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/DataLayout.h"
77 #include "llvm/Target/TargetLibraryInfo.h"
78 #include "llvm/Support/CommandLine.h"
79 #include "llvm/Support/ConstantRange.h"
80 #include "llvm/Support/Debug.h"
81 #include "llvm/Support/ErrorHandling.h"
82 #include "llvm/Support/GetElementPtrTypeIterator.h"
83 #include "llvm/Support/InstIterator.h"
84 #include "llvm/Support/MathExtras.h"
85 #include "llvm/Support/raw_ostream.h"
86 #include "llvm/ADT/Statistic.h"
87 #include "llvm/ADT/STLExtras.h"
88 #include "llvm/ADT/SmallPtrSet.h"
92 STATISTIC(NumArrayLenItCounts,
93 "Number of trip counts computed with array length");
94 STATISTIC(NumTripCountsComputed,
95 "Number of loops with predictable loop counts");
96 STATISTIC(NumTripCountsNotComputed,
97 "Number of loops without predictable loop counts");
98 STATISTIC(NumBruteForceTripCountsComputed,
99 "Number of loops with trip counts computed by force");
101 static cl::opt<unsigned>
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will "
104 "symbolically execute a constant "
108 // FIXME: Enable this with XDEBUG when the test suite is clean.
110 VerifySCEV("verify-scev",
111 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
113 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
114 "Scalar Evolution Analysis", false, true)
115 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
116 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
117 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
118 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
119 "Scalar Evolution Analysis", false, true)
120 char ScalarEvolution::ID = 0;
122 //===----------------------------------------------------------------------===//
123 // SCEV class definitions
124 //===----------------------------------------------------------------------===//
126 //===----------------------------------------------------------------------===//
127 // Implementation of the SCEV class.
130 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
131 void SCEV::dump() const {
137 void SCEV::print(raw_ostream &OS) const {
138 switch (getSCEVType()) {
140 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
143 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
144 const SCEV *Op = Trunc->getOperand();
145 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
146 << *Trunc->getType() << ")";
150 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
151 const SCEV *Op = ZExt->getOperand();
152 OS << "(zext " << *Op->getType() << " " << *Op << " to "
153 << *ZExt->getType() << ")";
157 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
158 const SCEV *Op = SExt->getOperand();
159 OS << "(sext " << *Op->getType() << " " << *Op << " to "
160 << *SExt->getType() << ")";
164 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
165 OS << "{" << *AR->getOperand(0);
166 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
167 OS << ",+," << *AR->getOperand(i);
169 if (AR->getNoWrapFlags(FlagNUW))
171 if (AR->getNoWrapFlags(FlagNSW))
173 if (AR->getNoWrapFlags(FlagNW) &&
174 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
176 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
184 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
185 const char *OpStr = 0;
186 switch (NAry->getSCEVType()) {
187 case scAddExpr: OpStr = " + "; break;
188 case scMulExpr: OpStr = " * "; break;
189 case scUMaxExpr: OpStr = " umax "; break;
190 case scSMaxExpr: OpStr = " smax "; break;
193 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
196 if (llvm::next(I) != E)
200 switch (NAry->getSCEVType()) {
203 if (NAry->getNoWrapFlags(FlagNUW))
205 if (NAry->getNoWrapFlags(FlagNSW))
211 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
212 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
216 const SCEVUnknown *U = cast<SCEVUnknown>(this);
218 if (U->isSizeOf(AllocTy)) {
219 OS << "sizeof(" << *AllocTy << ")";
222 if (U->isAlignOf(AllocTy)) {
223 OS << "alignof(" << *AllocTy << ")";
229 if (U->isOffsetOf(CTy, FieldNo)) {
230 OS << "offsetof(" << *CTy << ", ";
231 WriteAsOperand(OS, FieldNo, false);
236 // Otherwise just print it normally.
237 WriteAsOperand(OS, U->getValue(), false);
240 case scCouldNotCompute:
241 OS << "***COULDNOTCOMPUTE***";
245 llvm_unreachable("Unknown SCEV kind!");
248 Type *SCEV::getType() const {
249 switch (getSCEVType()) {
251 return cast<SCEVConstant>(this)->getType();
255 return cast<SCEVCastExpr>(this)->getType();
260 return cast<SCEVNAryExpr>(this)->getType();
262 return cast<SCEVAddExpr>(this)->getType();
264 return cast<SCEVUDivExpr>(this)->getType();
266 return cast<SCEVUnknown>(this)->getType();
267 case scCouldNotCompute:
268 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
270 llvm_unreachable("Unknown SCEV kind!");
274 bool SCEV::isZero() const {
275 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
276 return SC->getValue()->isZero();
280 bool SCEV::isOne() const {
281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
282 return SC->getValue()->isOne();
286 bool SCEV::isAllOnesValue() const {
287 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
288 return SC->getValue()->isAllOnesValue();
292 /// isNonConstantNegative - Return true if the specified scev is negated, but
294 bool SCEV::isNonConstantNegative() const {
295 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
296 if (!Mul) return false;
298 // If there is a constant factor, it will be first.
299 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
300 if (!SC) return false;
302 // Return true if the value is negative, this matches things like (-42 * V).
303 return SC->getValue()->getValue().isNegative();
306 SCEVCouldNotCompute::SCEVCouldNotCompute() :
307 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
309 bool SCEVCouldNotCompute::classof(const SCEV *S) {
310 return S->getSCEVType() == scCouldNotCompute;
313 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
315 ID.AddInteger(scConstant);
318 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
319 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
320 UniqueSCEVs.InsertNode(S, IP);
324 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
325 return getConstant(ConstantInt::get(getContext(), Val));
329 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
330 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
331 return getConstant(ConstantInt::get(ITy, V, isSigned));
334 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
335 unsigned SCEVTy, const SCEV *op, Type *ty)
336 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
338 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
339 const SCEV *op, Type *ty)
340 : SCEVCastExpr(ID, scTruncate, op, ty) {
341 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
342 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
343 "Cannot truncate non-integer value!");
346 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
347 const SCEV *op, Type *ty)
348 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
349 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
350 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
351 "Cannot zero extend non-integer value!");
354 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
355 const SCEV *op, Type *ty)
356 : SCEVCastExpr(ID, scSignExtend, op, ty) {
357 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
358 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
359 "Cannot sign extend non-integer value!");
362 void SCEVUnknown::deleted() {
363 // Clear this SCEVUnknown from various maps.
364 SE->forgetMemoizedResults(this);
366 // Remove this SCEVUnknown from the uniquing map.
367 SE->UniqueSCEVs.RemoveNode(this);
369 // Release the value.
373 void SCEVUnknown::allUsesReplacedWith(Value *New) {
374 // Clear this SCEVUnknown from various maps.
375 SE->forgetMemoizedResults(this);
377 // Remove this SCEVUnknown from the uniquing map.
378 SE->UniqueSCEVs.RemoveNode(this);
380 // Update this SCEVUnknown to point to the new value. This is needed
381 // because there may still be outstanding SCEVs which still point to
386 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
387 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
388 if (VCE->getOpcode() == Instruction::PtrToInt)
389 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
390 if (CE->getOpcode() == Instruction::GetElementPtr &&
391 CE->getOperand(0)->isNullValue() &&
392 CE->getNumOperands() == 2)
393 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
395 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
403 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
404 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
405 if (VCE->getOpcode() == Instruction::PtrToInt)
406 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
407 if (CE->getOpcode() == Instruction::GetElementPtr &&
408 CE->getOperand(0)->isNullValue()) {
410 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
411 if (StructType *STy = dyn_cast<StructType>(Ty))
412 if (!STy->isPacked() &&
413 CE->getNumOperands() == 3 &&
414 CE->getOperand(1)->isNullValue()) {
415 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
417 STy->getNumElements() == 2 &&
418 STy->getElementType(0)->isIntegerTy(1)) {
419 AllocTy = STy->getElementType(1);
428 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
429 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
430 if (VCE->getOpcode() == Instruction::PtrToInt)
431 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
432 if (CE->getOpcode() == Instruction::GetElementPtr &&
433 CE->getNumOperands() == 3 &&
434 CE->getOperand(0)->isNullValue() &&
435 CE->getOperand(1)->isNullValue()) {
437 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
438 // Ignore vector types here so that ScalarEvolutionExpander doesn't
439 // emit getelementptrs that index into vectors.
440 if (Ty->isStructTy() || Ty->isArrayTy()) {
442 FieldNo = CE->getOperand(2);
450 //===----------------------------------------------------------------------===//
452 //===----------------------------------------------------------------------===//
455 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
456 /// than the complexity of the RHS. This comparator is used to canonicalize
458 class SCEVComplexityCompare {
459 const LoopInfo *const LI;
461 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
463 // Return true or false if LHS is less than, or at least RHS, respectively.
464 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
465 return compare(LHS, RHS) < 0;
468 // Return negative, zero, or positive, if LHS is less than, equal to, or
469 // greater than RHS, respectively. A three-way result allows recursive
470 // comparisons to be more efficient.
471 int compare(const SCEV *LHS, const SCEV *RHS) const {
472 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
476 // Primarily, sort the SCEVs by their getSCEVType().
477 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
479 return (int)LType - (int)RType;
481 // Aside from the getSCEVType() ordering, the particular ordering
482 // isn't very important except that it's beneficial to be consistent,
483 // so that (a + b) and (b + a) don't end up as different expressions.
486 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
487 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
489 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
490 // not as complete as it could be.
491 const Value *LV = LU->getValue(), *RV = RU->getValue();
493 // Order pointer values after integer values. This helps SCEVExpander
495 bool LIsPointer = LV->getType()->isPointerTy(),
496 RIsPointer = RV->getType()->isPointerTy();
497 if (LIsPointer != RIsPointer)
498 return (int)LIsPointer - (int)RIsPointer;
500 // Compare getValueID values.
501 unsigned LID = LV->getValueID(),
502 RID = RV->getValueID();
504 return (int)LID - (int)RID;
506 // Sort arguments by their position.
507 if (const Argument *LA = dyn_cast<Argument>(LV)) {
508 const Argument *RA = cast<Argument>(RV);
509 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
510 return (int)LArgNo - (int)RArgNo;
513 // For instructions, compare their loop depth, and their operand
514 // count. This is pretty loose.
515 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
516 const Instruction *RInst = cast<Instruction>(RV);
518 // Compare loop depths.
519 const BasicBlock *LParent = LInst->getParent(),
520 *RParent = RInst->getParent();
521 if (LParent != RParent) {
522 unsigned LDepth = LI->getLoopDepth(LParent),
523 RDepth = LI->getLoopDepth(RParent);
524 if (LDepth != RDepth)
525 return (int)LDepth - (int)RDepth;
528 // Compare the number of operands.
529 unsigned LNumOps = LInst->getNumOperands(),
530 RNumOps = RInst->getNumOperands();
531 return (int)LNumOps - (int)RNumOps;
538 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
539 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
541 // Compare constant values.
542 const APInt &LA = LC->getValue()->getValue();
543 const APInt &RA = RC->getValue()->getValue();
544 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
545 if (LBitWidth != RBitWidth)
546 return (int)LBitWidth - (int)RBitWidth;
547 return LA.ult(RA) ? -1 : 1;
551 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
552 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
554 // Compare addrec loop depths.
555 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
556 if (LLoop != RLoop) {
557 unsigned LDepth = LLoop->getLoopDepth(),
558 RDepth = RLoop->getLoopDepth();
559 if (LDepth != RDepth)
560 return (int)LDepth - (int)RDepth;
563 // Addrec complexity grows with operand count.
564 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
565 if (LNumOps != RNumOps)
566 return (int)LNumOps - (int)RNumOps;
568 // Lexicographically compare.
569 for (unsigned i = 0; i != LNumOps; ++i) {
570 long X = compare(LA->getOperand(i), RA->getOperand(i));
582 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
583 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
585 // Lexicographically compare n-ary expressions.
586 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
587 for (unsigned i = 0; i != LNumOps; ++i) {
590 long X = compare(LC->getOperand(i), RC->getOperand(i));
594 return (int)LNumOps - (int)RNumOps;
598 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
599 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
601 // Lexicographically compare udiv expressions.
602 long X = compare(LC->getLHS(), RC->getLHS());
605 return compare(LC->getRHS(), RC->getRHS());
611 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
612 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
614 // Compare cast expressions by operand.
615 return compare(LC->getOperand(), RC->getOperand());
619 llvm_unreachable("Unknown SCEV kind!");
625 /// GroupByComplexity - Given a list of SCEV objects, order them by their
626 /// complexity, and group objects of the same complexity together by value.
627 /// When this routine is finished, we know that any duplicates in the vector are
628 /// consecutive and that complexity is monotonically increasing.
630 /// Note that we go take special precautions to ensure that we get deterministic
631 /// results from this routine. In other words, we don't want the results of
632 /// this to depend on where the addresses of various SCEV objects happened to
635 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
637 if (Ops.size() < 2) return; // Noop
638 if (Ops.size() == 2) {
639 // This is the common case, which also happens to be trivially simple.
641 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
642 if (SCEVComplexityCompare(LI)(RHS, LHS))
647 // Do the rough sort by complexity.
648 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
650 // Now that we are sorted by complexity, group elements of the same
651 // complexity. Note that this is, at worst, N^2, but the vector is likely to
652 // be extremely short in practice. Note that we take this approach because we
653 // do not want to depend on the addresses of the objects we are grouping.
654 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
655 const SCEV *S = Ops[i];
656 unsigned Complexity = S->getSCEVType();
658 // If there are any objects of the same complexity and same value as this
660 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
661 if (Ops[j] == S) { // Found a duplicate.
662 // Move it to immediately after i'th element.
663 std::swap(Ops[i+1], Ops[j]);
664 ++i; // no need to rescan it.
665 if (i == e-2) return; // Done!
673 //===----------------------------------------------------------------------===//
674 // Simple SCEV method implementations
675 //===----------------------------------------------------------------------===//
677 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
679 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
682 // Handle the simplest case efficiently.
684 return SE.getTruncateOrZeroExtend(It, ResultTy);
686 // We are using the following formula for BC(It, K):
688 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
690 // Suppose, W is the bitwidth of the return value. We must be prepared for
691 // overflow. Hence, we must assure that the result of our computation is
692 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
693 // safe in modular arithmetic.
695 // However, this code doesn't use exactly that formula; the formula it uses
696 // is something like the following, where T is the number of factors of 2 in
697 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
700 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
702 // This formula is trivially equivalent to the previous formula. However,
703 // this formula can be implemented much more efficiently. The trick is that
704 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
705 // arithmetic. To do exact division in modular arithmetic, all we have
706 // to do is multiply by the inverse. Therefore, this step can be done at
709 // The next issue is how to safely do the division by 2^T. The way this
710 // is done is by doing the multiplication step at a width of at least W + T
711 // bits. This way, the bottom W+T bits of the product are accurate. Then,
712 // when we perform the division by 2^T (which is equivalent to a right shift
713 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
714 // truncated out after the division by 2^T.
716 // In comparison to just directly using the first formula, this technique
717 // is much more efficient; using the first formula requires W * K bits,
718 // but this formula less than W + K bits. Also, the first formula requires
719 // a division step, whereas this formula only requires multiplies and shifts.
721 // It doesn't matter whether the subtraction step is done in the calculation
722 // width or the input iteration count's width; if the subtraction overflows,
723 // the result must be zero anyway. We prefer here to do it in the width of
724 // the induction variable because it helps a lot for certain cases; CodeGen
725 // isn't smart enough to ignore the overflow, which leads to much less
726 // efficient code if the width of the subtraction is wider than the native
729 // (It's possible to not widen at all by pulling out factors of 2 before
730 // the multiplication; for example, K=2 can be calculated as
731 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
732 // extra arithmetic, so it's not an obvious win, and it gets
733 // much more complicated for K > 3.)
735 // Protection from insane SCEVs; this bound is conservative,
736 // but it probably doesn't matter.
738 return SE.getCouldNotCompute();
740 unsigned W = SE.getTypeSizeInBits(ResultTy);
742 // Calculate K! / 2^T and T; we divide out the factors of two before
743 // multiplying for calculating K! / 2^T to avoid overflow.
744 // Other overflow doesn't matter because we only care about the bottom
745 // W bits of the result.
746 APInt OddFactorial(W, 1);
748 for (unsigned i = 3; i <= K; ++i) {
750 unsigned TwoFactors = Mult.countTrailingZeros();
752 Mult = Mult.lshr(TwoFactors);
753 OddFactorial *= Mult;
756 // We need at least W + T bits for the multiplication step
757 unsigned CalculationBits = W + T;
759 // Calculate 2^T, at width T+W.
760 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
762 // Calculate the multiplicative inverse of K! / 2^T;
763 // this multiplication factor will perform the exact division by
765 APInt Mod = APInt::getSignedMinValue(W+1);
766 APInt MultiplyFactor = OddFactorial.zext(W+1);
767 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
768 MultiplyFactor = MultiplyFactor.trunc(W);
770 // Calculate the product, at width T+W
771 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
773 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
774 for (unsigned i = 1; i != K; ++i) {
775 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
776 Dividend = SE.getMulExpr(Dividend,
777 SE.getTruncateOrZeroExtend(S, CalculationTy));
781 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
783 // Truncate the result, and divide by K! / 2^T.
785 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
786 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
789 /// evaluateAtIteration - Return the value of this chain of recurrences at
790 /// the specified iteration number. We can evaluate this recurrence by
791 /// multiplying each element in the chain by the binomial coefficient
792 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
794 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
796 /// where BC(It, k) stands for binomial coefficient.
798 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
799 ScalarEvolution &SE) const {
800 const SCEV *Result = getStart();
801 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
802 // The computation is correct in the face of overflow provided that the
803 // multiplication is performed _after_ the evaluation of the binomial
805 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
806 if (isa<SCEVCouldNotCompute>(Coeff))
809 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
814 //===----------------------------------------------------------------------===//
815 // SCEV Expression folder implementations
816 //===----------------------------------------------------------------------===//
818 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
820 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
821 "This is not a truncating conversion!");
822 assert(isSCEVable(Ty) &&
823 "This is not a conversion to a SCEVable type!");
824 Ty = getEffectiveSCEVType(Ty);
827 ID.AddInteger(scTruncate);
831 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
833 // Fold if the operand is constant.
834 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
836 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
838 // trunc(trunc(x)) --> trunc(x)
839 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
840 return getTruncateExpr(ST->getOperand(), Ty);
842 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
843 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
844 return getTruncateOrSignExtend(SS->getOperand(), Ty);
846 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
847 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
848 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
850 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
851 // eliminate all the truncates.
852 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
853 SmallVector<const SCEV *, 4> Operands;
854 bool hasTrunc = false;
855 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
856 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
857 hasTrunc = isa<SCEVTruncateExpr>(S);
858 Operands.push_back(S);
861 return getAddExpr(Operands);
862 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
865 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
866 // eliminate all the truncates.
867 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
868 SmallVector<const SCEV *, 4> Operands;
869 bool hasTrunc = false;
870 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
871 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
872 hasTrunc = isa<SCEVTruncateExpr>(S);
873 Operands.push_back(S);
876 return getMulExpr(Operands);
877 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
880 // If the input value is a chrec scev, truncate the chrec's operands.
881 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
882 SmallVector<const SCEV *, 4> Operands;
883 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
884 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
885 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
888 // The cast wasn't folded; create an explicit cast node. We can reuse
889 // the existing insert position since if we get here, we won't have
890 // made any changes which would invalidate it.
891 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
893 UniqueSCEVs.InsertNode(S, IP);
897 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
899 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
900 "This is not an extending conversion!");
901 assert(isSCEVable(Ty) &&
902 "This is not a conversion to a SCEVable type!");
903 Ty = getEffectiveSCEVType(Ty);
905 // Fold if the operand is constant.
906 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
908 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
910 // zext(zext(x)) --> zext(x)
911 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
912 return getZeroExtendExpr(SZ->getOperand(), Ty);
914 // Before doing any expensive analysis, check to see if we've already
915 // computed a SCEV for this Op and Ty.
917 ID.AddInteger(scZeroExtend);
921 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
923 // zext(trunc(x)) --> zext(x) or x or trunc(x)
924 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
925 // It's possible the bits taken off by the truncate were all zero bits. If
926 // so, we should be able to simplify this further.
927 const SCEV *X = ST->getOperand();
928 ConstantRange CR = getUnsignedRange(X);
929 unsigned TruncBits = getTypeSizeInBits(ST->getType());
930 unsigned NewBits = getTypeSizeInBits(Ty);
931 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
932 CR.zextOrTrunc(NewBits)))
933 return getTruncateOrZeroExtend(X, Ty);
936 // If the input value is a chrec scev, and we can prove that the value
937 // did not overflow the old, smaller, value, we can zero extend all of the
938 // operands (often constants). This allows analysis of something like
939 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
940 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
941 if (AR->isAffine()) {
942 const SCEV *Start = AR->getStart();
943 const SCEV *Step = AR->getStepRecurrence(*this);
944 unsigned BitWidth = getTypeSizeInBits(AR->getType());
945 const Loop *L = AR->getLoop();
947 // If we have special knowledge that this addrec won't overflow,
948 // we don't need to do any further analysis.
949 if (AR->getNoWrapFlags(SCEV::FlagNUW))
950 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
951 getZeroExtendExpr(Step, Ty),
952 L, AR->getNoWrapFlags());
954 // Check whether the backedge-taken count is SCEVCouldNotCompute.
955 // Note that this serves two purposes: It filters out loops that are
956 // simply not analyzable, and it covers the case where this code is
957 // being called from within backedge-taken count analysis, such that
958 // attempting to ask for the backedge-taken count would likely result
959 // in infinite recursion. In the later case, the analysis code will
960 // cope with a conservative value, and it will take care to purge
961 // that value once it has finished.
962 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
963 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
964 // Manually compute the final value for AR, checking for
967 // Check whether the backedge-taken count can be losslessly casted to
968 // the addrec's type. The count is always unsigned.
969 const SCEV *CastedMaxBECount =
970 getTruncateOrZeroExtend(MaxBECount, Start->getType());
971 const SCEV *RecastedMaxBECount =
972 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
973 if (MaxBECount == RecastedMaxBECount) {
974 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
975 // Check whether Start+Step*MaxBECount has no unsigned overflow.
976 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
977 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
978 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
979 const SCEV *WideMaxBECount =
980 getZeroExtendExpr(CastedMaxBECount, WideTy);
981 const SCEV *OperandExtendedAdd =
982 getAddExpr(WideStart,
983 getMulExpr(WideMaxBECount,
984 getZeroExtendExpr(Step, WideTy)));
985 if (ZAdd == OperandExtendedAdd) {
986 // Cache knowledge of AR NUW, which is propagated to this AddRec.
987 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
988 // Return the expression with the addrec on the outside.
989 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
990 getZeroExtendExpr(Step, Ty),
991 L, AR->getNoWrapFlags());
993 // Similar to above, only this time treat the step value as signed.
994 // This covers loops that count down.
996 getAddExpr(WideStart,
997 getMulExpr(WideMaxBECount,
998 getSignExtendExpr(Step, WideTy)));
999 if (ZAdd == OperandExtendedAdd) {
1000 // Cache knowledge of AR NW, which is propagated to this AddRec.
1001 // Negative step causes unsigned wrap, but it still can't self-wrap.
1002 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1003 // Return the expression with the addrec on the outside.
1004 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1005 getSignExtendExpr(Step, Ty),
1006 L, AR->getNoWrapFlags());
1010 // If the backedge is guarded by a comparison with the pre-inc value
1011 // the addrec is safe. Also, if the entry is guarded by a comparison
1012 // with the start value and the backedge is guarded by a comparison
1013 // with the post-inc value, the addrec is safe.
1014 if (isKnownPositive(Step)) {
1015 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1016 getUnsignedRange(Step).getUnsignedMax());
1017 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1018 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1019 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1020 AR->getPostIncExpr(*this), N))) {
1021 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1022 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1023 // Return the expression with the addrec on the outside.
1024 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1025 getZeroExtendExpr(Step, Ty),
1026 L, AR->getNoWrapFlags());
1028 } else if (isKnownNegative(Step)) {
1029 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1030 getSignedRange(Step).getSignedMin());
1031 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1032 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1033 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1034 AR->getPostIncExpr(*this), N))) {
1035 // Cache knowledge of AR NW, which is propagated to this AddRec.
1036 // Negative step causes unsigned wrap, but it still can't self-wrap.
1037 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1038 // Return the expression with the addrec on the outside.
1039 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1040 getSignExtendExpr(Step, Ty),
1041 L, AR->getNoWrapFlags());
1047 // The cast wasn't folded; create an explicit cast node.
1048 // Recompute the insert position, as it may have been invalidated.
1049 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1050 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1052 UniqueSCEVs.InsertNode(S, IP);
1056 // Get the limit of a recurrence such that incrementing by Step cannot cause
1057 // signed overflow as long as the value of the recurrence within the loop does
1058 // not exceed this limit before incrementing.
1059 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1060 ICmpInst::Predicate *Pred,
1061 ScalarEvolution *SE) {
1062 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1063 if (SE->isKnownPositive(Step)) {
1064 *Pred = ICmpInst::ICMP_SLT;
1065 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1066 SE->getSignedRange(Step).getSignedMax());
1068 if (SE->isKnownNegative(Step)) {
1069 *Pred = ICmpInst::ICMP_SGT;
1070 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1071 SE->getSignedRange(Step).getSignedMin());
1076 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1077 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1078 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1079 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1080 // result, the expression "Step + sext(PreIncAR)" is congruent with
1081 // "sext(PostIncAR)"
1082 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1084 ScalarEvolution *SE) {
1085 const Loop *L = AR->getLoop();
1086 const SCEV *Start = AR->getStart();
1087 const SCEV *Step = AR->getStepRecurrence(*SE);
1089 // Check for a simple looking step prior to loop entry.
1090 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1094 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1095 // subtraction is expensive. For this purpose, perform a quick and dirty
1096 // difference, by checking for Step in the operand list.
1097 SmallVector<const SCEV *, 4> DiffOps;
1098 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1101 DiffOps.push_back(*I);
1103 if (DiffOps.size() == SA->getNumOperands())
1106 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1107 // same three conditions that getSignExtendedExpr checks.
1109 // 1. NSW flags on the step increment.
1110 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1111 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1112 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1114 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1117 // 2. Direct overflow check on the step operation's expression.
1118 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1119 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1120 const SCEV *OperandExtendedStart =
1121 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1122 SE->getSignExtendExpr(Step, WideTy));
1123 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1124 // Cache knowledge of PreAR NSW.
1126 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1127 // FIXME: this optimization needs a unit test
1128 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1132 // 3. Loop precondition.
1133 ICmpInst::Predicate Pred;
1134 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1136 if (OverflowLimit &&
1137 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1143 // Get the normalized sign-extended expression for this AddRec's Start.
1144 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1146 ScalarEvolution *SE) {
1147 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1149 return SE->getSignExtendExpr(AR->getStart(), Ty);
1151 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1152 SE->getSignExtendExpr(PreStart, Ty));
1155 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1157 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1158 "This is not an extending conversion!");
1159 assert(isSCEVable(Ty) &&
1160 "This is not a conversion to a SCEVable type!");
1161 Ty = getEffectiveSCEVType(Ty);
1163 // Fold if the operand is constant.
1164 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1166 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1168 // sext(sext(x)) --> sext(x)
1169 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1170 return getSignExtendExpr(SS->getOperand(), Ty);
1172 // sext(zext(x)) --> zext(x)
1173 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1174 return getZeroExtendExpr(SZ->getOperand(), Ty);
1176 // Before doing any expensive analysis, check to see if we've already
1177 // computed a SCEV for this Op and Ty.
1178 FoldingSetNodeID ID;
1179 ID.AddInteger(scSignExtend);
1183 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1185 // If the input value is provably positive, build a zext instead.
1186 if (isKnownNonNegative(Op))
1187 return getZeroExtendExpr(Op, Ty);
1189 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1190 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1191 // It's possible the bits taken off by the truncate were all sign bits. If
1192 // so, we should be able to simplify this further.
1193 const SCEV *X = ST->getOperand();
1194 ConstantRange CR = getSignedRange(X);
1195 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1196 unsigned NewBits = getTypeSizeInBits(Ty);
1197 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1198 CR.sextOrTrunc(NewBits)))
1199 return getTruncateOrSignExtend(X, Ty);
1202 // If the input value is a chrec scev, and we can prove that the value
1203 // did not overflow the old, smaller, value, we can sign extend all of the
1204 // operands (often constants). This allows analysis of something like
1205 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1206 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1207 if (AR->isAffine()) {
1208 const SCEV *Start = AR->getStart();
1209 const SCEV *Step = AR->getStepRecurrence(*this);
1210 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1211 const Loop *L = AR->getLoop();
1213 // If we have special knowledge that this addrec won't overflow,
1214 // we don't need to do any further analysis.
1215 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1216 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1217 getSignExtendExpr(Step, Ty),
1220 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1221 // Note that this serves two purposes: It filters out loops that are
1222 // simply not analyzable, and it covers the case where this code is
1223 // being called from within backedge-taken count analysis, such that
1224 // attempting to ask for the backedge-taken count would likely result
1225 // in infinite recursion. In the later case, the analysis code will
1226 // cope with a conservative value, and it will take care to purge
1227 // that value once it has finished.
1228 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1229 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1230 // Manually compute the final value for AR, checking for
1233 // Check whether the backedge-taken count can be losslessly casted to
1234 // the addrec's type. The count is always unsigned.
1235 const SCEV *CastedMaxBECount =
1236 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1237 const SCEV *RecastedMaxBECount =
1238 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1239 if (MaxBECount == RecastedMaxBECount) {
1240 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1241 // Check whether Start+Step*MaxBECount has no signed overflow.
1242 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1243 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1244 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1245 const SCEV *WideMaxBECount =
1246 getZeroExtendExpr(CastedMaxBECount, WideTy);
1247 const SCEV *OperandExtendedAdd =
1248 getAddExpr(WideStart,
1249 getMulExpr(WideMaxBECount,
1250 getSignExtendExpr(Step, WideTy)));
1251 if (SAdd == OperandExtendedAdd) {
1252 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1253 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1254 // Return the expression with the addrec on the outside.
1255 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1256 getSignExtendExpr(Step, Ty),
1257 L, AR->getNoWrapFlags());
1259 // Similar to above, only this time treat the step value as unsigned.
1260 // This covers loops that count up with an unsigned step.
1261 OperandExtendedAdd =
1262 getAddExpr(WideStart,
1263 getMulExpr(WideMaxBECount,
1264 getZeroExtendExpr(Step, WideTy)));
1265 if (SAdd == OperandExtendedAdd) {
1266 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1267 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1268 // Return the expression with the addrec on the outside.
1269 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1270 getZeroExtendExpr(Step, Ty),
1271 L, AR->getNoWrapFlags());
1275 // If the backedge is guarded by a comparison with the pre-inc value
1276 // the addrec is safe. Also, if the entry is guarded by a comparison
1277 // with the start value and the backedge is guarded by a comparison
1278 // with the post-inc value, the addrec is safe.
1279 ICmpInst::Predicate Pred;
1280 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1281 if (OverflowLimit &&
1282 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1283 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1284 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1286 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1287 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1288 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1289 getSignExtendExpr(Step, Ty),
1290 L, AR->getNoWrapFlags());
1295 // The cast wasn't folded; create an explicit cast node.
1296 // Recompute the insert position, as it may have been invalidated.
1297 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1298 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1300 UniqueSCEVs.InsertNode(S, IP);
1304 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1305 /// unspecified bits out to the given type.
1307 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1309 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1310 "This is not an extending conversion!");
1311 assert(isSCEVable(Ty) &&
1312 "This is not a conversion to a SCEVable type!");
1313 Ty = getEffectiveSCEVType(Ty);
1315 // Sign-extend negative constants.
1316 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1317 if (SC->getValue()->getValue().isNegative())
1318 return getSignExtendExpr(Op, Ty);
1320 // Peel off a truncate cast.
1321 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1322 const SCEV *NewOp = T->getOperand();
1323 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1324 return getAnyExtendExpr(NewOp, Ty);
1325 return getTruncateOrNoop(NewOp, Ty);
1328 // Next try a zext cast. If the cast is folded, use it.
1329 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1330 if (!isa<SCEVZeroExtendExpr>(ZExt))
1333 // Next try a sext cast. If the cast is folded, use it.
1334 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1335 if (!isa<SCEVSignExtendExpr>(SExt))
1338 // Force the cast to be folded into the operands of an addrec.
1339 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1340 SmallVector<const SCEV *, 4> Ops;
1341 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1343 Ops.push_back(getAnyExtendExpr(*I, Ty));
1344 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1347 // If the expression is obviously signed, use the sext cast value.
1348 if (isa<SCEVSMaxExpr>(Op))
1351 // Absent any other information, use the zext cast value.
1355 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1356 /// a list of operands to be added under the given scale, update the given
1357 /// map. This is a helper function for getAddRecExpr. As an example of
1358 /// what it does, given a sequence of operands that would form an add
1359 /// expression like this:
1361 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1363 /// where A and B are constants, update the map with these values:
1365 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1367 /// and add 13 + A*B*29 to AccumulatedConstant.
1368 /// This will allow getAddRecExpr to produce this:
1370 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1372 /// This form often exposes folding opportunities that are hidden in
1373 /// the original operand list.
1375 /// Return true iff it appears that any interesting folding opportunities
1376 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1377 /// the common case where no interesting opportunities are present, and
1378 /// is also used as a check to avoid infinite recursion.
1381 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1382 SmallVector<const SCEV *, 8> &NewOps,
1383 APInt &AccumulatedConstant,
1384 const SCEV *const *Ops, size_t NumOperands,
1386 ScalarEvolution &SE) {
1387 bool Interesting = false;
1389 // Iterate over the add operands. They are sorted, with constants first.
1391 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1393 // Pull a buried constant out to the outside.
1394 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1396 AccumulatedConstant += Scale * C->getValue()->getValue();
1399 // Next comes everything else. We're especially interested in multiplies
1400 // here, but they're in the middle, so just visit the rest with one loop.
1401 for (; i != NumOperands; ++i) {
1402 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1403 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1405 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1406 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1407 // A multiplication of a constant with another add; recurse.
1408 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1410 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1411 Add->op_begin(), Add->getNumOperands(),
1414 // A multiplication of a constant with some other value. Update
1416 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1417 const SCEV *Key = SE.getMulExpr(MulOps);
1418 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1419 M.insert(std::make_pair(Key, NewScale));
1421 NewOps.push_back(Pair.first->first);
1423 Pair.first->second += NewScale;
1424 // The map already had an entry for this value, which may indicate
1425 // a folding opportunity.
1430 // An ordinary operand. Update the map.
1431 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1432 M.insert(std::make_pair(Ops[i], Scale));
1434 NewOps.push_back(Pair.first->first);
1436 Pair.first->second += Scale;
1437 // The map already had an entry for this value, which may indicate
1438 // a folding opportunity.
1448 struct APIntCompare {
1449 bool operator()(const APInt &LHS, const APInt &RHS) const {
1450 return LHS.ult(RHS);
1455 /// getAddExpr - Get a canonical add expression, or something simpler if
1457 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1458 SCEV::NoWrapFlags Flags) {
1459 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1460 "only nuw or nsw allowed");
1461 assert(!Ops.empty() && "Cannot get empty add!");
1462 if (Ops.size() == 1) return Ops[0];
1464 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1465 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1466 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1467 "SCEVAddExpr operand types don't match!");
1470 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1472 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1473 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1474 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1476 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1477 E = Ops.end(); I != E; ++I)
1478 if (!isKnownNonNegative(*I)) {
1482 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1485 // Sort by complexity, this groups all similar expression types together.
1486 GroupByComplexity(Ops, LI);
1488 // If there are any constants, fold them together.
1490 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1492 assert(Idx < Ops.size());
1493 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1494 // We found two constants, fold them together!
1495 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1496 RHSC->getValue()->getValue());
1497 if (Ops.size() == 2) return Ops[0];
1498 Ops.erase(Ops.begin()+1); // Erase the folded element
1499 LHSC = cast<SCEVConstant>(Ops[0]);
1502 // If we are left with a constant zero being added, strip it off.
1503 if (LHSC->getValue()->isZero()) {
1504 Ops.erase(Ops.begin());
1508 if (Ops.size() == 1) return Ops[0];
1511 // Okay, check to see if the same value occurs in the operand list more than
1512 // once. If so, merge them together into an multiply expression. Since we
1513 // sorted the list, these values are required to be adjacent.
1514 Type *Ty = Ops[0]->getType();
1515 bool FoundMatch = false;
1516 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1517 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1518 // Scan ahead to count how many equal operands there are.
1520 while (i+Count != e && Ops[i+Count] == Ops[i])
1522 // Merge the values into a multiply.
1523 const SCEV *Scale = getConstant(Ty, Count);
1524 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1525 if (Ops.size() == Count)
1528 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1529 --i; e -= Count - 1;
1533 return getAddExpr(Ops, Flags);
1535 // Check for truncates. If all the operands are truncated from the same
1536 // type, see if factoring out the truncate would permit the result to be
1537 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1538 // if the contents of the resulting outer trunc fold to something simple.
1539 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1540 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1541 Type *DstType = Trunc->getType();
1542 Type *SrcType = Trunc->getOperand()->getType();
1543 SmallVector<const SCEV *, 8> LargeOps;
1545 // Check all the operands to see if they can be represented in the
1546 // source type of the truncate.
1547 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1548 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1549 if (T->getOperand()->getType() != SrcType) {
1553 LargeOps.push_back(T->getOperand());
1554 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1555 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1556 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1557 SmallVector<const SCEV *, 8> LargeMulOps;
1558 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1559 if (const SCEVTruncateExpr *T =
1560 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1561 if (T->getOperand()->getType() != SrcType) {
1565 LargeMulOps.push_back(T->getOperand());
1566 } else if (const SCEVConstant *C =
1567 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1568 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1575 LargeOps.push_back(getMulExpr(LargeMulOps));
1582 // Evaluate the expression in the larger type.
1583 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1584 // If it folds to something simple, use it. Otherwise, don't.
1585 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1586 return getTruncateExpr(Fold, DstType);
1590 // Skip past any other cast SCEVs.
1591 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1594 // If there are add operands they would be next.
1595 if (Idx < Ops.size()) {
1596 bool DeletedAdd = false;
1597 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1598 // If we have an add, expand the add operands onto the end of the operands
1600 Ops.erase(Ops.begin()+Idx);
1601 Ops.append(Add->op_begin(), Add->op_end());
1605 // If we deleted at least one add, we added operands to the end of the list,
1606 // and they are not necessarily sorted. Recurse to resort and resimplify
1607 // any operands we just acquired.
1609 return getAddExpr(Ops);
1612 // Skip over the add expression until we get to a multiply.
1613 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1616 // Check to see if there are any folding opportunities present with
1617 // operands multiplied by constant values.
1618 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1619 uint64_t BitWidth = getTypeSizeInBits(Ty);
1620 DenseMap<const SCEV *, APInt> M;
1621 SmallVector<const SCEV *, 8> NewOps;
1622 APInt AccumulatedConstant(BitWidth, 0);
1623 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1624 Ops.data(), Ops.size(),
1625 APInt(BitWidth, 1), *this)) {
1626 // Some interesting folding opportunity is present, so its worthwhile to
1627 // re-generate the operands list. Group the operands by constant scale,
1628 // to avoid multiplying by the same constant scale multiple times.
1629 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1630 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1631 E = NewOps.end(); I != E; ++I)
1632 MulOpLists[M.find(*I)->second].push_back(*I);
1633 // Re-generate the operands list.
1635 if (AccumulatedConstant != 0)
1636 Ops.push_back(getConstant(AccumulatedConstant));
1637 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1638 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1640 Ops.push_back(getMulExpr(getConstant(I->first),
1641 getAddExpr(I->second)));
1643 return getConstant(Ty, 0);
1644 if (Ops.size() == 1)
1646 return getAddExpr(Ops);
1650 // If we are adding something to a multiply expression, make sure the
1651 // something is not already an operand of the multiply. If so, merge it into
1653 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1654 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1655 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1656 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1657 if (isa<SCEVConstant>(MulOpSCEV))
1659 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1660 if (MulOpSCEV == Ops[AddOp]) {
1661 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1662 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1663 if (Mul->getNumOperands() != 2) {
1664 // If the multiply has more than two operands, we must get the
1666 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1667 Mul->op_begin()+MulOp);
1668 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1669 InnerMul = getMulExpr(MulOps);
1671 const SCEV *One = getConstant(Ty, 1);
1672 const SCEV *AddOne = getAddExpr(One, InnerMul);
1673 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1674 if (Ops.size() == 2) return OuterMul;
1676 Ops.erase(Ops.begin()+AddOp);
1677 Ops.erase(Ops.begin()+Idx-1);
1679 Ops.erase(Ops.begin()+Idx);
1680 Ops.erase(Ops.begin()+AddOp-1);
1682 Ops.push_back(OuterMul);
1683 return getAddExpr(Ops);
1686 // Check this multiply against other multiplies being added together.
1687 for (unsigned OtherMulIdx = Idx+1;
1688 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1690 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1691 // If MulOp occurs in OtherMul, we can fold the two multiplies
1693 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1694 OMulOp != e; ++OMulOp)
1695 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1696 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1697 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1698 if (Mul->getNumOperands() != 2) {
1699 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1700 Mul->op_begin()+MulOp);
1701 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1702 InnerMul1 = getMulExpr(MulOps);
1704 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1705 if (OtherMul->getNumOperands() != 2) {
1706 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1707 OtherMul->op_begin()+OMulOp);
1708 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1709 InnerMul2 = getMulExpr(MulOps);
1711 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1712 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1713 if (Ops.size() == 2) return OuterMul;
1714 Ops.erase(Ops.begin()+Idx);
1715 Ops.erase(Ops.begin()+OtherMulIdx-1);
1716 Ops.push_back(OuterMul);
1717 return getAddExpr(Ops);
1723 // If there are any add recurrences in the operands list, see if any other
1724 // added values are loop invariant. If so, we can fold them into the
1726 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1729 // Scan over all recurrences, trying to fold loop invariants into them.
1730 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1731 // Scan all of the other operands to this add and add them to the vector if
1732 // they are loop invariant w.r.t. the recurrence.
1733 SmallVector<const SCEV *, 8> LIOps;
1734 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1735 const Loop *AddRecLoop = AddRec->getLoop();
1736 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1737 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1738 LIOps.push_back(Ops[i]);
1739 Ops.erase(Ops.begin()+i);
1743 // If we found some loop invariants, fold them into the recurrence.
1744 if (!LIOps.empty()) {
1745 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1746 LIOps.push_back(AddRec->getStart());
1748 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1750 AddRecOps[0] = getAddExpr(LIOps);
1752 // Build the new addrec. Propagate the NUW and NSW flags if both the
1753 // outer add and the inner addrec are guaranteed to have no overflow.
1754 // Always propagate NW.
1755 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1756 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1758 // If all of the other operands were loop invariant, we are done.
1759 if (Ops.size() == 1) return NewRec;
1761 // Otherwise, add the folded AddRec by the non-invariant parts.
1762 for (unsigned i = 0;; ++i)
1763 if (Ops[i] == AddRec) {
1767 return getAddExpr(Ops);
1770 // Okay, if there weren't any loop invariants to be folded, check to see if
1771 // there are multiple AddRec's with the same loop induction variable being
1772 // added together. If so, we can fold them.
1773 for (unsigned OtherIdx = Idx+1;
1774 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1776 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1777 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1778 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1780 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1782 if (const SCEVAddRecExpr *OtherAddRec =
1783 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1784 if (OtherAddRec->getLoop() == AddRecLoop) {
1785 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1787 if (i >= AddRecOps.size()) {
1788 AddRecOps.append(OtherAddRec->op_begin()+i,
1789 OtherAddRec->op_end());
1792 AddRecOps[i] = getAddExpr(AddRecOps[i],
1793 OtherAddRec->getOperand(i));
1795 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1797 // Step size has changed, so we cannot guarantee no self-wraparound.
1798 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1799 return getAddExpr(Ops);
1802 // Otherwise couldn't fold anything into this recurrence. Move onto the
1806 // Okay, it looks like we really DO need an add expr. Check to see if we
1807 // already have one, otherwise create a new one.
1808 FoldingSetNodeID ID;
1809 ID.AddInteger(scAddExpr);
1810 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1811 ID.AddPointer(Ops[i]);
1814 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1816 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1817 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1818 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1820 UniqueSCEVs.InsertNode(S, IP);
1822 S->setNoWrapFlags(Flags);
1826 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1828 if (j > 1 && k / j != i) Overflow = true;
1832 /// Compute the result of "n choose k", the binomial coefficient. If an
1833 /// intermediate computation overflows, Overflow will be set and the return will
1834 /// be garbage. Overflow is not cleared on absence of overflow.
1835 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1836 // We use the multiplicative formula:
1837 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1838 // At each iteration, we take the n-th term of the numeral and divide by the
1839 // (k-n)th term of the denominator. This division will always produce an
1840 // integral result, and helps reduce the chance of overflow in the
1841 // intermediate computations. However, we can still overflow even when the
1842 // final result would fit.
1844 if (n == 0 || n == k) return 1;
1845 if (k > n) return 0;
1851 for (uint64_t i = 1; i <= k; ++i) {
1852 r = umul_ov(r, n-(i-1), Overflow);
1858 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1860 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1861 SCEV::NoWrapFlags Flags) {
1862 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1863 "only nuw or nsw allowed");
1864 assert(!Ops.empty() && "Cannot get empty mul!");
1865 if (Ops.size() == 1) return Ops[0];
1867 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1868 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1869 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1870 "SCEVMulExpr operand types don't match!");
1873 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1875 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1876 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1877 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1879 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1880 E = Ops.end(); I != E; ++I)
1881 if (!isKnownNonNegative(*I)) {
1885 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1888 // Sort by complexity, this groups all similar expression types together.
1889 GroupByComplexity(Ops, LI);
1891 // If there are any constants, fold them together.
1893 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1895 // C1*(C2+V) -> C1*C2 + C1*V
1896 if (Ops.size() == 2)
1897 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1898 if (Add->getNumOperands() == 2 &&
1899 isa<SCEVConstant>(Add->getOperand(0)))
1900 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1901 getMulExpr(LHSC, Add->getOperand(1)));
1904 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1905 // We found two constants, fold them together!
1906 ConstantInt *Fold = ConstantInt::get(getContext(),
1907 LHSC->getValue()->getValue() *
1908 RHSC->getValue()->getValue());
1909 Ops[0] = getConstant(Fold);
1910 Ops.erase(Ops.begin()+1); // Erase the folded element
1911 if (Ops.size() == 1) return Ops[0];
1912 LHSC = cast<SCEVConstant>(Ops[0]);
1915 // If we are left with a constant one being multiplied, strip it off.
1916 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1917 Ops.erase(Ops.begin());
1919 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1920 // If we have a multiply of zero, it will always be zero.
1922 } else if (Ops[0]->isAllOnesValue()) {
1923 // If we have a mul by -1 of an add, try distributing the -1 among the
1925 if (Ops.size() == 2) {
1926 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1927 SmallVector<const SCEV *, 4> NewOps;
1928 bool AnyFolded = false;
1929 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1930 E = Add->op_end(); I != E; ++I) {
1931 const SCEV *Mul = getMulExpr(Ops[0], *I);
1932 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1933 NewOps.push_back(Mul);
1936 return getAddExpr(NewOps);
1938 else if (const SCEVAddRecExpr *
1939 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1940 // Negation preserves a recurrence's no self-wrap property.
1941 SmallVector<const SCEV *, 4> Operands;
1942 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1943 E = AddRec->op_end(); I != E; ++I) {
1944 Operands.push_back(getMulExpr(Ops[0], *I));
1946 return getAddRecExpr(Operands, AddRec->getLoop(),
1947 AddRec->getNoWrapFlags(SCEV::FlagNW));
1952 if (Ops.size() == 1)
1956 // Skip over the add expression until we get to a multiply.
1957 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1960 // If there are mul operands inline them all into this expression.
1961 if (Idx < Ops.size()) {
1962 bool DeletedMul = false;
1963 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1964 // If we have an mul, expand the mul operands onto the end of the operands
1966 Ops.erase(Ops.begin()+Idx);
1967 Ops.append(Mul->op_begin(), Mul->op_end());
1971 // If we deleted at least one mul, we added operands to the end of the list,
1972 // and they are not necessarily sorted. Recurse to resort and resimplify
1973 // any operands we just acquired.
1975 return getMulExpr(Ops);
1978 // If there are any add recurrences in the operands list, see if any other
1979 // added values are loop invariant. If so, we can fold them into the
1981 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1984 // Scan over all recurrences, trying to fold loop invariants into them.
1985 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1986 // Scan all of the other operands to this mul and add them to the vector if
1987 // they are loop invariant w.r.t. the recurrence.
1988 SmallVector<const SCEV *, 8> LIOps;
1989 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1990 const Loop *AddRecLoop = AddRec->getLoop();
1991 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1992 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1993 LIOps.push_back(Ops[i]);
1994 Ops.erase(Ops.begin()+i);
1998 // If we found some loop invariants, fold them into the recurrence.
1999 if (!LIOps.empty()) {
2000 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2001 SmallVector<const SCEV *, 4> NewOps;
2002 NewOps.reserve(AddRec->getNumOperands());
2003 const SCEV *Scale = getMulExpr(LIOps);
2004 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2005 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2007 // Build the new addrec. Propagate the NUW and NSW flags if both the
2008 // outer mul and the inner addrec are guaranteed to have no overflow.
2010 // No self-wrap cannot be guaranteed after changing the step size, but
2011 // will be inferred if either NUW or NSW is true.
2012 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2013 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2015 // If all of the other operands were loop invariant, we are done.
2016 if (Ops.size() == 1) return NewRec;
2018 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2019 for (unsigned i = 0;; ++i)
2020 if (Ops[i] == AddRec) {
2024 return getMulExpr(Ops);
2027 // Okay, if there weren't any loop invariants to be folded, check to see if
2028 // there are multiple AddRec's with the same loop induction variable being
2029 // multiplied together. If so, we can fold them.
2030 for (unsigned OtherIdx = Idx+1;
2031 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2033 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2036 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2037 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2038 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2039 // ]]],+,...up to x=2n}.
2040 // Note that the arguments to choose() are always integers with values
2041 // known at compile time, never SCEV objects.
2043 // The implementation avoids pointless extra computations when the two
2044 // addrec's are of different length (mathematically, it's equivalent to
2045 // an infinite stream of zeros on the right).
2046 bool OpsModified = false;
2047 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2049 const SCEVAddRecExpr *OtherAddRec =
2050 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2051 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2054 bool Overflow = false;
2055 Type *Ty = AddRec->getType();
2056 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2057 SmallVector<const SCEV*, 7> AddRecOps;
2058 for (int x = 0, xe = AddRec->getNumOperands() +
2059 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2060 const SCEV *Term = getConstant(Ty, 0);
2061 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2062 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2063 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2064 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2065 z < ze && !Overflow; ++z) {
2066 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2068 if (LargerThan64Bits)
2069 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2071 Coeff = Coeff1*Coeff2;
2072 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2073 const SCEV *Term1 = AddRec->getOperand(y-z);
2074 const SCEV *Term2 = OtherAddRec->getOperand(z);
2075 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2078 AddRecOps.push_back(Term);
2081 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2083 if (Ops.size() == 2) return NewAddRec;
2084 Ops[Idx] = NewAddRec;
2085 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2087 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2093 return getMulExpr(Ops);
2096 // Otherwise couldn't fold anything into this recurrence. Move onto the
2100 // Okay, it looks like we really DO need an mul expr. Check to see if we
2101 // already have one, otherwise create a new one.
2102 FoldingSetNodeID ID;
2103 ID.AddInteger(scMulExpr);
2104 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2105 ID.AddPointer(Ops[i]);
2108 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2110 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2111 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2112 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2114 UniqueSCEVs.InsertNode(S, IP);
2116 S->setNoWrapFlags(Flags);
2120 /// getUDivExpr - Get a canonical unsigned division expression, or something
2121 /// simpler if possible.
2122 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2124 assert(getEffectiveSCEVType(LHS->getType()) ==
2125 getEffectiveSCEVType(RHS->getType()) &&
2126 "SCEVUDivExpr operand types don't match!");
2128 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2129 if (RHSC->getValue()->equalsInt(1))
2130 return LHS; // X udiv 1 --> x
2131 // If the denominator is zero, the result of the udiv is undefined. Don't
2132 // try to analyze it, because the resolution chosen here may differ from
2133 // the resolution chosen in other parts of the compiler.
2134 if (!RHSC->getValue()->isZero()) {
2135 // Determine if the division can be folded into the operands of
2137 // TODO: Generalize this to non-constants by using known-bits information.
2138 Type *Ty = LHS->getType();
2139 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2140 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2141 // For non-power-of-two values, effectively round the value up to the
2142 // nearest power of two.
2143 if (!RHSC->getValue()->getValue().isPowerOf2())
2145 IntegerType *ExtTy =
2146 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2147 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2148 if (const SCEVConstant *Step =
2149 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2150 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2151 const APInt &StepInt = Step->getValue()->getValue();
2152 const APInt &DivInt = RHSC->getValue()->getValue();
2153 if (!StepInt.urem(DivInt) &&
2154 getZeroExtendExpr(AR, ExtTy) ==
2155 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2156 getZeroExtendExpr(Step, ExtTy),
2157 AR->getLoop(), SCEV::FlagAnyWrap)) {
2158 SmallVector<const SCEV *, 4> Operands;
2159 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2160 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2161 return getAddRecExpr(Operands, AR->getLoop(),
2164 /// Get a canonical UDivExpr for a recurrence.
2165 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2166 // We can currently only fold X%N if X is constant.
2167 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2168 if (StartC && !DivInt.urem(StepInt) &&
2169 getZeroExtendExpr(AR, ExtTy) ==
2170 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2171 getZeroExtendExpr(Step, ExtTy),
2172 AR->getLoop(), SCEV::FlagAnyWrap)) {
2173 const APInt &StartInt = StartC->getValue()->getValue();
2174 const APInt &StartRem = StartInt.urem(StepInt);
2176 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2177 AR->getLoop(), SCEV::FlagNW);
2180 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2181 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2182 SmallVector<const SCEV *, 4> Operands;
2183 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2184 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2185 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2186 // Find an operand that's safely divisible.
2187 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2188 const SCEV *Op = M->getOperand(i);
2189 const SCEV *Div = getUDivExpr(Op, RHSC);
2190 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2191 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2194 return getMulExpr(Operands);
2198 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2199 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2200 SmallVector<const SCEV *, 4> Operands;
2201 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2202 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2203 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2205 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2206 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2207 if (isa<SCEVUDivExpr>(Op) ||
2208 getMulExpr(Op, RHS) != A->getOperand(i))
2210 Operands.push_back(Op);
2212 if (Operands.size() == A->getNumOperands())
2213 return getAddExpr(Operands);
2217 // Fold if both operands are constant.
2218 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2219 Constant *LHSCV = LHSC->getValue();
2220 Constant *RHSCV = RHSC->getValue();
2221 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2227 FoldingSetNodeID ID;
2228 ID.AddInteger(scUDivExpr);
2232 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2233 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2235 UniqueSCEVs.InsertNode(S, IP);
2240 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2241 /// Simplify the expression as much as possible.
2242 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2244 SCEV::NoWrapFlags Flags) {
2245 SmallVector<const SCEV *, 4> Operands;
2246 Operands.push_back(Start);
2247 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2248 if (StepChrec->getLoop() == L) {
2249 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2250 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2253 Operands.push_back(Step);
2254 return getAddRecExpr(Operands, L, Flags);
2257 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2258 /// Simplify the expression as much as possible.
2260 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2261 const Loop *L, SCEV::NoWrapFlags Flags) {
2262 if (Operands.size() == 1) return Operands[0];
2264 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2265 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2266 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2267 "SCEVAddRecExpr operand types don't match!");
2268 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2269 assert(isLoopInvariant(Operands[i], L) &&
2270 "SCEVAddRecExpr operand is not loop-invariant!");
2273 if (Operands.back()->isZero()) {
2274 Operands.pop_back();
2275 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2278 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2279 // use that information to infer NUW and NSW flags. However, computing a
2280 // BE count requires calling getAddRecExpr, so we may not yet have a
2281 // meaningful BE count at this point (and if we don't, we'd be stuck
2282 // with a SCEVCouldNotCompute as the cached BE count).
2284 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2286 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2287 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2288 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2290 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2291 E = Operands.end(); I != E; ++I)
2292 if (!isKnownNonNegative(*I)) {
2296 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2299 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2300 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2301 const Loop *NestedLoop = NestedAR->getLoop();
2302 if (L->contains(NestedLoop) ?
2303 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2304 (!NestedLoop->contains(L) &&
2305 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2306 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2307 NestedAR->op_end());
2308 Operands[0] = NestedAR->getStart();
2309 // AddRecs require their operands be loop-invariant with respect to their
2310 // loops. Don't perform this transformation if it would break this
2312 bool AllInvariant = true;
2313 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2314 if (!isLoopInvariant(Operands[i], L)) {
2315 AllInvariant = false;
2319 // Create a recurrence for the outer loop with the same step size.
2321 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2322 // inner recurrence has the same property.
2323 SCEV::NoWrapFlags OuterFlags =
2324 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2326 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2327 AllInvariant = true;
2328 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2329 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2330 AllInvariant = false;
2334 // Ok, both add recurrences are valid after the transformation.
2336 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2337 // the outer recurrence has the same property.
2338 SCEV::NoWrapFlags InnerFlags =
2339 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2340 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2343 // Reset Operands to its original state.
2344 Operands[0] = NestedAR;
2348 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2349 // already have one, otherwise create a new one.
2350 FoldingSetNodeID ID;
2351 ID.AddInteger(scAddRecExpr);
2352 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2353 ID.AddPointer(Operands[i]);
2357 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2359 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2360 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2361 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2362 O, Operands.size(), L);
2363 UniqueSCEVs.InsertNode(S, IP);
2365 S->setNoWrapFlags(Flags);
2369 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2371 SmallVector<const SCEV *, 2> Ops;
2374 return getSMaxExpr(Ops);
2378 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2379 assert(!Ops.empty() && "Cannot get empty smax!");
2380 if (Ops.size() == 1) return Ops[0];
2382 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2383 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2384 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2385 "SCEVSMaxExpr operand types don't match!");
2388 // Sort by complexity, this groups all similar expression types together.
2389 GroupByComplexity(Ops, LI);
2391 // If there are any constants, fold them together.
2393 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2395 assert(Idx < Ops.size());
2396 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2397 // We found two constants, fold them together!
2398 ConstantInt *Fold = ConstantInt::get(getContext(),
2399 APIntOps::smax(LHSC->getValue()->getValue(),
2400 RHSC->getValue()->getValue()));
2401 Ops[0] = getConstant(Fold);
2402 Ops.erase(Ops.begin()+1); // Erase the folded element
2403 if (Ops.size() == 1) return Ops[0];
2404 LHSC = cast<SCEVConstant>(Ops[0]);
2407 // If we are left with a constant minimum-int, strip it off.
2408 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2409 Ops.erase(Ops.begin());
2411 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2412 // If we have an smax with a constant maximum-int, it will always be
2417 if (Ops.size() == 1) return Ops[0];
2420 // Find the first SMax
2421 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2424 // Check to see if one of the operands is an SMax. If so, expand its operands
2425 // onto our operand list, and recurse to simplify.
2426 if (Idx < Ops.size()) {
2427 bool DeletedSMax = false;
2428 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2429 Ops.erase(Ops.begin()+Idx);
2430 Ops.append(SMax->op_begin(), SMax->op_end());
2435 return getSMaxExpr(Ops);
2438 // Okay, check to see if the same value occurs in the operand list twice. If
2439 // so, delete one. Since we sorted the list, these values are required to
2441 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2442 // X smax Y smax Y --> X smax Y
2443 // X smax Y --> X, if X is always greater than Y
2444 if (Ops[i] == Ops[i+1] ||
2445 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2446 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2448 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2449 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2453 if (Ops.size() == 1) return Ops[0];
2455 assert(!Ops.empty() && "Reduced smax down to nothing!");
2457 // Okay, it looks like we really DO need an smax expr. Check to see if we
2458 // already have one, otherwise create a new one.
2459 FoldingSetNodeID ID;
2460 ID.AddInteger(scSMaxExpr);
2461 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2462 ID.AddPointer(Ops[i]);
2464 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2465 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2466 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2467 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2469 UniqueSCEVs.InsertNode(S, IP);
2473 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2475 SmallVector<const SCEV *, 2> Ops;
2478 return getUMaxExpr(Ops);
2482 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2483 assert(!Ops.empty() && "Cannot get empty umax!");
2484 if (Ops.size() == 1) return Ops[0];
2486 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2487 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2488 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2489 "SCEVUMaxExpr operand types don't match!");
2492 // Sort by complexity, this groups all similar expression types together.
2493 GroupByComplexity(Ops, LI);
2495 // If there are any constants, fold them together.
2497 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2499 assert(Idx < Ops.size());
2500 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2501 // We found two constants, fold them together!
2502 ConstantInt *Fold = ConstantInt::get(getContext(),
2503 APIntOps::umax(LHSC->getValue()->getValue(),
2504 RHSC->getValue()->getValue()));
2505 Ops[0] = getConstant(Fold);
2506 Ops.erase(Ops.begin()+1); // Erase the folded element
2507 if (Ops.size() == 1) return Ops[0];
2508 LHSC = cast<SCEVConstant>(Ops[0]);
2511 // If we are left with a constant minimum-int, strip it off.
2512 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2513 Ops.erase(Ops.begin());
2515 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2516 // If we have an umax with a constant maximum-int, it will always be
2521 if (Ops.size() == 1) return Ops[0];
2524 // Find the first UMax
2525 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2528 // Check to see if one of the operands is a UMax. If so, expand its operands
2529 // onto our operand list, and recurse to simplify.
2530 if (Idx < Ops.size()) {
2531 bool DeletedUMax = false;
2532 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2533 Ops.erase(Ops.begin()+Idx);
2534 Ops.append(UMax->op_begin(), UMax->op_end());
2539 return getUMaxExpr(Ops);
2542 // Okay, check to see if the same value occurs in the operand list twice. If
2543 // so, delete one. Since we sorted the list, these values are required to
2545 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2546 // X umax Y umax Y --> X umax Y
2547 // X umax Y --> X, if X is always greater than Y
2548 if (Ops[i] == Ops[i+1] ||
2549 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2550 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2552 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2553 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2557 if (Ops.size() == 1) return Ops[0];
2559 assert(!Ops.empty() && "Reduced umax down to nothing!");
2561 // Okay, it looks like we really DO need a umax expr. Check to see if we
2562 // already have one, otherwise create a new one.
2563 FoldingSetNodeID ID;
2564 ID.AddInteger(scUMaxExpr);
2565 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2566 ID.AddPointer(Ops[i]);
2568 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2569 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2570 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2571 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2573 UniqueSCEVs.InsertNode(S, IP);
2577 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2579 // ~smax(~x, ~y) == smin(x, y).
2580 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2583 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2585 // ~umax(~x, ~y) == umin(x, y)
2586 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2589 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2590 // If we have DataLayout, we can bypass creating a target-independent
2591 // constant expression and then folding it back into a ConstantInt.
2592 // This is just a compile-time optimization.
2594 return getConstant(TD->getIntPtrType(getContext()),
2595 TD->getTypeAllocSize(AllocTy));
2597 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2598 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2599 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2601 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2602 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2605 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2606 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2607 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2608 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2610 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2611 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2614 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2616 // If we have DataLayout, we can bypass creating a target-independent
2617 // constant expression and then folding it back into a ConstantInt.
2618 // This is just a compile-time optimization.
2620 return getConstant(TD->getIntPtrType(getContext()),
2621 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2623 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2624 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2625 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2627 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2628 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2631 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2632 Constant *FieldNo) {
2633 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2634 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2635 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2637 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2638 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2641 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2642 // Don't attempt to do anything other than create a SCEVUnknown object
2643 // here. createSCEV only calls getUnknown after checking for all other
2644 // interesting possibilities, and any other code that calls getUnknown
2645 // is doing so in order to hide a value from SCEV canonicalization.
2647 FoldingSetNodeID ID;
2648 ID.AddInteger(scUnknown);
2651 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2652 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2653 "Stale SCEVUnknown in uniquing map!");
2656 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2658 FirstUnknown = cast<SCEVUnknown>(S);
2659 UniqueSCEVs.InsertNode(S, IP);
2663 //===----------------------------------------------------------------------===//
2664 // Basic SCEV Analysis and PHI Idiom Recognition Code
2667 /// isSCEVable - Test if values of the given type are analyzable within
2668 /// the SCEV framework. This primarily includes integer types, and it
2669 /// can optionally include pointer types if the ScalarEvolution class
2670 /// has access to target-specific information.
2671 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2672 // Integers and pointers are always SCEVable.
2673 return Ty->isIntegerTy() || Ty->isPointerTy();
2676 /// getTypeSizeInBits - Return the size in bits of the specified type,
2677 /// for which isSCEVable must return true.
2678 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2679 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2681 // If we have a DataLayout, use it!
2683 return TD->getTypeSizeInBits(Ty);
2685 // Integer types have fixed sizes.
2686 if (Ty->isIntegerTy())
2687 return Ty->getPrimitiveSizeInBits();
2689 // The only other support type is pointer. Without DataLayout, conservatively
2690 // assume pointers are 64-bit.
2691 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2695 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2696 /// the given type and which represents how SCEV will treat the given
2697 /// type, for which isSCEVable must return true. For pointer types,
2698 /// this is the pointer-sized integer type.
2699 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2700 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2702 if (Ty->isIntegerTy())
2705 // The only other support type is pointer.
2706 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2707 if (TD) return TD->getIntPtrType(getContext());
2709 // Without DataLayout, conservatively assume pointers are 64-bit.
2710 return Type::getInt64Ty(getContext());
2713 const SCEV *ScalarEvolution::getCouldNotCompute() {
2714 return &CouldNotCompute;
2717 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2718 /// expression and create a new one.
2719 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2720 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2722 ValueExprMapType::const_iterator I = ValueExprMap.find_as(V);
2723 if (I != ValueExprMap.end()) return I->second;
2724 const SCEV *S = createSCEV(V);
2726 // The process of creating a SCEV for V may have caused other SCEVs
2727 // to have been created, so it's necessary to insert the new entry
2728 // from scratch, rather than trying to remember the insert position
2730 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2734 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2736 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2737 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2739 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2741 Type *Ty = V->getType();
2742 Ty = getEffectiveSCEVType(Ty);
2743 return getMulExpr(V,
2744 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2747 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2748 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2749 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2751 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2753 Type *Ty = V->getType();
2754 Ty = getEffectiveSCEVType(Ty);
2755 const SCEV *AllOnes =
2756 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2757 return getMinusSCEV(AllOnes, V);
2760 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2761 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2762 SCEV::NoWrapFlags Flags) {
2763 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2765 // Fast path: X - X --> 0.
2767 return getConstant(LHS->getType(), 0);
2770 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2773 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2774 /// input value to the specified type. If the type must be extended, it is zero
2777 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2778 Type *SrcTy = V->getType();
2779 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2780 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2781 "Cannot truncate or zero extend with non-integer arguments!");
2782 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2783 return V; // No conversion
2784 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2785 return getTruncateExpr(V, Ty);
2786 return getZeroExtendExpr(V, Ty);
2789 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2790 /// input value to the specified type. If the type must be extended, it is sign
2793 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2795 Type *SrcTy = V->getType();
2796 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2797 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2798 "Cannot truncate or zero extend with non-integer arguments!");
2799 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2800 return V; // No conversion
2801 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2802 return getTruncateExpr(V, Ty);
2803 return getSignExtendExpr(V, Ty);
2806 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2807 /// input value to the specified type. If the type must be extended, it is zero
2808 /// extended. The conversion must not be narrowing.
2810 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2811 Type *SrcTy = V->getType();
2812 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2813 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2814 "Cannot noop or zero extend with non-integer arguments!");
2815 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2816 "getNoopOrZeroExtend cannot truncate!");
2817 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2818 return V; // No conversion
2819 return getZeroExtendExpr(V, Ty);
2822 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2823 /// input value to the specified type. If the type must be extended, it is sign
2824 /// extended. The conversion must not be narrowing.
2826 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2827 Type *SrcTy = V->getType();
2828 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2829 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2830 "Cannot noop or sign extend with non-integer arguments!");
2831 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2832 "getNoopOrSignExtend cannot truncate!");
2833 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2834 return V; // No conversion
2835 return getSignExtendExpr(V, Ty);
2838 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2839 /// the input value to the specified type. If the type must be extended,
2840 /// it is extended with unspecified bits. The conversion must not be
2843 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2844 Type *SrcTy = V->getType();
2845 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2846 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2847 "Cannot noop or any extend with non-integer arguments!");
2848 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2849 "getNoopOrAnyExtend cannot truncate!");
2850 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2851 return V; // No conversion
2852 return getAnyExtendExpr(V, Ty);
2855 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2856 /// input value to the specified type. The conversion must not be widening.
2858 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2859 Type *SrcTy = V->getType();
2860 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2861 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2862 "Cannot truncate or noop with non-integer arguments!");
2863 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2864 "getTruncateOrNoop cannot extend!");
2865 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2866 return V; // No conversion
2867 return getTruncateExpr(V, Ty);
2870 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2871 /// the types using zero-extension, and then perform a umax operation
2873 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2875 const SCEV *PromotedLHS = LHS;
2876 const SCEV *PromotedRHS = RHS;
2878 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2879 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2881 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2883 return getUMaxExpr(PromotedLHS, PromotedRHS);
2886 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2887 /// the types using zero-extension, and then perform a umin operation
2889 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2891 const SCEV *PromotedLHS = LHS;
2892 const SCEV *PromotedRHS = RHS;
2894 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2895 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2897 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2899 return getUMinExpr(PromotedLHS, PromotedRHS);
2902 /// getPointerBase - Transitively follow the chain of pointer-type operands
2903 /// until reaching a SCEV that does not have a single pointer operand. This
2904 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2905 /// but corner cases do exist.
2906 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2907 // A pointer operand may evaluate to a nonpointer expression, such as null.
2908 if (!V->getType()->isPointerTy())
2911 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2912 return getPointerBase(Cast->getOperand());
2914 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2915 const SCEV *PtrOp = 0;
2916 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2918 if ((*I)->getType()->isPointerTy()) {
2919 // Cannot find the base of an expression with multiple pointer operands.
2927 return getPointerBase(PtrOp);
2932 /// PushDefUseChildren - Push users of the given Instruction
2933 /// onto the given Worklist.
2935 PushDefUseChildren(Instruction *I,
2936 SmallVectorImpl<Instruction *> &Worklist) {
2937 // Push the def-use children onto the Worklist stack.
2938 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2940 Worklist.push_back(cast<Instruction>(*UI));
2943 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2944 /// instructions that depend on the given instruction and removes them from
2945 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2948 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2949 SmallVector<Instruction *, 16> Worklist;
2950 PushDefUseChildren(PN, Worklist);
2952 SmallPtrSet<Instruction *, 8> Visited;
2954 while (!Worklist.empty()) {
2955 Instruction *I = Worklist.pop_back_val();
2956 if (!Visited.insert(I)) continue;
2958 ValueExprMapType::iterator It =
2959 ValueExprMap.find_as(static_cast<Value *>(I));
2960 if (It != ValueExprMap.end()) {
2961 const SCEV *Old = It->second;
2963 // Short-circuit the def-use traversal if the symbolic name
2964 // ceases to appear in expressions.
2965 if (Old != SymName && !hasOperand(Old, SymName))
2968 // SCEVUnknown for a PHI either means that it has an unrecognized
2969 // structure, it's a PHI that's in the progress of being computed
2970 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2971 // additional loop trip count information isn't going to change anything.
2972 // In the second case, createNodeForPHI will perform the necessary
2973 // updates on its own when it gets to that point. In the third, we do
2974 // want to forget the SCEVUnknown.
2975 if (!isa<PHINode>(I) ||
2976 !isa<SCEVUnknown>(Old) ||
2977 (I != PN && Old == SymName)) {
2978 forgetMemoizedResults(Old);
2979 ValueExprMap.erase(It);
2983 PushDefUseChildren(I, Worklist);
2987 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2988 /// a loop header, making it a potential recurrence, or it doesn't.
2990 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2991 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2992 if (L->getHeader() == PN->getParent()) {
2993 // The loop may have multiple entrances or multiple exits; we can analyze
2994 // this phi as an addrec if it has a unique entry value and a unique
2996 Value *BEValueV = 0, *StartValueV = 0;
2997 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2998 Value *V = PN->getIncomingValue(i);
2999 if (L->contains(PN->getIncomingBlock(i))) {
3002 } else if (BEValueV != V) {
3006 } else if (!StartValueV) {
3008 } else if (StartValueV != V) {
3013 if (BEValueV && StartValueV) {
3014 // While we are analyzing this PHI node, handle its value symbolically.
3015 const SCEV *SymbolicName = getUnknown(PN);
3016 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3017 "PHI node already processed?");
3018 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3020 // Using this symbolic name for the PHI, analyze the value coming around
3022 const SCEV *BEValue = getSCEV(BEValueV);
3024 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3025 // has a special value for the first iteration of the loop.
3027 // If the value coming around the backedge is an add with the symbolic
3028 // value we just inserted, then we found a simple induction variable!
3029 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3030 // If there is a single occurrence of the symbolic value, replace it
3031 // with a recurrence.
3032 unsigned FoundIndex = Add->getNumOperands();
3033 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3034 if (Add->getOperand(i) == SymbolicName)
3035 if (FoundIndex == e) {
3040 if (FoundIndex != Add->getNumOperands()) {
3041 // Create an add with everything but the specified operand.
3042 SmallVector<const SCEV *, 8> Ops;
3043 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3044 if (i != FoundIndex)
3045 Ops.push_back(Add->getOperand(i));
3046 const SCEV *Accum = getAddExpr(Ops);
3048 // This is not a valid addrec if the step amount is varying each
3049 // loop iteration, but is not itself an addrec in this loop.
3050 if (isLoopInvariant(Accum, L) ||
3051 (isa<SCEVAddRecExpr>(Accum) &&
3052 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3053 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3055 // If the increment doesn't overflow, then neither the addrec nor
3056 // the post-increment will overflow.
3057 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3058 if (OBO->hasNoUnsignedWrap())
3059 Flags = setFlags(Flags, SCEV::FlagNUW);
3060 if (OBO->hasNoSignedWrap())
3061 Flags = setFlags(Flags, SCEV::FlagNSW);
3062 } else if (const GEPOperator *GEP =
3063 dyn_cast<GEPOperator>(BEValueV)) {
3064 // If the increment is an inbounds GEP, then we know the address
3065 // space cannot be wrapped around. We cannot make any guarantee
3066 // about signed or unsigned overflow because pointers are
3067 // unsigned but we may have a negative index from the base
3069 if (GEP->isInBounds())
3070 Flags = setFlags(Flags, SCEV::FlagNW);
3073 const SCEV *StartVal = getSCEV(StartValueV);
3074 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3076 // Since the no-wrap flags are on the increment, they apply to the
3077 // post-incremented value as well.
3078 if (isLoopInvariant(Accum, L))
3079 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3082 // Okay, for the entire analysis of this edge we assumed the PHI
3083 // to be symbolic. We now need to go back and purge all of the
3084 // entries for the scalars that use the symbolic expression.
3085 ForgetSymbolicName(PN, SymbolicName);
3086 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3090 } else if (const SCEVAddRecExpr *AddRec =
3091 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3092 // Otherwise, this could be a loop like this:
3093 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3094 // In this case, j = {1,+,1} and BEValue is j.
3095 // Because the other in-value of i (0) fits the evolution of BEValue
3096 // i really is an addrec evolution.
3097 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3098 const SCEV *StartVal = getSCEV(StartValueV);
3100 // If StartVal = j.start - j.stride, we can use StartVal as the
3101 // initial step of the addrec evolution.
3102 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3103 AddRec->getOperand(1))) {
3104 // FIXME: For constant StartVal, we should be able to infer
3106 const SCEV *PHISCEV =
3107 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3110 // Okay, for the entire analysis of this edge we assumed the PHI
3111 // to be symbolic. We now need to go back and purge all of the
3112 // entries for the scalars that use the symbolic expression.
3113 ForgetSymbolicName(PN, SymbolicName);
3114 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3122 // If the PHI has a single incoming value, follow that value, unless the
3123 // PHI's incoming blocks are in a different loop, in which case doing so
3124 // risks breaking LCSSA form. Instcombine would normally zap these, but
3125 // it doesn't have DominatorTree information, so it may miss cases.
3126 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3127 if (LI->replacementPreservesLCSSAForm(PN, V))
3130 // If it's not a loop phi, we can't handle it yet.
3131 return getUnknown(PN);
3134 /// createNodeForGEP - Expand GEP instructions into add and multiply
3135 /// operations. This allows them to be analyzed by regular SCEV code.
3137 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3139 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3140 // Add expression, because the Instruction may be guarded by control flow
3141 // and the no-overflow bits may not be valid for the expression in any
3143 bool isInBounds = GEP->isInBounds();
3145 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3146 Value *Base = GEP->getOperand(0);
3147 // Don't attempt to analyze GEPs over unsized objects.
3148 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3149 return getUnknown(GEP);
3150 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3151 gep_type_iterator GTI = gep_type_begin(GEP);
3152 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3156 // Compute the (potentially symbolic) offset in bytes for this index.
3157 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3158 // For a struct, add the member offset.
3159 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3160 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3162 // Add the field offset to the running total offset.
3163 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3165 // For an array, add the element offset, explicitly scaled.
3166 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3167 const SCEV *IndexS = getSCEV(Index);
3168 // Getelementptr indices are signed.
3169 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3171 // Multiply the index by the element size to compute the element offset.
3172 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3173 isInBounds ? SCEV::FlagNSW :
3176 // Add the element offset to the running total offset.
3177 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3181 // Get the SCEV for the GEP base.
3182 const SCEV *BaseS = getSCEV(Base);
3184 // Add the total offset from all the GEP indices to the base.
3185 return getAddExpr(BaseS, TotalOffset,
3186 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3189 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3190 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3191 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3192 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3194 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3195 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3196 return C->getValue()->getValue().countTrailingZeros();
3198 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3199 return std::min(GetMinTrailingZeros(T->getOperand()),
3200 (uint32_t)getTypeSizeInBits(T->getType()));
3202 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3203 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3204 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3205 getTypeSizeInBits(E->getType()) : OpRes;
3208 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3209 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3210 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3211 getTypeSizeInBits(E->getType()) : OpRes;
3214 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3215 // The result is the min of all operands results.
3216 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3217 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3218 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3222 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3223 // The result is the sum of all operands results.
3224 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3225 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3226 for (unsigned i = 1, e = M->getNumOperands();
3227 SumOpRes != BitWidth && i != e; ++i)
3228 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3233 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3234 // The result is the min of all operands results.
3235 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3236 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3237 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3241 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3242 // The result is the min of all operands results.
3243 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3244 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3245 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3249 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3250 // The result is the min of all operands results.
3251 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3252 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3253 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3257 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3258 // For a SCEVUnknown, ask ValueTracking.
3259 unsigned BitWidth = getTypeSizeInBits(U->getType());
3260 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3261 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3262 return Zeros.countTrailingOnes();
3269 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3272 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3273 // See if we've computed this range already.
3274 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3275 if (I != UnsignedRanges.end())
3278 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3279 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3281 unsigned BitWidth = getTypeSizeInBits(S->getType());
3282 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3284 // If the value has known zeros, the maximum unsigned value will have those
3285 // known zeros as well.
3286 uint32_t TZ = GetMinTrailingZeros(S);
3288 ConservativeResult =
3289 ConstantRange(APInt::getMinValue(BitWidth),
3290 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3292 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3293 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3294 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3295 X = X.add(getUnsignedRange(Add->getOperand(i)));
3296 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3299 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3300 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3301 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3302 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3303 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3306 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3307 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3308 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3309 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3310 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3313 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3314 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3315 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3316 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3317 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3320 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3321 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3322 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3323 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3326 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3327 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3328 return setUnsignedRange(ZExt,
3329 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3332 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3333 ConstantRange X = getUnsignedRange(SExt->getOperand());
3334 return setUnsignedRange(SExt,
3335 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3338 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3339 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3340 return setUnsignedRange(Trunc,
3341 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3344 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3345 // If there's no unsigned wrap, the value will never be less than its
3347 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3348 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3349 if (!C->getValue()->isZero())
3350 ConservativeResult =
3351 ConservativeResult.intersectWith(
3352 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3354 // TODO: non-affine addrec
3355 if (AddRec->isAffine()) {
3356 Type *Ty = AddRec->getType();
3357 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3358 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3359 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3360 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3362 const SCEV *Start = AddRec->getStart();
3363 const SCEV *Step = AddRec->getStepRecurrence(*this);
3365 ConstantRange StartRange = getUnsignedRange(Start);
3366 ConstantRange StepRange = getSignedRange(Step);
3367 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3368 ConstantRange EndRange =
3369 StartRange.add(MaxBECountRange.multiply(StepRange));
3371 // Check for overflow. This must be done with ConstantRange arithmetic
3372 // because we could be called from within the ScalarEvolution overflow
3374 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3375 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3376 ConstantRange ExtMaxBECountRange =
3377 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3378 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3379 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3381 return setUnsignedRange(AddRec, ConservativeResult);
3383 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3384 EndRange.getUnsignedMin());
3385 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3386 EndRange.getUnsignedMax());
3387 if (Min.isMinValue() && Max.isMaxValue())
3388 return setUnsignedRange(AddRec, ConservativeResult);
3389 return setUnsignedRange(AddRec,
3390 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3394 return setUnsignedRange(AddRec, ConservativeResult);
3397 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3398 // For a SCEVUnknown, ask ValueTracking.
3399 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3400 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3401 if (Ones == ~Zeros + 1)
3402 return setUnsignedRange(U, ConservativeResult);
3403 return setUnsignedRange(U,
3404 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3407 return setUnsignedRange(S, ConservativeResult);
3410 /// getSignedRange - Determine the signed range for a particular SCEV.
3413 ScalarEvolution::getSignedRange(const SCEV *S) {
3414 // See if we've computed this range already.
3415 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3416 if (I != SignedRanges.end())
3419 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3420 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3422 unsigned BitWidth = getTypeSizeInBits(S->getType());
3423 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3425 // If the value has known zeros, the maximum signed value will have those
3426 // known zeros as well.
3427 uint32_t TZ = GetMinTrailingZeros(S);
3429 ConservativeResult =
3430 ConstantRange(APInt::getSignedMinValue(BitWidth),
3431 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3433 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3434 ConstantRange X = getSignedRange(Add->getOperand(0));
3435 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3436 X = X.add(getSignedRange(Add->getOperand(i)));
3437 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3440 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3441 ConstantRange X = getSignedRange(Mul->getOperand(0));
3442 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3443 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3444 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3447 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3448 ConstantRange X = getSignedRange(SMax->getOperand(0));
3449 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3450 X = X.smax(getSignedRange(SMax->getOperand(i)));
3451 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3454 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3455 ConstantRange X = getSignedRange(UMax->getOperand(0));
3456 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3457 X = X.umax(getSignedRange(UMax->getOperand(i)));
3458 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3461 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3462 ConstantRange X = getSignedRange(UDiv->getLHS());
3463 ConstantRange Y = getSignedRange(UDiv->getRHS());
3464 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3467 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3468 ConstantRange X = getSignedRange(ZExt->getOperand());
3469 return setSignedRange(ZExt,
3470 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3473 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3474 ConstantRange X = getSignedRange(SExt->getOperand());
3475 return setSignedRange(SExt,
3476 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3479 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3480 ConstantRange X = getSignedRange(Trunc->getOperand());
3481 return setSignedRange(Trunc,
3482 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3485 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3486 // If there's no signed wrap, and all the operands have the same sign or
3487 // zero, the value won't ever change sign.
3488 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3489 bool AllNonNeg = true;
3490 bool AllNonPos = true;
3491 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3492 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3493 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3496 ConservativeResult = ConservativeResult.intersectWith(
3497 ConstantRange(APInt(BitWidth, 0),
3498 APInt::getSignedMinValue(BitWidth)));
3500 ConservativeResult = ConservativeResult.intersectWith(
3501 ConstantRange(APInt::getSignedMinValue(BitWidth),
3502 APInt(BitWidth, 1)));
3505 // TODO: non-affine addrec
3506 if (AddRec->isAffine()) {
3507 Type *Ty = AddRec->getType();
3508 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3509 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3510 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3511 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3513 const SCEV *Start = AddRec->getStart();
3514 const SCEV *Step = AddRec->getStepRecurrence(*this);
3516 ConstantRange StartRange = getSignedRange(Start);
3517 ConstantRange StepRange = getSignedRange(Step);
3518 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3519 ConstantRange EndRange =
3520 StartRange.add(MaxBECountRange.multiply(StepRange));
3522 // Check for overflow. This must be done with ConstantRange arithmetic
3523 // because we could be called from within the ScalarEvolution overflow
3525 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3526 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3527 ConstantRange ExtMaxBECountRange =
3528 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3529 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3530 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3532 return setSignedRange(AddRec, ConservativeResult);
3534 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3535 EndRange.getSignedMin());
3536 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3537 EndRange.getSignedMax());
3538 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3539 return setSignedRange(AddRec, ConservativeResult);
3540 return setSignedRange(AddRec,
3541 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3545 return setSignedRange(AddRec, ConservativeResult);
3548 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3549 // For a SCEVUnknown, ask ValueTracking.
3550 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3551 return setSignedRange(U, ConservativeResult);
3552 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3554 return setSignedRange(U, ConservativeResult);
3555 return setSignedRange(U, ConservativeResult.intersectWith(
3556 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3557 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3560 return setSignedRange(S, ConservativeResult);
3563 /// createSCEV - We know that there is no SCEV for the specified value.
3564 /// Analyze the expression.
3566 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3567 if (!isSCEVable(V->getType()))
3568 return getUnknown(V);
3570 unsigned Opcode = Instruction::UserOp1;
3571 if (Instruction *I = dyn_cast<Instruction>(V)) {
3572 Opcode = I->getOpcode();
3574 // Don't attempt to analyze instructions in blocks that aren't
3575 // reachable. Such instructions don't matter, and they aren't required
3576 // to obey basic rules for definitions dominating uses which this
3577 // analysis depends on.
3578 if (!DT->isReachableFromEntry(I->getParent()))
3579 return getUnknown(V);
3580 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3581 Opcode = CE->getOpcode();
3582 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3583 return getConstant(CI);
3584 else if (isa<ConstantPointerNull>(V))
3585 return getConstant(V->getType(), 0);
3586 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3587 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3589 return getUnknown(V);
3591 Operator *U = cast<Operator>(V);
3593 case Instruction::Add: {
3594 // The simple thing to do would be to just call getSCEV on both operands
3595 // and call getAddExpr with the result. However if we're looking at a
3596 // bunch of things all added together, this can be quite inefficient,
3597 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3598 // Instead, gather up all the operands and make a single getAddExpr call.
3599 // LLVM IR canonical form means we need only traverse the left operands.
3601 // Don't apply this instruction's NSW or NUW flags to the new
3602 // expression. The instruction may be guarded by control flow that the
3603 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3604 // mapped to the same SCEV expression, and it would be incorrect to transfer
3605 // NSW/NUW semantics to those operations.
3606 SmallVector<const SCEV *, 4> AddOps;
3607 AddOps.push_back(getSCEV(U->getOperand(1)));
3608 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3609 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3610 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3612 U = cast<Operator>(Op);
3613 const SCEV *Op1 = getSCEV(U->getOperand(1));
3614 if (Opcode == Instruction::Sub)
3615 AddOps.push_back(getNegativeSCEV(Op1));
3617 AddOps.push_back(Op1);
3619 AddOps.push_back(getSCEV(U->getOperand(0)));
3620 return getAddExpr(AddOps);
3622 case Instruction::Mul: {
3623 // Don't transfer NSW/NUW for the same reason as AddExpr.
3624 SmallVector<const SCEV *, 4> MulOps;
3625 MulOps.push_back(getSCEV(U->getOperand(1)));
3626 for (Value *Op = U->getOperand(0);
3627 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3628 Op = U->getOperand(0)) {
3629 U = cast<Operator>(Op);
3630 MulOps.push_back(getSCEV(U->getOperand(1)));
3632 MulOps.push_back(getSCEV(U->getOperand(0)));
3633 return getMulExpr(MulOps);
3635 case Instruction::UDiv:
3636 return getUDivExpr(getSCEV(U->getOperand(0)),
3637 getSCEV(U->getOperand(1)));
3638 case Instruction::Sub:
3639 return getMinusSCEV(getSCEV(U->getOperand(0)),
3640 getSCEV(U->getOperand(1)));
3641 case Instruction::And:
3642 // For an expression like x&255 that merely masks off the high bits,
3643 // use zext(trunc(x)) as the SCEV expression.
3644 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3645 if (CI->isNullValue())
3646 return getSCEV(U->getOperand(1));
3647 if (CI->isAllOnesValue())
3648 return getSCEV(U->getOperand(0));
3649 const APInt &A = CI->getValue();
3651 // Instcombine's ShrinkDemandedConstant may strip bits out of
3652 // constants, obscuring what would otherwise be a low-bits mask.
3653 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3654 // knew about to reconstruct a low-bits mask value.
3655 unsigned LZ = A.countLeadingZeros();
3656 unsigned BitWidth = A.getBitWidth();
3657 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3658 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3660 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3662 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3664 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3665 IntegerType::get(getContext(), BitWidth - LZ)),
3670 case Instruction::Or:
3671 // If the RHS of the Or is a constant, we may have something like:
3672 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3673 // optimizations will transparently handle this case.
3675 // In order for this transformation to be safe, the LHS must be of the
3676 // form X*(2^n) and the Or constant must be less than 2^n.
3677 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3678 const SCEV *LHS = getSCEV(U->getOperand(0));
3679 const APInt &CIVal = CI->getValue();
3680 if (GetMinTrailingZeros(LHS) >=
3681 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3682 // Build a plain add SCEV.
3683 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3684 // If the LHS of the add was an addrec and it has no-wrap flags,
3685 // transfer the no-wrap flags, since an or won't introduce a wrap.
3686 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3687 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3688 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3689 OldAR->getNoWrapFlags());
3695 case Instruction::Xor:
3696 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3697 // If the RHS of the xor is a signbit, then this is just an add.
3698 // Instcombine turns add of signbit into xor as a strength reduction step.
3699 if (CI->getValue().isSignBit())
3700 return getAddExpr(getSCEV(U->getOperand(0)),
3701 getSCEV(U->getOperand(1)));
3703 // If the RHS of xor is -1, then this is a not operation.
3704 if (CI->isAllOnesValue())
3705 return getNotSCEV(getSCEV(U->getOperand(0)));
3707 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3708 // This is a variant of the check for xor with -1, and it handles
3709 // the case where instcombine has trimmed non-demanded bits out
3710 // of an xor with -1.
3711 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3712 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3713 if (BO->getOpcode() == Instruction::And &&
3714 LCI->getValue() == CI->getValue())
3715 if (const SCEVZeroExtendExpr *Z =
3716 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3717 Type *UTy = U->getType();
3718 const SCEV *Z0 = Z->getOperand();
3719 Type *Z0Ty = Z0->getType();
3720 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3722 // If C is a low-bits mask, the zero extend is serving to
3723 // mask off the high bits. Complement the operand and
3724 // re-apply the zext.
3725 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3726 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3728 // If C is a single bit, it may be in the sign-bit position
3729 // before the zero-extend. In this case, represent the xor
3730 // using an add, which is equivalent, and re-apply the zext.
3731 APInt Trunc = CI->getValue().trunc(Z0TySize);
3732 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3734 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3740 case Instruction::Shl:
3741 // Turn shift left of a constant amount into a multiply.
3742 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3743 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3745 // If the shift count is not less than the bitwidth, the result of
3746 // the shift is undefined. Don't try to analyze it, because the
3747 // resolution chosen here may differ from the resolution chosen in
3748 // other parts of the compiler.
3749 if (SA->getValue().uge(BitWidth))
3752 Constant *X = ConstantInt::get(getContext(),
3753 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3754 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3758 case Instruction::LShr:
3759 // Turn logical shift right of a constant into a unsigned divide.
3760 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3761 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3763 // If the shift count is not less than the bitwidth, the result of
3764 // the shift is undefined. Don't try to analyze it, because the
3765 // resolution chosen here may differ from the resolution chosen in
3766 // other parts of the compiler.
3767 if (SA->getValue().uge(BitWidth))
3770 Constant *X = ConstantInt::get(getContext(),
3771 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3772 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3776 case Instruction::AShr:
3777 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3778 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3779 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3780 if (L->getOpcode() == Instruction::Shl &&
3781 L->getOperand(1) == U->getOperand(1)) {
3782 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3784 // If the shift count is not less than the bitwidth, the result of
3785 // the shift is undefined. Don't try to analyze it, because the
3786 // resolution chosen here may differ from the resolution chosen in
3787 // other parts of the compiler.
3788 if (CI->getValue().uge(BitWidth))
3791 uint64_t Amt = BitWidth - CI->getZExtValue();
3792 if (Amt == BitWidth)
3793 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3795 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3796 IntegerType::get(getContext(),
3802 case Instruction::Trunc:
3803 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3805 case Instruction::ZExt:
3806 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3808 case Instruction::SExt:
3809 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3811 case Instruction::BitCast:
3812 // BitCasts are no-op casts so we just eliminate the cast.
3813 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3814 return getSCEV(U->getOperand(0));
3817 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3818 // lead to pointer expressions which cannot safely be expanded to GEPs,
3819 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3820 // simplifying integer expressions.
3822 case Instruction::GetElementPtr:
3823 return createNodeForGEP(cast<GEPOperator>(U));
3825 case Instruction::PHI:
3826 return createNodeForPHI(cast<PHINode>(U));
3828 case Instruction::Select:
3829 // This could be a smax or umax that was lowered earlier.
3830 // Try to recover it.
3831 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3832 Value *LHS = ICI->getOperand(0);
3833 Value *RHS = ICI->getOperand(1);
3834 switch (ICI->getPredicate()) {
3835 case ICmpInst::ICMP_SLT:
3836 case ICmpInst::ICMP_SLE:
3837 std::swap(LHS, RHS);
3839 case ICmpInst::ICMP_SGT:
3840 case ICmpInst::ICMP_SGE:
3841 // a >s b ? a+x : b+x -> smax(a, b)+x
3842 // a >s b ? b+x : a+x -> smin(a, b)+x
3843 if (LHS->getType() == U->getType()) {
3844 const SCEV *LS = getSCEV(LHS);
3845 const SCEV *RS = getSCEV(RHS);
3846 const SCEV *LA = getSCEV(U->getOperand(1));
3847 const SCEV *RA = getSCEV(U->getOperand(2));
3848 const SCEV *LDiff = getMinusSCEV(LA, LS);
3849 const SCEV *RDiff = getMinusSCEV(RA, RS);
3851 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3852 LDiff = getMinusSCEV(LA, RS);
3853 RDiff = getMinusSCEV(RA, LS);
3855 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3858 case ICmpInst::ICMP_ULT:
3859 case ICmpInst::ICMP_ULE:
3860 std::swap(LHS, RHS);
3862 case ICmpInst::ICMP_UGT:
3863 case ICmpInst::ICMP_UGE:
3864 // a >u b ? a+x : b+x -> umax(a, b)+x
3865 // a >u b ? b+x : a+x -> umin(a, b)+x
3866 if (LHS->getType() == U->getType()) {
3867 const SCEV *LS = getSCEV(LHS);
3868 const SCEV *RS = getSCEV(RHS);
3869 const SCEV *LA = getSCEV(U->getOperand(1));
3870 const SCEV *RA = getSCEV(U->getOperand(2));
3871 const SCEV *LDiff = getMinusSCEV(LA, LS);
3872 const SCEV *RDiff = getMinusSCEV(RA, RS);
3874 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3875 LDiff = getMinusSCEV(LA, RS);
3876 RDiff = getMinusSCEV(RA, LS);
3878 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3881 case ICmpInst::ICMP_NE:
3882 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3883 if (LHS->getType() == U->getType() &&
3884 isa<ConstantInt>(RHS) &&
3885 cast<ConstantInt>(RHS)->isZero()) {
3886 const SCEV *One = getConstant(LHS->getType(), 1);
3887 const SCEV *LS = getSCEV(LHS);
3888 const SCEV *LA = getSCEV(U->getOperand(1));
3889 const SCEV *RA = getSCEV(U->getOperand(2));
3890 const SCEV *LDiff = getMinusSCEV(LA, LS);
3891 const SCEV *RDiff = getMinusSCEV(RA, One);
3893 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3896 case ICmpInst::ICMP_EQ:
3897 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3898 if (LHS->getType() == U->getType() &&
3899 isa<ConstantInt>(RHS) &&
3900 cast<ConstantInt>(RHS)->isZero()) {
3901 const SCEV *One = getConstant(LHS->getType(), 1);
3902 const SCEV *LS = getSCEV(LHS);
3903 const SCEV *LA = getSCEV(U->getOperand(1));
3904 const SCEV *RA = getSCEV(U->getOperand(2));
3905 const SCEV *LDiff = getMinusSCEV(LA, One);
3906 const SCEV *RDiff = getMinusSCEV(RA, LS);
3908 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3916 default: // We cannot analyze this expression.
3920 return getUnknown(V);
3925 //===----------------------------------------------------------------------===//
3926 // Iteration Count Computation Code
3929 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3930 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3931 /// constant. Will also return 0 if the maximum trip count is very large (>=
3934 /// This "trip count" assumes that control exits via ExitingBlock. More
3935 /// precisely, it is the number of times that control may reach ExitingBlock
3936 /// before taking the branch. For loops with multiple exits, it may not be the
3937 /// number times that the loop header executes because the loop may exit
3938 /// prematurely via another branch.
3939 unsigned ScalarEvolution::
3940 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3941 const SCEVConstant *ExitCount =
3942 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3946 ConstantInt *ExitConst = ExitCount->getValue();
3948 // Guard against huge trip counts.
3949 if (ExitConst->getValue().getActiveBits() > 32)
3952 // In case of integer overflow, this returns 0, which is correct.
3953 return ((unsigned)ExitConst->getZExtValue()) + 1;
3956 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3957 /// trip count of this loop as a normal unsigned value, if possible. This
3958 /// means that the actual trip count is always a multiple of the returned
3959 /// value (don't forget the trip count could very well be zero as well!).
3961 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3962 /// multiple of a constant (which is also the case if the trip count is simply
3963 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3964 /// if the trip count is very large (>= 2^32).
3966 /// As explained in the comments for getSmallConstantTripCount, this assumes
3967 /// that control exits the loop via ExitingBlock.
3968 unsigned ScalarEvolution::
3969 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3970 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3971 if (ExitCount == getCouldNotCompute())
3974 // Get the trip count from the BE count by adding 1.
3975 const SCEV *TCMul = getAddExpr(ExitCount,
3976 getConstant(ExitCount->getType(), 1));
3977 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3978 // to factor simple cases.
3979 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3980 TCMul = Mul->getOperand(0);
3982 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3986 ConstantInt *Result = MulC->getValue();
3988 // Guard against huge trip counts (this requires checking
3989 // for zero to handle the case where the trip count == -1 and the
3991 if (!Result || Result->getValue().getActiveBits() > 32 ||
3992 Result->getValue().getActiveBits() == 0)
3995 return (unsigned)Result->getZExtValue();
3998 // getExitCount - Get the expression for the number of loop iterations for which
3999 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
4000 // SCEVCouldNotCompute.
4001 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4002 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4005 /// getBackedgeTakenCount - If the specified loop has a predictable
4006 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4007 /// object. The backedge-taken count is the number of times the loop header
4008 /// will be branched to from within the loop. This is one less than the
4009 /// trip count of the loop, since it doesn't count the first iteration,
4010 /// when the header is branched to from outside the loop.
4012 /// Note that it is not valid to call this method on a loop without a
4013 /// loop-invariant backedge-taken count (see
4014 /// hasLoopInvariantBackedgeTakenCount).
4016 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4017 return getBackedgeTakenInfo(L).getExact(this);
4020 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4021 /// return the least SCEV value that is known never to be less than the
4022 /// actual backedge taken count.
4023 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4024 return getBackedgeTakenInfo(L).getMax(this);
4027 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4028 /// onto the given Worklist.
4030 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4031 BasicBlock *Header = L->getHeader();
4033 // Push all Loop-header PHIs onto the Worklist stack.
4034 for (BasicBlock::iterator I = Header->begin();
4035 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4036 Worklist.push_back(PN);
4039 const ScalarEvolution::BackedgeTakenInfo &
4040 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4041 // Initially insert an invalid entry for this loop. If the insertion
4042 // succeeds, proceed to actually compute a backedge-taken count and
4043 // update the value. The temporary CouldNotCompute value tells SCEV
4044 // code elsewhere that it shouldn't attempt to request a new
4045 // backedge-taken count, which could result in infinite recursion.
4046 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4047 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4049 return Pair.first->second;
4051 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4052 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4053 // must be cleared in this scope.
4054 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4056 if (Result.getExact(this) != getCouldNotCompute()) {
4057 assert(isLoopInvariant(Result.getExact(this), L) &&
4058 isLoopInvariant(Result.getMax(this), L) &&
4059 "Computed backedge-taken count isn't loop invariant for loop!");
4060 ++NumTripCountsComputed;
4062 else if (Result.getMax(this) == getCouldNotCompute() &&
4063 isa<PHINode>(L->getHeader()->begin())) {
4064 // Only count loops that have phi nodes as not being computable.
4065 ++NumTripCountsNotComputed;
4068 // Now that we know more about the trip count for this loop, forget any
4069 // existing SCEV values for PHI nodes in this loop since they are only
4070 // conservative estimates made without the benefit of trip count
4071 // information. This is similar to the code in forgetLoop, except that
4072 // it handles SCEVUnknown PHI nodes specially.
4073 if (Result.hasAnyInfo()) {
4074 SmallVector<Instruction *, 16> Worklist;
4075 PushLoopPHIs(L, Worklist);
4077 SmallPtrSet<Instruction *, 8> Visited;
4078 while (!Worklist.empty()) {
4079 Instruction *I = Worklist.pop_back_val();
4080 if (!Visited.insert(I)) continue;
4082 ValueExprMapType::iterator It =
4083 ValueExprMap.find_as(static_cast<Value *>(I));
4084 if (It != ValueExprMap.end()) {
4085 const SCEV *Old = It->second;
4087 // SCEVUnknown for a PHI either means that it has an unrecognized
4088 // structure, or it's a PHI that's in the progress of being computed
4089 // by createNodeForPHI. In the former case, additional loop trip
4090 // count information isn't going to change anything. In the later
4091 // case, createNodeForPHI will perform the necessary updates on its
4092 // own when it gets to that point.
4093 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4094 forgetMemoizedResults(Old);
4095 ValueExprMap.erase(It);
4097 if (PHINode *PN = dyn_cast<PHINode>(I))
4098 ConstantEvolutionLoopExitValue.erase(PN);
4101 PushDefUseChildren(I, Worklist);
4105 // Re-lookup the insert position, since the call to
4106 // ComputeBackedgeTakenCount above could result in a
4107 // recusive call to getBackedgeTakenInfo (on a different
4108 // loop), which would invalidate the iterator computed
4110 return BackedgeTakenCounts.find(L)->second = Result;
4113 /// forgetLoop - This method should be called by the client when it has
4114 /// changed a loop in a way that may effect ScalarEvolution's ability to
4115 /// compute a trip count, or if the loop is deleted.
4116 void ScalarEvolution::forgetLoop(const Loop *L) {
4117 // Drop any stored trip count value.
4118 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4119 BackedgeTakenCounts.find(L);
4120 if (BTCPos != BackedgeTakenCounts.end()) {
4121 BTCPos->second.clear();
4122 BackedgeTakenCounts.erase(BTCPos);
4125 // Drop information about expressions based on loop-header PHIs.
4126 SmallVector<Instruction *, 16> Worklist;
4127 PushLoopPHIs(L, Worklist);
4129 SmallPtrSet<Instruction *, 8> Visited;
4130 while (!Worklist.empty()) {
4131 Instruction *I = Worklist.pop_back_val();
4132 if (!Visited.insert(I)) continue;
4134 ValueExprMapType::iterator It =
4135 ValueExprMap.find_as(static_cast<Value *>(I));
4136 if (It != ValueExprMap.end()) {
4137 forgetMemoizedResults(It->second);
4138 ValueExprMap.erase(It);
4139 if (PHINode *PN = dyn_cast<PHINode>(I))
4140 ConstantEvolutionLoopExitValue.erase(PN);
4143 PushDefUseChildren(I, Worklist);
4146 // Forget all contained loops too, to avoid dangling entries in the
4147 // ValuesAtScopes map.
4148 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4152 /// forgetValue - This method should be called by the client when it has
4153 /// changed a value in a way that may effect its value, or which may
4154 /// disconnect it from a def-use chain linking it to a loop.
4155 void ScalarEvolution::forgetValue(Value *V) {
4156 Instruction *I = dyn_cast<Instruction>(V);
4159 // Drop information about expressions based on loop-header PHIs.
4160 SmallVector<Instruction *, 16> Worklist;
4161 Worklist.push_back(I);
4163 SmallPtrSet<Instruction *, 8> Visited;
4164 while (!Worklist.empty()) {
4165 I = Worklist.pop_back_val();
4166 if (!Visited.insert(I)) continue;
4168 ValueExprMapType::iterator It =
4169 ValueExprMap.find_as(static_cast<Value *>(I));
4170 if (It != ValueExprMap.end()) {
4171 forgetMemoizedResults(It->second);
4172 ValueExprMap.erase(It);
4173 if (PHINode *PN = dyn_cast<PHINode>(I))
4174 ConstantEvolutionLoopExitValue.erase(PN);
4177 PushDefUseChildren(I, Worklist);
4181 /// getExact - Get the exact loop backedge taken count considering all loop
4182 /// exits. A computable result can only be return for loops with a single exit.
4183 /// Returning the minimum taken count among all exits is incorrect because one
4184 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4185 /// the limit of each loop test is never skipped. This is a valid assumption as
4186 /// long as the loop exits via that test. For precise results, it is the
4187 /// caller's responsibility to specify the relevant loop exit using
4188 /// getExact(ExitingBlock, SE).
4190 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4191 // If any exits were not computable, the loop is not computable.
4192 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4194 // We need exactly one computable exit.
4195 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4196 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4198 const SCEV *BECount = 0;
4199 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4200 ENT != 0; ENT = ENT->getNextExit()) {
4202 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4205 BECount = ENT->ExactNotTaken;
4206 else if (BECount != ENT->ExactNotTaken)
4207 return SE->getCouldNotCompute();
4209 assert(BECount && "Invalid not taken count for loop exit");
4213 /// getExact - Get the exact not taken count for this loop exit.
4215 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4216 ScalarEvolution *SE) const {
4217 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4218 ENT != 0; ENT = ENT->getNextExit()) {
4220 if (ENT->ExitingBlock == ExitingBlock)
4221 return ENT->ExactNotTaken;
4223 return SE->getCouldNotCompute();
4226 /// getMax - Get the max backedge taken count for the loop.
4228 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4229 return Max ? Max : SE->getCouldNotCompute();
4232 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4233 /// computable exit into a persistent ExitNotTakenInfo array.
4234 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4235 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4236 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4239 ExitNotTaken.setIncomplete();
4241 unsigned NumExits = ExitCounts.size();
4242 if (NumExits == 0) return;
4244 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4245 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4246 if (NumExits == 1) return;
4248 // Handle the rare case of multiple computable exits.
4249 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4251 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4252 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4253 PrevENT->setNextExit(ENT);
4254 ENT->ExitingBlock = ExitCounts[i].first;
4255 ENT->ExactNotTaken = ExitCounts[i].second;
4259 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4260 void ScalarEvolution::BackedgeTakenInfo::clear() {
4261 ExitNotTaken.ExitingBlock = 0;
4262 ExitNotTaken.ExactNotTaken = 0;
4263 delete[] ExitNotTaken.getNextExit();
4266 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4267 /// of the specified loop will execute.
4268 ScalarEvolution::BackedgeTakenInfo
4269 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4270 SmallVector<BasicBlock *, 8> ExitingBlocks;
4271 L->getExitingBlocks(ExitingBlocks);
4273 // Examine all exits and pick the most conservative values.
4274 const SCEV *MaxBECount = getCouldNotCompute();
4275 bool CouldComputeBECount = true;
4276 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4277 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4278 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4279 if (EL.Exact == getCouldNotCompute())
4280 // We couldn't compute an exact value for this exit, so
4281 // we won't be able to compute an exact value for the loop.
4282 CouldComputeBECount = false;
4284 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4286 if (MaxBECount == getCouldNotCompute())
4287 MaxBECount = EL.Max;
4288 else if (EL.Max != getCouldNotCompute()) {
4289 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4290 // skip some loop tests. Taking the max over the exits is sufficiently
4291 // conservative. TODO: We could do better taking into consideration
4292 // that (1) the loop has unit stride (2) the last loop test is
4293 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4294 // falls-through some constant times less then the other tests.
4295 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4299 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4302 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4303 /// loop will execute if it exits via the specified block.
4304 ScalarEvolution::ExitLimit
4305 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4307 // Okay, we've chosen an exiting block. See what condition causes us to
4308 // exit at this block.
4310 // FIXME: we should be able to handle switch instructions (with a single exit)
4311 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4312 if (ExitBr == 0) return getCouldNotCompute();
4313 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4315 // At this point, we know we have a conditional branch that determines whether
4316 // the loop is exited. However, we don't know if the branch is executed each
4317 // time through the loop. If not, then the execution count of the branch will
4318 // not be equal to the trip count of the loop.
4320 // Currently we check for this by checking to see if the Exit branch goes to
4321 // the loop header. If so, we know it will always execute the same number of
4322 // times as the loop. We also handle the case where the exit block *is* the
4323 // loop header. This is common for un-rotated loops.
4325 // If both of those tests fail, walk up the unique predecessor chain to the
4326 // header, stopping if there is an edge that doesn't exit the loop. If the
4327 // header is reached, the execution count of the branch will be equal to the
4328 // trip count of the loop.
4330 // More extensive analysis could be done to handle more cases here.
4332 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4333 ExitBr->getSuccessor(1) != L->getHeader() &&
4334 ExitBr->getParent() != L->getHeader()) {
4335 // The simple checks failed, try climbing the unique predecessor chain
4336 // up to the header.
4338 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4339 BasicBlock *Pred = BB->getUniquePredecessor();
4341 return getCouldNotCompute();
4342 TerminatorInst *PredTerm = Pred->getTerminator();
4343 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4344 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4347 // If the predecessor has a successor that isn't BB and isn't
4348 // outside the loop, assume the worst.
4349 if (L->contains(PredSucc))
4350 return getCouldNotCompute();
4352 if (Pred == L->getHeader()) {
4359 return getCouldNotCompute();
4362 // Proceed to the next level to examine the exit condition expression.
4363 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4364 ExitBr->getSuccessor(0),
4365 ExitBr->getSuccessor(1));
4368 /// ComputeExitLimitFromCond - Compute the number of times the
4369 /// backedge of the specified loop will execute if its exit condition
4370 /// were a conditional branch of ExitCond, TBB, and FBB.
4371 ScalarEvolution::ExitLimit
4372 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4376 // Check if the controlling expression for this loop is an And or Or.
4377 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4378 if (BO->getOpcode() == Instruction::And) {
4379 // Recurse on the operands of the and.
4380 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4381 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4382 const SCEV *BECount = getCouldNotCompute();
4383 const SCEV *MaxBECount = getCouldNotCompute();
4384 if (L->contains(TBB)) {
4385 // Both conditions must be true for the loop to continue executing.
4386 // Choose the less conservative count.
4387 if (EL0.Exact == getCouldNotCompute() ||
4388 EL1.Exact == getCouldNotCompute())
4389 BECount = getCouldNotCompute();
4391 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4392 if (EL0.Max == getCouldNotCompute())
4393 MaxBECount = EL1.Max;
4394 else if (EL1.Max == getCouldNotCompute())
4395 MaxBECount = EL0.Max;
4397 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4399 // Both conditions must be true at the same time for the loop to exit.
4400 // For now, be conservative.
4401 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4402 if (EL0.Max == EL1.Max)
4403 MaxBECount = EL0.Max;
4404 if (EL0.Exact == EL1.Exact)
4405 BECount = EL0.Exact;
4408 return ExitLimit(BECount, MaxBECount);
4410 if (BO->getOpcode() == Instruction::Or) {
4411 // Recurse on the operands of the or.
4412 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4413 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4414 const SCEV *BECount = getCouldNotCompute();
4415 const SCEV *MaxBECount = getCouldNotCompute();
4416 if (L->contains(FBB)) {
4417 // Both conditions must be false for the loop to continue executing.
4418 // Choose the less conservative count.
4419 if (EL0.Exact == getCouldNotCompute() ||
4420 EL1.Exact == getCouldNotCompute())
4421 BECount = getCouldNotCompute();
4423 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4424 if (EL0.Max == getCouldNotCompute())
4425 MaxBECount = EL1.Max;
4426 else if (EL1.Max == getCouldNotCompute())
4427 MaxBECount = EL0.Max;
4429 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4431 // Both conditions must be false at the same time for the loop to exit.
4432 // For now, be conservative.
4433 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4434 if (EL0.Max == EL1.Max)
4435 MaxBECount = EL0.Max;
4436 if (EL0.Exact == EL1.Exact)
4437 BECount = EL0.Exact;
4440 return ExitLimit(BECount, MaxBECount);
4444 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4445 // Proceed to the next level to examine the icmp.
4446 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4447 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4449 // Check for a constant condition. These are normally stripped out by
4450 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4451 // preserve the CFG and is temporarily leaving constant conditions
4453 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4454 if (L->contains(FBB) == !CI->getZExtValue())
4455 // The backedge is always taken.
4456 return getCouldNotCompute();
4458 // The backedge is never taken.
4459 return getConstant(CI->getType(), 0);
4462 // If it's not an integer or pointer comparison then compute it the hard way.
4463 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4466 /// ComputeExitLimitFromICmp - Compute the number of times the
4467 /// backedge of the specified loop will execute if its exit condition
4468 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4469 ScalarEvolution::ExitLimit
4470 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4475 // If the condition was exit on true, convert the condition to exit on false
4476 ICmpInst::Predicate Cond;
4477 if (!L->contains(FBB))
4478 Cond = ExitCond->getPredicate();
4480 Cond = ExitCond->getInversePredicate();
4482 // Handle common loops like: for (X = "string"; *X; ++X)
4483 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4484 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4486 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4487 if (ItCnt.hasAnyInfo())
4491 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4492 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4494 // Try to evaluate any dependencies out of the loop.
4495 LHS = getSCEVAtScope(LHS, L);
4496 RHS = getSCEVAtScope(RHS, L);
4498 // At this point, we would like to compute how many iterations of the
4499 // loop the predicate will return true for these inputs.
4500 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4501 // If there is a loop-invariant, force it into the RHS.
4502 std::swap(LHS, RHS);
4503 Cond = ICmpInst::getSwappedPredicate(Cond);
4506 // Simplify the operands before analyzing them.
4507 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4509 // If we have a comparison of a chrec against a constant, try to use value
4510 // ranges to answer this query.
4511 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4512 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4513 if (AddRec->getLoop() == L) {
4514 // Form the constant range.
4515 ConstantRange CompRange(
4516 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4518 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4519 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4523 case ICmpInst::ICMP_NE: { // while (X != Y)
4524 // Convert to: while (X-Y != 0)
4525 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4526 if (EL.hasAnyInfo()) return EL;
4529 case ICmpInst::ICMP_EQ: { // while (X == Y)
4530 // Convert to: while (X-Y == 0)
4531 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4532 if (EL.hasAnyInfo()) return EL;
4535 case ICmpInst::ICMP_SLT: {
4536 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4537 if (EL.hasAnyInfo()) return EL;
4540 case ICmpInst::ICMP_SGT: {
4541 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4542 getNotSCEV(RHS), L, true);
4543 if (EL.hasAnyInfo()) return EL;
4546 case ICmpInst::ICMP_ULT: {
4547 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4548 if (EL.hasAnyInfo()) return EL;
4551 case ICmpInst::ICMP_UGT: {
4552 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4553 getNotSCEV(RHS), L, false);
4554 if (EL.hasAnyInfo()) return EL;
4559 dbgs() << "ComputeBackedgeTakenCount ";
4560 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4561 dbgs() << "[unsigned] ";
4562 dbgs() << *LHS << " "
4563 << Instruction::getOpcodeName(Instruction::ICmp)
4564 << " " << *RHS << "\n";
4568 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4571 static ConstantInt *
4572 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4573 ScalarEvolution &SE) {
4574 const SCEV *InVal = SE.getConstant(C);
4575 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4576 assert(isa<SCEVConstant>(Val) &&
4577 "Evaluation of SCEV at constant didn't fold correctly?");
4578 return cast<SCEVConstant>(Val)->getValue();
4581 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4582 /// 'icmp op load X, cst', try to see if we can compute the backedge
4583 /// execution count.
4584 ScalarEvolution::ExitLimit
4585 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4589 ICmpInst::Predicate predicate) {
4591 if (LI->isVolatile()) return getCouldNotCompute();
4593 // Check to see if the loaded pointer is a getelementptr of a global.
4594 // TODO: Use SCEV instead of manually grubbing with GEPs.
4595 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4596 if (!GEP) return getCouldNotCompute();
4598 // Make sure that it is really a constant global we are gepping, with an
4599 // initializer, and make sure the first IDX is really 0.
4600 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4601 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4602 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4603 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4604 return getCouldNotCompute();
4606 // Okay, we allow one non-constant index into the GEP instruction.
4608 std::vector<Constant*> Indexes;
4609 unsigned VarIdxNum = 0;
4610 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4611 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4612 Indexes.push_back(CI);
4613 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4614 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4615 VarIdx = GEP->getOperand(i);
4617 Indexes.push_back(0);
4620 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4622 return getCouldNotCompute();
4624 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4625 // Check to see if X is a loop variant variable value now.
4626 const SCEV *Idx = getSCEV(VarIdx);
4627 Idx = getSCEVAtScope(Idx, L);
4629 // We can only recognize very limited forms of loop index expressions, in
4630 // particular, only affine AddRec's like {C1,+,C2}.
4631 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4632 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4633 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4634 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4635 return getCouldNotCompute();
4637 unsigned MaxSteps = MaxBruteForceIterations;
4638 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4639 ConstantInt *ItCst = ConstantInt::get(
4640 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4641 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4643 // Form the GEP offset.
4644 Indexes[VarIdxNum] = Val;
4646 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4648 if (Result == 0) break; // Cannot compute!
4650 // Evaluate the condition for this iteration.
4651 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4652 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4653 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4655 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4656 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4659 ++NumArrayLenItCounts;
4660 return getConstant(ItCst); // Found terminating iteration!
4663 return getCouldNotCompute();
4667 /// CanConstantFold - Return true if we can constant fold an instruction of the
4668 /// specified type, assuming that all operands were constants.
4669 static bool CanConstantFold(const Instruction *I) {
4670 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4671 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4675 if (const CallInst *CI = dyn_cast<CallInst>(I))
4676 if (const Function *F = CI->getCalledFunction())
4677 return canConstantFoldCallTo(F);
4681 /// Determine whether this instruction can constant evolve within this loop
4682 /// assuming its operands can all constant evolve.
4683 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4684 // An instruction outside of the loop can't be derived from a loop PHI.
4685 if (!L->contains(I)) return false;
4687 if (isa<PHINode>(I)) {
4688 if (L->getHeader() == I->getParent())
4691 // We don't currently keep track of the control flow needed to evaluate
4692 // PHIs, so we cannot handle PHIs inside of loops.
4696 // If we won't be able to constant fold this expression even if the operands
4697 // are constants, bail early.
4698 return CanConstantFold(I);
4701 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4702 /// recursing through each instruction operand until reaching a loop header phi.
4704 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4705 DenseMap<Instruction *, PHINode *> &PHIMap) {
4707 // Otherwise, we can evaluate this instruction if all of its operands are
4708 // constant or derived from a PHI node themselves.
4710 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4711 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4713 if (isa<Constant>(*OpI)) continue;
4715 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4716 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4718 PHINode *P = dyn_cast<PHINode>(OpInst);
4720 // If this operand is already visited, reuse the prior result.
4721 // We may have P != PHI if this is the deepest point at which the
4722 // inconsistent paths meet.
4723 P = PHIMap.lookup(OpInst);
4725 // Recurse and memoize the results, whether a phi is found or not.
4726 // This recursive call invalidates pointers into PHIMap.
4727 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4730 if (P == 0) return 0; // Not evolving from PHI
4731 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4734 // This is a expression evolving from a constant PHI!
4738 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4739 /// in the loop that V is derived from. We allow arbitrary operations along the
4740 /// way, but the operands of an operation must either be constants or a value
4741 /// derived from a constant PHI. If this expression does not fit with these
4742 /// constraints, return null.
4743 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4744 Instruction *I = dyn_cast<Instruction>(V);
4745 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4747 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4751 // Record non-constant instructions contained by the loop.
4752 DenseMap<Instruction *, PHINode *> PHIMap;
4753 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4756 /// EvaluateExpression - Given an expression that passes the
4757 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4758 /// in the loop has the value PHIVal. If we can't fold this expression for some
4759 /// reason, return null.
4760 static Constant *EvaluateExpression(Value *V, const Loop *L,
4761 DenseMap<Instruction *, Constant *> &Vals,
4762 const DataLayout *TD,
4763 const TargetLibraryInfo *TLI) {
4764 // Convenient constant check, but redundant for recursive calls.
4765 if (Constant *C = dyn_cast<Constant>(V)) return C;
4766 Instruction *I = dyn_cast<Instruction>(V);
4769 if (Constant *C = Vals.lookup(I)) return C;
4771 // An instruction inside the loop depends on a value outside the loop that we
4772 // weren't given a mapping for, or a value such as a call inside the loop.
4773 if (!canConstantEvolve(I, L)) return 0;
4775 // An unmapped PHI can be due to a branch or another loop inside this loop,
4776 // or due to this not being the initial iteration through a loop where we
4777 // couldn't compute the evolution of this particular PHI last time.
4778 if (isa<PHINode>(I)) return 0;
4780 std::vector<Constant*> Operands(I->getNumOperands());
4782 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4783 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4785 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4786 if (!Operands[i]) return 0;
4789 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4795 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4796 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4797 Operands[1], TD, TLI);
4798 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4799 if (!LI->isVolatile())
4800 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4802 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4806 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4807 /// in the header of its containing loop, we know the loop executes a
4808 /// constant number of times, and the PHI node is just a recurrence
4809 /// involving constants, fold it.
4811 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4814 DenseMap<PHINode*, Constant*>::const_iterator I =
4815 ConstantEvolutionLoopExitValue.find(PN);
4816 if (I != ConstantEvolutionLoopExitValue.end())
4819 if (BEs.ugt(MaxBruteForceIterations))
4820 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4822 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4824 DenseMap<Instruction *, Constant *> CurrentIterVals;
4825 BasicBlock *Header = L->getHeader();
4826 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4828 // Since the loop is canonicalized, the PHI node must have two entries. One
4829 // entry must be a constant (coming in from outside of the loop), and the
4830 // second must be derived from the same PHI.
4831 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4833 for (BasicBlock::iterator I = Header->begin();
4834 (PHI = dyn_cast<PHINode>(I)); ++I) {
4835 Constant *StartCST =
4836 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4837 if (StartCST == 0) continue;
4838 CurrentIterVals[PHI] = StartCST;
4840 if (!CurrentIterVals.count(PN))
4843 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4845 // Execute the loop symbolically to determine the exit value.
4846 if (BEs.getActiveBits() >= 32)
4847 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4849 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4850 unsigned IterationNum = 0;
4851 for (; ; ++IterationNum) {
4852 if (IterationNum == NumIterations)
4853 return RetVal = CurrentIterVals[PN]; // Got exit value!
4855 // Compute the value of the PHIs for the next iteration.
4856 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4857 DenseMap<Instruction *, Constant *> NextIterVals;
4858 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4861 return 0; // Couldn't evaluate!
4862 NextIterVals[PN] = NextPHI;
4864 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4866 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4867 // cease to be able to evaluate one of them or if they stop evolving,
4868 // because that doesn't necessarily prevent us from computing PN.
4869 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4870 for (DenseMap<Instruction *, Constant *>::const_iterator
4871 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4872 PHINode *PHI = dyn_cast<PHINode>(I->first);
4873 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4874 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4876 // We use two distinct loops because EvaluateExpression may invalidate any
4877 // iterators into CurrentIterVals.
4878 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4879 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4880 PHINode *PHI = I->first;
4881 Constant *&NextPHI = NextIterVals[PHI];
4882 if (!NextPHI) { // Not already computed.
4883 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4884 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4886 if (NextPHI != I->second)
4887 StoppedEvolving = false;
4890 // If all entries in CurrentIterVals == NextIterVals then we can stop
4891 // iterating, the loop can't continue to change.
4892 if (StoppedEvolving)
4893 return RetVal = CurrentIterVals[PN];
4895 CurrentIterVals.swap(NextIterVals);
4899 /// ComputeExitCountExhaustively - If the loop is known to execute a
4900 /// constant number of times (the condition evolves only from constants),
4901 /// try to evaluate a few iterations of the loop until we get the exit
4902 /// condition gets a value of ExitWhen (true or false). If we cannot
4903 /// evaluate the trip count of the loop, return getCouldNotCompute().
4904 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4907 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4908 if (PN == 0) return getCouldNotCompute();
4910 // If the loop is canonicalized, the PHI will have exactly two entries.
4911 // That's the only form we support here.
4912 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4914 DenseMap<Instruction *, Constant *> CurrentIterVals;
4915 BasicBlock *Header = L->getHeader();
4916 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4918 // One entry must be a constant (coming in from outside of the loop), and the
4919 // second must be derived from the same PHI.
4920 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4922 for (BasicBlock::iterator I = Header->begin();
4923 (PHI = dyn_cast<PHINode>(I)); ++I) {
4924 Constant *StartCST =
4925 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4926 if (StartCST == 0) continue;
4927 CurrentIterVals[PHI] = StartCST;
4929 if (!CurrentIterVals.count(PN))
4930 return getCouldNotCompute();
4932 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4933 // the loop symbolically to determine when the condition gets a value of
4936 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4937 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4938 ConstantInt *CondVal =
4939 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4942 // Couldn't symbolically evaluate.
4943 if (!CondVal) return getCouldNotCompute();
4945 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4946 ++NumBruteForceTripCountsComputed;
4947 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4950 // Update all the PHI nodes for the next iteration.
4951 DenseMap<Instruction *, Constant *> NextIterVals;
4953 // Create a list of which PHIs we need to compute. We want to do this before
4954 // calling EvaluateExpression on them because that may invalidate iterators
4955 // into CurrentIterVals.
4956 SmallVector<PHINode *, 8> PHIsToCompute;
4957 for (DenseMap<Instruction *, Constant *>::const_iterator
4958 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4959 PHINode *PHI = dyn_cast<PHINode>(I->first);
4960 if (!PHI || PHI->getParent() != Header) continue;
4961 PHIsToCompute.push_back(PHI);
4963 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4964 E = PHIsToCompute.end(); I != E; ++I) {
4966 Constant *&NextPHI = NextIterVals[PHI];
4967 if (NextPHI) continue; // Already computed!
4969 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4970 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4972 CurrentIterVals.swap(NextIterVals);
4975 // Too many iterations were needed to evaluate.
4976 return getCouldNotCompute();
4979 /// getSCEVAtScope - Return a SCEV expression for the specified value
4980 /// at the specified scope in the program. The L value specifies a loop
4981 /// nest to evaluate the expression at, where null is the top-level or a
4982 /// specified loop is immediately inside of the loop.
4984 /// This method can be used to compute the exit value for a variable defined
4985 /// in a loop by querying what the value will hold in the parent loop.
4987 /// In the case that a relevant loop exit value cannot be computed, the
4988 /// original value V is returned.
4989 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4990 // Check to see if we've folded this expression at this loop before.
4991 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4992 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4993 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4995 return Pair.first->second ? Pair.first->second : V;
4997 // Otherwise compute it.
4998 const SCEV *C = computeSCEVAtScope(V, L);
4999 ValuesAtScopes[V][L] = C;
5003 /// This builds up a Constant using the ConstantExpr interface. That way, we
5004 /// will return Constants for objects which aren't represented by a
5005 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5006 /// Returns NULL if the SCEV isn't representable as a Constant.
5007 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5008 switch (V->getSCEVType()) {
5009 default: // TODO: smax, umax.
5010 case scCouldNotCompute:
5014 return cast<SCEVConstant>(V)->getValue();
5016 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5017 case scSignExtend: {
5018 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5019 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5020 return ConstantExpr::getSExt(CastOp, SS->getType());
5023 case scZeroExtend: {
5024 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5025 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5026 return ConstantExpr::getZExt(CastOp, SZ->getType());
5030 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5031 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5032 return ConstantExpr::getTrunc(CastOp, ST->getType());
5036 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5037 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5038 if (C->getType()->isPointerTy())
5039 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5040 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5041 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5045 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5047 // The offsets have been converted to bytes. We can add bytes to an
5048 // i8* by GEP with the byte count in the first index.
5049 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5052 // Don't bother trying to sum two pointers. We probably can't
5053 // statically compute a load that results from it anyway.
5054 if (C2->getType()->isPointerTy())
5057 if (C->getType()->isPointerTy()) {
5058 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5059 C2 = ConstantExpr::getIntegerCast(
5060 C2, Type::getInt32Ty(C->getContext()), true);
5061 C = ConstantExpr::getGetElementPtr(C, C2);
5063 C = ConstantExpr::getAdd(C, C2);
5070 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5071 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5072 // Don't bother with pointers at all.
5073 if (C->getType()->isPointerTy()) return 0;
5074 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5075 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5076 if (!C2 || C2->getType()->isPointerTy()) return 0;
5077 C = ConstantExpr::getMul(C, C2);
5084 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5085 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5086 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5087 if (LHS->getType() == RHS->getType())
5088 return ConstantExpr::getUDiv(LHS, RHS);
5095 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5096 if (isa<SCEVConstant>(V)) return V;
5098 // If this instruction is evolved from a constant-evolving PHI, compute the
5099 // exit value from the loop without using SCEVs.
5100 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5101 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5102 const Loop *LI = (*this->LI)[I->getParent()];
5103 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5104 if (PHINode *PN = dyn_cast<PHINode>(I))
5105 if (PN->getParent() == LI->getHeader()) {
5106 // Okay, there is no closed form solution for the PHI node. Check
5107 // to see if the loop that contains it has a known backedge-taken
5108 // count. If so, we may be able to force computation of the exit
5110 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5111 if (const SCEVConstant *BTCC =
5112 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5113 // Okay, we know how many times the containing loop executes. If
5114 // this is a constant evolving PHI node, get the final value at
5115 // the specified iteration number.
5116 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5117 BTCC->getValue()->getValue(),
5119 if (RV) return getSCEV(RV);
5123 // Okay, this is an expression that we cannot symbolically evaluate
5124 // into a SCEV. Check to see if it's possible to symbolically evaluate
5125 // the arguments into constants, and if so, try to constant propagate the
5126 // result. This is particularly useful for computing loop exit values.
5127 if (CanConstantFold(I)) {
5128 SmallVector<Constant *, 4> Operands;
5129 bool MadeImprovement = false;
5130 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5131 Value *Op = I->getOperand(i);
5132 if (Constant *C = dyn_cast<Constant>(Op)) {
5133 Operands.push_back(C);
5137 // If any of the operands is non-constant and if they are
5138 // non-integer and non-pointer, don't even try to analyze them
5139 // with scev techniques.
5140 if (!isSCEVable(Op->getType()))
5143 const SCEV *OrigV = getSCEV(Op);
5144 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5145 MadeImprovement |= OrigV != OpV;
5147 Constant *C = BuildConstantFromSCEV(OpV);
5149 if (C->getType() != Op->getType())
5150 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5154 Operands.push_back(C);
5157 // Check to see if getSCEVAtScope actually made an improvement.
5158 if (MadeImprovement) {
5160 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5161 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5162 Operands[0], Operands[1], TD,
5164 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5165 if (!LI->isVolatile())
5166 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5168 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5176 // This is some other type of SCEVUnknown, just return it.
5180 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5181 // Avoid performing the look-up in the common case where the specified
5182 // expression has no loop-variant portions.
5183 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5184 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5185 if (OpAtScope != Comm->getOperand(i)) {
5186 // Okay, at least one of these operands is loop variant but might be
5187 // foldable. Build a new instance of the folded commutative expression.
5188 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5189 Comm->op_begin()+i);
5190 NewOps.push_back(OpAtScope);
5192 for (++i; i != e; ++i) {
5193 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5194 NewOps.push_back(OpAtScope);
5196 if (isa<SCEVAddExpr>(Comm))
5197 return getAddExpr(NewOps);
5198 if (isa<SCEVMulExpr>(Comm))
5199 return getMulExpr(NewOps);
5200 if (isa<SCEVSMaxExpr>(Comm))
5201 return getSMaxExpr(NewOps);
5202 if (isa<SCEVUMaxExpr>(Comm))
5203 return getUMaxExpr(NewOps);
5204 llvm_unreachable("Unknown commutative SCEV type!");
5207 // If we got here, all operands are loop invariant.
5211 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5212 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5213 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5214 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5215 return Div; // must be loop invariant
5216 return getUDivExpr(LHS, RHS);
5219 // If this is a loop recurrence for a loop that does not contain L, then we
5220 // are dealing with the final value computed by the loop.
5221 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5222 // First, attempt to evaluate each operand.
5223 // Avoid performing the look-up in the common case where the specified
5224 // expression has no loop-variant portions.
5225 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5226 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5227 if (OpAtScope == AddRec->getOperand(i))
5230 // Okay, at least one of these operands is loop variant but might be
5231 // foldable. Build a new instance of the folded commutative expression.
5232 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5233 AddRec->op_begin()+i);
5234 NewOps.push_back(OpAtScope);
5235 for (++i; i != e; ++i)
5236 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5238 const SCEV *FoldedRec =
5239 getAddRecExpr(NewOps, AddRec->getLoop(),
5240 AddRec->getNoWrapFlags(SCEV::FlagNW));
5241 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5242 // The addrec may be folded to a nonrecurrence, for example, if the
5243 // induction variable is multiplied by zero after constant folding. Go
5244 // ahead and return the folded value.
5250 // If the scope is outside the addrec's loop, evaluate it by using the
5251 // loop exit value of the addrec.
5252 if (!AddRec->getLoop()->contains(L)) {
5253 // To evaluate this recurrence, we need to know how many times the AddRec
5254 // loop iterates. Compute this now.
5255 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5256 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5258 // Then, evaluate the AddRec.
5259 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5265 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5266 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5267 if (Op == Cast->getOperand())
5268 return Cast; // must be loop invariant
5269 return getZeroExtendExpr(Op, Cast->getType());
5272 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5273 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5274 if (Op == Cast->getOperand())
5275 return Cast; // must be loop invariant
5276 return getSignExtendExpr(Op, Cast->getType());
5279 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5280 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5281 if (Op == Cast->getOperand())
5282 return Cast; // must be loop invariant
5283 return getTruncateExpr(Op, Cast->getType());
5286 llvm_unreachable("Unknown SCEV type!");
5289 /// getSCEVAtScope - This is a convenience function which does
5290 /// getSCEVAtScope(getSCEV(V), L).
5291 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5292 return getSCEVAtScope(getSCEV(V), L);
5295 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5296 /// following equation:
5298 /// A * X = B (mod N)
5300 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5301 /// A and B isn't important.
5303 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5304 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5305 ScalarEvolution &SE) {
5306 uint32_t BW = A.getBitWidth();
5307 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5308 assert(A != 0 && "A must be non-zero.");
5312 // The gcd of A and N may have only one prime factor: 2. The number of
5313 // trailing zeros in A is its multiplicity
5314 uint32_t Mult2 = A.countTrailingZeros();
5317 // 2. Check if B is divisible by D.
5319 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5320 // is not less than multiplicity of this prime factor for D.
5321 if (B.countTrailingZeros() < Mult2)
5322 return SE.getCouldNotCompute();
5324 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5327 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5328 // bit width during computations.
5329 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5330 APInt Mod(BW + 1, 0);
5331 Mod.setBit(BW - Mult2); // Mod = N / D
5332 APInt I = AD.multiplicativeInverse(Mod);
5334 // 4. Compute the minimum unsigned root of the equation:
5335 // I * (B / D) mod (N / D)
5336 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5338 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5340 return SE.getConstant(Result.trunc(BW));
5343 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5344 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5345 /// might be the same) or two SCEVCouldNotCompute objects.
5347 static std::pair<const SCEV *,const SCEV *>
5348 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5349 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5350 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5351 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5352 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5354 // We currently can only solve this if the coefficients are constants.
5355 if (!LC || !MC || !NC) {
5356 const SCEV *CNC = SE.getCouldNotCompute();
5357 return std::make_pair(CNC, CNC);
5360 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5361 const APInt &L = LC->getValue()->getValue();
5362 const APInt &M = MC->getValue()->getValue();
5363 const APInt &N = NC->getValue()->getValue();
5364 APInt Two(BitWidth, 2);
5365 APInt Four(BitWidth, 4);
5368 using namespace APIntOps;
5370 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5371 // The B coefficient is M-N/2
5375 // The A coefficient is N/2
5376 APInt A(N.sdiv(Two));
5378 // Compute the B^2-4ac term.
5381 SqrtTerm -= Four * (A * C);
5383 if (SqrtTerm.isNegative()) {
5384 // The loop is provably infinite.
5385 const SCEV *CNC = SE.getCouldNotCompute();
5386 return std::make_pair(CNC, CNC);
5389 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5390 // integer value or else APInt::sqrt() will assert.
5391 APInt SqrtVal(SqrtTerm.sqrt());
5393 // Compute the two solutions for the quadratic formula.
5394 // The divisions must be performed as signed divisions.
5397 if (TwoA.isMinValue()) {
5398 const SCEV *CNC = SE.getCouldNotCompute();
5399 return std::make_pair(CNC, CNC);
5402 LLVMContext &Context = SE.getContext();
5404 ConstantInt *Solution1 =
5405 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5406 ConstantInt *Solution2 =
5407 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5409 return std::make_pair(SE.getConstant(Solution1),
5410 SE.getConstant(Solution2));
5411 } // end APIntOps namespace
5414 /// HowFarToZero - Return the number of times a backedge comparing the specified
5415 /// value to zero will execute. If not computable, return CouldNotCompute.
5417 /// This is only used for loops with a "x != y" exit test. The exit condition is
5418 /// now expressed as a single expression, V = x-y. So the exit test is
5419 /// effectively V != 0. We know and take advantage of the fact that this
5420 /// expression only being used in a comparison by zero context.
5421 ScalarEvolution::ExitLimit
5422 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5423 // If the value is a constant
5424 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5425 // If the value is already zero, the branch will execute zero times.
5426 if (C->getValue()->isZero()) return C;
5427 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5430 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5431 if (!AddRec || AddRec->getLoop() != L)
5432 return getCouldNotCompute();
5434 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5435 // the quadratic equation to solve it.
5436 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5437 std::pair<const SCEV *,const SCEV *> Roots =
5438 SolveQuadraticEquation(AddRec, *this);
5439 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5440 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5443 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5444 << " sol#2: " << *R2 << "\n";
5446 // Pick the smallest positive root value.
5447 if (ConstantInt *CB =
5448 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5451 if (CB->getZExtValue() == false)
5452 std::swap(R1, R2); // R1 is the minimum root now.
5454 // We can only use this value if the chrec ends up with an exact zero
5455 // value at this index. When solving for "X*X != 5", for example, we
5456 // should not accept a root of 2.
5457 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5459 return R1; // We found a quadratic root!
5462 return getCouldNotCompute();
5465 // Otherwise we can only handle this if it is affine.
5466 if (!AddRec->isAffine())
5467 return getCouldNotCompute();
5469 // If this is an affine expression, the execution count of this branch is
5470 // the minimum unsigned root of the following equation:
5472 // Start + Step*N = 0 (mod 2^BW)
5476 // Step*N = -Start (mod 2^BW)
5478 // where BW is the common bit width of Start and Step.
5480 // Get the initial value for the loop.
5481 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5482 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5484 // For now we handle only constant steps.
5486 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5487 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5488 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5489 // We have not yet seen any such cases.
5490 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5491 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5492 return getCouldNotCompute();
5494 // For positive steps (counting up until unsigned overflow):
5495 // N = -Start/Step (as unsigned)
5496 // For negative steps (counting down to zero):
5498 // First compute the unsigned distance from zero in the direction of Step.
5499 bool CountDown = StepC->getValue()->getValue().isNegative();
5500 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5502 // Handle unitary steps, which cannot wraparound.
5503 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5504 // N = Distance (as unsigned)
5505 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5506 ConstantRange CR = getUnsignedRange(Start);
5507 const SCEV *MaxBECount;
5508 if (!CountDown && CR.getUnsignedMin().isMinValue())
5509 // When counting up, the worst starting value is 1, not 0.
5510 MaxBECount = CR.getUnsignedMax().isMinValue()
5511 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5512 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5514 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5515 : -CR.getUnsignedMin());
5516 return ExitLimit(Distance, MaxBECount);
5519 // If the recurrence is known not to wraparound, unsigned divide computes the
5520 // back edge count. We know that the value will either become zero (and thus
5521 // the loop terminates), that the loop will terminate through some other exit
5522 // condition first, or that the loop has undefined behavior. This means
5523 // we can't "miss" the exit value, even with nonunit stride.
5525 // FIXME: Prove that loops always exhibits *acceptable* undefined
5526 // behavior. Loops must exhibit defined behavior until a wrapped value is
5527 // actually used. So the trip count computed by udiv could be smaller than the
5528 // number of well-defined iterations.
5529 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5530 // FIXME: We really want an "isexact" bit for udiv.
5531 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5533 // Then, try to solve the above equation provided that Start is constant.
5534 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5535 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5536 -StartC->getValue()->getValue(),
5538 return getCouldNotCompute();
5541 /// HowFarToNonZero - Return the number of times a backedge checking the
5542 /// specified value for nonzero will execute. If not computable, return
5544 ScalarEvolution::ExitLimit
5545 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5546 // Loops that look like: while (X == 0) are very strange indeed. We don't
5547 // handle them yet except for the trivial case. This could be expanded in the
5548 // future as needed.
5550 // If the value is a constant, check to see if it is known to be non-zero
5551 // already. If so, the backedge will execute zero times.
5552 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5553 if (!C->getValue()->isNullValue())
5554 return getConstant(C->getType(), 0);
5555 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5558 // We could implement others, but I really doubt anyone writes loops like
5559 // this, and if they did, they would already be constant folded.
5560 return getCouldNotCompute();
5563 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5564 /// (which may not be an immediate predecessor) which has exactly one
5565 /// successor from which BB is reachable, or null if no such block is
5568 std::pair<BasicBlock *, BasicBlock *>
5569 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5570 // If the block has a unique predecessor, then there is no path from the
5571 // predecessor to the block that does not go through the direct edge
5572 // from the predecessor to the block.
5573 if (BasicBlock *Pred = BB->getSinglePredecessor())
5574 return std::make_pair(Pred, BB);
5576 // A loop's header is defined to be a block that dominates the loop.
5577 // If the header has a unique predecessor outside the loop, it must be
5578 // a block that has exactly one successor that can reach the loop.
5579 if (Loop *L = LI->getLoopFor(BB))
5580 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5582 return std::pair<BasicBlock *, BasicBlock *>();
5585 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5586 /// testing whether two expressions are equal, however for the purposes of
5587 /// looking for a condition guarding a loop, it can be useful to be a little
5588 /// more general, since a front-end may have replicated the controlling
5591 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5592 // Quick check to see if they are the same SCEV.
5593 if (A == B) return true;
5595 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5596 // two different instructions with the same value. Check for this case.
5597 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5598 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5599 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5600 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5601 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5604 // Otherwise assume they may have a different value.
5608 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5609 /// predicate Pred. Return true iff any changes were made.
5611 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5612 const SCEV *&LHS, const SCEV *&RHS,
5614 bool Changed = false;
5616 // If we hit the max recursion limit bail out.
5620 // Canonicalize a constant to the right side.
5621 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5622 // Check for both operands constant.
5623 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5624 if (ConstantExpr::getICmp(Pred,
5626 RHSC->getValue())->isNullValue())
5627 goto trivially_false;
5629 goto trivially_true;
5631 // Otherwise swap the operands to put the constant on the right.
5632 std::swap(LHS, RHS);
5633 Pred = ICmpInst::getSwappedPredicate(Pred);
5637 // If we're comparing an addrec with a value which is loop-invariant in the
5638 // addrec's loop, put the addrec on the left. Also make a dominance check,
5639 // as both operands could be addrecs loop-invariant in each other's loop.
5640 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5641 const Loop *L = AR->getLoop();
5642 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5643 std::swap(LHS, RHS);
5644 Pred = ICmpInst::getSwappedPredicate(Pred);
5649 // If there's a constant operand, canonicalize comparisons with boundary
5650 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5651 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5652 const APInt &RA = RC->getValue()->getValue();
5654 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5655 case ICmpInst::ICMP_EQ:
5656 case ICmpInst::ICMP_NE:
5657 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5659 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5660 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5661 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5662 ME->getOperand(0)->isAllOnesValue()) {
5663 RHS = AE->getOperand(1);
5664 LHS = ME->getOperand(1);
5668 case ICmpInst::ICMP_UGE:
5669 if ((RA - 1).isMinValue()) {
5670 Pred = ICmpInst::ICMP_NE;
5671 RHS = getConstant(RA - 1);
5675 if (RA.isMaxValue()) {
5676 Pred = ICmpInst::ICMP_EQ;
5680 if (RA.isMinValue()) goto trivially_true;
5682 Pred = ICmpInst::ICMP_UGT;
5683 RHS = getConstant(RA - 1);
5686 case ICmpInst::ICMP_ULE:
5687 if ((RA + 1).isMaxValue()) {
5688 Pred = ICmpInst::ICMP_NE;
5689 RHS = getConstant(RA + 1);
5693 if (RA.isMinValue()) {
5694 Pred = ICmpInst::ICMP_EQ;
5698 if (RA.isMaxValue()) goto trivially_true;
5700 Pred = ICmpInst::ICMP_ULT;
5701 RHS = getConstant(RA + 1);
5704 case ICmpInst::ICMP_SGE:
5705 if ((RA - 1).isMinSignedValue()) {
5706 Pred = ICmpInst::ICMP_NE;
5707 RHS = getConstant(RA - 1);
5711 if (RA.isMaxSignedValue()) {
5712 Pred = ICmpInst::ICMP_EQ;
5716 if (RA.isMinSignedValue()) goto trivially_true;
5718 Pred = ICmpInst::ICMP_SGT;
5719 RHS = getConstant(RA - 1);
5722 case ICmpInst::ICMP_SLE:
5723 if ((RA + 1).isMaxSignedValue()) {
5724 Pred = ICmpInst::ICMP_NE;
5725 RHS = getConstant(RA + 1);
5729 if (RA.isMinSignedValue()) {
5730 Pred = ICmpInst::ICMP_EQ;
5734 if (RA.isMaxSignedValue()) goto trivially_true;
5736 Pred = ICmpInst::ICMP_SLT;
5737 RHS = getConstant(RA + 1);
5740 case ICmpInst::ICMP_UGT:
5741 if (RA.isMinValue()) {
5742 Pred = ICmpInst::ICMP_NE;
5746 if ((RA + 1).isMaxValue()) {
5747 Pred = ICmpInst::ICMP_EQ;
5748 RHS = getConstant(RA + 1);
5752 if (RA.isMaxValue()) goto trivially_false;
5754 case ICmpInst::ICMP_ULT:
5755 if (RA.isMaxValue()) {
5756 Pred = ICmpInst::ICMP_NE;
5760 if ((RA - 1).isMinValue()) {
5761 Pred = ICmpInst::ICMP_EQ;
5762 RHS = getConstant(RA - 1);
5766 if (RA.isMinValue()) goto trivially_false;
5768 case ICmpInst::ICMP_SGT:
5769 if (RA.isMinSignedValue()) {
5770 Pred = ICmpInst::ICMP_NE;
5774 if ((RA + 1).isMaxSignedValue()) {
5775 Pred = ICmpInst::ICMP_EQ;
5776 RHS = getConstant(RA + 1);
5780 if (RA.isMaxSignedValue()) goto trivially_false;
5782 case ICmpInst::ICMP_SLT:
5783 if (RA.isMaxSignedValue()) {
5784 Pred = ICmpInst::ICMP_NE;
5788 if ((RA - 1).isMinSignedValue()) {
5789 Pred = ICmpInst::ICMP_EQ;
5790 RHS = getConstant(RA - 1);
5794 if (RA.isMinSignedValue()) goto trivially_false;
5799 // Check for obvious equality.
5800 if (HasSameValue(LHS, RHS)) {
5801 if (ICmpInst::isTrueWhenEqual(Pred))
5802 goto trivially_true;
5803 if (ICmpInst::isFalseWhenEqual(Pred))
5804 goto trivially_false;
5807 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5808 // adding or subtracting 1 from one of the operands.
5810 case ICmpInst::ICMP_SLE:
5811 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5812 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5814 Pred = ICmpInst::ICMP_SLT;
5816 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5817 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5819 Pred = ICmpInst::ICMP_SLT;
5823 case ICmpInst::ICMP_SGE:
5824 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5825 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5827 Pred = ICmpInst::ICMP_SGT;
5829 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5830 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5832 Pred = ICmpInst::ICMP_SGT;
5836 case ICmpInst::ICMP_ULE:
5837 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5838 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5840 Pred = ICmpInst::ICMP_ULT;
5842 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5843 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5845 Pred = ICmpInst::ICMP_ULT;
5849 case ICmpInst::ICMP_UGE:
5850 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5851 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5853 Pred = ICmpInst::ICMP_UGT;
5855 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5856 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5858 Pred = ICmpInst::ICMP_UGT;
5866 // TODO: More simplifications are possible here.
5868 // Recursively simplify until we either hit a recursion limit or nothing
5871 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5877 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5878 Pred = ICmpInst::ICMP_EQ;
5883 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5884 Pred = ICmpInst::ICMP_NE;
5888 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5889 return getSignedRange(S).getSignedMax().isNegative();
5892 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5893 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5896 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5897 return !getSignedRange(S).getSignedMin().isNegative();
5900 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5901 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5904 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5905 return isKnownNegative(S) || isKnownPositive(S);
5908 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5909 const SCEV *LHS, const SCEV *RHS) {
5910 // Canonicalize the inputs first.
5911 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5913 // If LHS or RHS is an addrec, check to see if the condition is true in
5914 // every iteration of the loop.
5915 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5916 if (isLoopEntryGuardedByCond(
5917 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5918 isLoopBackedgeGuardedByCond(
5919 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5921 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5922 if (isLoopEntryGuardedByCond(
5923 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5924 isLoopBackedgeGuardedByCond(
5925 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5928 // Otherwise see what can be done with known constant ranges.
5929 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5933 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5934 const SCEV *LHS, const SCEV *RHS) {
5935 if (HasSameValue(LHS, RHS))
5936 return ICmpInst::isTrueWhenEqual(Pred);
5938 // This code is split out from isKnownPredicate because it is called from
5939 // within isLoopEntryGuardedByCond.
5942 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5943 case ICmpInst::ICMP_SGT:
5944 Pred = ICmpInst::ICMP_SLT;
5945 std::swap(LHS, RHS);
5946 case ICmpInst::ICMP_SLT: {
5947 ConstantRange LHSRange = getSignedRange(LHS);
5948 ConstantRange RHSRange = getSignedRange(RHS);
5949 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5951 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5955 case ICmpInst::ICMP_SGE:
5956 Pred = ICmpInst::ICMP_SLE;
5957 std::swap(LHS, RHS);
5958 case ICmpInst::ICMP_SLE: {
5959 ConstantRange LHSRange = getSignedRange(LHS);
5960 ConstantRange RHSRange = getSignedRange(RHS);
5961 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5963 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5967 case ICmpInst::ICMP_UGT:
5968 Pred = ICmpInst::ICMP_ULT;
5969 std::swap(LHS, RHS);
5970 case ICmpInst::ICMP_ULT: {
5971 ConstantRange LHSRange = getUnsignedRange(LHS);
5972 ConstantRange RHSRange = getUnsignedRange(RHS);
5973 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5975 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5979 case ICmpInst::ICMP_UGE:
5980 Pred = ICmpInst::ICMP_ULE;
5981 std::swap(LHS, RHS);
5982 case ICmpInst::ICMP_ULE: {
5983 ConstantRange LHSRange = getUnsignedRange(LHS);
5984 ConstantRange RHSRange = getUnsignedRange(RHS);
5985 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5987 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5991 case ICmpInst::ICMP_NE: {
5992 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5994 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5997 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5998 if (isKnownNonZero(Diff))
6002 case ICmpInst::ICMP_EQ:
6003 // The check at the top of the function catches the case where
6004 // the values are known to be equal.
6010 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6011 /// protected by a conditional between LHS and RHS. This is used to
6012 /// to eliminate casts.
6014 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6015 ICmpInst::Predicate Pred,
6016 const SCEV *LHS, const SCEV *RHS) {
6017 // Interpret a null as meaning no loop, where there is obviously no guard
6018 // (interprocedural conditions notwithstanding).
6019 if (!L) return true;
6021 BasicBlock *Latch = L->getLoopLatch();
6025 BranchInst *LoopContinuePredicate =
6026 dyn_cast<BranchInst>(Latch->getTerminator());
6027 if (!LoopContinuePredicate ||
6028 LoopContinuePredicate->isUnconditional())
6031 return isImpliedCond(Pred, LHS, RHS,
6032 LoopContinuePredicate->getCondition(),
6033 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6036 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6037 /// by a conditional between LHS and RHS. This is used to help avoid max
6038 /// expressions in loop trip counts, and to eliminate casts.
6040 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6041 ICmpInst::Predicate Pred,
6042 const SCEV *LHS, const SCEV *RHS) {
6043 // Interpret a null as meaning no loop, where there is obviously no guard
6044 // (interprocedural conditions notwithstanding).
6045 if (!L) return false;
6047 // Starting at the loop predecessor, climb up the predecessor chain, as long
6048 // as there are predecessors that can be found that have unique successors
6049 // leading to the original header.
6050 for (std::pair<BasicBlock *, BasicBlock *>
6051 Pair(L->getLoopPredecessor(), L->getHeader());
6053 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6055 BranchInst *LoopEntryPredicate =
6056 dyn_cast<BranchInst>(Pair.first->getTerminator());
6057 if (!LoopEntryPredicate ||
6058 LoopEntryPredicate->isUnconditional())
6061 if (isImpliedCond(Pred, LHS, RHS,
6062 LoopEntryPredicate->getCondition(),
6063 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6070 /// RAII wrapper to prevent recursive application of isImpliedCond.
6071 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6072 /// currently evaluating isImpliedCond.
6073 struct MarkPendingLoopPredicate {
6075 DenseSet<Value*> &LoopPreds;
6078 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6079 : Cond(C), LoopPreds(LP) {
6080 Pending = !LoopPreds.insert(Cond).second;
6082 ~MarkPendingLoopPredicate() {
6084 LoopPreds.erase(Cond);
6088 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6089 /// and RHS is true whenever the given Cond value evaluates to true.
6090 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6091 const SCEV *LHS, const SCEV *RHS,
6092 Value *FoundCondValue,
6094 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6098 // Recursively handle And and Or conditions.
6099 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6100 if (BO->getOpcode() == Instruction::And) {
6102 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6103 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6104 } else if (BO->getOpcode() == Instruction::Or) {
6106 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6107 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6111 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6112 if (!ICI) return false;
6114 // Bail if the ICmp's operands' types are wider than the needed type
6115 // before attempting to call getSCEV on them. This avoids infinite
6116 // recursion, since the analysis of widening casts can require loop
6117 // exit condition information for overflow checking, which would
6119 if (getTypeSizeInBits(LHS->getType()) <
6120 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6123 // Now that we found a conditional branch that dominates the loop or controls
6124 // the loop latch. Check to see if it is the comparison we are looking for.
6125 ICmpInst::Predicate FoundPred;
6127 FoundPred = ICI->getInversePredicate();
6129 FoundPred = ICI->getPredicate();
6131 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6132 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6134 // Balance the types. The case where FoundLHS' type is wider than
6135 // LHS' type is checked for above.
6136 if (getTypeSizeInBits(LHS->getType()) >
6137 getTypeSizeInBits(FoundLHS->getType())) {
6138 if (CmpInst::isSigned(Pred)) {
6139 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6140 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6142 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6143 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6147 // Canonicalize the query to match the way instcombine will have
6148 // canonicalized the comparison.
6149 if (SimplifyICmpOperands(Pred, LHS, RHS))
6151 return CmpInst::isTrueWhenEqual(Pred);
6152 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6153 if (FoundLHS == FoundRHS)
6154 return CmpInst::isFalseWhenEqual(FoundPred);
6156 // Check to see if we can make the LHS or RHS match.
6157 if (LHS == FoundRHS || RHS == FoundLHS) {
6158 if (isa<SCEVConstant>(RHS)) {
6159 std::swap(FoundLHS, FoundRHS);
6160 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6162 std::swap(LHS, RHS);
6163 Pred = ICmpInst::getSwappedPredicate(Pred);
6167 // Check whether the found predicate is the same as the desired predicate.
6168 if (FoundPred == Pred)
6169 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6171 // Check whether swapping the found predicate makes it the same as the
6172 // desired predicate.
6173 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6174 if (isa<SCEVConstant>(RHS))
6175 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6177 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6178 RHS, LHS, FoundLHS, FoundRHS);
6181 // Check whether the actual condition is beyond sufficient.
6182 if (FoundPred == ICmpInst::ICMP_EQ)
6183 if (ICmpInst::isTrueWhenEqual(Pred))
6184 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6186 if (Pred == ICmpInst::ICMP_NE)
6187 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6188 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6191 // Otherwise assume the worst.
6195 /// isImpliedCondOperands - Test whether the condition described by Pred,
6196 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6197 /// and FoundRHS is true.
6198 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6199 const SCEV *LHS, const SCEV *RHS,
6200 const SCEV *FoundLHS,
6201 const SCEV *FoundRHS) {
6202 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6203 FoundLHS, FoundRHS) ||
6204 // ~x < ~y --> x > y
6205 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6206 getNotSCEV(FoundRHS),
6207 getNotSCEV(FoundLHS));
6210 /// isImpliedCondOperandsHelper - Test whether the condition described by
6211 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6212 /// FoundLHS, and FoundRHS is true.
6214 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6215 const SCEV *LHS, const SCEV *RHS,
6216 const SCEV *FoundLHS,
6217 const SCEV *FoundRHS) {
6219 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6220 case ICmpInst::ICMP_EQ:
6221 case ICmpInst::ICMP_NE:
6222 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6225 case ICmpInst::ICMP_SLT:
6226 case ICmpInst::ICMP_SLE:
6227 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6228 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6231 case ICmpInst::ICMP_SGT:
6232 case ICmpInst::ICMP_SGE:
6233 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6234 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6237 case ICmpInst::ICMP_ULT:
6238 case ICmpInst::ICMP_ULE:
6239 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6240 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6243 case ICmpInst::ICMP_UGT:
6244 case ICmpInst::ICMP_UGE:
6245 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6246 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6254 /// getBECount - Subtract the end and start values and divide by the step,
6255 /// rounding up, to get the number of times the backedge is executed. Return
6256 /// CouldNotCompute if an intermediate computation overflows.
6257 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6261 assert(!isKnownNegative(Step) &&
6262 "This code doesn't handle negative strides yet!");
6264 Type *Ty = Start->getType();
6266 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6267 // here because SCEV may not be able to determine that the unsigned division
6268 // after rounding is zero.
6270 return getConstant(Ty, 0);
6272 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6273 const SCEV *Diff = getMinusSCEV(End, Start);
6274 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6276 // Add an adjustment to the difference between End and Start so that
6277 // the division will effectively round up.
6278 const SCEV *Add = getAddExpr(Diff, RoundUp);
6281 // Check Add for unsigned overflow.
6282 // TODO: More sophisticated things could be done here.
6283 Type *WideTy = IntegerType::get(getContext(),
6284 getTypeSizeInBits(Ty) + 1);
6285 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6286 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6287 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6288 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6289 return getCouldNotCompute();
6292 return getUDivExpr(Add, Step);
6295 /// HowManyLessThans - Return the number of times a backedge containing the
6296 /// specified less-than comparison will execute. If not computable, return
6297 /// CouldNotCompute.
6298 ScalarEvolution::ExitLimit
6299 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6300 const Loop *L, bool isSigned) {
6301 // Only handle: "ADDREC < LoopInvariant".
6302 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6304 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6305 if (!AddRec || AddRec->getLoop() != L)
6306 return getCouldNotCompute();
6308 // Check to see if we have a flag which makes analysis easy.
6309 bool NoWrap = isSigned ?
6310 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6311 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6313 if (AddRec->isAffine()) {
6314 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6315 const SCEV *Step = AddRec->getStepRecurrence(*this);
6318 return getCouldNotCompute();
6319 if (Step->isOne()) {
6320 // With unit stride, the iteration never steps past the limit value.
6321 } else if (isKnownPositive(Step)) {
6322 // Test whether a positive iteration can step past the limit
6323 // value and past the maximum value for its type in a single step.
6324 // Note that it's not sufficient to check NoWrap here, because even
6325 // though the value after a wrap is undefined, it's not undefined
6326 // behavior, so if wrap does occur, the loop could either terminate or
6327 // loop infinitely, but in either case, the loop is guaranteed to
6328 // iterate at least until the iteration where the wrapping occurs.
6329 const SCEV *One = getConstant(Step->getType(), 1);
6331 APInt Max = APInt::getSignedMaxValue(BitWidth);
6332 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6333 .slt(getSignedRange(RHS).getSignedMax()))
6334 return getCouldNotCompute();
6336 APInt Max = APInt::getMaxValue(BitWidth);
6337 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6338 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6339 return getCouldNotCompute();
6342 // TODO: Handle negative strides here and below.
6343 return getCouldNotCompute();
6345 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6346 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6347 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6348 // treat m-n as signed nor unsigned due to overflow possibility.
6350 // First, we get the value of the LHS in the first iteration: n
6351 const SCEV *Start = AddRec->getOperand(0);
6353 // Determine the minimum constant start value.
6354 const SCEV *MinStart = getConstant(isSigned ?
6355 getSignedRange(Start).getSignedMin() :
6356 getUnsignedRange(Start).getUnsignedMin());
6358 // If we know that the condition is true in order to enter the loop,
6359 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6360 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6361 // the division must round up.
6362 const SCEV *End = RHS;
6363 if (!isLoopEntryGuardedByCond(L,
6364 isSigned ? ICmpInst::ICMP_SLT :
6366 getMinusSCEV(Start, Step), RHS))
6367 End = isSigned ? getSMaxExpr(RHS, Start)
6368 : getUMaxExpr(RHS, Start);
6370 // Determine the maximum constant end value.
6371 const SCEV *MaxEnd = getConstant(isSigned ?
6372 getSignedRange(End).getSignedMax() :
6373 getUnsignedRange(End).getUnsignedMax());
6375 // If MaxEnd is within a step of the maximum integer value in its type,
6376 // adjust it down to the minimum value which would produce the same effect.
6377 // This allows the subsequent ceiling division of (N+(step-1))/step to
6378 // compute the correct value.
6379 const SCEV *StepMinusOne = getMinusSCEV(Step,
6380 getConstant(Step->getType(), 1));
6383 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6386 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6389 // Finally, we subtract these two values and divide, rounding up, to get
6390 // the number of times the backedge is executed.
6391 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6393 // The maximum backedge count is similar, except using the minimum start
6394 // value and the maximum end value.
6395 // If we already have an exact constant BECount, use it instead.
6396 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6397 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6399 // If the stride is nonconstant, and NoWrap == true, then
6400 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6401 // exact BECount and invalid MaxBECount, which should be avoided to catch
6402 // more optimization opportunities.
6403 if (isa<SCEVCouldNotCompute>(MaxBECount))
6404 MaxBECount = BECount;
6406 return ExitLimit(BECount, MaxBECount);
6409 return getCouldNotCompute();
6412 /// getNumIterationsInRange - Return the number of iterations of this loop that
6413 /// produce values in the specified constant range. Another way of looking at
6414 /// this is that it returns the first iteration number where the value is not in
6415 /// the condition, thus computing the exit count. If the iteration count can't
6416 /// be computed, an instance of SCEVCouldNotCompute is returned.
6417 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6418 ScalarEvolution &SE) const {
6419 if (Range.isFullSet()) // Infinite loop.
6420 return SE.getCouldNotCompute();
6422 // If the start is a non-zero constant, shift the range to simplify things.
6423 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6424 if (!SC->getValue()->isZero()) {
6425 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6426 Operands[0] = SE.getConstant(SC->getType(), 0);
6427 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6428 getNoWrapFlags(FlagNW));
6429 if (const SCEVAddRecExpr *ShiftedAddRec =
6430 dyn_cast<SCEVAddRecExpr>(Shifted))
6431 return ShiftedAddRec->getNumIterationsInRange(
6432 Range.subtract(SC->getValue()->getValue()), SE);
6433 // This is strange and shouldn't happen.
6434 return SE.getCouldNotCompute();
6437 // The only time we can solve this is when we have all constant indices.
6438 // Otherwise, we cannot determine the overflow conditions.
6439 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6440 if (!isa<SCEVConstant>(getOperand(i)))
6441 return SE.getCouldNotCompute();
6444 // Okay at this point we know that all elements of the chrec are constants and
6445 // that the start element is zero.
6447 // First check to see if the range contains zero. If not, the first
6449 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6450 if (!Range.contains(APInt(BitWidth, 0)))
6451 return SE.getConstant(getType(), 0);
6454 // If this is an affine expression then we have this situation:
6455 // Solve {0,+,A} in Range === Ax in Range
6457 // We know that zero is in the range. If A is positive then we know that
6458 // the upper value of the range must be the first possible exit value.
6459 // If A is negative then the lower of the range is the last possible loop
6460 // value. Also note that we already checked for a full range.
6461 APInt One(BitWidth,1);
6462 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6463 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6465 // The exit value should be (End+A)/A.
6466 APInt ExitVal = (End + A).udiv(A);
6467 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6469 // Evaluate at the exit value. If we really did fall out of the valid
6470 // range, then we computed our trip count, otherwise wrap around or other
6471 // things must have happened.
6472 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6473 if (Range.contains(Val->getValue()))
6474 return SE.getCouldNotCompute(); // Something strange happened
6476 // Ensure that the previous value is in the range. This is a sanity check.
6477 assert(Range.contains(
6478 EvaluateConstantChrecAtConstant(this,
6479 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6480 "Linear scev computation is off in a bad way!");
6481 return SE.getConstant(ExitValue);
6482 } else if (isQuadratic()) {
6483 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6484 // quadratic equation to solve it. To do this, we must frame our problem in
6485 // terms of figuring out when zero is crossed, instead of when
6486 // Range.getUpper() is crossed.
6487 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6488 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6489 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6490 // getNoWrapFlags(FlagNW)
6493 // Next, solve the constructed addrec
6494 std::pair<const SCEV *,const SCEV *> Roots =
6495 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6496 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6497 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6499 // Pick the smallest positive root value.
6500 if (ConstantInt *CB =
6501 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6502 R1->getValue(), R2->getValue()))) {
6503 if (CB->getZExtValue() == false)
6504 std::swap(R1, R2); // R1 is the minimum root now.
6506 // Make sure the root is not off by one. The returned iteration should
6507 // not be in the range, but the previous one should be. When solving
6508 // for "X*X < 5", for example, we should not return a root of 2.
6509 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6512 if (Range.contains(R1Val->getValue())) {
6513 // The next iteration must be out of the range...
6514 ConstantInt *NextVal =
6515 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6517 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6518 if (!Range.contains(R1Val->getValue()))
6519 return SE.getConstant(NextVal);
6520 return SE.getCouldNotCompute(); // Something strange happened
6523 // If R1 was not in the range, then it is a good return value. Make
6524 // sure that R1-1 WAS in the range though, just in case.
6525 ConstantInt *NextVal =
6526 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6527 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6528 if (Range.contains(R1Val->getValue()))
6530 return SE.getCouldNotCompute(); // Something strange happened
6535 return SE.getCouldNotCompute();
6540 //===----------------------------------------------------------------------===//
6541 // SCEVCallbackVH Class Implementation
6542 //===----------------------------------------------------------------------===//
6544 void ScalarEvolution::SCEVCallbackVH::deleted() {
6545 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6546 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6547 SE->ConstantEvolutionLoopExitValue.erase(PN);
6548 SE->ValueExprMap.erase(getValPtr());
6549 // this now dangles!
6552 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6553 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6555 // Forget all the expressions associated with users of the old value,
6556 // so that future queries will recompute the expressions using the new
6558 Value *Old = getValPtr();
6559 SmallVector<User *, 16> Worklist;
6560 SmallPtrSet<User *, 8> Visited;
6561 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6563 Worklist.push_back(*UI);
6564 while (!Worklist.empty()) {
6565 User *U = Worklist.pop_back_val();
6566 // Deleting the Old value will cause this to dangle. Postpone
6567 // that until everything else is done.
6570 if (!Visited.insert(U))
6572 if (PHINode *PN = dyn_cast<PHINode>(U))
6573 SE->ConstantEvolutionLoopExitValue.erase(PN);
6574 SE->ValueExprMap.erase(U);
6575 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6577 Worklist.push_back(*UI);
6579 // Delete the Old value.
6580 if (PHINode *PN = dyn_cast<PHINode>(Old))
6581 SE->ConstantEvolutionLoopExitValue.erase(PN);
6582 SE->ValueExprMap.erase(Old);
6583 // this now dangles!
6586 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6587 : CallbackVH(V), SE(se) {}
6589 //===----------------------------------------------------------------------===//
6590 // ScalarEvolution Class Implementation
6591 //===----------------------------------------------------------------------===//
6593 ScalarEvolution::ScalarEvolution()
6594 : FunctionPass(ID), FirstUnknown(0) {
6595 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6598 bool ScalarEvolution::runOnFunction(Function &F) {
6600 LI = &getAnalysis<LoopInfo>();
6601 TD = getAnalysisIfAvailable<DataLayout>();
6602 TLI = &getAnalysis<TargetLibraryInfo>();
6603 DT = &getAnalysis<DominatorTree>();
6607 void ScalarEvolution::releaseMemory() {
6608 // Iterate through all the SCEVUnknown instances and call their
6609 // destructors, so that they release their references to their values.
6610 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6614 ValueExprMap.clear();
6616 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6617 // that a loop had multiple computable exits.
6618 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6619 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6624 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6626 BackedgeTakenCounts.clear();
6627 ConstantEvolutionLoopExitValue.clear();
6628 ValuesAtScopes.clear();
6629 LoopDispositions.clear();
6630 BlockDispositions.clear();
6631 UnsignedRanges.clear();
6632 SignedRanges.clear();
6633 UniqueSCEVs.clear();
6634 SCEVAllocator.Reset();
6637 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6638 AU.setPreservesAll();
6639 AU.addRequiredTransitive<LoopInfo>();
6640 AU.addRequiredTransitive<DominatorTree>();
6641 AU.addRequired<TargetLibraryInfo>();
6644 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6645 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6648 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6650 // Print all inner loops first
6651 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6652 PrintLoopInfo(OS, SE, *I);
6655 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6658 SmallVector<BasicBlock *, 8> ExitBlocks;
6659 L->getExitBlocks(ExitBlocks);
6660 if (ExitBlocks.size() != 1)
6661 OS << "<multiple exits> ";
6663 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6664 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6666 OS << "Unpredictable backedge-taken count. ";
6671 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6674 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6675 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6677 OS << "Unpredictable max backedge-taken count. ";
6683 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6684 // ScalarEvolution's implementation of the print method is to print
6685 // out SCEV values of all instructions that are interesting. Doing
6686 // this potentially causes it to create new SCEV objects though,
6687 // which technically conflicts with the const qualifier. This isn't
6688 // observable from outside the class though, so casting away the
6689 // const isn't dangerous.
6690 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6692 OS << "Classifying expressions for: ";
6693 WriteAsOperand(OS, F, /*PrintType=*/false);
6695 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6696 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6699 const SCEV *SV = SE.getSCEV(&*I);
6702 const Loop *L = LI->getLoopFor((*I).getParent());
6704 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6711 OS << "\t\t" "Exits: ";
6712 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6713 if (!SE.isLoopInvariant(ExitValue, L)) {
6714 OS << "<<Unknown>>";
6723 OS << "Determining loop execution counts for: ";
6724 WriteAsOperand(OS, F, /*PrintType=*/false);
6726 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6727 PrintLoopInfo(OS, &SE, *I);
6730 ScalarEvolution::LoopDisposition
6731 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6732 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6733 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6734 Values.insert(std::make_pair(L, LoopVariant));
6736 return Pair.first->second;
6738 LoopDisposition D = computeLoopDisposition(S, L);
6739 return LoopDispositions[S][L] = D;
6742 ScalarEvolution::LoopDisposition
6743 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6744 switch (S->getSCEVType()) {
6746 return LoopInvariant;
6750 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6751 case scAddRecExpr: {
6752 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6754 // If L is the addrec's loop, it's computable.
6755 if (AR->getLoop() == L)
6756 return LoopComputable;
6758 // Add recurrences are never invariant in the function-body (null loop).
6762 // This recurrence is variant w.r.t. L if L contains AR's loop.
6763 if (L->contains(AR->getLoop()))
6766 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6767 if (AR->getLoop()->contains(L))
6768 return LoopInvariant;
6770 // This recurrence is variant w.r.t. L if any of its operands
6772 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6774 if (!isLoopInvariant(*I, L))
6777 // Otherwise it's loop-invariant.
6778 return LoopInvariant;
6784 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6785 bool HasVarying = false;
6786 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6788 LoopDisposition D = getLoopDisposition(*I, L);
6789 if (D == LoopVariant)
6791 if (D == LoopComputable)
6794 return HasVarying ? LoopComputable : LoopInvariant;
6797 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6798 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6799 if (LD == LoopVariant)
6801 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6802 if (RD == LoopVariant)
6804 return (LD == LoopInvariant && RD == LoopInvariant) ?
6805 LoopInvariant : LoopComputable;
6808 // All non-instruction values are loop invariant. All instructions are loop
6809 // invariant if they are not contained in the specified loop.
6810 // Instructions are never considered invariant in the function body
6811 // (null loop) because they are defined within the "loop".
6812 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6813 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6814 return LoopInvariant;
6815 case scCouldNotCompute:
6816 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6817 default: llvm_unreachable("Unknown SCEV kind!");
6821 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6822 return getLoopDisposition(S, L) == LoopInvariant;
6825 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6826 return getLoopDisposition(S, L) == LoopComputable;
6829 ScalarEvolution::BlockDisposition
6830 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6831 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6832 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6833 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6835 return Pair.first->second;
6837 BlockDisposition D = computeBlockDisposition(S, BB);
6838 return BlockDispositions[S][BB] = D;
6841 ScalarEvolution::BlockDisposition
6842 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6843 switch (S->getSCEVType()) {
6845 return ProperlyDominatesBlock;
6849 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6850 case scAddRecExpr: {
6851 // This uses a "dominates" query instead of "properly dominates" query
6852 // to test for proper dominance too, because the instruction which
6853 // produces the addrec's value is a PHI, and a PHI effectively properly
6854 // dominates its entire containing block.
6855 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6856 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6857 return DoesNotDominateBlock;
6859 // FALL THROUGH into SCEVNAryExpr handling.
6864 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6866 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6868 BlockDisposition D = getBlockDisposition(*I, BB);
6869 if (D == DoesNotDominateBlock)
6870 return DoesNotDominateBlock;
6871 if (D == DominatesBlock)
6874 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6877 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6878 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6879 BlockDisposition LD = getBlockDisposition(LHS, BB);
6880 if (LD == DoesNotDominateBlock)
6881 return DoesNotDominateBlock;
6882 BlockDisposition RD = getBlockDisposition(RHS, BB);
6883 if (RD == DoesNotDominateBlock)
6884 return DoesNotDominateBlock;
6885 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6886 ProperlyDominatesBlock : DominatesBlock;
6889 if (Instruction *I =
6890 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6891 if (I->getParent() == BB)
6892 return DominatesBlock;
6893 if (DT->properlyDominates(I->getParent(), BB))
6894 return ProperlyDominatesBlock;
6895 return DoesNotDominateBlock;
6897 return ProperlyDominatesBlock;
6898 case scCouldNotCompute:
6899 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6901 llvm_unreachable("Unknown SCEV kind!");
6905 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6906 return getBlockDisposition(S, BB) >= DominatesBlock;
6909 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6910 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6914 // Search for a SCEV expression node within an expression tree.
6915 // Implements SCEVTraversal::Visitor.
6920 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
6922 bool follow(const SCEV *S) {
6923 IsFound |= (S == Node);
6926 bool isDone() const { return IsFound; }
6930 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6931 SCEVSearch Search(Op);
6932 visitAll(S, Search);
6933 return Search.IsFound;
6936 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6937 ValuesAtScopes.erase(S);
6938 LoopDispositions.erase(S);
6939 BlockDispositions.erase(S);
6940 UnsignedRanges.erase(S);
6941 SignedRanges.erase(S);
6944 typedef DenseMap<const Loop *, std::string> VerifyMap;
6946 /// replaceSubString - Replaces all occurences of From in Str with To.
6947 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
6949 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
6950 Str.replace(Pos, From.size(), To.data(), To.size());
6955 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
6957 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
6958 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
6959 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
6961 std::string &S = Map[L];
6963 raw_string_ostream OS(S);
6964 SE.getBackedgeTakenCount(L)->print(OS);
6966 // false and 0 are semantically equivalent. This can happen in dead loops.
6967 replaceSubString(OS.str(), "false", "0");
6968 // Remove wrap flags, their use in SCEV is highly fragile.
6969 // FIXME: Remove this when SCEV gets smarter about them.
6970 replaceSubString(OS.str(), "<nw>", "");
6971 replaceSubString(OS.str(), "<nsw>", "");
6972 replaceSubString(OS.str(), "<nuw>", "");
6977 void ScalarEvolution::verifyAnalysis() const {
6981 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6983 // Gather stringified backedge taken counts for all loops using SCEV's caches.
6984 // FIXME: It would be much better to store actual values instead of strings,
6985 // but SCEV pointers will change if we drop the caches.
6986 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
6987 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
6988 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
6990 // Gather stringified backedge taken counts for all loops without using
6993 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
6994 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
6996 // Now compare whether they're the same with and without caches. This allows
6997 // verifying that no pass changed the cache.
6998 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
6999 "New loops suddenly appeared!");
7001 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7002 OldE = BackedgeDumpsOld.end(),
7003 NewI = BackedgeDumpsNew.begin();
7004 OldI != OldE; ++OldI, ++NewI) {
7005 assert(OldI->first == NewI->first && "Loop order changed!");
7007 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7009 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7010 // means that a pass is buggy or SCEV has to learn a new pattern but is
7011 // usually not harmful.
7012 if (OldI->second != NewI->second &&
7013 OldI->second.find("undef") == std::string::npos &&
7014 NewI->second.find("undef") == std::string::npos &&
7015 OldI->second != "***COULDNOTCOMPUTE***" &&
7016 NewI->second != "***COULDNOTCOMPUTE***") {
7017 dbgs() << "SCEVValidator: SCEV for loop '"
7018 << OldI->first->getHeader()->getName()
7019 << "' changed from '" << OldI->second
7020 << "' to '" << NewI->second << "'!\n";
7025 // TODO: Verify more things.