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 // If the input value is a chrec scev, truncate the chrec's operands.
823 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
824 SmallVector<const SCEV *, 4> Operands;
825 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
826 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
827 return getAddRecExpr(Operands, AddRec->getLoop());
830 // As a special case, fold trunc(undef) to undef. We don't want to
831 // know too much about SCEVUnknowns, but this special case is handy
833 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
834 if (isa<UndefValue>(U->getValue()))
835 return getSCEV(UndefValue::get(Ty));
837 // The cast wasn't folded; create an explicit cast node. We can reuse
838 // the existing insert position since if we get here, we won't have
839 // made any changes which would invalidate it.
840 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
842 UniqueSCEVs.InsertNode(S, IP);
846 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
848 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
849 "This is not an extending conversion!");
850 assert(isSCEVable(Ty) &&
851 "This is not a conversion to a SCEVable type!");
852 Ty = getEffectiveSCEVType(Ty);
854 // Fold if the operand is constant.
855 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
857 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
858 getEffectiveSCEVType(Ty))));
860 // zext(zext(x)) --> zext(x)
861 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
862 return getZeroExtendExpr(SZ->getOperand(), Ty);
864 // Before doing any expensive analysis, check to see if we've already
865 // computed a SCEV for this Op and Ty.
867 ID.AddInteger(scZeroExtend);
871 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
873 // If the input value is a chrec scev, and we can prove that the value
874 // did not overflow the old, smaller, value, we can zero extend all of the
875 // operands (often constants). This allows analysis of something like
876 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
877 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
878 if (AR->isAffine()) {
879 const SCEV *Start = AR->getStart();
880 const SCEV *Step = AR->getStepRecurrence(*this);
881 unsigned BitWidth = getTypeSizeInBits(AR->getType());
882 const Loop *L = AR->getLoop();
884 // If we have special knowledge that this addrec won't overflow,
885 // we don't need to do any further analysis.
886 if (AR->hasNoUnsignedWrap())
887 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
888 getZeroExtendExpr(Step, Ty),
891 // Check whether the backedge-taken count is SCEVCouldNotCompute.
892 // Note that this serves two purposes: It filters out loops that are
893 // simply not analyzable, and it covers the case where this code is
894 // being called from within backedge-taken count analysis, such that
895 // attempting to ask for the backedge-taken count would likely result
896 // in infinite recursion. In the later case, the analysis code will
897 // cope with a conservative value, and it will take care to purge
898 // that value once it has finished.
899 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
900 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
901 // Manually compute the final value for AR, checking for
904 // Check whether the backedge-taken count can be losslessly casted to
905 // the addrec's type. The count is always unsigned.
906 const SCEV *CastedMaxBECount =
907 getTruncateOrZeroExtend(MaxBECount, Start->getType());
908 const SCEV *RecastedMaxBECount =
909 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
910 if (MaxBECount == RecastedMaxBECount) {
911 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
912 // Check whether Start+Step*MaxBECount has no unsigned overflow.
913 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
914 const SCEV *Add = getAddExpr(Start, ZMul);
915 const SCEV *OperandExtendedAdd =
916 getAddExpr(getZeroExtendExpr(Start, WideTy),
917 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
918 getZeroExtendExpr(Step, WideTy)));
919 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
920 // Return the expression with the addrec on the outside.
921 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
922 getZeroExtendExpr(Step, Ty),
925 // Similar to above, only this time treat the step value as signed.
926 // This covers loops that count down.
927 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
928 Add = getAddExpr(Start, SMul);
930 getAddExpr(getZeroExtendExpr(Start, WideTy),
931 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
932 getSignExtendExpr(Step, WideTy)));
933 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
934 // Return the expression with the addrec on the outside.
935 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
936 getSignExtendExpr(Step, Ty),
940 // If the backedge is guarded by a comparison with the pre-inc value
941 // the addrec is safe. Also, if the entry is guarded by a comparison
942 // with the start value and the backedge is guarded by a comparison
943 // with the post-inc value, the addrec is safe.
944 if (isKnownPositive(Step)) {
945 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
946 getUnsignedRange(Step).getUnsignedMax());
947 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
948 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
949 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
950 AR->getPostIncExpr(*this), N)))
951 // Return the expression with the addrec on the outside.
952 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
953 getZeroExtendExpr(Step, Ty),
955 } else if (isKnownNegative(Step)) {
956 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
957 getSignedRange(Step).getSignedMin());
958 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
959 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
960 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
961 AR->getPostIncExpr(*this), N)))
962 // Return the expression with the addrec on the outside.
963 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
964 getSignExtendExpr(Step, Ty),
970 // The cast wasn't folded; create an explicit cast node.
971 // Recompute the insert position, as it may have been invalidated.
972 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
973 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
975 UniqueSCEVs.InsertNode(S, IP);
979 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
981 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
982 "This is not an extending conversion!");
983 assert(isSCEVable(Ty) &&
984 "This is not a conversion to a SCEVable type!");
985 Ty = getEffectiveSCEVType(Ty);
987 // Fold if the operand is constant.
988 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
990 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
991 getEffectiveSCEVType(Ty))));
993 // sext(sext(x)) --> sext(x)
994 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
995 return getSignExtendExpr(SS->getOperand(), Ty);
997 // Before doing any expensive analysis, check to see if we've already
998 // computed a SCEV for this Op and Ty.
1000 ID.AddInteger(scSignExtend);
1004 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1006 // If the input value is a chrec scev, and we can prove that the value
1007 // did not overflow the old, smaller, value, we can sign extend all of the
1008 // operands (often constants). This allows analysis of something like
1009 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1010 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1011 if (AR->isAffine()) {
1012 const SCEV *Start = AR->getStart();
1013 const SCEV *Step = AR->getStepRecurrence(*this);
1014 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1015 const Loop *L = AR->getLoop();
1017 // If we have special knowledge that this addrec won't overflow,
1018 // we don't need to do any further analysis.
1019 if (AR->hasNoSignedWrap())
1020 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1021 getSignExtendExpr(Step, Ty),
1024 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1025 // Note that this serves two purposes: It filters out loops that are
1026 // simply not analyzable, and it covers the case where this code is
1027 // being called from within backedge-taken count analysis, such that
1028 // attempting to ask for the backedge-taken count would likely result
1029 // in infinite recursion. In the later case, the analysis code will
1030 // cope with a conservative value, and it will take care to purge
1031 // that value once it has finished.
1032 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1033 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1034 // Manually compute the final value for AR, checking for
1037 // Check whether the backedge-taken count can be losslessly casted to
1038 // the addrec's type. The count is always unsigned.
1039 const SCEV *CastedMaxBECount =
1040 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1041 const SCEV *RecastedMaxBECount =
1042 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1043 if (MaxBECount == RecastedMaxBECount) {
1044 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1045 // Check whether Start+Step*MaxBECount has no signed overflow.
1046 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1047 const SCEV *Add = getAddExpr(Start, SMul);
1048 const SCEV *OperandExtendedAdd =
1049 getAddExpr(getSignExtendExpr(Start, WideTy),
1050 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1051 getSignExtendExpr(Step, WideTy)));
1052 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1053 // Return the expression with the addrec on the outside.
1054 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1055 getSignExtendExpr(Step, Ty),
1058 // Similar to above, only this time treat the step value as unsigned.
1059 // This covers loops that count up with an unsigned step.
1060 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1061 Add = getAddExpr(Start, UMul);
1062 OperandExtendedAdd =
1063 getAddExpr(getSignExtendExpr(Start, WideTy),
1064 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1065 getZeroExtendExpr(Step, WideTy)));
1066 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
1067 // Return the expression with the addrec on the outside.
1068 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1069 getZeroExtendExpr(Step, Ty),
1073 // If the backedge is guarded by a comparison with the pre-inc value
1074 // the addrec is safe. Also, if the entry is guarded by a comparison
1075 // with the start value and the backedge is guarded by a comparison
1076 // with the post-inc value, the addrec is safe.
1077 if (isKnownPositive(Step)) {
1078 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1079 getSignedRange(Step).getSignedMax());
1080 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1081 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1082 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1083 AR->getPostIncExpr(*this), N)))
1084 // Return the expression with the addrec on the outside.
1085 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1086 getSignExtendExpr(Step, Ty),
1088 } else if (isKnownNegative(Step)) {
1089 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1090 getSignedRange(Step).getSignedMin());
1091 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1092 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1093 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1094 AR->getPostIncExpr(*this), N)))
1095 // Return the expression with the addrec on the outside.
1096 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1097 getSignExtendExpr(Step, Ty),
1103 // The cast wasn't folded; create an explicit cast node.
1104 // Recompute the insert position, as it may have been invalidated.
1105 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1106 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1108 UniqueSCEVs.InsertNode(S, IP);
1112 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1113 /// unspecified bits out to the given type.
1115 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1117 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1118 "This is not an extending conversion!");
1119 assert(isSCEVable(Ty) &&
1120 "This is not a conversion to a SCEVable type!");
1121 Ty = getEffectiveSCEVType(Ty);
1123 // Sign-extend negative constants.
1124 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1125 if (SC->getValue()->getValue().isNegative())
1126 return getSignExtendExpr(Op, Ty);
1128 // Peel off a truncate cast.
1129 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1130 const SCEV *NewOp = T->getOperand();
1131 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1132 return getAnyExtendExpr(NewOp, Ty);
1133 return getTruncateOrNoop(NewOp, Ty);
1136 // Next try a zext cast. If the cast is folded, use it.
1137 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1138 if (!isa<SCEVZeroExtendExpr>(ZExt))
1141 // Next try a sext cast. If the cast is folded, use it.
1142 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1143 if (!isa<SCEVSignExtendExpr>(SExt))
1146 // Force the cast to be folded into the operands of an addrec.
1147 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1148 SmallVector<const SCEV *, 4> Ops;
1149 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1151 Ops.push_back(getAnyExtendExpr(*I, Ty));
1152 return getAddRecExpr(Ops, AR->getLoop());
1155 // As a special case, fold anyext(undef) to undef. We don't want to
1156 // know too much about SCEVUnknowns, but this special case is handy
1158 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1159 if (isa<UndefValue>(U->getValue()))
1160 return getSCEV(UndefValue::get(Ty));
1162 // If the expression is obviously signed, use the sext cast value.
1163 if (isa<SCEVSMaxExpr>(Op))
1166 // Absent any other information, use the zext cast value.
1170 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1171 /// a list of operands to be added under the given scale, update the given
1172 /// map. This is a helper function for getAddRecExpr. As an example of
1173 /// what it does, given a sequence of operands that would form an add
1174 /// expression like this:
1176 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1178 /// where A and B are constants, update the map with these values:
1180 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1182 /// and add 13 + A*B*29 to AccumulatedConstant.
1183 /// This will allow getAddRecExpr to produce this:
1185 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1187 /// This form often exposes folding opportunities that are hidden in
1188 /// the original operand list.
1190 /// Return true iff it appears that any interesting folding opportunities
1191 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1192 /// the common case where no interesting opportunities are present, and
1193 /// is also used as a check to avoid infinite recursion.
1196 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1197 SmallVector<const SCEV *, 8> &NewOps,
1198 APInt &AccumulatedConstant,
1199 const SCEV *const *Ops, size_t NumOperands,
1201 ScalarEvolution &SE) {
1202 bool Interesting = false;
1204 // Iterate over the add operands. They are sorted, with constants first.
1206 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1208 // Pull a buried constant out to the outside.
1209 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1211 AccumulatedConstant += Scale * C->getValue()->getValue();
1214 // Next comes everything else. We're especially interested in multiplies
1215 // here, but they're in the middle, so just visit the rest with one loop.
1216 for (; i != NumOperands; ++i) {
1217 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1218 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1220 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1221 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1222 // A multiplication of a constant with another add; recurse.
1223 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1225 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1226 Add->op_begin(), Add->getNumOperands(),
1229 // A multiplication of a constant with some other value. Update
1231 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1232 const SCEV *Key = SE.getMulExpr(MulOps);
1233 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1234 M.insert(std::make_pair(Key, NewScale));
1236 NewOps.push_back(Pair.first->first);
1238 Pair.first->second += NewScale;
1239 // The map already had an entry for this value, which may indicate
1240 // a folding opportunity.
1245 // An ordinary operand. Update the map.
1246 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1247 M.insert(std::make_pair(Ops[i], Scale));
1249 NewOps.push_back(Pair.first->first);
1251 Pair.first->second += Scale;
1252 // The map already had an entry for this value, which may indicate
1253 // a folding opportunity.
1263 struct APIntCompare {
1264 bool operator()(const APInt &LHS, const APInt &RHS) const {
1265 return LHS.ult(RHS);
1270 /// getAddExpr - Get a canonical add expression, or something simpler if
1272 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1273 bool HasNUW, bool HasNSW) {
1274 assert(!Ops.empty() && "Cannot get empty add!");
1275 if (Ops.size() == 1) return Ops[0];
1277 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1278 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1279 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1280 "SCEVAddExpr operand types don't match!");
1283 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1284 if (!HasNUW && HasNSW) {
1286 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1287 E = Ops.end(); I != E; ++I)
1288 if (!isKnownNonNegative(*I)) {
1292 if (All) HasNUW = true;
1295 // Sort by complexity, this groups all similar expression types together.
1296 GroupByComplexity(Ops, LI);
1298 // If there are any constants, fold them together.
1300 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1302 assert(Idx < Ops.size());
1303 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1304 // We found two constants, fold them together!
1305 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1306 RHSC->getValue()->getValue());
1307 if (Ops.size() == 2) return Ops[0];
1308 Ops.erase(Ops.begin()+1); // Erase the folded element
1309 LHSC = cast<SCEVConstant>(Ops[0]);
1312 // If we are left with a constant zero being added, strip it off.
1313 if (LHSC->getValue()->isZero()) {
1314 Ops.erase(Ops.begin());
1318 if (Ops.size() == 1) return Ops[0];
1321 // Okay, check to see if the same value occurs in the operand list more than
1322 // once. If so, merge them together into an multiply expression. Since we
1323 // sorted the list, these values are required to be adjacent.
1324 const Type *Ty = Ops[0]->getType();
1325 bool FoundMatch = false;
1326 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1327 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1328 // Scan ahead to count how many equal operands there are.
1330 while (i+Count != e && Ops[i+Count] == Ops[i])
1332 // Merge the values into a multiply.
1333 const SCEV *Scale = getConstant(Ty, Count);
1334 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1335 if (Ops.size() == Count)
1338 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1339 --i; e -= Count - 1;
1343 return getAddExpr(Ops, HasNUW, HasNSW);
1345 // Check for truncates. If all the operands are truncated from the same
1346 // type, see if factoring out the truncate would permit the result to be
1347 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1348 // if the contents of the resulting outer trunc fold to something simple.
1349 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1350 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1351 const Type *DstType = Trunc->getType();
1352 const Type *SrcType = Trunc->getOperand()->getType();
1353 SmallVector<const SCEV *, 8> LargeOps;
1355 // Check all the operands to see if they can be represented in the
1356 // source type of the truncate.
1357 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1358 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1359 if (T->getOperand()->getType() != SrcType) {
1363 LargeOps.push_back(T->getOperand());
1364 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1365 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1366 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1367 SmallVector<const SCEV *, 8> LargeMulOps;
1368 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1369 if (const SCEVTruncateExpr *T =
1370 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1371 if (T->getOperand()->getType() != SrcType) {
1375 LargeMulOps.push_back(T->getOperand());
1376 } else if (const SCEVConstant *C =
1377 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1378 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1385 LargeOps.push_back(getMulExpr(LargeMulOps));
1392 // Evaluate the expression in the larger type.
1393 const SCEV *Fold = getAddExpr(LargeOps, HasNUW, HasNSW);
1394 // If it folds to something simple, use it. Otherwise, don't.
1395 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1396 return getTruncateExpr(Fold, DstType);
1400 // Skip past any other cast SCEVs.
1401 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1404 // If there are add operands they would be next.
1405 if (Idx < Ops.size()) {
1406 bool DeletedAdd = false;
1407 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1408 // If we have an add, expand the add operands onto the end of the operands
1410 Ops.erase(Ops.begin()+Idx);
1411 Ops.append(Add->op_begin(), Add->op_end());
1415 // If we deleted at least one add, we added operands to the end of the list,
1416 // and they are not necessarily sorted. Recurse to resort and resimplify
1417 // any operands we just acquired.
1419 return getAddExpr(Ops);
1422 // Skip over the add expression until we get to a multiply.
1423 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1426 // Check to see if there are any folding opportunities present with
1427 // operands multiplied by constant values.
1428 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1429 uint64_t BitWidth = getTypeSizeInBits(Ty);
1430 DenseMap<const SCEV *, APInt> M;
1431 SmallVector<const SCEV *, 8> NewOps;
1432 APInt AccumulatedConstant(BitWidth, 0);
1433 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1434 Ops.data(), Ops.size(),
1435 APInt(BitWidth, 1), *this)) {
1436 // Some interesting folding opportunity is present, so its worthwhile to
1437 // re-generate the operands list. Group the operands by constant scale,
1438 // to avoid multiplying by the same constant scale multiple times.
1439 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1440 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1441 E = NewOps.end(); I != E; ++I)
1442 MulOpLists[M.find(*I)->second].push_back(*I);
1443 // Re-generate the operands list.
1445 if (AccumulatedConstant != 0)
1446 Ops.push_back(getConstant(AccumulatedConstant));
1447 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1448 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1450 Ops.push_back(getMulExpr(getConstant(I->first),
1451 getAddExpr(I->second)));
1453 return getConstant(Ty, 0);
1454 if (Ops.size() == 1)
1456 return getAddExpr(Ops);
1460 // If we are adding something to a multiply expression, make sure the
1461 // something is not already an operand of the multiply. If so, merge it into
1463 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1464 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1465 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1466 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1467 if (isa<SCEVConstant>(MulOpSCEV))
1469 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1470 if (MulOpSCEV == Ops[AddOp]) {
1471 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1472 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1473 if (Mul->getNumOperands() != 2) {
1474 // If the multiply has more than two operands, we must get the
1476 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1477 Mul->op_begin()+MulOp);
1478 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1479 InnerMul = getMulExpr(MulOps);
1481 const SCEV *One = getConstant(Ty, 1);
1482 const SCEV *AddOne = getAddExpr(One, InnerMul);
1483 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1484 if (Ops.size() == 2) return OuterMul;
1486 Ops.erase(Ops.begin()+AddOp);
1487 Ops.erase(Ops.begin()+Idx-1);
1489 Ops.erase(Ops.begin()+Idx);
1490 Ops.erase(Ops.begin()+AddOp-1);
1492 Ops.push_back(OuterMul);
1493 return getAddExpr(Ops);
1496 // Check this multiply against other multiplies being added together.
1497 for (unsigned OtherMulIdx = Idx+1;
1498 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1500 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1501 // If MulOp occurs in OtherMul, we can fold the two multiplies
1503 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1504 OMulOp != e; ++OMulOp)
1505 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1506 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1507 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1508 if (Mul->getNumOperands() != 2) {
1509 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1510 Mul->op_begin()+MulOp);
1511 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1512 InnerMul1 = getMulExpr(MulOps);
1514 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1515 if (OtherMul->getNumOperands() != 2) {
1516 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1517 OtherMul->op_begin()+OMulOp);
1518 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1519 InnerMul2 = getMulExpr(MulOps);
1521 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1522 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1523 if (Ops.size() == 2) return OuterMul;
1524 Ops.erase(Ops.begin()+Idx);
1525 Ops.erase(Ops.begin()+OtherMulIdx-1);
1526 Ops.push_back(OuterMul);
1527 return getAddExpr(Ops);
1533 // If there are any add recurrences in the operands list, see if any other
1534 // added values are loop invariant. If so, we can fold them into the
1536 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1539 // Scan over all recurrences, trying to fold loop invariants into them.
1540 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1541 // Scan all of the other operands to this add and add them to the vector if
1542 // they are loop invariant w.r.t. the recurrence.
1543 SmallVector<const SCEV *, 8> LIOps;
1544 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1545 const Loop *AddRecLoop = AddRec->getLoop();
1546 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1547 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1548 LIOps.push_back(Ops[i]);
1549 Ops.erase(Ops.begin()+i);
1553 // If we found some loop invariants, fold them into the recurrence.
1554 if (!LIOps.empty()) {
1555 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1556 LIOps.push_back(AddRec->getStart());
1558 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1560 AddRecOps[0] = getAddExpr(LIOps);
1562 // Build the new addrec. Propagate the NUW and NSW flags if both the
1563 // outer add and the inner addrec are guaranteed to have no overflow.
1564 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop,
1565 HasNUW && AddRec->hasNoUnsignedWrap(),
1566 HasNSW && AddRec->hasNoSignedWrap());
1568 // If all of the other operands were loop invariant, we are done.
1569 if (Ops.size() == 1) return NewRec;
1571 // Otherwise, add the folded AddRec by the non-liv parts.
1572 for (unsigned i = 0;; ++i)
1573 if (Ops[i] == AddRec) {
1577 return getAddExpr(Ops);
1580 // Okay, if there weren't any loop invariants to be folded, check to see if
1581 // there are multiple AddRec's with the same loop induction variable being
1582 // added together. If so, we can fold them.
1583 for (unsigned OtherIdx = Idx+1;
1584 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1586 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1587 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1588 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1590 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1592 if (const SCEVAddRecExpr *OtherAddRec =
1593 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1594 if (OtherAddRec->getLoop() == AddRecLoop) {
1595 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1597 if (i >= AddRecOps.size()) {
1598 AddRecOps.append(OtherAddRec->op_begin()+i,
1599 OtherAddRec->op_end());
1602 AddRecOps[i] = getAddExpr(AddRecOps[i],
1603 OtherAddRec->getOperand(i));
1605 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1607 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop);
1608 return getAddExpr(Ops);
1611 // Otherwise couldn't fold anything into this recurrence. Move onto the
1615 // Okay, it looks like we really DO need an add expr. Check to see if we
1616 // already have one, otherwise create a new one.
1617 FoldingSetNodeID ID;
1618 ID.AddInteger(scAddExpr);
1619 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1620 ID.AddPointer(Ops[i]);
1623 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1625 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1626 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1627 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1629 UniqueSCEVs.InsertNode(S, IP);
1631 if (HasNUW) S->setHasNoUnsignedWrap(true);
1632 if (HasNSW) S->setHasNoSignedWrap(true);
1636 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1638 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1639 bool HasNUW, bool HasNSW) {
1640 assert(!Ops.empty() && "Cannot get empty mul!");
1641 if (Ops.size() == 1) return Ops[0];
1643 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1644 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1645 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1646 "SCEVMulExpr operand types don't match!");
1649 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1650 if (!HasNUW && HasNSW) {
1652 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1653 E = Ops.end(); I != E; ++I)
1654 if (!isKnownNonNegative(*I)) {
1658 if (All) HasNUW = true;
1661 // Sort by complexity, this groups all similar expression types together.
1662 GroupByComplexity(Ops, LI);
1664 // If there are any constants, fold them together.
1666 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1668 // C1*(C2+V) -> C1*C2 + C1*V
1669 if (Ops.size() == 2)
1670 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1671 if (Add->getNumOperands() == 2 &&
1672 isa<SCEVConstant>(Add->getOperand(0)))
1673 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1674 getMulExpr(LHSC, Add->getOperand(1)));
1677 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1678 // We found two constants, fold them together!
1679 ConstantInt *Fold = ConstantInt::get(getContext(),
1680 LHSC->getValue()->getValue() *
1681 RHSC->getValue()->getValue());
1682 Ops[0] = getConstant(Fold);
1683 Ops.erase(Ops.begin()+1); // Erase the folded element
1684 if (Ops.size() == 1) return Ops[0];
1685 LHSC = cast<SCEVConstant>(Ops[0]);
1688 // If we are left with a constant one being multiplied, strip it off.
1689 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1690 Ops.erase(Ops.begin());
1692 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1693 // If we have a multiply of zero, it will always be zero.
1695 } else if (Ops[0]->isAllOnesValue()) {
1696 // If we have a mul by -1 of an add, try distributing the -1 among the
1698 if (Ops.size() == 2)
1699 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1700 SmallVector<const SCEV *, 4> NewOps;
1701 bool AnyFolded = false;
1702 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
1704 const SCEV *Mul = getMulExpr(Ops[0], *I);
1705 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1706 NewOps.push_back(Mul);
1709 return getAddExpr(NewOps);
1713 if (Ops.size() == 1)
1717 // Skip over the add expression until we get to a multiply.
1718 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1721 // If there are mul operands inline them all into this expression.
1722 if (Idx < Ops.size()) {
1723 bool DeletedMul = false;
1724 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1725 // If we have an mul, expand the mul operands onto the end of the operands
1727 Ops.erase(Ops.begin()+Idx);
1728 Ops.append(Mul->op_begin(), Mul->op_end());
1732 // If we deleted at least one mul, we added operands to the end of the list,
1733 // and they are not necessarily sorted. Recurse to resort and resimplify
1734 // any operands we just acquired.
1736 return getMulExpr(Ops);
1739 // If there are any add recurrences in the operands list, see if any other
1740 // added values are loop invariant. If so, we can fold them into the
1742 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1745 // Scan over all recurrences, trying to fold loop invariants into them.
1746 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1747 // Scan all of the other operands to this mul and add them to the vector if
1748 // they are loop invariant w.r.t. the recurrence.
1749 SmallVector<const SCEV *, 8> LIOps;
1750 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1751 const Loop *AddRecLoop = AddRec->getLoop();
1752 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1753 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1754 LIOps.push_back(Ops[i]);
1755 Ops.erase(Ops.begin()+i);
1759 // If we found some loop invariants, fold them into the recurrence.
1760 if (!LIOps.empty()) {
1761 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1762 SmallVector<const SCEV *, 4> NewOps;
1763 NewOps.reserve(AddRec->getNumOperands());
1764 const SCEV *Scale = getMulExpr(LIOps);
1765 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1766 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1768 // Build the new addrec. Propagate the NUW and NSW flags if both the
1769 // outer mul and the inner addrec are guaranteed to have no overflow.
1770 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop,
1771 HasNUW && AddRec->hasNoUnsignedWrap(),
1772 HasNSW && AddRec->hasNoSignedWrap());
1774 // If all of the other operands were loop invariant, we are done.
1775 if (Ops.size() == 1) return NewRec;
1777 // Otherwise, multiply the folded AddRec by the non-liv parts.
1778 for (unsigned i = 0;; ++i)
1779 if (Ops[i] == AddRec) {
1783 return getMulExpr(Ops);
1786 // Okay, if there weren't any loop invariants to be folded, check to see if
1787 // there are multiple AddRec's with the same loop induction variable being
1788 // multiplied together. If so, we can fold them.
1789 for (unsigned OtherIdx = Idx+1;
1790 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1792 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1793 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> -->
1794 // {A*C,+,F*D + G*B + B*D}<L>
1795 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1797 if (const SCEVAddRecExpr *OtherAddRec =
1798 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1799 if (OtherAddRec->getLoop() == AddRecLoop) {
1800 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1801 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1802 const SCEV *B = F->getStepRecurrence(*this);
1803 const SCEV *D = G->getStepRecurrence(*this);
1804 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1807 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1809 if (Ops.size() == 2) return NewAddRec;
1810 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
1811 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1813 return getMulExpr(Ops);
1816 // Otherwise couldn't fold anything into this recurrence. Move onto the
1820 // Okay, it looks like we really DO need an mul expr. Check to see if we
1821 // already have one, otherwise create a new one.
1822 FoldingSetNodeID ID;
1823 ID.AddInteger(scMulExpr);
1824 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1825 ID.AddPointer(Ops[i]);
1828 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1830 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1831 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1832 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1834 UniqueSCEVs.InsertNode(S, IP);
1836 if (HasNUW) S->setHasNoUnsignedWrap(true);
1837 if (HasNSW) S->setHasNoSignedWrap(true);
1841 /// getUDivExpr - Get a canonical unsigned division expression, or something
1842 /// simpler if possible.
1843 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1845 assert(getEffectiveSCEVType(LHS->getType()) ==
1846 getEffectiveSCEVType(RHS->getType()) &&
1847 "SCEVUDivExpr operand types don't match!");
1849 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1850 if (RHSC->getValue()->equalsInt(1))
1851 return LHS; // X udiv 1 --> x
1852 // If the denominator is zero, the result of the udiv is undefined. Don't
1853 // try to analyze it, because the resolution chosen here may differ from
1854 // the resolution chosen in other parts of the compiler.
1855 if (!RHSC->getValue()->isZero()) {
1856 // Determine if the division can be folded into the operands of
1858 // TODO: Generalize this to non-constants by using known-bits information.
1859 const Type *Ty = LHS->getType();
1860 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1861 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1862 // For non-power-of-two values, effectively round the value up to the
1863 // nearest power of two.
1864 if (!RHSC->getValue()->getValue().isPowerOf2())
1866 const IntegerType *ExtTy =
1867 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1868 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1869 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1870 if (const SCEVConstant *Step =
1871 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1872 if (!Step->getValue()->getValue()
1873 .urem(RHSC->getValue()->getValue()) &&
1874 getZeroExtendExpr(AR, ExtTy) ==
1875 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1876 getZeroExtendExpr(Step, ExtTy),
1878 SmallVector<const SCEV *, 4> Operands;
1879 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1880 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1881 return getAddRecExpr(Operands, AR->getLoop());
1883 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1884 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1885 SmallVector<const SCEV *, 4> Operands;
1886 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1887 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1888 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1889 // Find an operand that's safely divisible.
1890 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1891 const SCEV *Op = M->getOperand(i);
1892 const SCEV *Div = getUDivExpr(Op, RHSC);
1893 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1894 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
1897 return getMulExpr(Operands);
1901 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1902 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1903 SmallVector<const SCEV *, 4> Operands;
1904 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1905 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1906 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1908 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1909 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1910 if (isa<SCEVUDivExpr>(Op) ||
1911 getMulExpr(Op, RHS) != A->getOperand(i))
1913 Operands.push_back(Op);
1915 if (Operands.size() == A->getNumOperands())
1916 return getAddExpr(Operands);
1920 // Fold if both operands are constant.
1921 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1922 Constant *LHSCV = LHSC->getValue();
1923 Constant *RHSCV = RHSC->getValue();
1924 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1930 FoldingSetNodeID ID;
1931 ID.AddInteger(scUDivExpr);
1935 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1936 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
1938 UniqueSCEVs.InsertNode(S, IP);
1943 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1944 /// Simplify the expression as much as possible.
1945 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1946 const SCEV *Step, const Loop *L,
1947 bool HasNUW, bool HasNSW) {
1948 SmallVector<const SCEV *, 4> Operands;
1949 Operands.push_back(Start);
1950 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1951 if (StepChrec->getLoop() == L) {
1952 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
1953 return getAddRecExpr(Operands, L);
1956 Operands.push_back(Step);
1957 return getAddRecExpr(Operands, L, HasNUW, HasNSW);
1960 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1961 /// Simplify the expression as much as possible.
1963 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1965 bool HasNUW, bool HasNSW) {
1966 if (Operands.size() == 1) return Operands[0];
1968 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
1969 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1970 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
1971 "SCEVAddRecExpr operand types don't match!");
1972 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1973 assert(isLoopInvariant(Operands[i], L) &&
1974 "SCEVAddRecExpr operand is not loop-invariant!");
1977 if (Operands.back()->isZero()) {
1978 Operands.pop_back();
1979 return getAddRecExpr(Operands, L, HasNUW, HasNSW); // {X,+,0} --> X
1982 // It's tempting to want to call getMaxBackedgeTakenCount count here and
1983 // use that information to infer NUW and NSW flags. However, computing a
1984 // BE count requires calling getAddRecExpr, so we may not yet have a
1985 // meaningful BE count at this point (and if we don't, we'd be stuck
1986 // with a SCEVCouldNotCompute as the cached BE count).
1988 // If HasNSW is true and all the operands are non-negative, infer HasNUW.
1989 if (!HasNUW && HasNSW) {
1991 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
1992 E = Operands.end(); I != E; ++I)
1993 if (!isKnownNonNegative(*I)) {
1997 if (All) HasNUW = true;
2000 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2001 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2002 const Loop *NestedLoop = NestedAR->getLoop();
2003 if (L->contains(NestedLoop) ?
2004 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2005 (!NestedLoop->contains(L) &&
2006 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2007 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2008 NestedAR->op_end());
2009 Operands[0] = NestedAR->getStart();
2010 // AddRecs require their operands be loop-invariant with respect to their
2011 // loops. Don't perform this transformation if it would break this
2013 bool AllInvariant = true;
2014 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2015 if (!isLoopInvariant(Operands[i], L)) {
2016 AllInvariant = false;
2020 NestedOperands[0] = getAddRecExpr(Operands, L);
2021 AllInvariant = true;
2022 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2023 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2024 AllInvariant = false;
2028 // Ok, both add recurrences are valid after the transformation.
2029 return getAddRecExpr(NestedOperands, NestedLoop, HasNUW, HasNSW);
2031 // Reset Operands to its original state.
2032 Operands[0] = NestedAR;
2036 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2037 // already have one, otherwise create a new one.
2038 FoldingSetNodeID ID;
2039 ID.AddInteger(scAddRecExpr);
2040 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2041 ID.AddPointer(Operands[i]);
2045 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2047 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2048 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2049 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2050 O, Operands.size(), L);
2051 UniqueSCEVs.InsertNode(S, IP);
2053 if (HasNUW) S->setHasNoUnsignedWrap(true);
2054 if (HasNSW) S->setHasNoSignedWrap(true);
2058 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2060 SmallVector<const SCEV *, 2> Ops;
2063 return getSMaxExpr(Ops);
2067 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2068 assert(!Ops.empty() && "Cannot get empty smax!");
2069 if (Ops.size() == 1) return Ops[0];
2071 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2072 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2073 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2074 "SCEVSMaxExpr operand types don't match!");
2077 // Sort by complexity, this groups all similar expression types together.
2078 GroupByComplexity(Ops, LI);
2080 // If there are any constants, fold them together.
2082 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2084 assert(Idx < Ops.size());
2085 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2086 // We found two constants, fold them together!
2087 ConstantInt *Fold = ConstantInt::get(getContext(),
2088 APIntOps::smax(LHSC->getValue()->getValue(),
2089 RHSC->getValue()->getValue()));
2090 Ops[0] = getConstant(Fold);
2091 Ops.erase(Ops.begin()+1); // Erase the folded element
2092 if (Ops.size() == 1) return Ops[0];
2093 LHSC = cast<SCEVConstant>(Ops[0]);
2096 // If we are left with a constant minimum-int, strip it off.
2097 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2098 Ops.erase(Ops.begin());
2100 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2101 // If we have an smax with a constant maximum-int, it will always be
2106 if (Ops.size() == 1) return Ops[0];
2109 // Find the first SMax
2110 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2113 // Check to see if one of the operands is an SMax. If so, expand its operands
2114 // onto our operand list, and recurse to simplify.
2115 if (Idx < Ops.size()) {
2116 bool DeletedSMax = false;
2117 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2118 Ops.erase(Ops.begin()+Idx);
2119 Ops.append(SMax->op_begin(), SMax->op_end());
2124 return getSMaxExpr(Ops);
2127 // Okay, check to see if the same value occurs in the operand list twice. If
2128 // so, delete one. Since we sorted the list, these values are required to
2130 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2131 // X smax Y smax Y --> X smax Y
2132 // X smax Y --> X, if X is always greater than Y
2133 if (Ops[i] == Ops[i+1] ||
2134 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2135 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2137 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2138 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2142 if (Ops.size() == 1) return Ops[0];
2144 assert(!Ops.empty() && "Reduced smax down to nothing!");
2146 // Okay, it looks like we really DO need an smax expr. Check to see if we
2147 // already have one, otherwise create a new one.
2148 FoldingSetNodeID ID;
2149 ID.AddInteger(scSMaxExpr);
2150 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2151 ID.AddPointer(Ops[i]);
2153 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2154 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2155 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2156 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2158 UniqueSCEVs.InsertNode(S, IP);
2162 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2164 SmallVector<const SCEV *, 2> Ops;
2167 return getUMaxExpr(Ops);
2171 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2172 assert(!Ops.empty() && "Cannot get empty umax!");
2173 if (Ops.size() == 1) return Ops[0];
2175 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2176 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2177 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2178 "SCEVUMaxExpr operand types don't match!");
2181 // Sort by complexity, this groups all similar expression types together.
2182 GroupByComplexity(Ops, LI);
2184 // If there are any constants, fold them together.
2186 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2188 assert(Idx < Ops.size());
2189 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2190 // We found two constants, fold them together!
2191 ConstantInt *Fold = ConstantInt::get(getContext(),
2192 APIntOps::umax(LHSC->getValue()->getValue(),
2193 RHSC->getValue()->getValue()));
2194 Ops[0] = getConstant(Fold);
2195 Ops.erase(Ops.begin()+1); // Erase the folded element
2196 if (Ops.size() == 1) return Ops[0];
2197 LHSC = cast<SCEVConstant>(Ops[0]);
2200 // If we are left with a constant minimum-int, strip it off.
2201 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2202 Ops.erase(Ops.begin());
2204 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2205 // If we have an umax with a constant maximum-int, it will always be
2210 if (Ops.size() == 1) return Ops[0];
2213 // Find the first UMax
2214 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2217 // Check to see if one of the operands is a UMax. If so, expand its operands
2218 // onto our operand list, and recurse to simplify.
2219 if (Idx < Ops.size()) {
2220 bool DeletedUMax = false;
2221 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2222 Ops.erase(Ops.begin()+Idx);
2223 Ops.append(UMax->op_begin(), UMax->op_end());
2228 return getUMaxExpr(Ops);
2231 // Okay, check to see if the same value occurs in the operand list twice. If
2232 // so, delete one. Since we sorted the list, these values are required to
2234 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2235 // X umax Y umax Y --> X umax Y
2236 // X umax Y --> X, if X is always greater than Y
2237 if (Ops[i] == Ops[i+1] ||
2238 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2239 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2241 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2242 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2246 if (Ops.size() == 1) return Ops[0];
2248 assert(!Ops.empty() && "Reduced umax down to nothing!");
2250 // Okay, it looks like we really DO need a umax expr. Check to see if we
2251 // already have one, otherwise create a new one.
2252 FoldingSetNodeID ID;
2253 ID.AddInteger(scUMaxExpr);
2254 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2255 ID.AddPointer(Ops[i]);
2257 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2258 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2259 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2260 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2262 UniqueSCEVs.InsertNode(S, IP);
2266 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2268 // ~smax(~x, ~y) == smin(x, y).
2269 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2272 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2274 // ~umax(~x, ~y) == umin(x, y)
2275 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2278 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2279 // If we have TargetData, we can bypass creating a target-independent
2280 // constant expression and then folding it back into a ConstantInt.
2281 // This is just a compile-time optimization.
2283 return getConstant(TD->getIntPtrType(getContext()),
2284 TD->getTypeAllocSize(AllocTy));
2286 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2287 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2288 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2290 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2291 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2294 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2295 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2296 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2297 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2299 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2300 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2303 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2305 // If we have TargetData, we can bypass creating a target-independent
2306 // constant expression and then folding it back into a ConstantInt.
2307 // This is just a compile-time optimization.
2309 return getConstant(TD->getIntPtrType(getContext()),
2310 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2312 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2313 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2314 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2316 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2317 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2320 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2321 Constant *FieldNo) {
2322 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2323 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2324 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2326 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2327 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2330 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2331 // Don't attempt to do anything other than create a SCEVUnknown object
2332 // here. createSCEV only calls getUnknown after checking for all other
2333 // interesting possibilities, and any other code that calls getUnknown
2334 // is doing so in order to hide a value from SCEV canonicalization.
2336 FoldingSetNodeID ID;
2337 ID.AddInteger(scUnknown);
2340 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2341 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2342 "Stale SCEVUnknown in uniquing map!");
2345 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2347 FirstUnknown = cast<SCEVUnknown>(S);
2348 UniqueSCEVs.InsertNode(S, IP);
2352 //===----------------------------------------------------------------------===//
2353 // Basic SCEV Analysis and PHI Idiom Recognition Code
2356 /// isSCEVable - Test if values of the given type are analyzable within
2357 /// the SCEV framework. This primarily includes integer types, and it
2358 /// can optionally include pointer types if the ScalarEvolution class
2359 /// has access to target-specific information.
2360 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2361 // Integers and pointers are always SCEVable.
2362 return Ty->isIntegerTy() || Ty->isPointerTy();
2365 /// getTypeSizeInBits - Return the size in bits of the specified type,
2366 /// for which isSCEVable must return true.
2367 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2368 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2370 // If we have a TargetData, use it!
2372 return TD->getTypeSizeInBits(Ty);
2374 // Integer types have fixed sizes.
2375 if (Ty->isIntegerTy())
2376 return Ty->getPrimitiveSizeInBits();
2378 // The only other support type is pointer. Without TargetData, conservatively
2379 // assume pointers are 64-bit.
2380 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2384 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2385 /// the given type and which represents how SCEV will treat the given
2386 /// type, for which isSCEVable must return true. For pointer types,
2387 /// this is the pointer-sized integer type.
2388 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2389 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2391 if (Ty->isIntegerTy())
2394 // The only other support type is pointer.
2395 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2396 if (TD) return TD->getIntPtrType(getContext());
2398 // Without TargetData, conservatively assume pointers are 64-bit.
2399 return Type::getInt64Ty(getContext());
2402 const SCEV *ScalarEvolution::getCouldNotCompute() {
2403 return &CouldNotCompute;
2406 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2407 /// expression and create a new one.
2408 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2409 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2411 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2412 if (I != ValueExprMap.end()) return I->second;
2413 const SCEV *S = createSCEV(V);
2415 // The process of creating a SCEV for V may have caused other SCEVs
2416 // to have been created, so it's necessary to insert the new entry
2417 // from scratch, rather than trying to remember the insert position
2419 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2423 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2425 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2426 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2428 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2430 const Type *Ty = V->getType();
2431 Ty = getEffectiveSCEVType(Ty);
2432 return getMulExpr(V,
2433 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2436 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2437 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2438 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2440 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2442 const Type *Ty = V->getType();
2443 Ty = getEffectiveSCEVType(Ty);
2444 const SCEV *AllOnes =
2445 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2446 return getMinusSCEV(AllOnes, V);
2449 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2451 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2452 bool HasNUW, bool HasNSW) {
2453 // Fast path: X - X --> 0.
2455 return getConstant(LHS->getType(), 0);
2458 return getAddExpr(LHS, getNegativeSCEV(RHS), HasNUW, HasNSW);
2461 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2462 /// input value to the specified type. If the type must be extended, it is zero
2465 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) {
2466 const Type *SrcTy = V->getType();
2467 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2468 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2469 "Cannot truncate or zero extend with non-integer arguments!");
2470 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2471 return V; // No conversion
2472 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2473 return getTruncateExpr(V, Ty);
2474 return getZeroExtendExpr(V, Ty);
2477 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2478 /// input value to the specified type. If the type must be extended, it is sign
2481 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2483 const Type *SrcTy = V->getType();
2484 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2485 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2486 "Cannot truncate or zero extend with non-integer arguments!");
2487 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2488 return V; // No conversion
2489 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2490 return getTruncateExpr(V, Ty);
2491 return getSignExtendExpr(V, Ty);
2494 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2495 /// input value to the specified type. If the type must be extended, it is zero
2496 /// extended. The conversion must not be narrowing.
2498 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2499 const Type *SrcTy = V->getType();
2500 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2501 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2502 "Cannot noop or zero extend with non-integer arguments!");
2503 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2504 "getNoopOrZeroExtend cannot truncate!");
2505 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2506 return V; // No conversion
2507 return getZeroExtendExpr(V, Ty);
2510 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2511 /// input value to the specified type. If the type must be extended, it is sign
2512 /// extended. The conversion must not be narrowing.
2514 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2515 const Type *SrcTy = V->getType();
2516 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2517 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2518 "Cannot noop or sign extend with non-integer arguments!");
2519 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2520 "getNoopOrSignExtend cannot truncate!");
2521 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2522 return V; // No conversion
2523 return getSignExtendExpr(V, Ty);
2526 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2527 /// the input value to the specified type. If the type must be extended,
2528 /// it is extended with unspecified bits. The conversion must not be
2531 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2532 const Type *SrcTy = V->getType();
2533 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2534 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2535 "Cannot noop or any extend with non-integer arguments!");
2536 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2537 "getNoopOrAnyExtend cannot truncate!");
2538 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2539 return V; // No conversion
2540 return getAnyExtendExpr(V, Ty);
2543 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2544 /// input value to the specified type. The conversion must not be widening.
2546 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2547 const Type *SrcTy = V->getType();
2548 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2549 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2550 "Cannot truncate or noop with non-integer arguments!");
2551 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2552 "getTruncateOrNoop cannot extend!");
2553 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2554 return V; // No conversion
2555 return getTruncateExpr(V, Ty);
2558 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2559 /// the types using zero-extension, and then perform a umax operation
2561 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2563 const SCEV *PromotedLHS = LHS;
2564 const SCEV *PromotedRHS = RHS;
2566 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2567 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2569 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2571 return getUMaxExpr(PromotedLHS, PromotedRHS);
2574 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2575 /// the types using zero-extension, and then perform a umin operation
2577 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2579 const SCEV *PromotedLHS = LHS;
2580 const SCEV *PromotedRHS = RHS;
2582 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2583 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2585 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2587 return getUMinExpr(PromotedLHS, PromotedRHS);
2590 /// PushDefUseChildren - Push users of the given Instruction
2591 /// onto the given Worklist.
2593 PushDefUseChildren(Instruction *I,
2594 SmallVectorImpl<Instruction *> &Worklist) {
2595 // Push the def-use children onto the Worklist stack.
2596 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2598 Worklist.push_back(cast<Instruction>(*UI));
2601 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2602 /// instructions that depend on the given instruction and removes them from
2603 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2606 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2607 SmallVector<Instruction *, 16> Worklist;
2608 PushDefUseChildren(PN, Worklist);
2610 SmallPtrSet<Instruction *, 8> Visited;
2612 while (!Worklist.empty()) {
2613 Instruction *I = Worklist.pop_back_val();
2614 if (!Visited.insert(I)) continue;
2616 ValueExprMapType::iterator It =
2617 ValueExprMap.find(static_cast<Value *>(I));
2618 if (It != ValueExprMap.end()) {
2619 const SCEV *Old = It->second;
2621 // Short-circuit the def-use traversal if the symbolic name
2622 // ceases to appear in expressions.
2623 if (Old != SymName && !hasOperand(Old, SymName))
2626 // SCEVUnknown for a PHI either means that it has an unrecognized
2627 // structure, it's a PHI that's in the progress of being computed
2628 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2629 // additional loop trip count information isn't going to change anything.
2630 // In the second case, createNodeForPHI will perform the necessary
2631 // updates on its own when it gets to that point. In the third, we do
2632 // want to forget the SCEVUnknown.
2633 if (!isa<PHINode>(I) ||
2634 !isa<SCEVUnknown>(Old) ||
2635 (I != PN && Old == SymName)) {
2636 forgetMemoizedResults(Old);
2637 ValueExprMap.erase(It);
2641 PushDefUseChildren(I, Worklist);
2645 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2646 /// a loop header, making it a potential recurrence, or it doesn't.
2648 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2649 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2650 if (L->getHeader() == PN->getParent()) {
2651 // The loop may have multiple entrances or multiple exits; we can analyze
2652 // this phi as an addrec if it has a unique entry value and a unique
2654 Value *BEValueV = 0, *StartValueV = 0;
2655 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2656 Value *V = PN->getIncomingValue(i);
2657 if (L->contains(PN->getIncomingBlock(i))) {
2660 } else if (BEValueV != V) {
2664 } else if (!StartValueV) {
2666 } else if (StartValueV != V) {
2671 if (BEValueV && StartValueV) {
2672 // While we are analyzing this PHI node, handle its value symbolically.
2673 const SCEV *SymbolicName = getUnknown(PN);
2674 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2675 "PHI node already processed?");
2676 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2678 // Using this symbolic name for the PHI, analyze the value coming around
2680 const SCEV *BEValue = getSCEV(BEValueV);
2682 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2683 // has a special value for the first iteration of the loop.
2685 // If the value coming around the backedge is an add with the symbolic
2686 // value we just inserted, then we found a simple induction variable!
2687 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2688 // If there is a single occurrence of the symbolic value, replace it
2689 // with a recurrence.
2690 unsigned FoundIndex = Add->getNumOperands();
2691 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2692 if (Add->getOperand(i) == SymbolicName)
2693 if (FoundIndex == e) {
2698 if (FoundIndex != Add->getNumOperands()) {
2699 // Create an add with everything but the specified operand.
2700 SmallVector<const SCEV *, 8> Ops;
2701 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2702 if (i != FoundIndex)
2703 Ops.push_back(Add->getOperand(i));
2704 const SCEV *Accum = getAddExpr(Ops);
2706 // This is not a valid addrec if the step amount is varying each
2707 // loop iteration, but is not itself an addrec in this loop.
2708 if (isLoopInvariant(Accum, L) ||
2709 (isa<SCEVAddRecExpr>(Accum) &&
2710 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2711 bool HasNUW = false;
2712 bool HasNSW = false;
2714 // If the increment doesn't overflow, then neither the addrec nor
2715 // the post-increment will overflow.
2716 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2717 if (OBO->hasNoUnsignedWrap())
2719 if (OBO->hasNoSignedWrap())
2721 } else if (isa<GEPOperator>(BEValueV)) {
2722 // If the increment is a GEP, then we know it won't perform an
2723 // unsigned overflow, because the address space cannot be
2728 const SCEV *StartVal = getSCEV(StartValueV);
2729 const SCEV *PHISCEV =
2730 getAddRecExpr(StartVal, Accum, L, HasNUW, HasNSW);
2732 // Since the no-wrap flags are on the increment, they apply to the
2733 // post-incremented value as well.
2734 if (isLoopInvariant(Accum, L))
2735 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2736 Accum, L, HasNUW, HasNSW);
2738 // Okay, for the entire analysis of this edge we assumed the PHI
2739 // to be symbolic. We now need to go back and purge all of the
2740 // entries for the scalars that use the symbolic expression.
2741 ForgetSymbolicName(PN, SymbolicName);
2742 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2746 } else if (const SCEVAddRecExpr *AddRec =
2747 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2748 // Otherwise, this could be a loop like this:
2749 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2750 // In this case, j = {1,+,1} and BEValue is j.
2751 // Because the other in-value of i (0) fits the evolution of BEValue
2752 // i really is an addrec evolution.
2753 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2754 const SCEV *StartVal = getSCEV(StartValueV);
2756 // If StartVal = j.start - j.stride, we can use StartVal as the
2757 // initial step of the addrec evolution.
2758 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2759 AddRec->getOperand(1))) {
2760 const SCEV *PHISCEV =
2761 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2763 // Okay, for the entire analysis of this edge we assumed the PHI
2764 // to be symbolic. We now need to go back and purge all of the
2765 // entries for the scalars that use the symbolic expression.
2766 ForgetSymbolicName(PN, SymbolicName);
2767 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2775 // If the PHI has a single incoming value, follow that value, unless the
2776 // PHI's incoming blocks are in a different loop, in which case doing so
2777 // risks breaking LCSSA form. Instcombine would normally zap these, but
2778 // it doesn't have DominatorTree information, so it may miss cases.
2779 if (Value *V = SimplifyInstruction(PN, TD, DT))
2780 if (LI->replacementPreservesLCSSAForm(PN, V))
2783 // If it's not a loop phi, we can't handle it yet.
2784 return getUnknown(PN);
2787 /// createNodeForGEP - Expand GEP instructions into add and multiply
2788 /// operations. This allows them to be analyzed by regular SCEV code.
2790 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2792 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2793 // Add expression, because the Instruction may be guarded by control flow
2794 // and the no-overflow bits may not be valid for the expression in any
2797 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2798 Value *Base = GEP->getOperand(0);
2799 // Don't attempt to analyze GEPs over unsized objects.
2800 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2801 return getUnknown(GEP);
2802 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2803 gep_type_iterator GTI = gep_type_begin(GEP);
2804 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2808 // Compute the (potentially symbolic) offset in bytes for this index.
2809 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2810 // For a struct, add the member offset.
2811 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2812 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2814 // Add the field offset to the running total offset.
2815 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2817 // For an array, add the element offset, explicitly scaled.
2818 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2819 const SCEV *IndexS = getSCEV(Index);
2820 // Getelementptr indices are signed.
2821 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2823 // Multiply the index by the element size to compute the element offset.
2824 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize);
2826 // Add the element offset to the running total offset.
2827 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2831 // Get the SCEV for the GEP base.
2832 const SCEV *BaseS = getSCEV(Base);
2834 // Add the total offset from all the GEP indices to the base.
2835 return getAddExpr(BaseS, TotalOffset);
2838 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2839 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2840 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2841 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2843 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2844 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2845 return C->getValue()->getValue().countTrailingZeros();
2847 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2848 return std::min(GetMinTrailingZeros(T->getOperand()),
2849 (uint32_t)getTypeSizeInBits(T->getType()));
2851 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2852 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2853 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2854 getTypeSizeInBits(E->getType()) : OpRes;
2857 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2858 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2859 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2860 getTypeSizeInBits(E->getType()) : OpRes;
2863 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2864 // The result is the min of all operands results.
2865 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2866 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2867 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2871 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2872 // The result is the sum of all operands results.
2873 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2874 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2875 for (unsigned i = 1, e = M->getNumOperands();
2876 SumOpRes != BitWidth && i != e; ++i)
2877 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2882 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2883 // The result is the min of all operands results.
2884 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2885 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2886 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2890 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2891 // The result is the min of all operands results.
2892 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2893 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2894 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2898 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2899 // The result is the min of all operands results.
2900 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2901 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2902 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2906 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2907 // For a SCEVUnknown, ask ValueTracking.
2908 unsigned BitWidth = getTypeSizeInBits(U->getType());
2909 APInt Mask = APInt::getAllOnesValue(BitWidth);
2910 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2911 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2912 return Zeros.countTrailingOnes();
2919 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2922 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2923 // See if we've computed this range already.
2924 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
2925 if (I != UnsignedRanges.end())
2928 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2929 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
2931 unsigned BitWidth = getTypeSizeInBits(S->getType());
2932 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
2934 // If the value has known zeros, the maximum unsigned value will have those
2935 // known zeros as well.
2936 uint32_t TZ = GetMinTrailingZeros(S);
2938 ConservativeResult =
2939 ConstantRange(APInt::getMinValue(BitWidth),
2940 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
2942 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2943 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2944 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2945 X = X.add(getUnsignedRange(Add->getOperand(i)));
2946 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
2949 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2950 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2951 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2952 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2953 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
2956 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2957 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2958 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2959 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2960 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
2963 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2964 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2965 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2966 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2967 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
2970 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2971 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2972 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2973 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
2976 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2977 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2978 return setUnsignedRange(ZExt,
2979 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
2982 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2983 ConstantRange X = getUnsignedRange(SExt->getOperand());
2984 return setUnsignedRange(SExt,
2985 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
2988 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2989 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2990 return setUnsignedRange(Trunc,
2991 ConservativeResult.intersectWith(X.truncate(BitWidth)));
2994 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2995 // If there's no unsigned wrap, the value will never be less than its
2997 if (AddRec->hasNoUnsignedWrap())
2998 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
2999 if (!C->getValue()->isZero())
3000 ConservativeResult =
3001 ConservativeResult.intersectWith(
3002 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3004 // TODO: non-affine addrec
3005 if (AddRec->isAffine()) {
3006 const Type *Ty = AddRec->getType();
3007 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3008 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3009 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3010 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3012 const SCEV *Start = AddRec->getStart();
3013 const SCEV *Step = AddRec->getStepRecurrence(*this);
3015 ConstantRange StartRange = getUnsignedRange(Start);
3016 ConstantRange StepRange = getSignedRange(Step);
3017 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3018 ConstantRange EndRange =
3019 StartRange.add(MaxBECountRange.multiply(StepRange));
3021 // Check for overflow. This must be done with ConstantRange arithmetic
3022 // because we could be called from within the ScalarEvolution overflow
3024 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3025 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3026 ConstantRange ExtMaxBECountRange =
3027 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3028 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3029 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3031 return setUnsignedRange(AddRec, ConservativeResult);
3033 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3034 EndRange.getUnsignedMin());
3035 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3036 EndRange.getUnsignedMax());
3037 if (Min.isMinValue() && Max.isMaxValue())
3038 return setUnsignedRange(AddRec, ConservativeResult);
3039 return setUnsignedRange(AddRec,
3040 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3044 return setUnsignedRange(AddRec, ConservativeResult);
3047 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3048 // For a SCEVUnknown, ask ValueTracking.
3049 APInt Mask = APInt::getAllOnesValue(BitWidth);
3050 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3051 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3052 if (Ones == ~Zeros + 1)
3053 return setUnsignedRange(U, ConservativeResult);
3054 return setUnsignedRange(U,
3055 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3058 return setUnsignedRange(S, ConservativeResult);
3061 /// getSignedRange - Determine the signed range for a particular SCEV.
3064 ScalarEvolution::getSignedRange(const SCEV *S) {
3065 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3066 if (I != SignedRanges.end())
3069 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3070 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3072 unsigned BitWidth = getTypeSizeInBits(S->getType());
3073 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3075 // If the value has known zeros, the maximum signed value will have those
3076 // known zeros as well.
3077 uint32_t TZ = GetMinTrailingZeros(S);
3079 ConservativeResult =
3080 ConstantRange(APInt::getSignedMinValue(BitWidth),
3081 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3083 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3084 ConstantRange X = getSignedRange(Add->getOperand(0));
3085 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3086 X = X.add(getSignedRange(Add->getOperand(i)));
3087 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3090 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3091 ConstantRange X = getSignedRange(Mul->getOperand(0));
3092 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3093 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3094 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3097 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3098 ConstantRange X = getSignedRange(SMax->getOperand(0));
3099 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3100 X = X.smax(getSignedRange(SMax->getOperand(i)));
3101 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3104 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3105 ConstantRange X = getSignedRange(UMax->getOperand(0));
3106 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3107 X = X.umax(getSignedRange(UMax->getOperand(i)));
3108 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3111 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3112 ConstantRange X = getSignedRange(UDiv->getLHS());
3113 ConstantRange Y = getSignedRange(UDiv->getRHS());
3114 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3117 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3118 ConstantRange X = getSignedRange(ZExt->getOperand());
3119 return setSignedRange(ZExt,
3120 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3123 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3124 ConstantRange X = getSignedRange(SExt->getOperand());
3125 return setSignedRange(SExt,
3126 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3129 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3130 ConstantRange X = getSignedRange(Trunc->getOperand());
3131 return setSignedRange(Trunc,
3132 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3135 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3136 // If there's no signed wrap, and all the operands have the same sign or
3137 // zero, the value won't ever change sign.
3138 if (AddRec->hasNoSignedWrap()) {
3139 bool AllNonNeg = true;
3140 bool AllNonPos = true;
3141 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3142 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3143 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3146 ConservativeResult = ConservativeResult.intersectWith(
3147 ConstantRange(APInt(BitWidth, 0),
3148 APInt::getSignedMinValue(BitWidth)));
3150 ConservativeResult = ConservativeResult.intersectWith(
3151 ConstantRange(APInt::getSignedMinValue(BitWidth),
3152 APInt(BitWidth, 1)));
3155 // TODO: non-affine addrec
3156 if (AddRec->isAffine()) {
3157 const Type *Ty = AddRec->getType();
3158 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3159 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3160 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3161 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3163 const SCEV *Start = AddRec->getStart();
3164 const SCEV *Step = AddRec->getStepRecurrence(*this);
3166 ConstantRange StartRange = getSignedRange(Start);
3167 ConstantRange StepRange = getSignedRange(Step);
3168 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3169 ConstantRange EndRange =
3170 StartRange.add(MaxBECountRange.multiply(StepRange));
3172 // Check for overflow. This must be done with ConstantRange arithmetic
3173 // because we could be called from within the ScalarEvolution overflow
3175 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3176 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3177 ConstantRange ExtMaxBECountRange =
3178 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3179 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3180 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3182 return setSignedRange(AddRec, ConservativeResult);
3184 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3185 EndRange.getSignedMin());
3186 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3187 EndRange.getSignedMax());
3188 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3189 return setSignedRange(AddRec, ConservativeResult);
3190 return setSignedRange(AddRec,
3191 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3195 return setSignedRange(AddRec, ConservativeResult);
3198 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3199 // For a SCEVUnknown, ask ValueTracking.
3200 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3201 return setSignedRange(U, ConservativeResult);
3202 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3204 return setSignedRange(U, ConservativeResult);
3205 return setSignedRange(U, ConservativeResult.intersectWith(
3206 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3207 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3210 return setSignedRange(S, ConservativeResult);
3213 /// createSCEV - We know that there is no SCEV for the specified value.
3214 /// Analyze the expression.
3216 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3217 if (!isSCEVable(V->getType()))
3218 return getUnknown(V);
3220 unsigned Opcode = Instruction::UserOp1;
3221 if (Instruction *I = dyn_cast<Instruction>(V)) {
3222 Opcode = I->getOpcode();
3224 // Don't attempt to analyze instructions in blocks that aren't
3225 // reachable. Such instructions don't matter, and they aren't required
3226 // to obey basic rules for definitions dominating uses which this
3227 // analysis depends on.
3228 if (!DT->isReachableFromEntry(I->getParent()))
3229 return getUnknown(V);
3230 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3231 Opcode = CE->getOpcode();
3232 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3233 return getConstant(CI);
3234 else if (isa<ConstantPointerNull>(V))
3235 return getConstant(V->getType(), 0);
3236 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3237 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3239 return getUnknown(V);
3241 Operator *U = cast<Operator>(V);
3243 case Instruction::Add: {
3244 // The simple thing to do would be to just call getSCEV on both operands
3245 // and call getAddExpr with the result. However if we're looking at a
3246 // bunch of things all added together, this can be quite inefficient,
3247 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3248 // Instead, gather up all the operands and make a single getAddExpr call.
3249 // LLVM IR canonical form means we need only traverse the left operands.
3250 SmallVector<const SCEV *, 4> AddOps;
3251 AddOps.push_back(getSCEV(U->getOperand(1)));
3252 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3253 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3254 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3256 U = cast<Operator>(Op);
3257 const SCEV *Op1 = getSCEV(U->getOperand(1));
3258 if (Opcode == Instruction::Sub)
3259 AddOps.push_back(getNegativeSCEV(Op1));
3261 AddOps.push_back(Op1);
3263 AddOps.push_back(getSCEV(U->getOperand(0)));
3264 return getAddExpr(AddOps);
3266 case Instruction::Mul: {
3267 // See the Add code above.
3268 SmallVector<const SCEV *, 4> MulOps;
3269 MulOps.push_back(getSCEV(U->getOperand(1)));
3270 for (Value *Op = U->getOperand(0);
3271 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3272 Op = U->getOperand(0)) {
3273 U = cast<Operator>(Op);
3274 MulOps.push_back(getSCEV(U->getOperand(1)));
3276 MulOps.push_back(getSCEV(U->getOperand(0)));
3277 return getMulExpr(MulOps);
3279 case Instruction::UDiv:
3280 return getUDivExpr(getSCEV(U->getOperand(0)),
3281 getSCEV(U->getOperand(1)));
3282 case Instruction::Sub:
3283 return getMinusSCEV(getSCEV(U->getOperand(0)),
3284 getSCEV(U->getOperand(1)));
3285 case Instruction::And:
3286 // For an expression like x&255 that merely masks off the high bits,
3287 // use zext(trunc(x)) as the SCEV expression.
3288 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3289 if (CI->isNullValue())
3290 return getSCEV(U->getOperand(1));
3291 if (CI->isAllOnesValue())
3292 return getSCEV(U->getOperand(0));
3293 const APInt &A = CI->getValue();
3295 // Instcombine's ShrinkDemandedConstant may strip bits out of
3296 // constants, obscuring what would otherwise be a low-bits mask.
3297 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3298 // knew about to reconstruct a low-bits mask value.
3299 unsigned LZ = A.countLeadingZeros();
3300 unsigned BitWidth = A.getBitWidth();
3301 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3302 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3303 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3305 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3307 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3309 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3310 IntegerType::get(getContext(), BitWidth - LZ)),
3315 case Instruction::Or:
3316 // If the RHS of the Or is a constant, we may have something like:
3317 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3318 // optimizations will transparently handle this case.
3320 // In order for this transformation to be safe, the LHS must be of the
3321 // form X*(2^n) and the Or constant must be less than 2^n.
3322 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3323 const SCEV *LHS = getSCEV(U->getOperand(0));
3324 const APInt &CIVal = CI->getValue();
3325 if (GetMinTrailingZeros(LHS) >=
3326 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3327 // Build a plain add SCEV.
3328 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3329 // If the LHS of the add was an addrec and it has no-wrap flags,
3330 // transfer the no-wrap flags, since an or won't introduce a wrap.
3331 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3332 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3333 if (OldAR->hasNoUnsignedWrap())
3334 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoUnsignedWrap(true);
3335 if (OldAR->hasNoSignedWrap())
3336 const_cast<SCEVAddRecExpr *>(NewAR)->setHasNoSignedWrap(true);
3342 case Instruction::Xor:
3343 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3344 // If the RHS of the xor is a signbit, then this is just an add.
3345 // Instcombine turns add of signbit into xor as a strength reduction step.
3346 if (CI->getValue().isSignBit())
3347 return getAddExpr(getSCEV(U->getOperand(0)),
3348 getSCEV(U->getOperand(1)));
3350 // If the RHS of xor is -1, then this is a not operation.
3351 if (CI->isAllOnesValue())
3352 return getNotSCEV(getSCEV(U->getOperand(0)));
3354 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3355 // This is a variant of the check for xor with -1, and it handles
3356 // the case where instcombine has trimmed non-demanded bits out
3357 // of an xor with -1.
3358 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3359 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3360 if (BO->getOpcode() == Instruction::And &&
3361 LCI->getValue() == CI->getValue())
3362 if (const SCEVZeroExtendExpr *Z =
3363 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3364 const Type *UTy = U->getType();
3365 const SCEV *Z0 = Z->getOperand();
3366 const Type *Z0Ty = Z0->getType();
3367 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3369 // If C is a low-bits mask, the zero extend is serving to
3370 // mask off the high bits. Complement the operand and
3371 // re-apply the zext.
3372 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3373 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3375 // If C is a single bit, it may be in the sign-bit position
3376 // before the zero-extend. In this case, represent the xor
3377 // using an add, which is equivalent, and re-apply the zext.
3378 APInt Trunc = CI->getValue().trunc(Z0TySize);
3379 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3381 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3387 case Instruction::Shl:
3388 // Turn shift left of a constant amount into a multiply.
3389 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3390 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3392 // If the shift count is not less than the bitwidth, the result of
3393 // the shift is undefined. Don't try to analyze it, because the
3394 // resolution chosen here may differ from the resolution chosen in
3395 // other parts of the compiler.
3396 if (SA->getValue().uge(BitWidth))
3399 Constant *X = ConstantInt::get(getContext(),
3400 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3401 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3405 case Instruction::LShr:
3406 // Turn logical shift right of a constant into a unsigned divide.
3407 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3408 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3410 // If the shift count is not less than the bitwidth, the result of
3411 // the shift is undefined. Don't try to analyze it, because the
3412 // resolution chosen here may differ from the resolution chosen in
3413 // other parts of the compiler.
3414 if (SA->getValue().uge(BitWidth))
3417 Constant *X = ConstantInt::get(getContext(),
3418 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3419 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3423 case Instruction::AShr:
3424 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3425 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3426 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3427 if (L->getOpcode() == Instruction::Shl &&
3428 L->getOperand(1) == U->getOperand(1)) {
3429 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3431 // If the shift count is not less than the bitwidth, the result of
3432 // the shift is undefined. Don't try to analyze it, because the
3433 // resolution chosen here may differ from the resolution chosen in
3434 // other parts of the compiler.
3435 if (CI->getValue().uge(BitWidth))
3438 uint64_t Amt = BitWidth - CI->getZExtValue();
3439 if (Amt == BitWidth)
3440 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3442 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3443 IntegerType::get(getContext(),
3449 case Instruction::Trunc:
3450 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3452 case Instruction::ZExt:
3453 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3455 case Instruction::SExt:
3456 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3458 case Instruction::BitCast:
3459 // BitCasts are no-op casts so we just eliminate the cast.
3460 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3461 return getSCEV(U->getOperand(0));
3464 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3465 // lead to pointer expressions which cannot safely be expanded to GEPs,
3466 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3467 // simplifying integer expressions.
3469 case Instruction::GetElementPtr:
3470 return createNodeForGEP(cast<GEPOperator>(U));
3472 case Instruction::PHI:
3473 return createNodeForPHI(cast<PHINode>(U));
3475 case Instruction::Select:
3476 // This could be a smax or umax that was lowered earlier.
3477 // Try to recover it.
3478 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3479 Value *LHS = ICI->getOperand(0);
3480 Value *RHS = ICI->getOperand(1);
3481 switch (ICI->getPredicate()) {
3482 case ICmpInst::ICMP_SLT:
3483 case ICmpInst::ICMP_SLE:
3484 std::swap(LHS, RHS);
3486 case ICmpInst::ICMP_SGT:
3487 case ICmpInst::ICMP_SGE:
3488 // a >s b ? a+x : b+x -> smax(a, b)+x
3489 // a >s b ? b+x : a+x -> smin(a, b)+x
3490 if (LHS->getType() == U->getType()) {
3491 const SCEV *LS = getSCEV(LHS);
3492 const SCEV *RS = getSCEV(RHS);
3493 const SCEV *LA = getSCEV(U->getOperand(1));
3494 const SCEV *RA = getSCEV(U->getOperand(2));
3495 const SCEV *LDiff = getMinusSCEV(LA, LS);
3496 const SCEV *RDiff = getMinusSCEV(RA, RS);
3498 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3499 LDiff = getMinusSCEV(LA, RS);
3500 RDiff = getMinusSCEV(RA, LS);
3502 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3505 case ICmpInst::ICMP_ULT:
3506 case ICmpInst::ICMP_ULE:
3507 std::swap(LHS, RHS);
3509 case ICmpInst::ICMP_UGT:
3510 case ICmpInst::ICMP_UGE:
3511 // a >u b ? a+x : b+x -> umax(a, b)+x
3512 // a >u b ? b+x : a+x -> umin(a, b)+x
3513 if (LHS->getType() == U->getType()) {
3514 const SCEV *LS = getSCEV(LHS);
3515 const SCEV *RS = getSCEV(RHS);
3516 const SCEV *LA = getSCEV(U->getOperand(1));
3517 const SCEV *RA = getSCEV(U->getOperand(2));
3518 const SCEV *LDiff = getMinusSCEV(LA, LS);
3519 const SCEV *RDiff = getMinusSCEV(RA, RS);
3521 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3522 LDiff = getMinusSCEV(LA, RS);
3523 RDiff = getMinusSCEV(RA, LS);
3525 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3528 case ICmpInst::ICMP_NE:
3529 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3530 if (LHS->getType() == U->getType() &&
3531 isa<ConstantInt>(RHS) &&
3532 cast<ConstantInt>(RHS)->isZero()) {
3533 const SCEV *One = getConstant(LHS->getType(), 1);
3534 const SCEV *LS = getSCEV(LHS);
3535 const SCEV *LA = getSCEV(U->getOperand(1));
3536 const SCEV *RA = getSCEV(U->getOperand(2));
3537 const SCEV *LDiff = getMinusSCEV(LA, LS);
3538 const SCEV *RDiff = getMinusSCEV(RA, One);
3540 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3543 case ICmpInst::ICMP_EQ:
3544 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3545 if (LHS->getType() == U->getType() &&
3546 isa<ConstantInt>(RHS) &&
3547 cast<ConstantInt>(RHS)->isZero()) {
3548 const SCEV *One = getConstant(LHS->getType(), 1);
3549 const SCEV *LS = getSCEV(LHS);
3550 const SCEV *LA = getSCEV(U->getOperand(1));
3551 const SCEV *RA = getSCEV(U->getOperand(2));
3552 const SCEV *LDiff = getMinusSCEV(LA, One);
3553 const SCEV *RDiff = getMinusSCEV(RA, LS);
3555 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3563 default: // We cannot analyze this expression.
3567 return getUnknown(V);
3572 //===----------------------------------------------------------------------===//
3573 // Iteration Count Computation Code
3576 /// getBackedgeTakenCount - If the specified loop has a predictable
3577 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3578 /// object. The backedge-taken count is the number of times the loop header
3579 /// will be branched to from within the loop. This is one less than the
3580 /// trip count of the loop, since it doesn't count the first iteration,
3581 /// when the header is branched to from outside the loop.
3583 /// Note that it is not valid to call this method on a loop without a
3584 /// loop-invariant backedge-taken count (see
3585 /// hasLoopInvariantBackedgeTakenCount).
3587 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3588 return getBackedgeTakenInfo(L).Exact;
3591 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3592 /// return the least SCEV value that is known never to be less than the
3593 /// actual backedge taken count.
3594 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3595 return getBackedgeTakenInfo(L).Max;
3598 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3599 /// onto the given Worklist.
3601 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3602 BasicBlock *Header = L->getHeader();
3604 // Push all Loop-header PHIs onto the Worklist stack.
3605 for (BasicBlock::iterator I = Header->begin();
3606 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3607 Worklist.push_back(PN);
3610 const ScalarEvolution::BackedgeTakenInfo &
3611 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3612 // Initially insert a CouldNotCompute for this loop. If the insertion
3613 // succeeds, proceed to actually compute a backedge-taken count and
3614 // update the value. The temporary CouldNotCompute value tells SCEV
3615 // code elsewhere that it shouldn't attempt to request a new
3616 // backedge-taken count, which could result in infinite recursion.
3617 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3618 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3620 return Pair.first->second;
3622 BackedgeTakenInfo BECount = ComputeBackedgeTakenCount(L);
3623 if (BECount.Exact != getCouldNotCompute()) {
3624 assert(isLoopInvariant(BECount.Exact, L) &&
3625 isLoopInvariant(BECount.Max, L) &&
3626 "Computed backedge-taken count isn't loop invariant for loop!");
3627 ++NumTripCountsComputed;
3629 // Update the value in the map.
3630 Pair.first->second = BECount;
3632 if (BECount.Max != getCouldNotCompute())
3633 // Update the value in the map.
3634 Pair.first->second = BECount;
3635 if (isa<PHINode>(L->getHeader()->begin()))
3636 // Only count loops that have phi nodes as not being computable.
3637 ++NumTripCountsNotComputed;
3640 // Now that we know more about the trip count for this loop, forget any
3641 // existing SCEV values for PHI nodes in this loop since they are only
3642 // conservative estimates made without the benefit of trip count
3643 // information. This is similar to the code in forgetLoop, except that
3644 // it handles SCEVUnknown PHI nodes specially.
3645 if (BECount.hasAnyInfo()) {
3646 SmallVector<Instruction *, 16> Worklist;
3647 PushLoopPHIs(L, Worklist);
3649 SmallPtrSet<Instruction *, 8> Visited;
3650 while (!Worklist.empty()) {
3651 Instruction *I = Worklist.pop_back_val();
3652 if (!Visited.insert(I)) continue;
3654 ValueExprMapType::iterator It =
3655 ValueExprMap.find(static_cast<Value *>(I));
3656 if (It != ValueExprMap.end()) {
3657 const SCEV *Old = It->second;
3659 // SCEVUnknown for a PHI either means that it has an unrecognized
3660 // structure, or it's a PHI that's in the progress of being computed
3661 // by createNodeForPHI. In the former case, additional loop trip
3662 // count information isn't going to change anything. In the later
3663 // case, createNodeForPHI will perform the necessary updates on its
3664 // own when it gets to that point.
3665 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
3666 forgetMemoizedResults(Old);
3667 ValueExprMap.erase(It);
3669 if (PHINode *PN = dyn_cast<PHINode>(I))
3670 ConstantEvolutionLoopExitValue.erase(PN);
3673 PushDefUseChildren(I, Worklist);
3676 return Pair.first->second;
3679 /// forgetLoop - This method should be called by the client when it has
3680 /// changed a loop in a way that may effect ScalarEvolution's ability to
3681 /// compute a trip count, or if the loop is deleted.
3682 void ScalarEvolution::forgetLoop(const Loop *L) {
3683 // Drop any stored trip count value.
3684 BackedgeTakenCounts.erase(L);
3686 // Drop information about expressions based on loop-header PHIs.
3687 SmallVector<Instruction *, 16> Worklist;
3688 PushLoopPHIs(L, Worklist);
3690 SmallPtrSet<Instruction *, 8> Visited;
3691 while (!Worklist.empty()) {
3692 Instruction *I = Worklist.pop_back_val();
3693 if (!Visited.insert(I)) continue;
3695 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3696 if (It != ValueExprMap.end()) {
3697 forgetMemoizedResults(It->second);
3698 ValueExprMap.erase(It);
3699 if (PHINode *PN = dyn_cast<PHINode>(I))
3700 ConstantEvolutionLoopExitValue.erase(PN);
3703 PushDefUseChildren(I, Worklist);
3706 // Forget all contained loops too, to avoid dangling entries in the
3707 // ValuesAtScopes map.
3708 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3712 /// forgetValue - This method should be called by the client when it has
3713 /// changed a value in a way that may effect its value, or which may
3714 /// disconnect it from a def-use chain linking it to a loop.
3715 void ScalarEvolution::forgetValue(Value *V) {
3716 Instruction *I = dyn_cast<Instruction>(V);
3719 // Drop information about expressions based on loop-header PHIs.
3720 SmallVector<Instruction *, 16> Worklist;
3721 Worklist.push_back(I);
3723 SmallPtrSet<Instruction *, 8> Visited;
3724 while (!Worklist.empty()) {
3725 I = Worklist.pop_back_val();
3726 if (!Visited.insert(I)) continue;
3728 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3729 if (It != ValueExprMap.end()) {
3730 forgetMemoizedResults(It->second);
3731 ValueExprMap.erase(It);
3732 if (PHINode *PN = dyn_cast<PHINode>(I))
3733 ConstantEvolutionLoopExitValue.erase(PN);
3736 PushDefUseChildren(I, Worklist);
3740 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3741 /// of the specified loop will execute.
3742 ScalarEvolution::BackedgeTakenInfo
3743 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3744 SmallVector<BasicBlock *, 8> ExitingBlocks;
3745 L->getExitingBlocks(ExitingBlocks);
3747 // Examine all exits and pick the most conservative values.
3748 const SCEV *BECount = getCouldNotCompute();
3749 const SCEV *MaxBECount = getCouldNotCompute();
3750 bool CouldNotComputeBECount = false;
3751 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3752 BackedgeTakenInfo NewBTI =
3753 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3755 if (NewBTI.Exact == getCouldNotCompute()) {
3756 // We couldn't compute an exact value for this exit, so
3757 // we won't be able to compute an exact value for the loop.
3758 CouldNotComputeBECount = true;
3759 BECount = getCouldNotCompute();
3760 } else if (!CouldNotComputeBECount) {
3761 if (BECount == getCouldNotCompute())
3762 BECount = NewBTI.Exact;
3764 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3766 if (MaxBECount == getCouldNotCompute())
3767 MaxBECount = NewBTI.Max;
3768 else if (NewBTI.Max != getCouldNotCompute())
3769 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3772 return BackedgeTakenInfo(BECount, MaxBECount);
3775 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3776 /// of the specified loop will execute if it exits via the specified block.
3777 ScalarEvolution::BackedgeTakenInfo
3778 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3779 BasicBlock *ExitingBlock) {
3781 // Okay, we've chosen an exiting block. See what condition causes us to
3782 // exit at this block.
3784 // FIXME: we should be able to handle switch instructions (with a single exit)
3785 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3786 if (ExitBr == 0) return getCouldNotCompute();
3787 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3789 // At this point, we know we have a conditional branch that determines whether
3790 // the loop is exited. However, we don't know if the branch is executed each
3791 // time through the loop. If not, then the execution count of the branch will
3792 // not be equal to the trip count of the loop.
3794 // Currently we check for this by checking to see if the Exit branch goes to
3795 // the loop header. If so, we know it will always execute the same number of
3796 // times as the loop. We also handle the case where the exit block *is* the
3797 // loop header. This is common for un-rotated loops.
3799 // If both of those tests fail, walk up the unique predecessor chain to the
3800 // header, stopping if there is an edge that doesn't exit the loop. If the
3801 // header is reached, the execution count of the branch will be equal to the
3802 // trip count of the loop.
3804 // More extensive analysis could be done to handle more cases here.
3806 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3807 ExitBr->getSuccessor(1) != L->getHeader() &&
3808 ExitBr->getParent() != L->getHeader()) {
3809 // The simple checks failed, try climbing the unique predecessor chain
3810 // up to the header.
3812 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3813 BasicBlock *Pred = BB->getUniquePredecessor();
3815 return getCouldNotCompute();
3816 TerminatorInst *PredTerm = Pred->getTerminator();
3817 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3818 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3821 // If the predecessor has a successor that isn't BB and isn't
3822 // outside the loop, assume the worst.
3823 if (L->contains(PredSucc))
3824 return getCouldNotCompute();
3826 if (Pred == L->getHeader()) {
3833 return getCouldNotCompute();
3836 // Proceed to the next level to examine the exit condition expression.
3837 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3838 ExitBr->getSuccessor(0),
3839 ExitBr->getSuccessor(1));
3842 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3843 /// backedge of the specified loop will execute if its exit condition
3844 /// were a conditional branch of ExitCond, TBB, and FBB.
3845 ScalarEvolution::BackedgeTakenInfo
3846 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3850 // Check if the controlling expression for this loop is an And or Or.
3851 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3852 if (BO->getOpcode() == Instruction::And) {
3853 // Recurse on the operands of the and.
3854 BackedgeTakenInfo BTI0 =
3855 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3856 BackedgeTakenInfo BTI1 =
3857 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3858 const SCEV *BECount = getCouldNotCompute();
3859 const SCEV *MaxBECount = getCouldNotCompute();
3860 if (L->contains(TBB)) {
3861 // Both conditions must be true for the loop to continue executing.
3862 // Choose the less conservative count.
3863 if (BTI0.Exact == getCouldNotCompute() ||
3864 BTI1.Exact == getCouldNotCompute())
3865 BECount = getCouldNotCompute();
3867 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3868 if (BTI0.Max == getCouldNotCompute())
3869 MaxBECount = BTI1.Max;
3870 else if (BTI1.Max == getCouldNotCompute())
3871 MaxBECount = BTI0.Max;
3873 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3875 // Both conditions must be true at the same time for the loop to exit.
3876 // For now, be conservative.
3877 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3878 if (BTI0.Max == BTI1.Max)
3879 MaxBECount = BTI0.Max;
3880 if (BTI0.Exact == BTI1.Exact)
3881 BECount = BTI0.Exact;
3884 return BackedgeTakenInfo(BECount, MaxBECount);
3886 if (BO->getOpcode() == Instruction::Or) {
3887 // Recurse on the operands of the or.
3888 BackedgeTakenInfo BTI0 =
3889 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3890 BackedgeTakenInfo BTI1 =
3891 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3892 const SCEV *BECount = getCouldNotCompute();
3893 const SCEV *MaxBECount = getCouldNotCompute();
3894 if (L->contains(FBB)) {
3895 // Both conditions must be false for the loop to continue executing.
3896 // Choose the less conservative count.
3897 if (BTI0.Exact == getCouldNotCompute() ||
3898 BTI1.Exact == getCouldNotCompute())
3899 BECount = getCouldNotCompute();
3901 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3902 if (BTI0.Max == getCouldNotCompute())
3903 MaxBECount = BTI1.Max;
3904 else if (BTI1.Max == getCouldNotCompute())
3905 MaxBECount = BTI0.Max;
3907 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3909 // Both conditions must be false at the same time for the loop to exit.
3910 // For now, be conservative.
3911 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3912 if (BTI0.Max == BTI1.Max)
3913 MaxBECount = BTI0.Max;
3914 if (BTI0.Exact == BTI1.Exact)
3915 BECount = BTI0.Exact;
3918 return BackedgeTakenInfo(BECount, MaxBECount);
3922 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3923 // Proceed to the next level to examine the icmp.
3924 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3925 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3927 // Check for a constant condition. These are normally stripped out by
3928 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
3929 // preserve the CFG and is temporarily leaving constant conditions
3931 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
3932 if (L->contains(FBB) == !CI->getZExtValue())
3933 // The backedge is always taken.
3934 return getCouldNotCompute();
3936 // The backedge is never taken.
3937 return getConstant(CI->getType(), 0);
3940 // If it's not an integer or pointer comparison then compute it the hard way.
3941 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3944 static const SCEVAddRecExpr *
3945 isSimpleUnwrappingAddRec(const SCEV *S, const Loop *L) {
3946 const SCEVAddRecExpr *SA = dyn_cast<SCEVAddRecExpr>(S);
3948 // The SCEV must be an addrec of this loop.
3949 if (!SA || SA->getLoop() != L || !SA->isAffine())
3952 // The SCEV must be known to not wrap in some way to be interesting.
3953 if (!SA->hasNoUnsignedWrap() && !SA->hasNoSignedWrap())
3956 // The stride must be a constant so that we know if it is striding up or down.
3957 if (!isa<SCEVConstant>(SA->getOperand(1)))
3962 /// getMinusSCEVForExitTest - When considering an exit test for a loop with a
3963 /// "x != y" exit test, we turn this into a computation that evaluates x-y != 0,
3964 /// and this function returns the expression to use for x-y. We know and take
3965 /// advantage of the fact that this subtraction is only being used in a
3966 /// comparison by zero context.
3968 static const SCEV *getMinusSCEVForExitTest(const SCEV *LHS, const SCEV *RHS,
3969 const Loop *L, ScalarEvolution &SE) {
3970 // If either LHS or RHS is an AddRec SCEV (of this loop) that is known to not
3971 // wrap (either NSW or NUW), then we know that the value will either become
3972 // the other one (and thus the loop terminates), that the loop will terminate
3973 // through some other exit condition first, or that the loop has undefined
3974 // behavior. This information is useful when the addrec has a stride that is
3975 // != 1 or -1, because it means we can't "miss" the exit value.
3977 // In any of these three cases, it is safe to turn the exit condition into a
3978 // "counting down" AddRec (to zero) by subtracting the two inputs as normal,
3979 // but since we know that the "end cannot be missed" we can force the
3980 // resulting AddRec to be a NUW addrec. Since it is counting down, this means
3981 // that the AddRec *cannot* pass zero.
3983 // See if LHS and RHS are addrec's we can handle.
3984 const SCEVAddRecExpr *LHSA = isSimpleUnwrappingAddRec(LHS, L);
3985 const SCEVAddRecExpr *RHSA = isSimpleUnwrappingAddRec(RHS, L);
3987 // If neither addrec is interesting, just return a minus.
3988 if (RHSA == 0 && LHSA == 0)
3989 return SE.getMinusSCEV(LHS, RHS);
3991 // If only one of LHS and RHS are an AddRec of this loop, make sure it is LHS.
3992 if (RHSA && LHSA == 0) {
3993 // Safe because a-b === b-a for comparisons against zero.
3994 std::swap(LHS, RHS);
3995 std::swap(LHSA, RHSA);
3998 // Handle the case when only one is advancing in a non-overflowing way.
4000 // If RHS is loop varying, then we can't predict when LHS will cross it.
4001 if (!SE.isLoopInvariant(RHS, L))
4002 return SE.getMinusSCEV(LHS, RHS);
4004 // If LHS has a positive stride, then we compute RHS-LHS, because the loop
4005 // is counting up until it crosses RHS (which must be larger than LHS). If
4006 // it is negative, we compute LHS-RHS because we're counting down to RHS.
4007 const ConstantInt *Stride =
4008 cast<SCEVConstant>(LHSA->getOperand(1))->getValue();
4009 if (Stride->getValue().isNegative())
4010 std::swap(LHS, RHS);
4012 return SE.getMinusSCEV(RHS, LHS, true /*HasNUW*/);
4015 // If both LHS and RHS are interesting, we have something like:
4017 const ConstantInt *LHSStride =
4018 cast<SCEVConstant>(LHSA->getOperand(1))->getValue();
4019 const ConstantInt *RHSStride =
4020 cast<SCEVConstant>(RHSA->getOperand(1))->getValue();
4022 // If the strides are equal, then this is just a (complex) loop invariant
4023 // comparison of a/b.
4024 if (LHSStride == RHSStride)
4025 return SE.getMinusSCEV(LHSA->getStart(), RHSA->getStart());
4027 // If the signs of the strides differ, then the negative stride is counting
4028 // down to the positive stride.
4029 if (LHSStride->getValue().isNegative() != RHSStride->getValue().isNegative()){
4030 if (RHSStride->getValue().isNegative())
4031 std::swap(LHS, RHS);
4033 // If LHS's stride is smaller than RHS's stride, then "b" must be less than
4034 // "a" and "b" is RHS is counting up (catching up) to LHS. This is true
4035 // whether the strides are positive or negative.
4036 if (RHSStride->getValue().slt(LHSStride->getValue()))
4037 std::swap(LHS, RHS);
4040 return SE.getMinusSCEV(LHS, RHS, true /*HasNUW*/);
4043 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4044 /// backedge of the specified loop will execute if its exit condition
4045 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4046 ScalarEvolution::BackedgeTakenInfo
4047 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4052 // If the condition was exit on true, convert the condition to exit on false
4053 ICmpInst::Predicate Cond;
4054 if (!L->contains(FBB))
4055 Cond = ExitCond->getPredicate();
4057 Cond = ExitCond->getInversePredicate();
4059 // Handle common loops like: for (X = "string"; *X; ++X)
4060 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4061 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4062 BackedgeTakenInfo ItCnt =
4063 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4064 if (ItCnt.hasAnyInfo())
4068 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4069 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4071 // Try to evaluate any dependencies out of the loop.
4072 LHS = getSCEVAtScope(LHS, L);
4073 RHS = getSCEVAtScope(RHS, L);
4075 // At this point, we would like to compute how many iterations of the
4076 // loop the predicate will return true for these inputs.
4077 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4078 // If there is a loop-invariant, force it into the RHS.
4079 std::swap(LHS, RHS);
4080 Cond = ICmpInst::getSwappedPredicate(Cond);
4083 // Simplify the operands before analyzing them.
4084 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4086 // If we have a comparison of a chrec against a constant, try to use value
4087 // ranges to answer this query.
4088 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4089 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4090 if (AddRec->getLoop() == L) {
4091 // Form the constant range.
4092 ConstantRange CompRange(
4093 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4095 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4096 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4100 case ICmpInst::ICMP_NE: { // while (X != Y)
4101 // Convert to: while (X-Y != 0)
4102 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEVForExitTest(LHS, RHS, L,
4104 if (BTI.hasAnyInfo()) return BTI;
4107 case ICmpInst::ICMP_EQ: { // while (X == Y)
4108 // Convert to: while (X-Y == 0)
4109 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4110 if (BTI.hasAnyInfo()) return BTI;
4113 case ICmpInst::ICMP_SLT: {
4114 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4115 if (BTI.hasAnyInfo()) return BTI;
4118 case ICmpInst::ICMP_SGT: {
4119 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4120 getNotSCEV(RHS), L, true);
4121 if (BTI.hasAnyInfo()) return BTI;
4124 case ICmpInst::ICMP_ULT: {
4125 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4126 if (BTI.hasAnyInfo()) return BTI;
4129 case ICmpInst::ICMP_UGT: {
4130 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4131 getNotSCEV(RHS), L, false);
4132 if (BTI.hasAnyInfo()) return BTI;
4137 dbgs() << "ComputeBackedgeTakenCount ";
4138 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4139 dbgs() << "[unsigned] ";
4140 dbgs() << *LHS << " "
4141 << Instruction::getOpcodeName(Instruction::ICmp)
4142 << " " << *RHS << "\n";
4147 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4150 static ConstantInt *
4151 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4152 ScalarEvolution &SE) {
4153 const SCEV *InVal = SE.getConstant(C);
4154 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4155 assert(isa<SCEVConstant>(Val) &&
4156 "Evaluation of SCEV at constant didn't fold correctly?");
4157 return cast<SCEVConstant>(Val)->getValue();
4160 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4161 /// and a GEP expression (missing the pointer index) indexing into it, return
4162 /// the addressed element of the initializer or null if the index expression is
4165 GetAddressedElementFromGlobal(GlobalVariable *GV,
4166 const std::vector<ConstantInt*> &Indices) {
4167 Constant *Init = GV->getInitializer();
4168 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4169 uint64_t Idx = Indices[i]->getZExtValue();
4170 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4171 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4172 Init = cast<Constant>(CS->getOperand(Idx));
4173 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4174 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4175 Init = cast<Constant>(CA->getOperand(Idx));
4176 } else if (isa<ConstantAggregateZero>(Init)) {
4177 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4178 assert(Idx < STy->getNumElements() && "Bad struct index!");
4179 Init = Constant::getNullValue(STy->getElementType(Idx));
4180 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4181 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4182 Init = Constant::getNullValue(ATy->getElementType());
4184 llvm_unreachable("Unknown constant aggregate type!");
4188 return 0; // Unknown initializer type
4194 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4195 /// 'icmp op load X, cst', try to see if we can compute the backedge
4196 /// execution count.
4197 ScalarEvolution::BackedgeTakenInfo
4198 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4202 ICmpInst::Predicate predicate) {
4203 if (LI->isVolatile()) return getCouldNotCompute();
4205 // Check to see if the loaded pointer is a getelementptr of a global.
4206 // TODO: Use SCEV instead of manually grubbing with GEPs.
4207 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4208 if (!GEP) return getCouldNotCompute();
4210 // Make sure that it is really a constant global we are gepping, with an
4211 // initializer, and make sure the first IDX is really 0.
4212 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4213 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4214 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4215 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4216 return getCouldNotCompute();
4218 // Okay, we allow one non-constant index into the GEP instruction.
4220 std::vector<ConstantInt*> Indexes;
4221 unsigned VarIdxNum = 0;
4222 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4223 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4224 Indexes.push_back(CI);
4225 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4226 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4227 VarIdx = GEP->getOperand(i);
4229 Indexes.push_back(0);
4232 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4233 // Check to see if X is a loop variant variable value now.
4234 const SCEV *Idx = getSCEV(VarIdx);
4235 Idx = getSCEVAtScope(Idx, L);
4237 // We can only recognize very limited forms of loop index expressions, in
4238 // particular, only affine AddRec's like {C1,+,C2}.
4239 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4240 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4241 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4242 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4243 return getCouldNotCompute();
4245 unsigned MaxSteps = MaxBruteForceIterations;
4246 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4247 ConstantInt *ItCst = ConstantInt::get(
4248 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4249 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4251 // Form the GEP offset.
4252 Indexes[VarIdxNum] = Val;
4254 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4255 if (Result == 0) break; // Cannot compute!
4257 // Evaluate the condition for this iteration.
4258 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4259 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4260 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4262 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4263 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4266 ++NumArrayLenItCounts;
4267 return getConstant(ItCst); // Found terminating iteration!
4270 return getCouldNotCompute();
4274 /// CanConstantFold - Return true if we can constant fold an instruction of the
4275 /// specified type, assuming that all operands were constants.
4276 static bool CanConstantFold(const Instruction *I) {
4277 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4278 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4281 if (const CallInst *CI = dyn_cast<CallInst>(I))
4282 if (const Function *F = CI->getCalledFunction())
4283 return canConstantFoldCallTo(F);
4287 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4288 /// in the loop that V is derived from. We allow arbitrary operations along the
4289 /// way, but the operands of an operation must either be constants or a value
4290 /// derived from a constant PHI. If this expression does not fit with these
4291 /// constraints, return null.
4292 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4293 // If this is not an instruction, or if this is an instruction outside of the
4294 // loop, it can't be derived from a loop PHI.
4295 Instruction *I = dyn_cast<Instruction>(V);
4296 if (I == 0 || !L->contains(I)) return 0;
4298 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4299 if (L->getHeader() == I->getParent())
4302 // We don't currently keep track of the control flow needed to evaluate
4303 // PHIs, so we cannot handle PHIs inside of loops.
4307 // If we won't be able to constant fold this expression even if the operands
4308 // are constants, return early.
4309 if (!CanConstantFold(I)) return 0;
4311 // Otherwise, we can evaluate this instruction if all of its operands are
4312 // constant or derived from a PHI node themselves.
4314 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4315 if (!isa<Constant>(I->getOperand(Op))) {
4316 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4317 if (P == 0) return 0; // Not evolving from PHI
4321 return 0; // Evolving from multiple different PHIs.
4324 // This is a expression evolving from a constant PHI!
4328 /// EvaluateExpression - Given an expression that passes the
4329 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4330 /// in the loop has the value PHIVal. If we can't fold this expression for some
4331 /// reason, return null.
4332 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4333 const TargetData *TD) {
4334 if (isa<PHINode>(V)) return PHIVal;
4335 if (Constant *C = dyn_cast<Constant>(V)) return C;
4336 Instruction *I = cast<Instruction>(V);
4338 std::vector<Constant*> Operands(I->getNumOperands());
4340 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4341 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4342 if (Operands[i] == 0) return 0;
4345 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4346 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4348 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4349 &Operands[0], Operands.size(), TD);
4352 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4353 /// in the header of its containing loop, we know the loop executes a
4354 /// constant number of times, and the PHI node is just a recurrence
4355 /// involving constants, fold it.
4357 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4360 std::map<PHINode*, Constant*>::const_iterator I =
4361 ConstantEvolutionLoopExitValue.find(PN);
4362 if (I != ConstantEvolutionLoopExitValue.end())
4365 if (BEs.ugt(MaxBruteForceIterations))
4366 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4368 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4370 // Since the loop is canonicalized, the PHI node must have two entries. One
4371 // entry must be a constant (coming in from outside of the loop), and the
4372 // second must be derived from the same PHI.
4373 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4374 Constant *StartCST =
4375 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4377 return RetVal = 0; // Must be a constant.
4379 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4380 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4381 !isa<Constant>(BEValue))
4382 return RetVal = 0; // Not derived from same PHI.
4384 // Execute the loop symbolically to determine the exit value.
4385 if (BEs.getActiveBits() >= 32)
4386 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4388 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4389 unsigned IterationNum = 0;
4390 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4391 if (IterationNum == NumIterations)
4392 return RetVal = PHIVal; // Got exit value!
4394 // Compute the value of the PHI node for the next iteration.
4395 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4396 if (NextPHI == PHIVal)
4397 return RetVal = NextPHI; // Stopped evolving!
4399 return 0; // Couldn't evaluate!
4404 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4405 /// constant number of times (the condition evolves only from constants),
4406 /// try to evaluate a few iterations of the loop until we get the exit
4407 /// condition gets a value of ExitWhen (true or false). If we cannot
4408 /// evaluate the trip count of the loop, return getCouldNotCompute().
4410 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4413 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4414 if (PN == 0) return getCouldNotCompute();
4416 // If the loop is canonicalized, the PHI will have exactly two entries.
4417 // That's the only form we support here.
4418 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4420 // One entry must be a constant (coming in from outside of the loop), and the
4421 // second must be derived from the same PHI.
4422 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4423 Constant *StartCST =
4424 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4425 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4427 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4428 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4429 !isa<Constant>(BEValue))
4430 return getCouldNotCompute(); // Not derived from same PHI.
4432 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4433 // the loop symbolically to determine when the condition gets a value of
4435 unsigned IterationNum = 0;
4436 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4437 for (Constant *PHIVal = StartCST;
4438 IterationNum != MaxIterations; ++IterationNum) {
4439 ConstantInt *CondVal =
4440 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4442 // Couldn't symbolically evaluate.
4443 if (!CondVal) return getCouldNotCompute();
4445 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4446 ++NumBruteForceTripCountsComputed;
4447 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4450 // Compute the value of the PHI node for the next iteration.
4451 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4452 if (NextPHI == 0 || NextPHI == PHIVal)
4453 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4457 // Too many iterations were needed to evaluate.
4458 return getCouldNotCompute();
4461 /// getSCEVAtScope - Return a SCEV expression for the specified value
4462 /// at the specified scope in the program. The L value specifies a loop
4463 /// nest to evaluate the expression at, where null is the top-level or a
4464 /// specified loop is immediately inside of the loop.
4466 /// This method can be used to compute the exit value for a variable defined
4467 /// in a loop by querying what the value will hold in the parent loop.
4469 /// In the case that a relevant loop exit value cannot be computed, the
4470 /// original value V is returned.
4471 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4472 // Check to see if we've folded this expression at this loop before.
4473 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4474 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4475 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4477 return Pair.first->second ? Pair.first->second : V;
4479 // Otherwise compute it.
4480 const SCEV *C = computeSCEVAtScope(V, L);
4481 ValuesAtScopes[V][L] = C;
4485 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4486 if (isa<SCEVConstant>(V)) return V;
4488 // If this instruction is evolved from a constant-evolving PHI, compute the
4489 // exit value from the loop without using SCEVs.
4490 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4491 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4492 const Loop *LI = (*this->LI)[I->getParent()];
4493 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4494 if (PHINode *PN = dyn_cast<PHINode>(I))
4495 if (PN->getParent() == LI->getHeader()) {
4496 // Okay, there is no closed form solution for the PHI node. Check
4497 // to see if the loop that contains it has a known backedge-taken
4498 // count. If so, we may be able to force computation of the exit
4500 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4501 if (const SCEVConstant *BTCC =
4502 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4503 // Okay, we know how many times the containing loop executes. If
4504 // this is a constant evolving PHI node, get the final value at
4505 // the specified iteration number.
4506 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4507 BTCC->getValue()->getValue(),
4509 if (RV) return getSCEV(RV);
4513 // Okay, this is an expression that we cannot symbolically evaluate
4514 // into a SCEV. Check to see if it's possible to symbolically evaluate
4515 // the arguments into constants, and if so, try to constant propagate the
4516 // result. This is particularly useful for computing loop exit values.
4517 if (CanConstantFold(I)) {
4518 SmallVector<Constant *, 4> Operands;
4519 bool MadeImprovement = false;
4520 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4521 Value *Op = I->getOperand(i);
4522 if (Constant *C = dyn_cast<Constant>(Op)) {
4523 Operands.push_back(C);
4527 // If any of the operands is non-constant and if they are
4528 // non-integer and non-pointer, don't even try to analyze them
4529 // with scev techniques.
4530 if (!isSCEVable(Op->getType()))
4533 const SCEV *OrigV = getSCEV(Op);
4534 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4535 MadeImprovement |= OrigV != OpV;
4538 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4540 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4541 C = dyn_cast<Constant>(SU->getValue());
4543 if (C->getType() != Op->getType())
4544 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4548 Operands.push_back(C);
4551 // Check to see if getSCEVAtScope actually made an improvement.
4552 if (MadeImprovement) {
4554 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4555 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4556 Operands[0], Operands[1], TD);
4558 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4559 &Operands[0], Operands.size(), TD);
4566 // This is some other type of SCEVUnknown, just return it.
4570 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4571 // Avoid performing the look-up in the common case where the specified
4572 // expression has no loop-variant portions.
4573 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4574 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4575 if (OpAtScope != Comm->getOperand(i)) {
4576 // Okay, at least one of these operands is loop variant but might be
4577 // foldable. Build a new instance of the folded commutative expression.
4578 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4579 Comm->op_begin()+i);
4580 NewOps.push_back(OpAtScope);
4582 for (++i; i != e; ++i) {
4583 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4584 NewOps.push_back(OpAtScope);
4586 if (isa<SCEVAddExpr>(Comm))
4587 return getAddExpr(NewOps);
4588 if (isa<SCEVMulExpr>(Comm))
4589 return getMulExpr(NewOps);
4590 if (isa<SCEVSMaxExpr>(Comm))
4591 return getSMaxExpr(NewOps);
4592 if (isa<SCEVUMaxExpr>(Comm))
4593 return getUMaxExpr(NewOps);
4594 llvm_unreachable("Unknown commutative SCEV type!");
4597 // If we got here, all operands are loop invariant.
4601 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4602 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4603 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4604 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4605 return Div; // must be loop invariant
4606 return getUDivExpr(LHS, RHS);
4609 // If this is a loop recurrence for a loop that does not contain L, then we
4610 // are dealing with the final value computed by the loop.
4611 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4612 // First, attempt to evaluate each operand.
4613 // Avoid performing the look-up in the common case where the specified
4614 // expression has no loop-variant portions.
4615 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4616 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4617 if (OpAtScope == AddRec->getOperand(i))
4620 // Okay, at least one of these operands is loop variant but might be
4621 // foldable. Build a new instance of the folded commutative expression.
4622 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4623 AddRec->op_begin()+i);
4624 NewOps.push_back(OpAtScope);
4625 for (++i; i != e; ++i)
4626 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4628 AddRec = cast<SCEVAddRecExpr>(getAddRecExpr(NewOps, AddRec->getLoop()));
4632 // If the scope is outside the addrec's loop, evaluate it by using the
4633 // loop exit value of the addrec.
4634 if (!AddRec->getLoop()->contains(L)) {
4635 // To evaluate this recurrence, we need to know how many times the AddRec
4636 // loop iterates. Compute this now.
4637 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4638 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4640 // Then, evaluate the AddRec.
4641 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4647 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4648 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4649 if (Op == Cast->getOperand())
4650 return Cast; // must be loop invariant
4651 return getZeroExtendExpr(Op, Cast->getType());
4654 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4655 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4656 if (Op == Cast->getOperand())
4657 return Cast; // must be loop invariant
4658 return getSignExtendExpr(Op, Cast->getType());
4661 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4662 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4663 if (Op == Cast->getOperand())
4664 return Cast; // must be loop invariant
4665 return getTruncateExpr(Op, Cast->getType());
4668 llvm_unreachable("Unknown SCEV type!");
4672 /// getSCEVAtScope - This is a convenience function which does
4673 /// getSCEVAtScope(getSCEV(V), L).
4674 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4675 return getSCEVAtScope(getSCEV(V), L);
4678 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4679 /// following equation:
4681 /// A * X = B (mod N)
4683 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4684 /// A and B isn't important.
4686 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4687 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4688 ScalarEvolution &SE) {
4689 uint32_t BW = A.getBitWidth();
4690 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4691 assert(A != 0 && "A must be non-zero.");
4695 // The gcd of A and N may have only one prime factor: 2. The number of
4696 // trailing zeros in A is its multiplicity
4697 uint32_t Mult2 = A.countTrailingZeros();
4700 // 2. Check if B is divisible by D.
4702 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4703 // is not less than multiplicity of this prime factor for D.
4704 if (B.countTrailingZeros() < Mult2)
4705 return SE.getCouldNotCompute();
4707 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4710 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4711 // bit width during computations.
4712 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4713 APInt Mod(BW + 1, 0);
4714 Mod.setBit(BW - Mult2); // Mod = N / D
4715 APInt I = AD.multiplicativeInverse(Mod);
4717 // 4. Compute the minimum unsigned root of the equation:
4718 // I * (B / D) mod (N / D)
4719 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4721 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4723 return SE.getConstant(Result.trunc(BW));
4726 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4727 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4728 /// might be the same) or two SCEVCouldNotCompute objects.
4730 static std::pair<const SCEV *,const SCEV *>
4731 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4732 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4733 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4734 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4735 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4737 // We currently can only solve this if the coefficients are constants.
4738 if (!LC || !MC || !NC) {
4739 const SCEV *CNC = SE.getCouldNotCompute();
4740 return std::make_pair(CNC, CNC);
4743 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4744 const APInt &L = LC->getValue()->getValue();
4745 const APInt &M = MC->getValue()->getValue();
4746 const APInt &N = NC->getValue()->getValue();
4747 APInt Two(BitWidth, 2);
4748 APInt Four(BitWidth, 4);
4751 using namespace APIntOps;
4753 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4754 // The B coefficient is M-N/2
4758 // The A coefficient is N/2
4759 APInt A(N.sdiv(Two));
4761 // Compute the B^2-4ac term.
4764 SqrtTerm -= Four * (A * C);
4766 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4767 // integer value or else APInt::sqrt() will assert.
4768 APInt SqrtVal(SqrtTerm.sqrt());
4770 // Compute the two solutions for the quadratic formula.
4771 // The divisions must be performed as signed divisions.
4773 APInt TwoA( A << 1 );
4774 if (TwoA.isMinValue()) {
4775 const SCEV *CNC = SE.getCouldNotCompute();
4776 return std::make_pair(CNC, CNC);
4779 LLVMContext &Context = SE.getContext();
4781 ConstantInt *Solution1 =
4782 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4783 ConstantInt *Solution2 =
4784 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4786 return std::make_pair(SE.getConstant(Solution1),
4787 SE.getConstant(Solution2));
4788 } // end APIntOps namespace
4791 /// HowFarToZero - Return the number of times a backedge comparing the specified
4792 /// value to zero will execute. If not computable, return CouldNotCompute.
4793 ScalarEvolution::BackedgeTakenInfo
4794 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4795 // If the value is a constant
4796 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4797 // If the value is already zero, the branch will execute zero times.
4798 if (C->getValue()->isZero()) return C;
4799 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4802 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4803 if (!AddRec || AddRec->getLoop() != L)
4804 return getCouldNotCompute();
4806 if (AddRec->isAffine()) {
4807 // If this is an affine expression, the execution count of this branch is
4808 // the minimum unsigned root of the following equation:
4810 // Start + Step*N = 0 (mod 2^BW)
4814 // Step*N = -Start (mod 2^BW)
4816 // where BW is the common bit width of Start and Step.
4818 // Get the initial value for the loop.
4819 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4820 L->getParentLoop());
4821 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4822 L->getParentLoop());
4824 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4825 // For now we handle only constant steps.
4827 // First, handle unitary steps.
4828 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4829 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4830 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4831 return Start; // N = Start (as unsigned)
4833 // Then, try to solve the above equation provided that Start is constant.
4834 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4835 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4836 -StartC->getValue()->getValue(),
4839 } else if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4840 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4841 // the quadratic equation to solve it.
4842 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4844 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4845 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4848 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4849 << " sol#2: " << *R2 << "\n";
4851 // Pick the smallest positive root value.
4852 if (ConstantInt *CB =
4853 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4854 R1->getValue(), R2->getValue()))) {
4855 if (CB->getZExtValue() == false)
4856 std::swap(R1, R2); // R1 is the minimum root now.
4858 // We can only use this value if the chrec ends up with an exact zero
4859 // value at this index. When solving for "X*X != 5", for example, we
4860 // should not accept a root of 2.
4861 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4863 return R1; // We found a quadratic root!
4868 return getCouldNotCompute();
4871 /// HowFarToNonZero - Return the number of times a backedge checking the
4872 /// specified value for nonzero will execute. If not computable, return
4874 ScalarEvolution::BackedgeTakenInfo
4875 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4876 // Loops that look like: while (X == 0) are very strange indeed. We don't
4877 // handle them yet except for the trivial case. This could be expanded in the
4878 // future as needed.
4880 // If the value is a constant, check to see if it is known to be non-zero
4881 // already. If so, the backedge will execute zero times.
4882 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4883 if (!C->getValue()->isNullValue())
4884 return getConstant(C->getType(), 0);
4885 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4888 // We could implement others, but I really doubt anyone writes loops like
4889 // this, and if they did, they would already be constant folded.
4890 return getCouldNotCompute();
4893 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4894 /// (which may not be an immediate predecessor) which has exactly one
4895 /// successor from which BB is reachable, or null if no such block is
4898 std::pair<BasicBlock *, BasicBlock *>
4899 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4900 // If the block has a unique predecessor, then there is no path from the
4901 // predecessor to the block that does not go through the direct edge
4902 // from the predecessor to the block.
4903 if (BasicBlock *Pred = BB->getSinglePredecessor())
4904 return std::make_pair(Pred, BB);
4906 // A loop's header is defined to be a block that dominates the loop.
4907 // If the header has a unique predecessor outside the loop, it must be
4908 // a block that has exactly one successor that can reach the loop.
4909 if (Loop *L = LI->getLoopFor(BB))
4910 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
4912 return std::pair<BasicBlock *, BasicBlock *>();
4915 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4916 /// testing whether two expressions are equal, however for the purposes of
4917 /// looking for a condition guarding a loop, it can be useful to be a little
4918 /// more general, since a front-end may have replicated the controlling
4921 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4922 // Quick check to see if they are the same SCEV.
4923 if (A == B) return true;
4925 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4926 // two different instructions with the same value. Check for this case.
4927 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4928 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4929 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4930 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4931 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
4934 // Otherwise assume they may have a different value.
4938 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
4939 /// predicate Pred. Return true iff any changes were made.
4941 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
4942 const SCEV *&LHS, const SCEV *&RHS) {
4943 bool Changed = false;
4945 // Canonicalize a constant to the right side.
4946 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
4947 // Check for both operands constant.
4948 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
4949 if (ConstantExpr::getICmp(Pred,
4951 RHSC->getValue())->isNullValue())
4952 goto trivially_false;
4954 goto trivially_true;
4956 // Otherwise swap the operands to put the constant on the right.
4957 std::swap(LHS, RHS);
4958 Pred = ICmpInst::getSwappedPredicate(Pred);
4962 // If we're comparing an addrec with a value which is loop-invariant in the
4963 // addrec's loop, put the addrec on the left. Also make a dominance check,
4964 // as both operands could be addrecs loop-invariant in each other's loop.
4965 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
4966 const Loop *L = AR->getLoop();
4967 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
4968 std::swap(LHS, RHS);
4969 Pred = ICmpInst::getSwappedPredicate(Pred);
4974 // If there's a constant operand, canonicalize comparisons with boundary
4975 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
4976 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4977 const APInt &RA = RC->getValue()->getValue();
4979 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4980 case ICmpInst::ICMP_EQ:
4981 case ICmpInst::ICMP_NE:
4983 case ICmpInst::ICMP_UGE:
4984 if ((RA - 1).isMinValue()) {
4985 Pred = ICmpInst::ICMP_NE;
4986 RHS = getConstant(RA - 1);
4990 if (RA.isMaxValue()) {
4991 Pred = ICmpInst::ICMP_EQ;
4995 if (RA.isMinValue()) goto trivially_true;
4997 Pred = ICmpInst::ICMP_UGT;
4998 RHS = getConstant(RA - 1);
5001 case ICmpInst::ICMP_ULE:
5002 if ((RA + 1).isMaxValue()) {
5003 Pred = ICmpInst::ICMP_NE;
5004 RHS = getConstant(RA + 1);
5008 if (RA.isMinValue()) {
5009 Pred = ICmpInst::ICMP_EQ;
5013 if (RA.isMaxValue()) goto trivially_true;
5015 Pred = ICmpInst::ICMP_ULT;
5016 RHS = getConstant(RA + 1);
5019 case ICmpInst::ICMP_SGE:
5020 if ((RA - 1).isMinSignedValue()) {
5021 Pred = ICmpInst::ICMP_NE;
5022 RHS = getConstant(RA - 1);
5026 if (RA.isMaxSignedValue()) {
5027 Pred = ICmpInst::ICMP_EQ;
5031 if (RA.isMinSignedValue()) goto trivially_true;
5033 Pred = ICmpInst::ICMP_SGT;
5034 RHS = getConstant(RA - 1);
5037 case ICmpInst::ICMP_SLE:
5038 if ((RA + 1).isMaxSignedValue()) {
5039 Pred = ICmpInst::ICMP_NE;
5040 RHS = getConstant(RA + 1);
5044 if (RA.isMinSignedValue()) {
5045 Pred = ICmpInst::ICMP_EQ;
5049 if (RA.isMaxSignedValue()) goto trivially_true;
5051 Pred = ICmpInst::ICMP_SLT;
5052 RHS = getConstant(RA + 1);
5055 case ICmpInst::ICMP_UGT:
5056 if (RA.isMinValue()) {
5057 Pred = ICmpInst::ICMP_NE;
5061 if ((RA + 1).isMaxValue()) {
5062 Pred = ICmpInst::ICMP_EQ;
5063 RHS = getConstant(RA + 1);
5067 if (RA.isMaxValue()) goto trivially_false;
5069 case ICmpInst::ICMP_ULT:
5070 if (RA.isMaxValue()) {
5071 Pred = ICmpInst::ICMP_NE;
5075 if ((RA - 1).isMinValue()) {
5076 Pred = ICmpInst::ICMP_EQ;
5077 RHS = getConstant(RA - 1);
5081 if (RA.isMinValue()) goto trivially_false;
5083 case ICmpInst::ICMP_SGT:
5084 if (RA.isMinSignedValue()) {
5085 Pred = ICmpInst::ICMP_NE;
5089 if ((RA + 1).isMaxSignedValue()) {
5090 Pred = ICmpInst::ICMP_EQ;
5091 RHS = getConstant(RA + 1);
5095 if (RA.isMaxSignedValue()) goto trivially_false;
5097 case ICmpInst::ICMP_SLT:
5098 if (RA.isMaxSignedValue()) {
5099 Pred = ICmpInst::ICMP_NE;
5103 if ((RA - 1).isMinSignedValue()) {
5104 Pred = ICmpInst::ICMP_EQ;
5105 RHS = getConstant(RA - 1);
5109 if (RA.isMinSignedValue()) goto trivially_false;
5114 // Check for obvious equality.
5115 if (HasSameValue(LHS, RHS)) {
5116 if (ICmpInst::isTrueWhenEqual(Pred))
5117 goto trivially_true;
5118 if (ICmpInst::isFalseWhenEqual(Pred))
5119 goto trivially_false;
5122 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5123 // adding or subtracting 1 from one of the operands.
5125 case ICmpInst::ICMP_SLE:
5126 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5127 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5128 /*HasNUW=*/false, /*HasNSW=*/true);
5129 Pred = ICmpInst::ICMP_SLT;
5131 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5132 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5133 /*HasNUW=*/false, /*HasNSW=*/true);
5134 Pred = ICmpInst::ICMP_SLT;
5138 case ICmpInst::ICMP_SGE:
5139 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5140 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5141 /*HasNUW=*/false, /*HasNSW=*/true);
5142 Pred = ICmpInst::ICMP_SGT;
5144 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5145 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5146 /*HasNUW=*/false, /*HasNSW=*/true);
5147 Pred = ICmpInst::ICMP_SGT;
5151 case ICmpInst::ICMP_ULE:
5152 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5153 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5154 /*HasNUW=*/true, /*HasNSW=*/false);
5155 Pred = ICmpInst::ICMP_ULT;
5157 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5158 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5159 /*HasNUW=*/true, /*HasNSW=*/false);
5160 Pred = ICmpInst::ICMP_ULT;
5164 case ICmpInst::ICMP_UGE:
5165 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5166 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5167 /*HasNUW=*/true, /*HasNSW=*/false);
5168 Pred = ICmpInst::ICMP_UGT;
5170 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5171 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5172 /*HasNUW=*/true, /*HasNSW=*/false);
5173 Pred = ICmpInst::ICMP_UGT;
5181 // TODO: More simplifications are possible here.
5187 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5188 Pred = ICmpInst::ICMP_EQ;
5193 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5194 Pred = ICmpInst::ICMP_NE;
5198 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5199 return getSignedRange(S).getSignedMax().isNegative();
5202 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5203 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5206 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5207 return !getSignedRange(S).getSignedMin().isNegative();
5210 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5211 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5214 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5215 return isKnownNegative(S) || isKnownPositive(S);
5218 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5219 const SCEV *LHS, const SCEV *RHS) {
5220 // Canonicalize the inputs first.
5221 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5223 // If LHS or RHS is an addrec, check to see if the condition is true in
5224 // every iteration of the loop.
5225 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5226 if (isLoopEntryGuardedByCond(
5227 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5228 isLoopBackedgeGuardedByCond(
5229 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5231 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5232 if (isLoopEntryGuardedByCond(
5233 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5234 isLoopBackedgeGuardedByCond(
5235 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5238 // Otherwise see what can be done with known constant ranges.
5239 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5243 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5244 const SCEV *LHS, const SCEV *RHS) {
5245 if (HasSameValue(LHS, RHS))
5246 return ICmpInst::isTrueWhenEqual(Pred);
5248 // This code is split out from isKnownPredicate because it is called from
5249 // within isLoopEntryGuardedByCond.
5252 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5254 case ICmpInst::ICMP_SGT:
5255 Pred = ICmpInst::ICMP_SLT;
5256 std::swap(LHS, RHS);
5257 case ICmpInst::ICMP_SLT: {
5258 ConstantRange LHSRange = getSignedRange(LHS);
5259 ConstantRange RHSRange = getSignedRange(RHS);
5260 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5262 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5266 case ICmpInst::ICMP_SGE:
5267 Pred = ICmpInst::ICMP_SLE;
5268 std::swap(LHS, RHS);
5269 case ICmpInst::ICMP_SLE: {
5270 ConstantRange LHSRange = getSignedRange(LHS);
5271 ConstantRange RHSRange = getSignedRange(RHS);
5272 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5274 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5278 case ICmpInst::ICMP_UGT:
5279 Pred = ICmpInst::ICMP_ULT;
5280 std::swap(LHS, RHS);
5281 case ICmpInst::ICMP_ULT: {
5282 ConstantRange LHSRange = getUnsignedRange(LHS);
5283 ConstantRange RHSRange = getUnsignedRange(RHS);
5284 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5286 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5290 case ICmpInst::ICMP_UGE:
5291 Pred = ICmpInst::ICMP_ULE;
5292 std::swap(LHS, RHS);
5293 case ICmpInst::ICMP_ULE: {
5294 ConstantRange LHSRange = getUnsignedRange(LHS);
5295 ConstantRange RHSRange = getUnsignedRange(RHS);
5296 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5298 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5302 case ICmpInst::ICMP_NE: {
5303 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5305 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5308 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5309 if (isKnownNonZero(Diff))
5313 case ICmpInst::ICMP_EQ:
5314 // The check at the top of the function catches the case where
5315 // the values are known to be equal.
5321 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5322 /// protected by a conditional between LHS and RHS. This is used to
5323 /// to eliminate casts.
5325 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5326 ICmpInst::Predicate Pred,
5327 const SCEV *LHS, const SCEV *RHS) {
5328 // Interpret a null as meaning no loop, where there is obviously no guard
5329 // (interprocedural conditions notwithstanding).
5330 if (!L) return true;
5332 BasicBlock *Latch = L->getLoopLatch();
5336 BranchInst *LoopContinuePredicate =
5337 dyn_cast<BranchInst>(Latch->getTerminator());
5338 if (!LoopContinuePredicate ||
5339 LoopContinuePredicate->isUnconditional())
5342 return isImpliedCond(Pred, LHS, RHS,
5343 LoopContinuePredicate->getCondition(),
5344 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5347 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5348 /// by a conditional between LHS and RHS. This is used to help avoid max
5349 /// expressions in loop trip counts, and to eliminate casts.
5351 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5352 ICmpInst::Predicate Pred,
5353 const SCEV *LHS, const SCEV *RHS) {
5354 // Interpret a null as meaning no loop, where there is obviously no guard
5355 // (interprocedural conditions notwithstanding).
5356 if (!L) return false;
5358 // Starting at the loop predecessor, climb up the predecessor chain, as long
5359 // as there are predecessors that can be found that have unique successors
5360 // leading to the original header.
5361 for (std::pair<BasicBlock *, BasicBlock *>
5362 Pair(L->getLoopPredecessor(), L->getHeader());
5364 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5366 BranchInst *LoopEntryPredicate =
5367 dyn_cast<BranchInst>(Pair.first->getTerminator());
5368 if (!LoopEntryPredicate ||
5369 LoopEntryPredicate->isUnconditional())
5372 if (isImpliedCond(Pred, LHS, RHS,
5373 LoopEntryPredicate->getCondition(),
5374 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5381 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5382 /// and RHS is true whenever the given Cond value evaluates to true.
5383 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5384 const SCEV *LHS, const SCEV *RHS,
5385 Value *FoundCondValue,
5387 // Recursively handle And and Or conditions.
5388 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5389 if (BO->getOpcode() == Instruction::And) {
5391 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5392 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5393 } else if (BO->getOpcode() == Instruction::Or) {
5395 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5396 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5400 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5401 if (!ICI) return false;
5403 // Bail if the ICmp's operands' types are wider than the needed type
5404 // before attempting to call getSCEV on them. This avoids infinite
5405 // recursion, since the analysis of widening casts can require loop
5406 // exit condition information for overflow checking, which would
5408 if (getTypeSizeInBits(LHS->getType()) <
5409 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5412 // Now that we found a conditional branch that dominates the loop, check to
5413 // see if it is the comparison we are looking for.
5414 ICmpInst::Predicate FoundPred;
5416 FoundPred = ICI->getInversePredicate();
5418 FoundPred = ICI->getPredicate();
5420 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5421 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5423 // Balance the types. The case where FoundLHS' type is wider than
5424 // LHS' type is checked for above.
5425 if (getTypeSizeInBits(LHS->getType()) >
5426 getTypeSizeInBits(FoundLHS->getType())) {
5427 if (CmpInst::isSigned(Pred)) {
5428 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5429 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5431 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5432 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5436 // Canonicalize the query to match the way instcombine will have
5437 // canonicalized the comparison.
5438 if (SimplifyICmpOperands(Pred, LHS, RHS))
5440 return CmpInst::isTrueWhenEqual(Pred);
5441 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5442 if (FoundLHS == FoundRHS)
5443 return CmpInst::isFalseWhenEqual(Pred);
5445 // Check to see if we can make the LHS or RHS match.
5446 if (LHS == FoundRHS || RHS == FoundLHS) {
5447 if (isa<SCEVConstant>(RHS)) {
5448 std::swap(FoundLHS, FoundRHS);
5449 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5451 std::swap(LHS, RHS);
5452 Pred = ICmpInst::getSwappedPredicate(Pred);
5456 // Check whether the found predicate is the same as the desired predicate.
5457 if (FoundPred == Pred)
5458 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5460 // Check whether swapping the found predicate makes it the same as the
5461 // desired predicate.
5462 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5463 if (isa<SCEVConstant>(RHS))
5464 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5466 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5467 RHS, LHS, FoundLHS, FoundRHS);
5470 // Check whether the actual condition is beyond sufficient.
5471 if (FoundPred == ICmpInst::ICMP_EQ)
5472 if (ICmpInst::isTrueWhenEqual(Pred))
5473 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5475 if (Pred == ICmpInst::ICMP_NE)
5476 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5477 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5480 // Otherwise assume the worst.
5484 /// isImpliedCondOperands - Test whether the condition described by Pred,
5485 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5486 /// and FoundRHS is true.
5487 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5488 const SCEV *LHS, const SCEV *RHS,
5489 const SCEV *FoundLHS,
5490 const SCEV *FoundRHS) {
5491 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5492 FoundLHS, FoundRHS) ||
5493 // ~x < ~y --> x > y
5494 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5495 getNotSCEV(FoundRHS),
5496 getNotSCEV(FoundLHS));
5499 /// isImpliedCondOperandsHelper - Test whether the condition described by
5500 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5501 /// FoundLHS, and FoundRHS is true.
5503 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5504 const SCEV *LHS, const SCEV *RHS,
5505 const SCEV *FoundLHS,
5506 const SCEV *FoundRHS) {
5508 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5509 case ICmpInst::ICMP_EQ:
5510 case ICmpInst::ICMP_NE:
5511 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5514 case ICmpInst::ICMP_SLT:
5515 case ICmpInst::ICMP_SLE:
5516 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5517 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5520 case ICmpInst::ICMP_SGT:
5521 case ICmpInst::ICMP_SGE:
5522 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5523 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5526 case ICmpInst::ICMP_ULT:
5527 case ICmpInst::ICMP_ULE:
5528 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5529 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5532 case ICmpInst::ICMP_UGT:
5533 case ICmpInst::ICMP_UGE:
5534 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5535 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5543 /// getBECount - Subtract the end and start values and divide by the step,
5544 /// rounding up, to get the number of times the backedge is executed. Return
5545 /// CouldNotCompute if an intermediate computation overflows.
5546 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5550 assert(!isKnownNegative(Step) &&
5551 "This code doesn't handle negative strides yet!");
5553 const Type *Ty = Start->getType();
5554 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5555 const SCEV *Diff = getMinusSCEV(End, Start);
5556 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5558 // Add an adjustment to the difference between End and Start so that
5559 // the division will effectively round up.
5560 const SCEV *Add = getAddExpr(Diff, RoundUp);
5563 // Check Add for unsigned overflow.
5564 // TODO: More sophisticated things could be done here.
5565 const Type *WideTy = IntegerType::get(getContext(),
5566 getTypeSizeInBits(Ty) + 1);
5567 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5568 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5569 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5570 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5571 return getCouldNotCompute();
5574 return getUDivExpr(Add, Step);
5577 /// HowManyLessThans - Return the number of times a backedge containing the
5578 /// specified less-than comparison will execute. If not computable, return
5579 /// CouldNotCompute.
5580 ScalarEvolution::BackedgeTakenInfo
5581 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5582 const Loop *L, bool isSigned) {
5583 // Only handle: "ADDREC < LoopInvariant".
5584 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
5586 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5587 if (!AddRec || AddRec->getLoop() != L)
5588 return getCouldNotCompute();
5590 // Check to see if we have a flag which makes analysis easy.
5591 bool NoWrap = isSigned ? AddRec->hasNoSignedWrap() :
5592 AddRec->hasNoUnsignedWrap();
5594 if (AddRec->isAffine()) {
5595 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5596 const SCEV *Step = AddRec->getStepRecurrence(*this);
5599 return getCouldNotCompute();
5600 if (Step->isOne()) {
5601 // With unit stride, the iteration never steps past the limit value.
5602 } else if (isKnownPositive(Step)) {
5603 // Test whether a positive iteration can step past the limit
5604 // value and past the maximum value for its type in a single step.
5605 // Note that it's not sufficient to check NoWrap here, because even
5606 // though the value after a wrap is undefined, it's not undefined
5607 // behavior, so if wrap does occur, the loop could either terminate or
5608 // loop infinitely, but in either case, the loop is guaranteed to
5609 // iterate at least until the iteration where the wrapping occurs.
5610 const SCEV *One = getConstant(Step->getType(), 1);
5612 APInt Max = APInt::getSignedMaxValue(BitWidth);
5613 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5614 .slt(getSignedRange(RHS).getSignedMax()))
5615 return getCouldNotCompute();
5617 APInt Max = APInt::getMaxValue(BitWidth);
5618 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5619 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5620 return getCouldNotCompute();
5623 // TODO: Handle negative strides here and below.
5624 return getCouldNotCompute();
5626 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5627 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5628 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5629 // treat m-n as signed nor unsigned due to overflow possibility.
5631 // First, we get the value of the LHS in the first iteration: n
5632 const SCEV *Start = AddRec->getOperand(0);
5634 // Determine the minimum constant start value.
5635 const SCEV *MinStart = getConstant(isSigned ?
5636 getSignedRange(Start).getSignedMin() :
5637 getUnsignedRange(Start).getUnsignedMin());
5639 // If we know that the condition is true in order to enter the loop,
5640 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5641 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5642 // the division must round up.
5643 const SCEV *End = RHS;
5644 if (!isLoopEntryGuardedByCond(L,
5645 isSigned ? ICmpInst::ICMP_SLT :
5647 getMinusSCEV(Start, Step), RHS))
5648 End = isSigned ? getSMaxExpr(RHS, Start)
5649 : getUMaxExpr(RHS, Start);
5651 // Determine the maximum constant end value.
5652 const SCEV *MaxEnd = getConstant(isSigned ?
5653 getSignedRange(End).getSignedMax() :
5654 getUnsignedRange(End).getUnsignedMax());
5656 // If MaxEnd is within a step of the maximum integer value in its type,
5657 // adjust it down to the minimum value which would produce the same effect.
5658 // This allows the subsequent ceiling division of (N+(step-1))/step to
5659 // compute the correct value.
5660 const SCEV *StepMinusOne = getMinusSCEV(Step,
5661 getConstant(Step->getType(), 1));
5664 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5667 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5670 // Finally, we subtract these two values and divide, rounding up, to get
5671 // the number of times the backedge is executed.
5672 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5674 // The maximum backedge count is similar, except using the minimum start
5675 // value and the maximum end value.
5676 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step, NoWrap);
5678 return BackedgeTakenInfo(BECount, MaxBECount);
5681 return getCouldNotCompute();
5684 /// getNumIterationsInRange - Return the number of iterations of this loop that
5685 /// produce values in the specified constant range. Another way of looking at
5686 /// this is that it returns the first iteration number where the value is not in
5687 /// the condition, thus computing the exit count. If the iteration count can't
5688 /// be computed, an instance of SCEVCouldNotCompute is returned.
5689 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5690 ScalarEvolution &SE) const {
5691 if (Range.isFullSet()) // Infinite loop.
5692 return SE.getCouldNotCompute();
5694 // If the start is a non-zero constant, shift the range to simplify things.
5695 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5696 if (!SC->getValue()->isZero()) {
5697 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5698 Operands[0] = SE.getConstant(SC->getType(), 0);
5699 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
5700 if (const SCEVAddRecExpr *ShiftedAddRec =
5701 dyn_cast<SCEVAddRecExpr>(Shifted))
5702 return ShiftedAddRec->getNumIterationsInRange(
5703 Range.subtract(SC->getValue()->getValue()), SE);
5704 // This is strange and shouldn't happen.
5705 return SE.getCouldNotCompute();
5708 // The only time we can solve this is when we have all constant indices.
5709 // Otherwise, we cannot determine the overflow conditions.
5710 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5711 if (!isa<SCEVConstant>(getOperand(i)))
5712 return SE.getCouldNotCompute();
5715 // Okay at this point we know that all elements of the chrec are constants and
5716 // that the start element is zero.
5718 // First check to see if the range contains zero. If not, the first
5720 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5721 if (!Range.contains(APInt(BitWidth, 0)))
5722 return SE.getConstant(getType(), 0);
5725 // If this is an affine expression then we have this situation:
5726 // Solve {0,+,A} in Range === Ax in Range
5728 // We know that zero is in the range. If A is positive then we know that
5729 // the upper value of the range must be the first possible exit value.
5730 // If A is negative then the lower of the range is the last possible loop
5731 // value. Also note that we already checked for a full range.
5732 APInt One(BitWidth,1);
5733 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5734 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5736 // The exit value should be (End+A)/A.
5737 APInt ExitVal = (End + A).udiv(A);
5738 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5740 // Evaluate at the exit value. If we really did fall out of the valid
5741 // range, then we computed our trip count, otherwise wrap around or other
5742 // things must have happened.
5743 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5744 if (Range.contains(Val->getValue()))
5745 return SE.getCouldNotCompute(); // Something strange happened
5747 // Ensure that the previous value is in the range. This is a sanity check.
5748 assert(Range.contains(
5749 EvaluateConstantChrecAtConstant(this,
5750 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5751 "Linear scev computation is off in a bad way!");
5752 return SE.getConstant(ExitValue);
5753 } else if (isQuadratic()) {
5754 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5755 // quadratic equation to solve it. To do this, we must frame our problem in
5756 // terms of figuring out when zero is crossed, instead of when
5757 // Range.getUpper() is crossed.
5758 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5759 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5760 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
5762 // Next, solve the constructed addrec
5763 std::pair<const SCEV *,const SCEV *> Roots =
5764 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5765 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5766 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5768 // Pick the smallest positive root value.
5769 if (ConstantInt *CB =
5770 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5771 R1->getValue(), R2->getValue()))) {
5772 if (CB->getZExtValue() == false)
5773 std::swap(R1, R2); // R1 is the minimum root now.
5775 // Make sure the root is not off by one. The returned iteration should
5776 // not be in the range, but the previous one should be. When solving
5777 // for "X*X < 5", for example, we should not return a root of 2.
5778 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5781 if (Range.contains(R1Val->getValue())) {
5782 // The next iteration must be out of the range...
5783 ConstantInt *NextVal =
5784 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5786 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5787 if (!Range.contains(R1Val->getValue()))
5788 return SE.getConstant(NextVal);
5789 return SE.getCouldNotCompute(); // Something strange happened
5792 // If R1 was not in the range, then it is a good return value. Make
5793 // sure that R1-1 WAS in the range though, just in case.
5794 ConstantInt *NextVal =
5795 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5796 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5797 if (Range.contains(R1Val->getValue()))
5799 return SE.getCouldNotCompute(); // Something strange happened
5804 return SE.getCouldNotCompute();
5809 //===----------------------------------------------------------------------===//
5810 // SCEVCallbackVH Class Implementation
5811 //===----------------------------------------------------------------------===//
5813 void ScalarEvolution::SCEVCallbackVH::deleted() {
5814 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5815 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5816 SE->ConstantEvolutionLoopExitValue.erase(PN);
5817 SE->ValueExprMap.erase(getValPtr());
5818 // this now dangles!
5821 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5822 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5824 // Forget all the expressions associated with users of the old value,
5825 // so that future queries will recompute the expressions using the new
5827 Value *Old = getValPtr();
5828 SmallVector<User *, 16> Worklist;
5829 SmallPtrSet<User *, 8> Visited;
5830 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5832 Worklist.push_back(*UI);
5833 while (!Worklist.empty()) {
5834 User *U = Worklist.pop_back_val();
5835 // Deleting the Old value will cause this to dangle. Postpone
5836 // that until everything else is done.
5839 if (!Visited.insert(U))
5841 if (PHINode *PN = dyn_cast<PHINode>(U))
5842 SE->ConstantEvolutionLoopExitValue.erase(PN);
5843 SE->ValueExprMap.erase(U);
5844 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5846 Worklist.push_back(*UI);
5848 // Delete the Old value.
5849 if (PHINode *PN = dyn_cast<PHINode>(Old))
5850 SE->ConstantEvolutionLoopExitValue.erase(PN);
5851 SE->ValueExprMap.erase(Old);
5852 // this now dangles!
5855 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5856 : CallbackVH(V), SE(se) {}
5858 //===----------------------------------------------------------------------===//
5859 // ScalarEvolution Class Implementation
5860 //===----------------------------------------------------------------------===//
5862 ScalarEvolution::ScalarEvolution()
5863 : FunctionPass(ID), FirstUnknown(0) {
5864 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
5867 bool ScalarEvolution::runOnFunction(Function &F) {
5869 LI = &getAnalysis<LoopInfo>();
5870 TD = getAnalysisIfAvailable<TargetData>();
5871 DT = &getAnalysis<DominatorTree>();
5875 void ScalarEvolution::releaseMemory() {
5876 // Iterate through all the SCEVUnknown instances and call their
5877 // destructors, so that they release their references to their values.
5878 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
5882 ValueExprMap.clear();
5883 BackedgeTakenCounts.clear();
5884 ConstantEvolutionLoopExitValue.clear();
5885 ValuesAtScopes.clear();
5886 LoopDispositions.clear();
5887 BlockDispositions.clear();
5888 UnsignedRanges.clear();
5889 SignedRanges.clear();
5890 UniqueSCEVs.clear();
5891 SCEVAllocator.Reset();
5894 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
5895 AU.setPreservesAll();
5896 AU.addRequiredTransitive<LoopInfo>();
5897 AU.addRequiredTransitive<DominatorTree>();
5900 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
5901 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
5904 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
5906 // Print all inner loops first
5907 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
5908 PrintLoopInfo(OS, SE, *I);
5911 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5914 SmallVector<BasicBlock *, 8> ExitBlocks;
5915 L->getExitBlocks(ExitBlocks);
5916 if (ExitBlocks.size() != 1)
5917 OS << "<multiple exits> ";
5919 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5920 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5922 OS << "Unpredictable backedge-taken count. ";
5927 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
5930 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5931 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5933 OS << "Unpredictable max backedge-taken count. ";
5939 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
5940 // ScalarEvolution's implementation of the print method is to print
5941 // out SCEV values of all instructions that are interesting. Doing
5942 // this potentially causes it to create new SCEV objects though,
5943 // which technically conflicts with the const qualifier. This isn't
5944 // observable from outside the class though, so casting away the
5945 // const isn't dangerous.
5946 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
5948 OS << "Classifying expressions for: ";
5949 WriteAsOperand(OS, F, /*PrintType=*/false);
5951 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5952 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
5955 const SCEV *SV = SE.getSCEV(&*I);
5958 const Loop *L = LI->getLoopFor((*I).getParent());
5960 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5967 OS << "\t\t" "Exits: ";
5968 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5969 if (!SE.isLoopInvariant(ExitValue, L)) {
5970 OS << "<<Unknown>>";
5979 OS << "Determining loop execution counts for: ";
5980 WriteAsOperand(OS, F, /*PrintType=*/false);
5982 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5983 PrintLoopInfo(OS, &SE, *I);
5986 ScalarEvolution::LoopDisposition
5987 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
5988 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
5989 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
5990 Values.insert(std::make_pair(L, LoopVariant));
5992 return Pair.first->second;
5994 LoopDisposition D = computeLoopDisposition(S, L);
5995 return LoopDispositions[S][L] = D;
5998 ScalarEvolution::LoopDisposition
5999 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6000 switch (S->getSCEVType()) {
6002 return LoopInvariant;
6006 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6007 case scAddRecExpr: {
6008 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6010 // If L is the addrec's loop, it's computable.
6011 if (AR->getLoop() == L)
6012 return LoopComputable;
6014 // Add recurrences are never invariant in the function-body (null loop).
6018 // This recurrence is variant w.r.t. L if L contains AR's loop.
6019 if (L->contains(AR->getLoop()))
6022 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6023 if (AR->getLoop()->contains(L))
6024 return LoopInvariant;
6026 // This recurrence is variant w.r.t. L if any of its operands
6028 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6030 if (!isLoopInvariant(*I, L))
6033 // Otherwise it's loop-invariant.
6034 return LoopInvariant;
6040 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6041 bool HasVarying = false;
6042 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6044 LoopDisposition D = getLoopDisposition(*I, L);
6045 if (D == LoopVariant)
6047 if (D == LoopComputable)
6050 return HasVarying ? LoopComputable : LoopInvariant;
6053 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6054 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6055 if (LD == LoopVariant)
6057 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6058 if (RD == LoopVariant)
6060 return (LD == LoopInvariant && RD == LoopInvariant) ?
6061 LoopInvariant : LoopComputable;
6064 // All non-instruction values are loop invariant. All instructions are loop
6065 // invariant if they are not contained in the specified loop.
6066 // Instructions are never considered invariant in the function body
6067 // (null loop) because they are defined within the "loop".
6068 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6069 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6070 return LoopInvariant;
6071 case scCouldNotCompute:
6072 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6076 llvm_unreachable("Unknown SCEV kind!");
6080 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6081 return getLoopDisposition(S, L) == LoopInvariant;
6084 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6085 return getLoopDisposition(S, L) == LoopComputable;
6088 ScalarEvolution::BlockDisposition
6089 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6090 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6091 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6092 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6094 return Pair.first->second;
6096 BlockDisposition D = computeBlockDisposition(S, BB);
6097 return BlockDispositions[S][BB] = D;
6100 ScalarEvolution::BlockDisposition
6101 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6102 switch (S->getSCEVType()) {
6104 return ProperlyDominatesBlock;
6108 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6109 case scAddRecExpr: {
6110 // This uses a "dominates" query instead of "properly dominates" query
6111 // to test for proper dominance too, because the instruction which
6112 // produces the addrec's value is a PHI, and a PHI effectively properly
6113 // dominates its entire containing block.
6114 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6115 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6116 return DoesNotDominateBlock;
6118 // FALL THROUGH into SCEVNAryExpr handling.
6123 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6125 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6127 BlockDisposition D = getBlockDisposition(*I, BB);
6128 if (D == DoesNotDominateBlock)
6129 return DoesNotDominateBlock;
6130 if (D == DominatesBlock)
6133 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6136 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6137 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6138 BlockDisposition LD = getBlockDisposition(LHS, BB);
6139 if (LD == DoesNotDominateBlock)
6140 return DoesNotDominateBlock;
6141 BlockDisposition RD = getBlockDisposition(RHS, BB);
6142 if (RD == DoesNotDominateBlock)
6143 return DoesNotDominateBlock;
6144 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6145 ProperlyDominatesBlock : DominatesBlock;
6148 if (Instruction *I =
6149 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6150 if (I->getParent() == BB)
6151 return DominatesBlock;
6152 if (DT->properlyDominates(I->getParent(), BB))
6153 return ProperlyDominatesBlock;
6154 return DoesNotDominateBlock;
6156 return ProperlyDominatesBlock;
6157 case scCouldNotCompute:
6158 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6159 return DoesNotDominateBlock;
6162 llvm_unreachable("Unknown SCEV kind!");
6163 return DoesNotDominateBlock;
6166 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6167 return getBlockDisposition(S, BB) >= DominatesBlock;
6170 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6171 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6174 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6175 switch (S->getSCEVType()) {
6180 case scSignExtend: {
6181 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6182 const SCEV *CastOp = Cast->getOperand();
6183 return Op == CastOp || hasOperand(CastOp, Op);
6190 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6191 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6193 const SCEV *NAryOp = *I;
6194 if (NAryOp == Op || hasOperand(NAryOp, Op))
6200 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6201 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6202 return LHS == Op || hasOperand(LHS, Op) ||
6203 RHS == Op || hasOperand(RHS, Op);
6207 case scCouldNotCompute:
6208 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6212 llvm_unreachable("Unknown SCEV kind!");
6216 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6217 ValuesAtScopes.erase(S);
6218 LoopDispositions.erase(S);
6219 BlockDispositions.erase(S);
6220 UnsignedRanges.erase(S);
6221 SignedRanges.erase(S);