3264 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3265 EndRange.getSignedMax());
3266 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3267 return setSignedRange(AddRec, ConservativeResult);
3268 return setSignedRange(AddRec,
3269 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3273 return setSignedRange(AddRec, ConservativeResult);
3276 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3277 // For a SCEVUnknown, ask ValueTracking.
3278 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3279 return setSignedRange(U, ConservativeResult);
3280 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3282 return setSignedRange(U, ConservativeResult);
3283 return setSignedRange(U, ConservativeResult.intersectWith(
3284 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3285 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3288 return setSignedRange(S, ConservativeResult);
3291 /// createSCEV - We know that there is no SCEV for the specified value.
3292 /// Analyze the expression.
3294 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3295 if (!isSCEVable(V->getType()))
3296 return getUnknown(V);
3298 unsigned Opcode = Instruction::UserOp1;
3299 if (Instruction *I = dyn_cast<Instruction>(V)) {
3300 Opcode = I->getOpcode();
3302 // Don't attempt to analyze instructions in blocks that aren't
3303 // reachable. Such instructions don't matter, and they aren't required
3304 // to obey basic rules for definitions dominating uses which this
3305 // analysis depends on.
3306 if (!DT->isReachableFromEntry(I->getParent()))
3307 return getUnknown(V);
3308 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3309 Opcode = CE->getOpcode();
3310 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3311 return getConstant(CI);
3312 else if (isa<ConstantPointerNull>(V))
3313 return getConstant(V->getType(), 0);
3314 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3315 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3317 return getUnknown(V);
3319 Operator *U = cast<Operator>(V);
3321 case Instruction::Add: {
3322 // The simple thing to do would be to just call getSCEV on both operands
3323 // and call getAddExpr with the result. However if we're looking at a
3324 // bunch of things all added together, this can be quite inefficient,
3325 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3326 // Instead, gather up all the operands and make a single getAddExpr call.
3327 // LLVM IR canonical form means we need only traverse the left operands.
3328 SmallVector<const SCEV *, 4> AddOps;
3329 AddOps.push_back(getSCEV(U->getOperand(1)));
3330 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3331 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3332 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3334 U = cast<Operator>(Op);
3335 const SCEV *Op1 = getSCEV(U->getOperand(1));
3336 if (Opcode == Instruction::Sub)
3337 AddOps.push_back(getNegativeSCEV(Op1));
3339 AddOps.push_back(Op1);
3341 AddOps.push_back(getSCEV(U->getOperand(0)));
3342 return getAddExpr(AddOps);
3344 case Instruction::Mul: {
3345 // See the Add code above.
3346 SmallVector<const SCEV *, 4> MulOps;
3347 MulOps.push_back(getSCEV(U->getOperand(1)));
3348 for (Value *Op = U->getOperand(0);
3349 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3350 Op = U->getOperand(0)) {
3351 U = cast<Operator>(Op);
3352 MulOps.push_back(getSCEV(U->getOperand(1)));
3354 MulOps.push_back(getSCEV(U->getOperand(0)));
3355 return getMulExpr(MulOps);
3357 case Instruction::UDiv:
3358 return getUDivExpr(getSCEV(U->getOperand(0)),
3359 getSCEV(U->getOperand(1)));
3360 case Instruction::Sub:
3361 return getMinusSCEV(getSCEV(U->getOperand(0)),
3362 getSCEV(U->getOperand(1)));
3363 case Instruction::And:
3364 // For an expression like x&255 that merely masks off the high bits,
3365 // use zext(trunc(x)) as the SCEV expression.
3366 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3367 if (CI->isNullValue())
3368 return getSCEV(U->getOperand(1));
3369 if (CI->isAllOnesValue())
3370 return getSCEV(U->getOperand(0));
3371 const APInt &A = CI->getValue();
3373 // Instcombine's ShrinkDemandedConstant may strip bits out of
3374 // constants, obscuring what would otherwise be a low-bits mask.
3375 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3376 // knew about to reconstruct a low-bits mask value.
3377 unsigned LZ = A.countLeadingZeros();
3378 unsigned BitWidth = A.getBitWidth();
3379 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3380 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3381 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3383 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3385 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3387 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3388 IntegerType::get(getContext(), BitWidth - LZ)),
3393 case Instruction::Or:
3394 // If the RHS of the Or is a constant, we may have something like:
3395 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3396 // optimizations will transparently handle this case.
3398 // In order for this transformation to be safe, the LHS must be of the
3399 // form X*(2^n) and the Or constant must be less than 2^n.
3400 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3401 const SCEV *LHS = getSCEV(U->getOperand(0));
3402 const APInt &CIVal = CI->getValue();
3403 if (GetMinTrailingZeros(LHS) >=
3404 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3405 // Build a plain add SCEV.
3406 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3407 // If the LHS of the add was an addrec and it has no-wrap flags,
3408 // transfer the no-wrap flags, since an or won't introduce a wrap.
3409 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3410 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3411 if (OldAR->hasNoUnsignedWrap())
3412 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3413 if (OldAR->hasNoSignedWrap())
3414 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3420 case Instruction::Xor:
3421 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3422 // If the RHS of the xor is a signbit, then this is just an add.
3423 // Instcombine turns add of signbit into xor as a strength reduction step.
3424 if (CI->getValue().isSignBit())
3425 return getAddExpr(getSCEV(U->getOperand(0)),
3426 getSCEV(U->getOperand(1)));
3428 // If the RHS of xor is -1, then this is a not operation.
3429 if (CI->isAllOnesValue())
3430 return getNotSCEV(getSCEV(U->getOperand(0)));
3432 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3433 // This is a variant of the check for xor with -1, and it handles
3434 // the case where instcombine has trimmed non-demanded bits out
3435 // of an xor with -1.
3436 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3437 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3438 if (BO->getOpcode() == Instruction::And &&
3439 LCI->getValue() == CI->getValue())
3440 if (const SCEVZeroExtendExpr *Z =
3441 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3442 const Type *UTy = U->getType();
3443 const SCEV *Z0 = Z->getOperand();
3444 const Type *Z0Ty = Z0->getType();
3445 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3447 // If C is a low-bits mask, the zero extend is serving to
3448 // mask off the high bits. Complement the operand and
3449 // re-apply the zext.
3450 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3451 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3453 // If C is a single bit, it may be in the sign-bit position
3454 // before the zero-extend. In this case, represent the xor
3455 // using an add, which is equivalent, and re-apply the zext.
3456 APInt Trunc = CI->getValue().trunc(Z0TySize);
3457 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3459 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3465 case Instruction::Shl:
3466 // Turn shift left of a constant amount into a multiply.
3467 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3468 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3470 // If the shift count is not less than the bitwidth, the result of
3471 // the shift is undefined. Don't try to analyze it, because the
3472 // resolution chosen here may differ from the resolution chosen in
3473 // other parts of the compiler.
3474 if (SA->getValue().uge(BitWidth))
3477 Constant *X = ConstantInt::get(getContext(),
3478 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3479 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3483 case Instruction::LShr:
3484 // Turn logical shift right of a constant into a unsigned divide.
3485 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3486 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3488 // If the shift count is not less than the bitwidth, the result of
3489 // the shift is undefined. Don't try to analyze it, because the
3490 // resolution chosen here may differ from the resolution chosen in
3491 // other parts of the compiler.
3492 if (SA->getValue().uge(BitWidth))
3495 Constant *X = ConstantInt::get(getContext(),
3496 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3497 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3501 case Instruction::AShr:
3502 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3503 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3504 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3505 if (L->getOpcode() == Instruction::Shl &&
3506 L->getOperand(1) == U->getOperand(1)) {
3507 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3509 // If the shift count is not less than the bitwidth, the result of
3510 // the shift is undefined. Don't try to analyze it, because the
3511 // resolution chosen here may differ from the resolution chosen in
3512 // other parts of the compiler.
3513 if (CI->getValue().uge(BitWidth))
3516 uint64_t Amt = BitWidth - CI->getZExtValue();
3517 if (Amt == BitWidth)
3518 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3520 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3521 IntegerType::get(getContext(),
3527 case Instruction::Trunc:
3528 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3530 case Instruction::ZExt:
3531 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3533 case Instruction::SExt:
3534 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3536 case Instruction::BitCast:
3537 // BitCasts are no-op casts so we just eliminate the cast.
3538 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3539 return getSCEV(U->getOperand(0));
3542 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3543 // lead to pointer expressions which cannot safely be expanded to GEPs,
3544 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3545 // simplifying integer expressions.
3547 case Instruction::GetElementPtr:
3548 return createNodeForGEP(cast<GEPOperator>(U));
3550 case Instruction::PHI:
3551 return createNodeForPHI(cast<PHINode>(U));
3553 case Instruction::Select:
3554 // This could be a smax or umax that was lowered earlier.
3555 // Try to recover it.
3556 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3557 Value *LHS = ICI->getOperand(0);
3558 Value *RHS = ICI->getOperand(1);
3559 switch (ICI->getPredicate()) {
3560 case ICmpInst::ICMP_SLT:
3561 case ICmpInst::ICMP_SLE:
3562 std::swap(LHS, RHS);
3564 case ICmpInst::ICMP_SGT:
3565 case ICmpInst::ICMP_SGE:
3566 // a >s b ? a+x : b+x -> smax(a, b)+x
3567 // a >s b ? b+x : a+x -> smin(a, b)+x
3568 if (LHS->getType() == U->getType()) {
3569 const SCEV *LS = getSCEV(LHS);
3570 const SCEV *RS = getSCEV(RHS);
3571 const SCEV *LA = getSCEV(U->getOperand(1));
3572 const SCEV *RA = getSCEV(U->getOperand(2));
3573 const SCEV *LDiff = getMinusSCEV(LA, LS);
3574 const SCEV *RDiff = getMinusSCEV(RA, RS);
3576 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3577 LDiff = getMinusSCEV(LA, RS);
3578 RDiff = getMinusSCEV(RA, LS);
3580 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3583 case ICmpInst::ICMP_ULT:
3584 case ICmpInst::ICMP_ULE:
3585 std::swap(LHS, RHS);
3587 case ICmpInst::ICMP_UGT:
3588 case ICmpInst::ICMP_UGE:
3589 // a >u b ? a+x : b+x -> umax(a, b)+x
3590 // a >u b ? b+x : a+x -> umin(a, b)+x
3591 if (LHS->getType() == U->getType()) {
3592 const SCEV *LS = getSCEV(LHS);
3593 const SCEV *RS = getSCEV(RHS);
3594 const SCEV *LA = getSCEV(U->getOperand(1));
3595 const SCEV *RA = getSCEV(U->getOperand(2));
3596 const SCEV *LDiff = getMinusSCEV(LA, LS);
3597 const SCEV *RDiff = getMinusSCEV(RA, RS);
3599 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3600 LDiff = getMinusSCEV(LA, RS);
3601 RDiff = getMinusSCEV(RA, LS);
3603 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3606 case ICmpInst::ICMP_NE:
3607 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3608 if (LHS->getType() == U->getType() &&
3609 isa<ConstantInt>(RHS) &&
3610 cast<ConstantInt>(RHS)->isZero()) {
3611 const SCEV *One = getConstant(LHS->getType(), 1);
3612 const SCEV *LS = getSCEV(LHS);
3613 const SCEV *LA = getSCEV(U->getOperand(1));
3614 const SCEV *RA = getSCEV(U->getOperand(2));
3615 const SCEV *LDiff = getMinusSCEV(LA, LS);
3616 const SCEV *RDiff = getMinusSCEV(RA, One);
3618 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3621 case ICmpInst::ICMP_EQ:
3622 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3623 if (LHS->getType() == U->getType() &&
3624 isa<ConstantInt>(RHS) &&
3625 cast<ConstantInt>(RHS)->isZero()) {
3626 const SCEV *One = getConstant(LHS->getType(), 1);
3627 const SCEV *LS = getSCEV(LHS);
3628 const SCEV *LA = getSCEV(U->getOperand(1));
3629 const SCEV *RA = getSCEV(U->getOperand(2));
3630 const SCEV *LDiff = getMinusSCEV(LA, One);
3631 const SCEV *RDiff = getMinusSCEV(RA, LS);
3633 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3641 default: // We cannot analyze this expression.
3645 return getUnknown(V);
3650 //===----------------------------------------------------------------------===//
3651 // Iteration Count Computation Code
3654 /// getBackedgeTakenCount - If the specified loop has a predictable
3655 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3656 /// object. The backedge-taken count is the number of times the loop header
3657 /// will be branched to from within the loop. This is one less than the
3658 /// trip count of the loop, since it doesn't count the first iteration,
3659 /// when the header is branched to from outside the loop.
3661 /// Note that it is not valid to call this method on a loop without a
3662 /// loop-invariant backedge-taken count (see
3663 /// hasLoopInvariantBackedgeTakenCount).
3665 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3666 return getBackedgeTakenInfo(L).Exact;
3669 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3670 /// return the least SCEV value that is known never to be less than the
3671 /// actual backedge taken count.
3672 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3673 return getBackedgeTakenInfo(L).Max;
3676 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3677 /// onto the given Worklist.
3679 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3680 BasicBlock *Header = L->getHeader();
3682 // Push all Loop-header PHIs onto the Worklist stack.
3683 for (BasicBlock::iterator I = Header->begin();
3684 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3685 Worklist.push_back(PN);
3688 const ScalarEvolution::BackedgeTakenInfo &
3689 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3690 // Initially insert a CouldNotCompute for this loop. If the insertion
3691 // succeeds, proceed to actually compute a backedge-taken count and
3692 // update the value. The temporary CouldNotCompute value tells SCEV
3693 // code elsewhere that it shouldn't attempt to request a new
3694 // backedge-taken count, which could result in infinite recursion.
3695 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3696 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3698 return Pair.first->second;
3700 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3701 if (BECount.Exact != getCouldNotCompute()) {
3702 assert(isLoopInvariant(BECount.Exact, L) &&
3703 isLoopInvariant(BECount.Max, L) &&
3704 "Computed backedge-taken count isn't loop invariant for loop!");
3705 ++NumTripCountsComputed;
3707 // Update the value in the map.
3708 Pair.first->second = BECount;
3710 if (BECount.Max != getCouldNotCompute())
3711 // Update the value in the map.
3712 Pair.first->second = BECount;
3713 if (isa<PHINode>(L->getHeader()->begin()))
3714 // Only count loops that have phi nodes as not being computable.
3715 ++NumTripCountsNotComputed;
3718 // Now that we know more about the trip count for this loop, forget any
3719 // existing SCEV values for PHI nodes in this loop since they are only
3720 // conservative estimates made without the benefit of trip count
3721 // information. This is similar to the code in forgetLoop, except that
3722 // it handles SCEVUnknown PHI nodes specially.
3723 if (BECount.hasAnyInfo()) {
3724 SmallVector<Instruction *, 16> Worklist;
3725 PushLoopPHIs(L, Worklist);
3727 SmallPtrSet<Instruction *, 8> Visited;
3728 while (!Worklist.empty()) {
3729 Instruction *I = Worklist.pop_back_val();
3730 if (!Visited.insert(I)) continue;
3732 ValueExprMapType::iterator It =
3733 ValueExprMap.find(static_cast<Value *>(I));
3734 if (It != ValueExprMap.end()) {
3735 const SCEV *Old = It->second;
3737 // SCEVUnknown for a PHI either means that it has an unrecognized
3738 // structure, or it's a PHI that's in the progress of being computed
3739 // by createNodeForPHI. In the former case, additional loop trip
3740 // count information isn't going to change anything. In the later
3741 // case, createNodeForPHI will perform the necessary updates on its
3742 // own when it gets to that point.
3743 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
3744 forgetMemoizedResults(Old);
3745 ValueExprMap.erase(It);
3747 if (PHINode *PN = dyn_cast<PHINode>(I))
3748 ConstantEvolutionLoopExitValue.erase(PN);
3751 PushDefUseChildren(I, Worklist);
3754 return Pair.first->second;
3757 /// forgetLoop - This method should be called by the client when it has
3758 /// changed a loop in a way that may effect ScalarEvolution's ability to
3759 /// compute a trip count, or if the loop is deleted.
3760 void ScalarEvolution::forgetLoop(const Loop *L) {
3761 // Drop any stored trip count value.
3762 BackedgeTakenCounts.erase(L);
3764 // Drop information about expressions based on loop-header PHIs.
3765 SmallVector<Instruction *, 16> Worklist;
3766 PushLoopPHIs(L, Worklist);
3768 SmallPtrSet<Instruction *, 8> Visited;
3769 while (!Worklist.empty()) {
3770 Instruction *I = Worklist.pop_back_val();
3771 if (!Visited.insert(I)) continue;
3773 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3774 if (It != ValueExprMap.end()) {
3775 forgetMemoizedResults(It->second);
3776 ValueExprMap.erase(It);
3777 if (PHINode *PN = dyn_cast<PHINode>(I))
3778 ConstantEvolutionLoopExitValue.erase(PN);
3781 PushDefUseChildren(I, Worklist);
3784 // Forget all contained loops too, to avoid dangling entries in the
3785 // ValuesAtScopes map.
3786 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3790 /// forgetValue - This method should be called by the client when it has
3791 /// changed a value in a way that may effect its value, or which may
3792 /// disconnect it from a def-use chain linking it to a loop.
3793 void ScalarEvolution::forgetValue(Value *V) {
3794 Instruction *I = dyn_cast<Instruction>(V);
3797 // Drop information about expressions based on loop-header PHIs.
3798 SmallVector<Instruction *, 16> Worklist;
3799 Worklist.push_back(I);
3801 SmallPtrSet<Instruction *, 8> Visited;
3802 while (!Worklist.empty()) {
3803 I = Worklist.pop_back_val();
3804 if (!Visited.insert(I)) continue;
3806 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3807 if (It != ValueExprMap.end()) {
3808 forgetMemoizedResults(It->second);
3809 ValueExprMap.erase(It);
3810 if (PHINode *PN = dyn_cast<PHINode>(I))
3811 ConstantEvolutionLoopExitValue.erase(PN);
3814 PushDefUseChildren(I, Worklist);
3818 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3819 /// of the specified loop will execute.
3820 ScalarEvolution::BackedgeTakenInfo
3821 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3822 SmallVector<BasicBlock *, 8> ExitingBlocks;
3823 L->getExitingBlocks(ExitingBlocks);
3825 // Examine all exits and pick the most conservative values.
3826 const SCEV *BECount = getCouldNotCompute();
3827 const SCEV *MaxBECount = getCouldNotCompute();
3828 bool CouldNotComputeBECount = false;
3829 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3830 BackedgeTakenInfo NewBTI =
3831 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3833 if (NewBTI.Exact == getCouldNotCompute()) {
3834 // We couldn't compute an exact value for this exit, so
3835 // we won't be able to compute an exact value for the loop.
3836 CouldNotComputeBECount = true;
3837 BECount = getCouldNotCompute();
3838 } else if (!CouldNotComputeBECount) {
3839 if (BECount == getCouldNotCompute())
3840 BECount = NewBTI.Exact;
3842 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3844 if (MaxBECount == getCouldNotCompute())
3845 MaxBECount = NewBTI.Max;
3846 else if (NewBTI.Max != getCouldNotCompute())
3847 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3850 return BackedgeTakenInfo(BECount, MaxBECount);
3853 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3854 /// of the specified loop will execute if it exits via the specified block.
3855 ScalarEvolution::BackedgeTakenInfo
3856 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3857 BasicBlock *ExitingBlock) {
3859 // Okay, we've chosen an exiting block. See what condition causes us to
3860 // exit at this block.
3862 // FIXME: we should be able to handle switch instructions (with a single exit)
3863 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3864 if (ExitBr == 0) return getCouldNotCompute();
3865 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3867 // At this point, we know we have a conditional branch that determines whether
3868 // the loop is exited. However, we don't know if the branch is executed each
3869 // time through the loop. If not, then the execution count of the branch will
3870 // not be equal to the trip count of the loop.
3872 // Currently we check for this by checking to see if the Exit branch goes to
3873 // the loop header. If so, we know it will always execute the same number of
3874 // times as the loop. We also handle the case where the exit block *is* the
3875 // loop header. This is common for un-rotated loops.
3877 // If both of those tests fail, walk up the unique predecessor chain to the
3878 // header, stopping if there is an edge that doesn't exit the loop. If the
3879 // header is reached, the execution count of the branch will be equal to the
3880 // trip count of the loop.
3882 // More extensive analysis could be done to handle more cases here.
3884 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3885 ExitBr->getSuccessor(1) != L->getHeader() &&
3886 ExitBr->getParent() != L->getHeader()) {
3887 // The simple checks failed, try climbing the unique predecessor chain
3888 // up to the header.
3890 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3891 BasicBlock *Pred = BB->getUniquePredecessor();
3893 return getCouldNotCompute();
3894 TerminatorInst *PredTerm = Pred->getTerminator();
3895 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3896 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3899 // If the predecessor has a successor that isn't BB and isn't
3900 // outside the loop, assume the worst.
3901 if (L->contains(PredSucc))
3902 return getCouldNotCompute();
3904 if (Pred == L->getHeader()) {
3911 return getCouldNotCompute();
3914 // Proceed to the next level to examine the exit condition expression.
3915 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3916 ExitBr->getSuccessor(0),
3917 ExitBr->getSuccessor(1));
3920 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3921 /// backedge of the specified loop will execute if its exit condition
3922 /// were a conditional branch of ExitCond, TBB, and FBB.
3923 ScalarEvolution::BackedgeTakenInfo
3924 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3928 // Check if the controlling expression for this loop is an And or Or.
3929 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3930 if (BO->getOpcode() == Instruction::And) {
3931 // Recurse on the operands of the and.
3932 BackedgeTakenInfo BTI0 =
3933 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3934 BackedgeTakenInfo BTI1 =
3935 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3936 const SCEV *BECount = getCouldNotCompute();
3937 const SCEV *MaxBECount = getCouldNotCompute();
3938 if (L->contains(TBB)) {
3939 // Both conditions must be true for the loop to continue executing.
3940 // Choose the less conservative count.
3941 if (BTI0.Exact == getCouldNotCompute() ||
3942 BTI1.Exact == getCouldNotCompute())
3943 BECount = getCouldNotCompute();
3945 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3946 if (BTI0.Max == getCouldNotCompute())
3947 MaxBECount = BTI1.Max;
3948 else if (BTI1.Max == getCouldNotCompute())
3949 MaxBECount = BTI0.Max;
3951 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3953 // Both conditions must be true at the same time for the loop to exit.
3954 // For now, be conservative.
3955 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3956 if (BTI0.Max == BTI1.Max)
3957 MaxBECount = BTI0.Max;
3958 if (BTI0.Exact == BTI1.Exact)
3959 BECount = BTI0.Exact;
3962 return BackedgeTakenInfo(BECount, MaxBECount);
3964 if (BO->getOpcode() == Instruction::Or) {
3965 // Recurse on the operands of the or.
3966 BackedgeTakenInfo BTI0 =
3967 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3968 BackedgeTakenInfo BTI1 =
3969 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3970 const SCEV *BECount = getCouldNotCompute();
3971 const SCEV *MaxBECount = getCouldNotCompute();
3972 if (L->contains(FBB)) {
3973 // Both conditions must be false for the loop to continue executing.
3974 // Choose the less conservative count.
3975 if (BTI0.Exact == getCouldNotCompute() ||
3976 BTI1.Exact == getCouldNotCompute())
3977 BECount = getCouldNotCompute();
3979 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3980 if (BTI0.Max == getCouldNotCompute())
3981 MaxBECount = BTI1.Max;
3982 else if (BTI1.Max == getCouldNotCompute())
3983 MaxBECount = BTI0.Max;
3985 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3987 // Both conditions must be false at the same time for the loop to exit.
3988 // For now, be conservative.
3989 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3990 if (BTI0.Max == BTI1.Max)
3991 MaxBECount = BTI0.Max;
3992 if (BTI0.Exact == BTI1.Exact)
3993 BECount = BTI0.Exact;
3996 return BackedgeTakenInfo(BECount, MaxBECount);
4000 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4001 // Proceed to the next level to examine the icmp.
4002 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4003 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
4005 // Check for a constant condition. These are normally stripped out by
4006 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4007 // preserve the CFG and is temporarily leaving constant conditions
4009 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4010 if (L->contains(FBB) == !CI->getZExtValue())
4011 // The backedge is always taken.
4012 return getCouldNotCompute();
4014 // The backedge is never taken.
4015 return getConstant(CI->getType(), 0);
4018 // If it's not an integer or pointer comparison then compute it the hard way.
4019 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4022 static const SCEVAddRecExpr *
4023 isSimpleUnwrappingAddRec(const SCEV *S, const Loop *L) {
4024 const SCEVAddRecExpr *SA = dyn_cast<SCEVAddRecExpr>(S);
4026 // The SCEV must be an addrec of this loop.
4027 if (!SA || SA->getLoop() != L || !SA->isAffine())
4030 // The SCEV must be known to not wrap in some way to be interesting.
4031 if (!SA->hasNoUnsignedWrap() && !SA->hasNoSignedWrap())
4034 // The stride must be a constant so that we know if it is striding up or down.
4035 if (!isa<SCEVConstant>(SA->getOperand(1)))
4040 /// getMinusSCEVForExitTest - When considering an exit test for a loop with a
4041 /// "x != y" exit test, we turn this into a computation that evaluates x-y != 0,
4042 /// and this function returns the expression to use for x-y. We know and take
4043 /// advantage of the fact that this subtraction is only being used in a
4044 /// comparison by zero context.
4046 static const SCEV *getMinusSCEVForExitTest(const SCEV *LHS, const SCEV *RHS,
4047 const Loop *L, ScalarEvolution &SE) {
4048 // If either LHS or RHS is an AddRec SCEV (of this loop) that is known to not
4049 // wrap (either NSW or NUW), then we know that the value will either become
4050 // the other one (and thus the loop terminates), that the loop will terminate
4051 // through some other exit condition first, or that the loop has undefined
4052 // behavior. This information is useful when the addrec has a stride that is
4053 // != 1 or -1, because it means we can't "miss" the exit value.
4055 // In any of these three cases, it is safe to turn the exit condition into a
4056 // "counting down" AddRec (to zero) by subtracting the two inputs as normal,
4057 // but since we know that the "end cannot be missed" we can force the
4058 // resulting AddRec to be a NUW addrec. Since it is counting down, this means
4059 // that the AddRec *cannot* pass zero.
4061 // See if LHS and RHS are addrec's we can handle.
4062 const SCEVAddRecExpr *LHSA = isSimpleUnwrappingAddRec(LHS, L);
4063 const SCEVAddRecExpr *RHSA = isSimpleUnwrappingAddRec(RHS, L);
4065 // If neither addrec is interesting, just return a minus.
4066 if (RHSA == 0 && LHSA == 0)
4067 return SE.getMinusSCEV(LHS, RHS);
4069 // If only one of LHS and RHS are an AddRec of this loop, make sure it is LHS.
4070 if (RHSA && LHSA == 0) {
4071 // Safe because a-b === b-a for comparisons against zero.
4072 std::swap(LHS, RHS);
4073 std::swap(LHSA, RHSA);
4076 // Handle the case when only one is advancing in a non-overflowing way.
4078 // If RHS is loop varying, then we can't predict when LHS will cross it.
4079 if (!SE.isLoopInvariant(RHS, L))
4080 return SE.getMinusSCEV(LHS, RHS);
4082 // If LHS has a positive stride, then we compute RHS-LHS, because the loop
4083 // is counting up until it crosses RHS (which must be larger than LHS). If
4084 // it is negative, we compute LHS-RHS because we're counting down to RHS.
4085 const ConstantInt *Stride =
4086 cast<SCEVConstant>(LHSA->getOperand(1))->getValue();
4087 if (Stride->getValue().isNegative())
4088 std::swap(LHS, RHS);
4090 return SE.getMinusSCEV(RHS, LHS, true /*HasNUW*/);
4093 // If both LHS and RHS are interesting, we have something like:
4095 const ConstantInt *LHSStride =
4096 cast<SCEVConstant>(LHSA->getOperand(1))->getValue();
4097 const ConstantInt *RHSStride =
4098 cast<SCEVConstant>(RHSA->getOperand(1))->getValue();
4100 // If the strides are equal, then this is just a (complex) loop invariant
4101 // comparison of a and b.
4102 if (LHSStride == RHSStride)
4103 return SE.getMinusSCEV(LHSA->getStart(), RHSA->getStart());
4105 // If the signs of the strides differ, then the negative stride is counting
4106 // down to the positive stride.
4107 if (LHSStride->getValue().isNegative() != RHSStride->getValue().isNegative()){
4108 if (RHSStride->getValue().isNegative())
4109 std::swap(LHS, RHS);
4111 // If LHS's stride is smaller than RHS's stride, then "b" must be less than
4112 // "a" and "b" is RHS is counting up (catching up) to LHS. This is true
4113 // whether the strides are positive or negative.
4114 if (RHSStride->getValue().slt(LHSStride->getValue()))
4115 std::swap(LHS, RHS);
4118 return SE.getMinusSCEV(LHS, RHS, true /*HasNUW*/);
4121 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4122 /// backedge of the specified loop will execute if its exit condition
4123 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4124 ScalarEvolution::BackedgeTakenInfo
4125 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4130 // If the condition was exit on true, convert the condition to exit on false
4131 ICmpInst::Predicate Cond;
4132 if (!L->contains(FBB))
4133 Cond = ExitCond->getPredicate();
4135 Cond = ExitCond->getInversePredicate();
4137 // Handle common loops like: for (X = "string"; *X; ++X)
4138 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4139 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4140 BackedgeTakenInfo ItCnt =
4141 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4142 if (ItCnt.hasAnyInfo())
4146 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4147 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4149 // Try to evaluate any dependencies out of the loop.
4150 LHS = getSCEVAtScope(LHS, L);
4151 RHS = getSCEVAtScope(RHS, L);
4153 // At this point, we would like to compute how many iterations of the
4154 // loop the predicate will return true for these inputs.
4155 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4156 // If there is a loop-invariant, force it into the RHS.
4157 std::swap(LHS, RHS);
4158 Cond = ICmpInst::getSwappedPredicate(Cond);
4161 // Simplify the operands before analyzing them.
4162 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4164 // If we have a comparison of a chrec against a constant, try to use value
4165 // ranges to answer this query.
4166 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4167 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4168 if (AddRec->getLoop() == L) {
4169 // Form the constant range.
4170 ConstantRange CompRange(
4171 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4173 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4174 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4178 case ICmpInst::ICMP_NE: { // while (X != Y)
4179 // Convert to: while (X-Y != 0)
4180 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEVForExitTest(LHS, RHS, L,
4182 if (BTI.hasAnyInfo()) return BTI;
4185 case ICmpInst::ICMP_EQ: { // while (X == Y)
4186 // Convert to: while (X-Y == 0)
4187 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4188 if (BTI.hasAnyInfo()) return BTI;
4191 case ICmpInst::ICMP_SLT: {
4192 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4193 if (BTI.hasAnyInfo()) return BTI;
4196 case ICmpInst::ICMP_SGT: {
4197 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4198 getNotSCEV(RHS), L, true);
4199 if (BTI.hasAnyInfo()) return BTI;
4202 case ICmpInst::ICMP_ULT: {
4203 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4204 if (BTI.hasAnyInfo()) return BTI;
4207 case ICmpInst::ICMP_UGT: {
4208 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4209 getNotSCEV(RHS), L, false);
4210 if (BTI.hasAnyInfo()) return BTI;
4215 dbgs() << "ComputeBackedgeTakenCount ";
4216 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4217 dbgs() << "[unsigned] ";
4218 dbgs() << *LHS << " "
4219 << Instruction::getOpcodeName(Instruction::ICmp)
4220 << " " << *RHS << "\n";
4225 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4228 static ConstantInt *
4229 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4230 ScalarEvolution &SE) {
4231 const SCEV *InVal = SE.getConstant(C);
4232 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4233 assert(isa<SCEVConstant>(Val) &&
4234 "Evaluation of SCEV at constant didn't fold correctly?");
4235 return cast<SCEVConstant>(Val)->getValue();
4238 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4239 /// and a GEP expression (missing the pointer index) indexing into it, return
4240 /// the addressed element of the initializer or null if the index expression is
4243 GetAddressedElementFromGlobal(GlobalVariable *GV,
4244 const std::vector<ConstantInt*> &Indices) {
4245 Constant *Init = GV->getInitializer();
4246 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4247 uint64_t Idx = Indices[i]->getZExtValue();
4248 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4249 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4250 Init = cast<Constant>(CS->getOperand(Idx));
4251 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4252 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4253 Init = cast<Constant>(CA->getOperand(Idx));
4254 } else if (isa<ConstantAggregateZero>(Init)) {
4255 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4256 assert(Idx < STy->getNumElements() && "Bad struct index!");
4257 Init = Constant::getNullValue(STy->getElementType(Idx));
4258 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4259 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4260 Init = Constant::getNullValue(ATy->getElementType());
4262 llvm_unreachable("Unknown constant aggregate type!");
4266 return 0; // Unknown initializer type
4272 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4273 /// 'icmp op load X, cst', try to see if we can compute the backedge
4274 /// execution count.
4275 ScalarEvolution::BackedgeTakenInfo
4276 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4280 ICmpInst::Predicate predicate) {
4281 if (LI->isVolatile()) return getCouldNotCompute();
4283 // Check to see if the loaded pointer is a getelementptr of a global.
4284 // TODO: Use SCEV instead of manually grubbing with GEPs.
4285 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4286 if (!GEP) return getCouldNotCompute();
4288 // Make sure that it is really a constant global we are gepping, with an
4289 // initializer, and make sure the first IDX is really 0.
4290 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4291 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4292 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4293 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4294 return getCouldNotCompute();
4296 // Okay, we allow one non-constant index into the GEP instruction.
4298 std::vector<ConstantInt*> Indexes;
4299 unsigned VarIdxNum = 0;
4300 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4301 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4302 Indexes.push_back(CI);
4303 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4304 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4305 VarIdx = GEP->getOperand(i);
4307 Indexes.push_back(0);
4310 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4311 // Check to see if X is a loop variant variable value now.
4312 const SCEV *Idx = getSCEV(VarIdx);
4313 Idx = getSCEVAtScope(Idx, L);
4315 // We can only recognize very limited forms of loop index expressions, in
4316 // particular, only affine AddRec's like {C1,+,C2}.
4317 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4318 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4319 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4320 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4321 return getCouldNotCompute();
4323 unsigned MaxSteps = MaxBruteForceIterations;
4324 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4325 ConstantInt *ItCst = ConstantInt::get(
4326 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4327 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4329 // Form the GEP offset.
4330 Indexes[VarIdxNum] = Val;
4332 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4333 if (Result == 0) break; // Cannot compute!
4335 // Evaluate the condition for this iteration.
4336 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4337 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4338 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4340 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4341 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4344 ++NumArrayLenItCounts;
4345 return getConstant(ItCst); // Found terminating iteration!
4348 return getCouldNotCompute();
4352 /// CanConstantFold - Return true if we can constant fold an instruction of the
4353 /// specified type, assuming that all operands were constants.
4354 static bool CanConstantFold(const Instruction *I) {
4355 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4356 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4359 if (const CallInst *CI = dyn_cast<CallInst>(I))
4360 if (const Function *F = CI->getCalledFunction())
4361 return canConstantFoldCallTo(F);
4365 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4366 /// in the loop that V is derived from. We allow arbitrary operations along the
4367 /// way, but the operands of an operation must either be constants or a value
4368 /// derived from a constant PHI. If this expression does not fit with these
4369 /// constraints, return null.
4370 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4371 // If this is not an instruction, or if this is an instruction outside of the
4372 // loop, it can't be derived from a loop PHI.
4373 Instruction *I = dyn_cast<Instruction>(V);
4374 if (I == 0 || !L->contains(I)) return 0;
4376 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4377 if (L->getHeader() == I->getParent())
4380 // We don't currently keep track of the control flow needed to evaluate
4381 // PHIs, so we cannot handle PHIs inside of loops.
4385 // If we won't be able to constant fold this expression even if the operands
4386 // are constants, return early.
4387 if (!CanConstantFold(I)) return 0;
4389 // Otherwise, we can evaluate this instruction if all of its operands are
4390 // constant or derived from a PHI node themselves.
4392 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4393 if (!isa<Constant>(I->getOperand(Op))) {
4394 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4395 if (P == 0) return 0; // Not evolving from PHI
4399 return 0; // Evolving from multiple different PHIs.
4402 // This is a expression evolving from a constant PHI!
4406 /// EvaluateExpression - Given an expression that passes the
4407 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4408 /// in the loop has the value PHIVal. If we can't fold this expression for some
4409 /// reason, return null.
4410 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4411 const TargetData *TD) {
4412 if (isa<PHINode>(V)) return PHIVal;
4413 if (Constant *C = dyn_cast<Constant>(V)) return C;
4414 Instruction *I = cast<Instruction>(V);
4416 std::vector<Constant*> Operands(I->getNumOperands());
4418 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4419 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4420 if (Operands[i] == 0) return 0;
4423 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4424 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4426 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4427 &Operands[0], Operands.size(), TD);
4430 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4431 /// in the header of its containing loop, we know the loop executes a
4432 /// constant number of times, and the PHI node is just a recurrence
4433 /// involving constants, fold it.
4435 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4438 std::map<PHINode*, Constant*>::const_iterator I =
4439 ConstantEvolutionLoopExitValue.find(PN);
4440 if (I != ConstantEvolutionLoopExitValue.end())
4443 if (BEs.ugt(MaxBruteForceIterations))
4444 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4446 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4448 // Since the loop is canonicalized, the PHI node must have two entries. One
4449 // entry must be a constant (coming in from outside of the loop), and the
4450 // second must be derived from the same PHI.
4451 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4452 Constant *StartCST =
4453 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4455 return RetVal = 0; // Must be a constant.
4457 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4458 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4459 !isa<Constant>(BEValue))
4460 return RetVal = 0; // Not derived from same PHI.
4462 // Execute the loop symbolically to determine the exit value.
4463 if (BEs.getActiveBits() >= 32)
4464 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4466 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4467 unsigned IterationNum = 0;
4468 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4469 if (IterationNum == NumIterations)
4470 return RetVal = PHIVal; // Got exit value!
4472 // Compute the value of the PHI node for the next iteration.
4473 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4474 if (NextPHI == PHIVal)
4475 return RetVal = NextPHI; // Stopped evolving!
4477 return 0; // Couldn't evaluate!
4482 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4483 /// constant number of times (the condition evolves only from constants),
4484 /// try to evaluate a few iterations of the loop until we get the exit
4485 /// condition gets a value of ExitWhen (true or false). If we cannot
4486 /// evaluate the trip count of the loop, return getCouldNotCompute().
4488 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4491 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4492 if (PN == 0) return getCouldNotCompute();
4494 // If the loop is canonicalized, the PHI will have exactly two entries.
4495 // That's the only form we support here.
4496 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4498 // One entry must be a constant (coming in from outside of the loop), and the
4499 // second must be derived from the same PHI.
4500 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4501 Constant *StartCST =
4502 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4503 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4505 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4506 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4507 !isa<Constant>(BEValue))
4508 return getCouldNotCompute(); // Not derived from same PHI.
4510 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4511 // the loop symbolically to determine when the condition gets a value of
4513 unsigned IterationNum = 0;
4514 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4515 for (Constant *PHIVal = StartCST;
4516 IterationNum != MaxIterations; ++IterationNum) {
4517 ConstantInt *CondVal =
4518 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4520 // Couldn't symbolically evaluate.
4521 if (!CondVal) return getCouldNotCompute();
4523 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4524 ++NumBruteForceTripCountsComputed;
4525 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4528 // Compute the value of the PHI node for the next iteration.
4529 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4530 if (NextPHI == 0 || NextPHI == PHIVal)
4531 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4535 // Too many iterations were needed to evaluate.
4536 return getCouldNotCompute();
4539 /// getSCEVAtScope - Return a SCEV expression for the specified value
4540 /// at the specified scope in the program. The L value specifies a loop
4541 /// nest to evaluate the expression at, where null is the top-level or a
4542 /// specified loop is immediately inside of the loop.
4544 /// This method can be used to compute the exit value for a variable defined
4545 /// in a loop by querying what the value will hold in the parent loop.
4547 /// In the case that a relevant loop exit value cannot be computed, the
4548 /// original value V is returned.
4549 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4550 // Check to see if we've folded this expression at this loop before.
4551 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4552 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4553 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4555 return Pair.first->second ? Pair.first->second : V;
4557 // Otherwise compute it.
4558 const SCEV *C = computeSCEVAtScope(V, L);
4559 ValuesAtScopes[V][L] = C;
4563 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4564 if (isa<SCEVConstant>(V)) return V;
4566 // If this instruction is evolved from a constant-evolving PHI, compute the
4567 // exit value from the loop without using SCEVs.
4568 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4569 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4570 const Loop *LI = (*this->LI)[I->getParent()];
4571 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4572 if (PHINode *PN = dyn_cast<PHINode>(I))
4573 if (PN->getParent() == LI->getHeader()) {
4574 // Okay, there is no closed form solution for the PHI node. Check
4575 // to see if the loop that contains it has a known backedge-taken
4576 // count. If so, we may be able to force computation of the exit
4578 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4579 if (const SCEVConstant *BTCC =
4580 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4581 // Okay, we know how many times the containing loop executes. If
4582 // this is a constant evolving PHI node, get the final value at
4583 // the specified iteration number.
4584 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4585 BTCC->getValue()->getValue(),
4587 if (RV) return getSCEV(RV);
4591 // Okay, this is an expression that we cannot symbolically evaluate
4592 // into a SCEV. Check to see if it's possible to symbolically evaluate
4593 // the arguments into constants, and if so, try to constant propagate the
4594 // result. This is particularly useful for computing loop exit values.
4595 if (CanConstantFold(I)) {
4596 SmallVector<Constant *, 4> Operands;
4597 bool MadeImprovement = false;
4598 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4599 Value *Op = I->getOperand(i);
4600 if (Constant *C = dyn_cast<Constant>(Op)) {
4601 Operands.push_back(C);
4605 // If any of the operands is non-constant and if they are
4606 // non-integer and non-pointer, don't even try to analyze them
4607 // with scev techniques.
4608 if (!isSCEVable(Op->getType()))
4611 const SCEV *OrigV = getSCEV(Op);
4612 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4613 MadeImprovement |= OrigV != OpV;
4616 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4618 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4619 C = dyn_cast<Constant>(SU->getValue());
4621 if (C->getType() != Op->getType())
4622 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4626 Operands.push_back(C);
4629 // Check to see if getSCEVAtScope actually made an improvement.
4630 if (MadeImprovement) {
4632 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4633 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4634 Operands[0], Operands[1], TD);
4636 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4637 &Operands[0], Operands.size(), TD);
4644 // This is some other type of SCEVUnknown, just return it.
4648 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4649 // Avoid performing the look-up in the common case where the specified
4650 // expression has no loop-variant portions.
4651 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4652 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4653 if (OpAtScope != Comm->getOperand(i)) {
4654 // Okay, at least one of these operands is loop variant but might be
4655 // foldable. Build a new instance of the folded commutative expression.
4656 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4657 Comm->op_begin()+i);
4658 NewOps.push_back(OpAtScope);
4660 for (++i; i != e; ++i) {
4661 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4662 NewOps.push_back(OpAtScope);
4664 if (isa<SCEVAddExpr>(Comm))
4665 return getAddExpr(NewOps);
4666 if (isa<SCEVMulExpr>(Comm))
4667 return getMulExpr(NewOps);
4668 if (isa<SCEVSMaxExpr>(Comm))
4669 return getSMaxExpr(NewOps);
4670 if (isa<SCEVUMaxExpr>(Comm))
4671 return getUMaxExpr(NewOps);
4672 llvm_unreachable("Unknown commutative SCEV type!");
4675 // If we got here, all operands are loop invariant.
4679 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4680 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4681 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4682 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4683 return Div; // must be loop invariant
4684 return getUDivExpr(LHS, RHS);
4687 // If this is a loop recurrence for a loop that does not contain L, then we
4688 // are dealing with the final value computed by the loop.
4689 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4690 // First, attempt to evaluate each operand.
4691 // Avoid performing the look-up in the common case where the specified
4692 // expression has no loop-variant portions.
4693 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4694 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4695 if (OpAtScope == AddRec->getOperand(i))
4698 // Okay, at least one of these operands is loop variant but might be
4699 // foldable. Build a new instance of the folded commutative expression.
4700 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4701 AddRec->op_begin()+i);
4702 NewOps.push_back(OpAtScope);
4703 for (++i; i != e; ++i)
4704 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4706 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4710 // If the scope is outside the addrec's loop, evaluate it by using the
4711 // loop exit value of the addrec.
4712 if (!AddRec->getLoop()->contains(L)) {
4713 // To evaluate this recurrence, we need to know how many times the AddRec
4714 // loop iterates. Compute this now.
4715 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4716 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4718 // Then, evaluate the AddRec.
4719 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4725 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4726 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4727 if (Op == Cast->getOperand())
4728 return Cast; // must be loop invariant
4729 return getZeroExtendExpr(Op, Cast->getType());
4732 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4733 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4734 if (Op == Cast->getOperand())
4735 return Cast; // must be loop invariant
4736 return getSignExtendExpr(Op, Cast->getType());
4739 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4740 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4741 if (Op == Cast->getOperand())
4742 return Cast; // must be loop invariant
4743 return getTruncateExpr(Op, Cast->getType());
4746 llvm_unreachable("Unknown SCEV type!");
4750 /// getSCEVAtScope - This is a convenience function which does
4751 /// getSCEVAtScope(getSCEV(V), L).
4752 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4753 return getSCEVAtScope(getSCEV(V), L);
4756 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4757 /// following equation:
4759 /// A * X = B (mod N)
4761 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4762 /// A and B isn't important.
4764 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4765 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4766 ScalarEvolution &SE) {
4767 uint32_t BW = A.getBitWidth();
4768 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4769 assert(A != 0 && "A must be non-zero.");
4773 // The gcd of A and N may have only one prime factor: 2. The number of
4774 // trailing zeros in A is its multiplicity
4775 uint32_t Mult2 = A.countTrailingZeros();
4778 // 2. Check if B is divisible by D.
4780 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4781 // is not less than multiplicity of this prime factor for D.
4782 if (B.countTrailingZeros() < Mult2)
4783 return SE.getCouldNotCompute();
4785 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4788 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4789 // bit width during computations.
4790 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4791 APInt Mod(BW + 1, 0);
4792 Mod.setBit(BW - Mult2); // Mod = N / D
4793 APInt I = AD.multiplicativeInverse(Mod);
4795 // 4. Compute the minimum unsigned root of the equation:
4796 // I * (B / D) mod (N / D)
4797 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4799 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4801 return SE.getConstant(Result.trunc(BW));
4804 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4805 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4806 /// might be the same) or two SCEVCouldNotCompute objects.
4808 static std::pair<const SCEV *,const SCEV *>
4809 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4810 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4811 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4812 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4813 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4815 // We currently can only solve this if the coefficients are constants.
4816 if (!LC || !MC || !NC) {
4817 const SCEV *CNC = SE.getCouldNotCompute();
4818 return std::make_pair(CNC, CNC);
4821 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4822 const APInt &L = LC->getValue()->getValue();
4823 const APInt &M = MC->getValue()->getValue();
4824 const APInt &N = NC->getValue()->getValue();
4825 APInt Two(BitWidth, 2);
4826 APInt Four(BitWidth, 4);
4829 using namespace APIntOps;
4831 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4832 // The B coefficient is M-N/2
4836 // The A coefficient is N/2
4837 APInt A(N.sdiv(Two));
4839 // Compute the B^2-4ac term.
4842 SqrtTerm -= Four * (A * C);
4844 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4845 // integer value or else APInt::sqrt() will assert.
4846 APInt SqrtVal(SqrtTerm.sqrt());
4848 // Compute the two solutions for the quadratic formula.
4849 // The divisions must be performed as signed divisions.
4851 APInt TwoA( A << 1 );
4852 if (TwoA.isMinValue()) {
4853 const SCEV *CNC = SE.getCouldNotCompute();
4854 return std::make_pair(CNC, CNC);
4857 LLVMContext &Context = SE.getContext();
4859 ConstantInt *Solution1 =
4860 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4861 ConstantInt *Solution2 =
4862 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4864 return std::make_pair(SE.getConstant(Solution1),
4865 SE.getConstant(Solution2));
4866 } // end APIntOps namespace
4869 /// HowFarToZero - Return the number of times a backedge comparing the specified
4870 /// value to zero will execute. If not computable, return CouldNotCompute.
4871 ScalarEvolution::BackedgeTakenInfo
4872 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4873 // If the value is a constant
4874 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4875 // If the value is already zero, the branch will execute zero times.
4876 if (C->getValue()->isZero()) return C;
4877 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4880 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4881 if (!AddRec || AddRec->getLoop() != L)
4882 return getCouldNotCompute();
4884 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4885 // the quadratic equation to solve it.
4886 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4887 std::pair<const SCEV *,const SCEV *> Roots =
4888 SolveQuadraticEquation(AddRec, *this);
4889 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4890 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4893 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4894 << " sol#2: " << *R2 << "\n";
4896 // Pick the smallest positive root value.
4897 if (ConstantInt *CB =
4898 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
4901 if (CB->getZExtValue() == false)
4902 std::swap(R1, R2); // R1 is the minimum root now.
4904 // We can only use this value if the chrec ends up with an exact zero
4905 // value at this index. When solving for "X*X != 5", for example, we
4906 // should not accept a root of 2.
4907 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4909 return R1; // We found a quadratic root!
4912 return getCouldNotCompute();
4915 // Otherwise we can only handle this if it is affine.
4916 if (!AddRec->isAffine())
4917 return getCouldNotCompute();
4919 // If this is an affine expression, the execution count of this branch is
4920 // the minimum unsigned root of the following equation:
4922 // Start + Step*N = 0 (mod 2^BW)
4926 // Step*N = -Start (mod 2^BW)
4928 // where BW is the common bit width of Start and Step.
4930 // Get the initial value for the loop.
4931 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
4932 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
4934 // If the AddRec is NUW, then (in an unsigned sense) it cannot be counting up
4935 // to wrap to 0, it must be counting down to equal 0. Also, while counting
4936 // down, it cannot "miss" 0 (which would cause it to wrap), regardless of what
4937 // the stride is. As such, NUW addrec's will always become zero in
4938 // "start / -stride" steps, and we know that the division is exact.
4939 if (AddRec->hasNoUnsignedWrap())
4940 // FIXME: We really want an "isexact" bit for udiv.
4941 return getUDivExpr(Start, getNegativeSCEV(Step));
4943 // For now we handle only constant steps.
4944 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
4946 return getCouldNotCompute();
4948 // First, handle unitary steps.
4949 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4950 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4952 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4953 return Start; // N = Start (as unsigned)
4955 // Then, try to solve the above equation provided that Start is constant.
4956 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4957 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4958 -StartC->getValue()->getValue(),
4960 return getCouldNotCompute();
4963 /// HowFarToNonZero - Return the number of times a backedge checking the
4964 /// specified value for nonzero will execute. If not computable, return
4966 ScalarEvolution::BackedgeTakenInfo
4967 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4968 // Loops that look like: while (X == 0) are very strange indeed. We don't
4969 // handle them yet except for the trivial case. This could be expanded in the
4970 // future as needed.
4972 // If the value is a constant, check to see if it is known to be non-zero
4973 // already. If so, the backedge will execute zero times.
4974 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4975 if (!C->getValue()->isNullValue())
4976 return getConstant(C->getType(), 0);
4977 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4980 // We could implement others, but I really doubt anyone writes loops like
4981 // this, and if they did, they would already be constant folded.
4982 return getCouldNotCompute();
4985 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4986 /// (which may not be an immediate predecessor) which has exactly one
4987 /// successor from which BB is reachable, or null if no such block is
4990 std::pair<BasicBlock *, BasicBlock *>
4991 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4992 // If the block has a unique predecessor, then there is no path from the
4993 // predecessor to the block that does not go through the direct edge
4994 // from the predecessor to the block.
4995 if (BasicBlock *Pred = BB->getSinglePredecessor())
4996 return std::make_pair(Pred, BB);
4998 // A loop's header is defined to be a block that dominates the loop.
4999 // If the header has a unique predecessor outside the loop, it must be
5000 // a block that has exactly one successor that can reach the loop.
5001 if (Loop *L = LI->getLoopFor(BB))
5002 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5004 return std::pair<BasicBlock *, BasicBlock *>();
5007 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5008 /// testing whether two expressions are equal, however for the purposes of
5009 /// looking for a condition guarding a loop, it can be useful to be a little
5010 /// more general, since a front-end may have replicated the controlling
5013 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5014 // Quick check to see if they are the same SCEV.
5015 if (A == B) return true;
5017 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5018 // two different instructions with the same value. Check for this case.
5019 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5020 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5021 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5022 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5023 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5026 // Otherwise assume they may have a different value.
5030 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5031 /// predicate Pred. Return true iff any changes were made.
5033 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5034 const SCEV *&LHS, const SCEV *&RHS) {
5035 bool Changed = false;
5037 // Canonicalize a constant to the right side.
5038 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5039 // Check for both operands constant.
5040 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5041 if (ConstantExpr::getICmp(Pred,
5043 RHSC->getValue())->isNullValue())
5044 goto trivially_false;
5046 goto trivially_true;
5048 // Otherwise swap the operands to put the constant on the right.
5049 std::swap(LHS, RHS);
5050 Pred = ICmpInst::getSwappedPredicate(Pred);
5054 // If we're comparing an addrec with a value which is loop-invariant in the
5055 // addrec's loop, put the addrec on the left. Also make a dominance check,
5056 // as both operands could be addrecs loop-invariant in each other's loop.
5057 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5058 const Loop *L = AR->getLoop();
5059 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5060 std::swap(LHS, RHS);
5061 Pred = ICmpInst::getSwappedPredicate(Pred);
5066 // If there's a constant operand, canonicalize comparisons with boundary
5067 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5068 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5069 const APInt &RA = RC->getValue()->getValue();
5071 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5072 case ICmpInst::ICMP_EQ:
5073 case ICmpInst::ICMP_NE:
5075 case ICmpInst::ICMP_UGE:
5076 if ((RA - 1).isMinValue()) {
5077 Pred = ICmpInst::ICMP_NE;
5078 RHS = getConstant(RA - 1);
5082 if (RA.isMaxValue()) {
5083 Pred = ICmpInst::ICMP_EQ;
5087 if (RA.isMinValue()) goto trivially_true;
5089 Pred = ICmpInst::ICMP_UGT;
5090 RHS = getConstant(RA - 1);
5093 case ICmpInst::ICMP_ULE:
5094 if ((RA + 1).isMaxValue()) {
5095 Pred = ICmpInst::ICMP_NE;
5096 RHS = getConstant(RA + 1);
5100 if (RA.isMinValue()) {
5101 Pred = ICmpInst::ICMP_EQ;
5105 if (RA.isMaxValue()) goto trivially_true;
5107 Pred = ICmpInst::ICMP_ULT;
5108 RHS = getConstant(RA + 1);
5111 case ICmpInst::ICMP_SGE:
5112 if ((RA - 1).isMinSignedValue()) {
5113 Pred = ICmpInst::ICMP_NE;
5114 RHS = getConstant(RA - 1);
5118 if (RA.isMaxSignedValue()) {
5119 Pred = ICmpInst::ICMP_EQ;
5123 if (RA.isMinSignedValue()) goto trivially_true;
5125 Pred = ICmpInst::ICMP_SGT;
5126 RHS = getConstant(RA - 1);
5129 case ICmpInst::ICMP_SLE:
5130 if ((RA + 1).isMaxSignedValue()) {
5131 Pred = ICmpInst::ICMP_NE;
5132 RHS = getConstant(RA + 1);
5136 if (RA.isMinSignedValue()) {
5137 Pred = ICmpInst::ICMP_EQ;
5141 if (RA.isMaxSignedValue()) goto trivially_true;
5143 Pred = ICmpInst::ICMP_SLT;
5144 RHS = getConstant(RA + 1);
5147 case ICmpInst::ICMP_UGT:
5148 if (RA.isMinValue()) {
5149 Pred = ICmpInst::ICMP_NE;
5153 if ((RA + 1).isMaxValue()) {
5154 Pred = ICmpInst::ICMP_EQ;
5155 RHS = getConstant(RA + 1);
5159 if (RA.isMaxValue()) goto trivially_false;
5161 case ICmpInst::ICMP_ULT:
5162 if (RA.isMaxValue()) {
5163 Pred = ICmpInst::ICMP_NE;
5167 if ((RA - 1).isMinValue()) {
5168 Pred = ICmpInst::ICMP_EQ;
5169 RHS = getConstant(RA - 1);
5173 if (RA.isMinValue()) goto trivially_false;
5175 case ICmpInst::ICMP_SGT:
5176 if (RA.isMinSignedValue()) {
5177 Pred = ICmpInst::ICMP_NE;
5181 if ((RA + 1).isMaxSignedValue()) {
5182 Pred = ICmpInst::ICMP_EQ;
5183 RHS = getConstant(RA + 1);
5187 if (RA.isMaxSignedValue()) goto trivially_false;
5189 case ICmpInst::ICMP_SLT:
5190 if (RA.isMaxSignedValue()) {
5191 Pred = ICmpInst::ICMP_NE;
5195 if ((RA - 1).isMinSignedValue()) {
5196 Pred = ICmpInst::ICMP_EQ;
5197 RHS = getConstant(RA - 1);
5201 if (RA.isMinSignedValue()) goto trivially_false;
5206 // Check for obvious equality.
5207 if (HasSameValue(LHS, RHS)) {
5208 if (ICmpInst::isTrueWhenEqual(Pred))
5209 goto trivially_true;
5210 if (ICmpInst::isFalseWhenEqual(Pred))
5211 goto trivially_false;
5214 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5215 // adding or subtracting 1 from one of the operands.
5217 case ICmpInst::ICMP_SLE:
5218 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5219 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5220 /*HasNUW=*/false, /*HasNSW=*/true);
5221 Pred = ICmpInst::ICMP_SLT;
5223 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5224 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5225 /*HasNUW=*/false, /*HasNSW=*/true);
5226 Pred = ICmpInst::ICMP_SLT;
5230 case ICmpInst::ICMP_SGE:
5231 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5232 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5233 /*HasNUW=*/false, /*HasNSW=*/true);
5234 Pred = ICmpInst::ICMP_SGT;
5236 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5237 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5238 /*HasNUW=*/false, /*HasNSW=*/true);
5239 Pred = ICmpInst::ICMP_SGT;
5243 case ICmpInst::ICMP_ULE:
5244 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5245 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5246 /*HasNUW=*/true, /*HasNSW=*/false);
5247 Pred = ICmpInst::ICMP_ULT;
5249 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5250 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5251 /*HasNUW=*/true, /*HasNSW=*/false);
5252 Pred = ICmpInst::ICMP_ULT;
5256 case ICmpInst::ICMP_UGE:
5257 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5258 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5259 /*HasNUW=*/true, /*HasNSW=*/false);
5260 Pred = ICmpInst::ICMP_UGT;
5262 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5263 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5264 /*HasNUW=*/true, /*HasNSW=*/false);
5265 Pred = ICmpInst::ICMP_UGT;
5273 // TODO: More simplifications are possible here.
5279 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5280 Pred = ICmpInst::ICMP_EQ;
5285 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5286 Pred = ICmpInst::ICMP_NE;
5290 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5291 return getSignedRange(S).getSignedMax().isNegative();
5294 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5295 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5298 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5299 return !getSignedRange(S).getSignedMin().isNegative();
5302 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5303 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5306 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5307 return isKnownNegative(S) || isKnownPositive(S);
5310 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5311 const SCEV *LHS, const SCEV *RHS) {
5312 // Canonicalize the inputs first.
5313 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5315 // If LHS or RHS is an addrec, check to see if the condition is true in
5316 // every iteration of the loop.
5317 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5318 if (isLoopEntryGuardedByCond(
5319 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5320 isLoopBackedgeGuardedByCond(
5321 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5323 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5324 if (isLoopEntryGuardedByCond(
5325 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5326 isLoopBackedgeGuardedByCond(
5327 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5330 // Otherwise see what can be done with known constant ranges.
5331 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5335 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5336 const SCEV *LHS, const SCEV *RHS) {
5337 if (HasSameValue(LHS, RHS))
5338 return ICmpInst::isTrueWhenEqual(Pred);
5340 // This code is split out from isKnownPredicate because it is called from
5341 // within isLoopEntryGuardedByCond.
5344 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5346 case ICmpInst::ICMP_SGT:
5347 Pred = ICmpInst::ICMP_SLT;
5348 std::swap(LHS, RHS);
5349 case ICmpInst::ICMP_SLT: {
5350 ConstantRange LHSRange = getSignedRange(LHS);
5351 ConstantRange RHSRange = getSignedRange(RHS);
5352 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5354 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5358 case ICmpInst::ICMP_SGE:
5359 Pred = ICmpInst::ICMP_SLE;
5360 std::swap(LHS, RHS);
5361 case ICmpInst::ICMP_SLE: {
5362 ConstantRange LHSRange = getSignedRange(LHS);
5363 ConstantRange RHSRange = getSignedRange(RHS);
5364 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5366 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5370 case ICmpInst::ICMP_UGT:
5371 Pred = ICmpInst::ICMP_ULT;
5372 std::swap(LHS, RHS);
5373 case ICmpInst::ICMP_ULT: {
5374 ConstantRange LHSRange = getUnsignedRange(LHS);
5375 ConstantRange RHSRange = getUnsignedRange(RHS);
5376 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5378 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5382 case ICmpInst::ICMP_UGE:
5383 Pred = ICmpInst::ICMP_ULE;
5384 std::swap(LHS, RHS);
5385 case ICmpInst::ICMP_ULE: {
5386 ConstantRange LHSRange = getUnsignedRange(LHS);
5387 ConstantRange RHSRange = getUnsignedRange(RHS);
5388 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5390 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5394 case ICmpInst::ICMP_NE: {
5395 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5397 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5400 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5401 if (isKnownNonZero(Diff))
5405 case ICmpInst::ICMP_EQ:
5406 // The check at the top of the function catches the case where
5407 // the values are known to be equal.
5413 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5414 /// protected by a conditional between LHS and RHS. This is used to
5415 /// to eliminate casts.
5417 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5418 ICmpInst::Predicate Pred,
5419 const SCEV *LHS, const SCEV *RHS) {
5420 // Interpret a null as meaning no loop, where there is obviously no guard
5421 // (interprocedural conditions notwithstanding).
5422 if (!L) return true;
5424 BasicBlock *Latch = L->getLoopLatch();
5428 BranchInst *LoopContinuePredicate =
5429 dyn_cast<BranchInst>(Latch->getTerminator());
5430 if (!LoopContinuePredicate ||
5431 LoopContinuePredicate->isUnconditional())
5434 return isImpliedCond(Pred, LHS, RHS,
5435 LoopContinuePredicate->getCondition(),
5436 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5439 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5440 /// by a conditional between LHS and RHS. This is used to help avoid max
5441 /// expressions in loop trip counts, and to eliminate casts.
5443 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5444 ICmpInst::Predicate Pred,
5445 const SCEV *LHS, const SCEV *RHS) {
5446 // Interpret a null as meaning no loop, where there is obviously no guard
5447 // (interprocedural conditions notwithstanding).
5448 if (!L) return false;
5450 // Starting at the loop predecessor, climb up the predecessor chain, as long
5451 // as there are predecessors that can be found that have unique successors
5452 // leading to the original header.
5453 for (std::pair<BasicBlock *, BasicBlock *>
5454 Pair(L->getLoopPredecessor(), L->getHeader());
5456 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5458 BranchInst *LoopEntryPredicate =
5459 dyn_cast<BranchInst>(Pair.first->getTerminator());
5460 if (!LoopEntryPredicate ||
5461 LoopEntryPredicate->isUnconditional())
5464 if (isImpliedCond(Pred, LHS, RHS,
5465 LoopEntryPredicate->getCondition(),
5466 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5473 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5474 /// and RHS is true whenever the given Cond value evaluates to true.
5475 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5476 const SCEV *LHS, const SCEV *RHS,
5477 Value *FoundCondValue,
5479 // Recursively handle And and Or conditions.
5480 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5481 if (BO->getOpcode() == Instruction::And) {
5483 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5484 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5485 } else if (BO->getOpcode() == Instruction::Or) {
5487 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5488 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5492 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5493 if (!ICI) return false;
5495 // Bail if the ICmp's operands' types are wider than the needed type
5496 // before attempting to call getSCEV on them. This avoids infinite
5497 // recursion, since the analysis of widening casts can require loop
5498 // exit condition information for overflow checking, which would
5500 if (getTypeSizeInBits(LHS->getType()) <
5501 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5504 // Now that we found a conditional branch that dominates the loop, check to
5505 // see if it is the comparison we are looking for.
5506 ICmpInst::Predicate FoundPred;
5508 FoundPred = ICI->getInversePredicate();
5510 FoundPred = ICI->getPredicate();
5512 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5513 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5515 // Balance the types. The case where FoundLHS' type is wider than
5516 // LHS' type is checked for above.
5517 if (getTypeSizeInBits(LHS->getType()) >
5518 getTypeSizeInBits(FoundLHS->getType())) {
5519 if (CmpInst::isSigned(Pred)) {
5520 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5521 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5523 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5524 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5528 // Canonicalize the query to match the way instcombine will have
5529 // canonicalized the comparison.
5530 if (SimplifyICmpOperands(Pred, LHS, RHS))
5532 return CmpInst::isTrueWhenEqual(Pred);
5533 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5534 if (FoundLHS == FoundRHS)
5535 return CmpInst::isFalseWhenEqual(Pred);
5537 // Check to see if we can make the LHS or RHS match.
5538 if (LHS == FoundRHS || RHS == FoundLHS) {
5539 if (isa<SCEVConstant>(RHS)) {
5540 std::swap(FoundLHS, FoundRHS);
5541 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5543 std::swap(LHS, RHS);
5544 Pred = ICmpInst::getSwappedPredicate(Pred);
5548 // Check whether the found predicate is the same as the desired predicate.
5549 if (FoundPred == Pred)
5550 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5552 // Check whether swapping the found predicate makes it the same as the
5553 // desired predicate.
5554 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5555 if (isa<SCEVConstant>(RHS))
5556 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5558 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5559 RHS, LHS, FoundLHS, FoundRHS);
5562 // Check whether the actual condition is beyond sufficient.
5563 if (FoundPred == ICmpInst::ICMP_EQ)
5564 if (ICmpInst::isTrueWhenEqual(Pred))
5565 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5567 if (Pred == ICmpInst::ICMP_NE)
5568 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5569 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5572 // Otherwise assume the worst.
5576 /// isImpliedCondOperands - Test whether the condition described by Pred,
5577 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5578 /// and FoundRHS is true.
5579 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5580 const SCEV *LHS, const SCEV *RHS,
5581 const SCEV *FoundLHS,
5582 const SCEV *FoundRHS) {
5583 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5584 FoundLHS, FoundRHS) ||
5585 // ~x < ~y --> x > y
5586 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5587 getNotSCEV(FoundRHS),
5588 getNotSCEV(FoundLHS));
5591 /// isImpliedCondOperandsHelper - Test whether the condition described by
5592 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5593 /// FoundLHS, and FoundRHS is true.
5595 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5596 const SCEV *LHS, const SCEV *RHS,
5597 const SCEV *FoundLHS,
5598 const SCEV *FoundRHS) {
5600 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5601 case ICmpInst::ICMP_EQ:
5602 case ICmpInst::ICMP_NE:
5603 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5606 case ICmpInst::ICMP_SLT:
5607 case ICmpInst::ICMP_SLE:
5608 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5609 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5612 case ICmpInst::ICMP_SGT:
5613 case ICmpInst::ICMP_SGE:
5614 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5615 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5618 case ICmpInst::ICMP_ULT:
5619 case ICmpInst::ICMP_ULE:
5620 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5621 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5624 case ICmpInst::ICMP_UGT:
5625 case ICmpInst::ICMP_UGE:
5626 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5627 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5635 /// getBECount - Subtract the end and start values and divide by the step,
5636 /// rounding up, to get the number of times the backedge is executed. Return
5637 /// CouldNotCompute if an intermediate computation overflows.
5638 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5642 assert(!isKnownNegative(Step) &&
5643 "This code doesn't handle negative strides yet!");
5645 const Type *Ty = Start->getType();
5646 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5647 const SCEV *Diff = getMinusSCEV(End, Start);
5648 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5650 // Add an adjustment to the difference between End and Start so that
5651 // the division will effectively round up.
5652 const SCEV *Add = getAddExpr(Diff, RoundUp);
5655 // Check Add for unsigned overflow.
5656 // TODO: More sophisticated things could be done here.
5657 const Type *WideTy = IntegerType::get(getContext(),
5658 getTypeSizeInBits(Ty) + 1);
5659 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5660 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5661 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5662 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5663 return getCouldNotCompute();
5666 return getUDivExpr(Add, Step);
5669 /// HowManyLessThans - Return the number of times a backedge containing the
5670 /// specified less-than comparison will execute. If not computable, return
5671 /// CouldNotCompute.
5672 ScalarEvolution::BackedgeTakenInfo
5673 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5674 const Loop *L, bool isSigned) {
5675 // Only handle: "ADDREC < LoopInvariant".
5676 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
5678 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5679 if (!AddRec || AddRec->getLoop() != L)
5680 return getCouldNotCompute();
5682 // Check to see if we have a flag which makes analysis easy.
5683 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5684 AddRec->hasNoUnsignedWrap();
5686 if (AddRec->isAffine()) {
5687 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5688 const SCEV *Step = AddRec->getStepRecurrence(*this);
5691 return getCouldNotCompute();
5692 if (Step->isOne()) {
5693 // With unit stride, the iteration never steps past the limit value.
5694 } else if (isKnownPositive(Step)) {
5695 // Test whether a positive iteration can step past the limit
5696 // value and past the maximum value for its type in a single step.
5697 // Note that it's not sufficient to check NoWrap here, because even
5698 // though the value after a wrap is undefined, it's not undefined
5699 // behavior, so if wrap does occur, the loop could either terminate or
5700 // loop infinitely, but in either case, the loop is guaranteed to
5701 // iterate at least until the iteration where the wrapping occurs.
5702 const SCEV *One = getConstant(Step->getType(), 1);
5704 APInt Max = APInt::getSignedMaxValue(BitWidth);
5705 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5706 .slt(getSignedRange(RHS).getSignedMax()))
5707 return getCouldNotCompute();
5709 APInt Max = APInt::getMaxValue(BitWidth);
5710 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5711 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5712 return getCouldNotCompute();
5715 // TODO: Handle negative strides here and below.
5716 return getCouldNotCompute();
5718 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5719 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5720 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5721 // treat m-n as signed nor unsigned due to overflow possibility.
5723 // First, we get the value of the LHS in the first iteration: n
5724 const SCEV *Start = AddRec->getOperand(0);
5726 // Determine the minimum constant start value.
5727 const SCEV *MinStart = getConstant(isSigned ?
5728 getSignedRange(Start).getSignedMin() :
5729 getUnsignedRange(Start).getUnsignedMin());
5731 // If we know that the condition is true in order to enter the loop,
5732 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5733 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5734 // the division must round up.
5735 const SCEV *End = RHS;
5736 if (!isLoopEntryGuardedByCond(L,
5737 isSigned ? ICmpInst::ICMP_SLT :
5739 getMinusSCEV(Start, Step), RHS))
5740 End = isSigned ? getSMaxExpr(RHS, Start)
5741 : getUMaxExpr(RHS, Start);
5743 // Determine the maximum constant end value.
5744 const SCEV *MaxEnd = getConstant(isSigned ?
5745 getSignedRange(End).getSignedMax() :
5746 getUnsignedRange(End).getUnsignedMax());
5748 // If MaxEnd is within a step of the maximum integer value in its type,
5749 // adjust it down to the minimum value which would produce the same effect.
5750 // This allows the subsequent ceiling division of (N+(step-1))/step to
5751 // compute the correct value.
5752 const SCEV *StepMinusOne = getMinusSCEV(Step,
5753 getConstant(Step->getType(), 1));
5756 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5759 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5762 // Finally, we subtract these two values and divide, rounding up, to get
5763 // the number of times the backedge is executed.
5764 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5766 // The maximum backedge count is similar, except using the minimum start
5767 // value and the maximum end value.
5768 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5770 return BackedgeTakenInfo(BECount, MaxBECount);
5773 return getCouldNotCompute();
5776 /// getNumIterationsInRange - Return the number of iterations of this loop that
5777 /// produce values in the specified constant range. Another way of looking at
5778 /// this is that it returns the first iteration number where the value is not in
5779 /// the condition, thus computing the exit count. If the iteration count can't
5780 /// be computed, an instance of SCEVCouldNotCompute is returned.
5781 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5782 ScalarEvolution &SE) const {
5783 if (Range.isFullSet()) // Infinite loop.
5784 return SE.getCouldNotCompute();
5786 // If the start is a non-zero constant, shift the range to simplify things.
5787 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5788 if (!SC->getValue()->isZero()) {
5789 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5790 Operands[0] = SE.getConstant(SC->getType(), 0);
5791 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5792 if (const SCEVAddRecExpr *ShiftedAddRec =
5793 dyn_cast<SCEVAddRecExpr>(Shifted))
5794 return ShiftedAddRec->getNumIterationsInRange(
5795 Range.subtract(SC->getValue()->getValue()), SE);
5796 // This is strange and shouldn't happen.
5797 return SE.getCouldNotCompute();
5800 // The only time we can solve this is when we have all constant indices.
5801 // Otherwise, we cannot determine the overflow conditions.
5802 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5803 if (!isa<SCEVConstant>(getOperand(i)))
5804 return SE.getCouldNotCompute();
5807 // Okay at this point we know that all elements of the chrec are constants and
5808 // that the start element is zero.
5810 // First check to see if the range contains zero. If not, the first
5812 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5813 if (!Range.contains(APInt(BitWidth, 0)))
5814 return SE.getConstant(getType(), 0);
5817 // If this is an affine expression then we have this situation:
5818 // Solve {0,+,A} in Range === Ax in Range
5820 // We know that zero is in the range. If A is positive then we know that
5821 // the upper value of the range must be the first possible exit value.
5822 // If A is negative then the lower of the range is the last possible loop
5823 // value. Also note that we already checked for a full range.
5824 APInt One(BitWidth,1);
5825 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5826 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5828 // The exit value should be (End+A)/A.
5829 APInt ExitVal = (End + A).udiv(A);
5830 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5832 // Evaluate at the exit value. If we really did fall out of the valid
5833 // range, then we computed our trip count, otherwise wrap around or other
5834 // things must have happened.
5835 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5836 if (Range.contains(Val->getValue()))
5837 return SE.getCouldNotCompute(); // Something strange happened
5839 // Ensure that the previous value is in the range. This is a sanity check.
5840 assert(Range.contains(
5841 EvaluateConstantChrecAtConstant(this,
5842 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5843 "Linear scev computation is off in a bad way!");
5844 return SE.getConstant(ExitValue);
5845 } else if (isQuadratic()) {
5846 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5847 // quadratic equation to solve it. To do this, we must frame our problem in
5848 // terms of figuring out when zero is crossed, instead of when
5849 // Range.getUpper() is crossed.
5850 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5851 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5852 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5854 // Next, solve the constructed addrec
5855 std::pair<const SCEV *,const SCEV *> Roots =
5856 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5857 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5858 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5860 // Pick the smallest positive root value.
5861 if (ConstantInt *CB =
5862 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5863 R1->getValue(), R2->getValue()))) {
5864 if (CB->getZExtValue() == false)
5865 std::swap(R1, R2); // R1 is the minimum root now.
5867 // Make sure the root is not off by one. The returned iteration should
5868 // not be in the range, but the previous one should be. When solving
5869 // for "X*X < 5", for example, we should not return a root of 2.
5870 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5873 if (Range.contains(R1Val->getValue())) {
5874 // The next iteration must be out of the range...
5875 ConstantInt *NextVal =
5876 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5878 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5879 if (!Range.contains(R1Val->getValue()))
5880 return SE.getConstant(NextVal);
5881 return SE.getCouldNotCompute(); // Something strange happened
5884 // If R1 was not in the range, then it is a good return value. Make
5885 // sure that R1-1 WAS in the range though, just in case.
5886 ConstantInt *NextVal =
5887 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5888 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5889 if (Range.contains(R1Val->getValue()))
5891 return SE.getCouldNotCompute(); // Something strange happened
5896 return SE.getCouldNotCompute();
5901 //===----------------------------------------------------------------------===//
5902 // SCEVCallbackVH Class Implementation
5903 //===----------------------------------------------------------------------===//
5905 void ScalarEvolution::SCEVCallbackVH::deleted() {
5906 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5907 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5908 SE->ConstantEvolutionLoopExitValue.erase(PN);
5909 SE->ValueExprMap.erase(getValPtr());
5910 // this now dangles!
5913 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5914 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5916 // Forget all the expressions associated with users of the old value,
5917 // so that future queries will recompute the expressions using the new
5919 Value *Old = getValPtr();
5920 SmallVector<User *, 16> Worklist;
5921 SmallPtrSet<User *, 8> Visited;
5922 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5924 Worklist.push_back(*UI);
5925 while (!Worklist.empty()) {
5926 User *U = Worklist.pop_back_val();
5927 // Deleting the Old value will cause this to dangle. Postpone
5928 // that until everything else is done.
5931 if (!Visited.insert(U))
5933 if (PHINode *PN = dyn_cast<PHINode>(U))
5934 SE->ConstantEvolutionLoopExitValue.erase(PN);
5935 SE->ValueExprMap.erase(U);
5936 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5938 Worklist.push_back(*UI);
5940 // Delete the Old value.
5941 if (PHINode *PN = dyn_cast<PHINode>(Old))
5942 SE->ConstantEvolutionLoopExitValue.erase(PN);
5943 SE->ValueExprMap.erase(Old);
5944 // this now dangles!
5947 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5948 : CallbackVH(V), SE(se) {}
5950 //===----------------------------------------------------------------------===//
5951 // ScalarEvolution Class Implementation
5952 //===----------------------------------------------------------------------===//
5954 ScalarEvolution::ScalarEvolution()
5955 : FunctionPass(ID), FirstUnknown(0) {
5956 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
5959 bool ScalarEvolution::runOnFunction(Function &F) {
5961 LI = &getAnalysis<LoopInfo>();
5962 TD = getAnalysisIfAvailable<TargetData>();
5963 DT = &getAnalysis<DominatorTree>();
5967 void ScalarEvolution::releaseMemory() {
5968 // Iterate through all the SCEVUnknown instances and call their
5969 // destructors, so that they release their references to their values.
5970 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
5974 ValueExprMap.clear();
5975 BackedgeTakenCounts.clear();
5976 ConstantEvolutionLoopExitValue.clear();
5977 ValuesAtScopes.clear();
5978 LoopDispositions.clear();
5979 BlockDispositions.clear();
5980 UnsignedRanges.clear();
5981 SignedRanges.clear();
5982 UniqueSCEVs.clear();
5983 SCEVAllocator.Reset();
5986 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5987 AU.setPreservesAll();
5988 AU.addRequiredTransitive<LoopInfo>();
5989 AU.addRequiredTransitive<DominatorTree>();
5992 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5993 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5996 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5998 // Print all inner loops first
5999 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6000 PrintLoopInfo(OS, SE, *I);
6003 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6006 SmallVector<BasicBlock *, 8> ExitBlocks;
6007 L->getExitBlocks(ExitBlocks);
6008 if (ExitBlocks.size() != 1)
6009 OS << "<multiple exits> ";
6011 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6012 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6014 OS << "Unpredictable backedge-taken count. ";
6019 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6022 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6023 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6025 OS << "Unpredictable max backedge-taken count. ";
6031 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6032 // ScalarEvolution's implementation of the print method is to print
6033 // out SCEV values of all instructions that are interesting. Doing
6034 // this potentially causes it to create new SCEV objects though,
6035 // which technically conflicts with the const qualifier. This isn't
6036 // observable from outside the class though, so casting away the
6037 // const isn't dangerous.
6038 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6040 OS << "Classifying expressions for: ";
6041 WriteAsOperand(OS, F, /*PrintType=*/false);
6043 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6044 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6047 const SCEV *SV = SE.getSCEV(&*I);
6050 const Loop *L = LI->getLoopFor((*I).getParent());
6052 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6059 OS << "\t\t" "Exits: ";
6060 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6061 if (!SE.isLoopInvariant(ExitValue, L)) {
6062 OS << "<<Unknown>>";
6071 OS << "Determining loop execution counts for: ";
6072 WriteAsOperand(OS, F, /*PrintType=*/false);
6074 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6075 PrintLoopInfo(OS, &SE, *I);
6078 ScalarEvolution::LoopDisposition
6079 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6080 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6081 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6082 Values.insert(std::make_pair(L, LoopVariant));
6084 return Pair.first->second;
6086 LoopDisposition D = computeLoopDisposition(S, L);
6087 return LoopDispositions[S][L] = D;
6090 ScalarEvolution::LoopDisposition
6091 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6092 switch (S->getSCEVType()) {
6094 return LoopInvariant;
6098 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6099 case scAddRecExpr: {
6100 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6102 // If L is the addrec's loop, it's computable.
6103 if (AR->getLoop() == L)
6104 return LoopComputable;
6106 // Add recurrences are never invariant in the function-body (null loop).
6110 // This recurrence is variant w.r.t. L if L contains AR's loop.
6111 if (L->contains(AR->getLoop()))
6114 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6115 if (AR->getLoop()->contains(L))
6116 return LoopInvariant;
6118 // This recurrence is variant w.r.t. L if any of its operands
6120 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6122 if (!isLoopInvariant(*I, L))
6125 // Otherwise it's loop-invariant.
6126 return LoopInvariant;
6132 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6133 bool HasVarying = false;
6134 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6136 LoopDisposition D = getLoopDisposition(*I, L);
6137 if (D == LoopVariant)
6139 if (D == LoopComputable)
6142 return HasVarying ? LoopComputable : LoopInvariant;
6145 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6146 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6147 if (LD == LoopVariant)
6149 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6150 if (RD == LoopVariant)
6152 return (LD == LoopInvariant && RD == LoopInvariant) ?
6153 LoopInvariant : LoopComputable;
6156 // All non-instruction values are loop invariant. All instructions are loop
6157 // invariant if they are not contained in the specified loop.
6158 // Instructions are never considered invariant in the function body
6159 // (null loop) because they are defined within the "loop".
6160 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6161 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6162 return LoopInvariant;
6163 case scCouldNotCompute:
6164 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6168 llvm_unreachable("Unknown SCEV kind!");
6172 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6173 return getLoopDisposition(S, L) == LoopInvariant;
6176 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6177 return getLoopDisposition(S, L) == LoopComputable;
6180 ScalarEvolution::BlockDisposition
6181 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6182 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6183 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6184 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6186 return Pair.first->second;
6188 BlockDisposition D = computeBlockDisposition(S, BB);
6189 return BlockDispositions[S][BB] = D;
6192 ScalarEvolution::BlockDisposition
6193 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6194 switch (S->getSCEVType()) {
6196 return ProperlyDominatesBlock;
6200 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6201 case scAddRecExpr: {
6202 // This uses a "dominates" query instead of "properly dominates" query
6203 // to test for proper dominance too, because the instruction which
6204 // produces the addrec's value is a PHI, and a PHI effectively properly
6205 // dominates its entire containing block.
6206 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6207 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6208 return DoesNotDominateBlock;
6210 // FALL THROUGH into SCEVNAryExpr handling.
6215 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6217 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6219 BlockDisposition D = getBlockDisposition(*I, BB);
6220 if (D == DoesNotDominateBlock)
6221 return DoesNotDominateBlock;
6222 if (D == DominatesBlock)
6225 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6228 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6229 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6230 BlockDisposition LD = getBlockDisposition(LHS, BB);
6231 if (LD == DoesNotDominateBlock)
6232 return DoesNotDominateBlock;
6233 BlockDisposition RD = getBlockDisposition(RHS, BB);
6234 if (RD == DoesNotDominateBlock)
6235 return DoesNotDominateBlock;
6236 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6237 ProperlyDominatesBlock : DominatesBlock;
6240 if (Instruction *I =
6241 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6242 if (I->getParent() == BB)
6243 return DominatesBlock;
6244 if (DT->properlyDominates(I->getParent(), BB))
6245 return ProperlyDominatesBlock;
6246 return DoesNotDominateBlock;
6248 return ProperlyDominatesBlock;
6249 case scCouldNotCompute:
6250 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6251 return DoesNotDominateBlock;
6254 llvm_unreachable("Unknown SCEV kind!");
6255 return DoesNotDominateBlock;
6258 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6259 return getBlockDisposition(S, BB) >= DominatesBlock;
6262 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6263 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6266 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6267 switch (S->getSCEVType()) {
6272 case scSignExtend: {
6273 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6274 const SCEV *CastOp = Cast->getOperand();
6275 return Op == CastOp || hasOperand(CastOp, Op);
6282 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6283 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6285 const SCEV *NAryOp = *I;
6286 if (NAryOp == Op || hasOperand(NAryOp, Op))
6292 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6293 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6294 return LHS == Op || hasOperand(LHS, Op) ||
6295 RHS == Op || hasOperand(RHS, Op);
6299 case scCouldNotCompute:
6300 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6304 llvm_unreachable("Unknown SCEV kind!");
6308 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6309 ValuesAtScopes.erase(S);
6310 LoopDispositions.erase(S);
6311 BlockDispositions.erase(S);
6312 UnsignedRanges.erase(S);
6313 SignedRanges.erase(S);