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, Type *IntPtrTy) {
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(IntPtrTy, TD->getTypeAllocSize(AllocTy));
2596 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2597 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2598 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2600 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2601 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2604 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2605 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2606 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2607 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2609 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2610 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2613 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, Type *IntPtrTy,
2615 // If we have DataLayout, we can bypass creating a target-independent
2616 // constant expression and then folding it back into a ConstantInt.
2617 // This is just a compile-time optimization.
2619 return getConstant(IntPtrTy,
2620 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2622 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2623 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2624 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2626 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2627 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2630 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2631 Constant *FieldNo) {
2632 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2633 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2634 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2636 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2637 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2640 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2641 // Don't attempt to do anything other than create a SCEVUnknown object
2642 // here. createSCEV only calls getUnknown after checking for all other
2643 // interesting possibilities, and any other code that calls getUnknown
2644 // is doing so in order to hide a value from SCEV canonicalization.
2646 FoldingSetNodeID ID;
2647 ID.AddInteger(scUnknown);
2650 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2651 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2652 "Stale SCEVUnknown in uniquing map!");
2655 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2657 FirstUnknown = cast<SCEVUnknown>(S);
2658 UniqueSCEVs.InsertNode(S, IP);
2662 //===----------------------------------------------------------------------===//
2663 // Basic SCEV Analysis and PHI Idiom Recognition Code
2666 /// isSCEVable - Test if values of the given type are analyzable within
2667 /// the SCEV framework. This primarily includes integer types, and it
2668 /// can optionally include pointer types if the ScalarEvolution class
2669 /// has access to target-specific information.
2670 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2671 // Integers and pointers are always SCEVable.
2672 return Ty->isIntegerTy() || Ty->isPointerTy();
2675 /// getTypeSizeInBits - Return the size in bits of the specified type,
2676 /// for which isSCEVable must return true.
2677 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2678 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2680 // If we have a DataLayout, use it!
2682 return TD->getTypeSizeInBits(Ty);
2684 // Integer types have fixed sizes.
2685 if (Ty->isIntegerTy())
2686 return Ty->getPrimitiveSizeInBits();
2688 // The only other support type is pointer. Without DataLayout, conservatively
2689 // assume pointers are 64-bit.
2690 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2694 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2695 /// the given type and which represents how SCEV will treat the given
2696 /// type, for which isSCEVable must return true. For pointer types,
2697 /// this is the pointer-sized integer type.
2698 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2699 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2701 if (Ty->isIntegerTy())
2704 // The only other support type is pointer.
2705 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2706 if (TD) return TD->getIntPtrType(Ty);
2708 // Without DataLayout, conservatively assume pointers are 64-bit.
2709 return Type::getInt64Ty(getContext());
2712 const SCEV *ScalarEvolution::getCouldNotCompute() {
2713 return &CouldNotCompute;
2716 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2717 /// expression and create a new one.
2718 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2719 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2721 ValueExprMapType::const_iterator I = ValueExprMap.find_as(V);
2722 if (I != ValueExprMap.end()) return I->second;
2723 const SCEV *S = createSCEV(V);
2725 // The process of creating a SCEV for V may have caused other SCEVs
2726 // to have been created, so it's necessary to insert the new entry
2727 // from scratch, rather than trying to remember the insert position
2729 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2733 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2735 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2736 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2738 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2740 Type *Ty = V->getType();
2741 Ty = getEffectiveSCEVType(Ty);
2742 return getMulExpr(V,
2743 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2746 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2747 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2748 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2750 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2752 Type *Ty = V->getType();
2753 Ty = getEffectiveSCEVType(Ty);
2754 const SCEV *AllOnes =
2755 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2756 return getMinusSCEV(AllOnes, V);
2759 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2760 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2761 SCEV::NoWrapFlags Flags) {
2762 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2764 // Fast path: X - X --> 0.
2766 return getConstant(LHS->getType(), 0);
2769 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2772 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2773 /// input value to the specified type. If the type must be extended, it is zero
2776 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2777 Type *SrcTy = V->getType();
2778 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2779 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2780 "Cannot truncate or zero extend with non-integer arguments!");
2781 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2782 return V; // No conversion
2783 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2784 return getTruncateExpr(V, Ty);
2785 return getZeroExtendExpr(V, Ty);
2788 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2789 /// input value to the specified type. If the type must be extended, it is sign
2792 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2794 Type *SrcTy = V->getType();
2795 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2796 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2797 "Cannot truncate or zero extend with non-integer arguments!");
2798 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2799 return V; // No conversion
2800 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2801 return getTruncateExpr(V, Ty);
2802 return getSignExtendExpr(V, Ty);
2805 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2806 /// input value to the specified type. If the type must be extended, it is zero
2807 /// extended. The conversion must not be narrowing.
2809 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2810 Type *SrcTy = V->getType();
2811 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2812 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2813 "Cannot noop or zero extend with non-integer arguments!");
2814 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2815 "getNoopOrZeroExtend cannot truncate!");
2816 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2817 return V; // No conversion
2818 return getZeroExtendExpr(V, Ty);
2821 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2822 /// input value to the specified type. If the type must be extended, it is sign
2823 /// extended. The conversion must not be narrowing.
2825 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2826 Type *SrcTy = V->getType();
2827 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2828 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2829 "Cannot noop or sign extend with non-integer arguments!");
2830 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2831 "getNoopOrSignExtend cannot truncate!");
2832 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2833 return V; // No conversion
2834 return getSignExtendExpr(V, Ty);
2837 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2838 /// the input value to the specified type. If the type must be extended,
2839 /// it is extended with unspecified bits. The conversion must not be
2842 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2843 Type *SrcTy = V->getType();
2844 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2845 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2846 "Cannot noop or any extend with non-integer arguments!");
2847 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2848 "getNoopOrAnyExtend cannot truncate!");
2849 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2850 return V; // No conversion
2851 return getAnyExtendExpr(V, Ty);
2854 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2855 /// input value to the specified type. The conversion must not be widening.
2857 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2858 Type *SrcTy = V->getType();
2859 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2860 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2861 "Cannot truncate or noop with non-integer arguments!");
2862 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2863 "getTruncateOrNoop cannot extend!");
2864 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2865 return V; // No conversion
2866 return getTruncateExpr(V, Ty);
2869 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2870 /// the types using zero-extension, and then perform a umax operation
2872 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2874 const SCEV *PromotedLHS = LHS;
2875 const SCEV *PromotedRHS = RHS;
2877 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2878 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2880 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2882 return getUMaxExpr(PromotedLHS, PromotedRHS);
2885 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2886 /// the types using zero-extension, and then perform a umin operation
2888 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2890 const SCEV *PromotedLHS = LHS;
2891 const SCEV *PromotedRHS = RHS;
2893 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2894 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2896 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2898 return getUMinExpr(PromotedLHS, PromotedRHS);
2901 /// getPointerBase - Transitively follow the chain of pointer-type operands
2902 /// until reaching a SCEV that does not have a single pointer operand. This
2903 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2904 /// but corner cases do exist.
2905 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2906 // A pointer operand may evaluate to a nonpointer expression, such as null.
2907 if (!V->getType()->isPointerTy())
2910 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2911 return getPointerBase(Cast->getOperand());
2913 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2914 const SCEV *PtrOp = 0;
2915 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2917 if ((*I)->getType()->isPointerTy()) {
2918 // Cannot find the base of an expression with multiple pointer operands.
2926 return getPointerBase(PtrOp);
2931 /// PushDefUseChildren - Push users of the given Instruction
2932 /// onto the given Worklist.
2934 PushDefUseChildren(Instruction *I,
2935 SmallVectorImpl<Instruction *> &Worklist) {
2936 // Push the def-use children onto the Worklist stack.
2937 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2939 Worklist.push_back(cast<Instruction>(*UI));
2942 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2943 /// instructions that depend on the given instruction and removes them from
2944 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2947 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2948 SmallVector<Instruction *, 16> Worklist;
2949 PushDefUseChildren(PN, Worklist);
2951 SmallPtrSet<Instruction *, 8> Visited;
2953 while (!Worklist.empty()) {
2954 Instruction *I = Worklist.pop_back_val();
2955 if (!Visited.insert(I)) continue;
2957 ValueExprMapType::iterator It =
2958 ValueExprMap.find_as(static_cast<Value *>(I));
2959 if (It != ValueExprMap.end()) {
2960 const SCEV *Old = It->second;
2962 // Short-circuit the def-use traversal if the symbolic name
2963 // ceases to appear in expressions.
2964 if (Old != SymName && !hasOperand(Old, SymName))
2967 // SCEVUnknown for a PHI either means that it has an unrecognized
2968 // structure, it's a PHI that's in the progress of being computed
2969 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2970 // additional loop trip count information isn't going to change anything.
2971 // In the second case, createNodeForPHI will perform the necessary
2972 // updates on its own when it gets to that point. In the third, we do
2973 // want to forget the SCEVUnknown.
2974 if (!isa<PHINode>(I) ||
2975 !isa<SCEVUnknown>(Old) ||
2976 (I != PN && Old == SymName)) {
2977 forgetMemoizedResults(Old);
2978 ValueExprMap.erase(It);
2982 PushDefUseChildren(I, Worklist);
2986 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2987 /// a loop header, making it a potential recurrence, or it doesn't.
2989 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2990 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2991 if (L->getHeader() == PN->getParent()) {
2992 // The loop may have multiple entrances or multiple exits; we can analyze
2993 // this phi as an addrec if it has a unique entry value and a unique
2995 Value *BEValueV = 0, *StartValueV = 0;
2996 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2997 Value *V = PN->getIncomingValue(i);
2998 if (L->contains(PN->getIncomingBlock(i))) {
3001 } else if (BEValueV != V) {
3005 } else if (!StartValueV) {
3007 } else if (StartValueV != V) {
3012 if (BEValueV && StartValueV) {
3013 // While we are analyzing this PHI node, handle its value symbolically.
3014 const SCEV *SymbolicName = getUnknown(PN);
3015 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3016 "PHI node already processed?");
3017 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3019 // Using this symbolic name for the PHI, analyze the value coming around
3021 const SCEV *BEValue = getSCEV(BEValueV);
3023 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3024 // has a special value for the first iteration of the loop.
3026 // If the value coming around the backedge is an add with the symbolic
3027 // value we just inserted, then we found a simple induction variable!
3028 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3029 // If there is a single occurrence of the symbolic value, replace it
3030 // with a recurrence.
3031 unsigned FoundIndex = Add->getNumOperands();
3032 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3033 if (Add->getOperand(i) == SymbolicName)
3034 if (FoundIndex == e) {
3039 if (FoundIndex != Add->getNumOperands()) {
3040 // Create an add with everything but the specified operand.
3041 SmallVector<const SCEV *, 8> Ops;
3042 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3043 if (i != FoundIndex)
3044 Ops.push_back(Add->getOperand(i));
3045 const SCEV *Accum = getAddExpr(Ops);
3047 // This is not a valid addrec if the step amount is varying each
3048 // loop iteration, but is not itself an addrec in this loop.
3049 if (isLoopInvariant(Accum, L) ||
3050 (isa<SCEVAddRecExpr>(Accum) &&
3051 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3052 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3054 // If the increment doesn't overflow, then neither the addrec nor
3055 // the post-increment will overflow.
3056 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3057 if (OBO->hasNoUnsignedWrap())
3058 Flags = setFlags(Flags, SCEV::FlagNUW);
3059 if (OBO->hasNoSignedWrap())
3060 Flags = setFlags(Flags, SCEV::FlagNSW);
3061 } else if (const GEPOperator *GEP =
3062 dyn_cast<GEPOperator>(BEValueV)) {
3063 // If the increment is an inbounds GEP, then we know the address
3064 // space cannot be wrapped around. We cannot make any guarantee
3065 // about signed or unsigned overflow because pointers are
3066 // unsigned but we may have a negative index from the base
3068 if (GEP->isInBounds())
3069 Flags = setFlags(Flags, SCEV::FlagNW);
3072 const SCEV *StartVal = getSCEV(StartValueV);
3073 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3075 // Since the no-wrap flags are on the increment, they apply to the
3076 // post-incremented value as well.
3077 if (isLoopInvariant(Accum, L))
3078 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3081 // Okay, for the entire analysis of this edge we assumed the PHI
3082 // to be symbolic. We now need to go back and purge all of the
3083 // entries for the scalars that use the symbolic expression.
3084 ForgetSymbolicName(PN, SymbolicName);
3085 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3089 } else if (const SCEVAddRecExpr *AddRec =
3090 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3091 // Otherwise, this could be a loop like this:
3092 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3093 // In this case, j = {1,+,1} and BEValue is j.
3094 // Because the other in-value of i (0) fits the evolution of BEValue
3095 // i really is an addrec evolution.
3096 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3097 const SCEV *StartVal = getSCEV(StartValueV);
3099 // If StartVal = j.start - j.stride, we can use StartVal as the
3100 // initial step of the addrec evolution.
3101 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3102 AddRec->getOperand(1))) {
3103 // FIXME: For constant StartVal, we should be able to infer
3105 const SCEV *PHISCEV =
3106 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3109 // Okay, for the entire analysis of this edge we assumed the PHI
3110 // to be symbolic. We now need to go back and purge all of the
3111 // entries for the scalars that use the symbolic expression.
3112 ForgetSymbolicName(PN, SymbolicName);
3113 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3121 // If the PHI has a single incoming value, follow that value, unless the
3122 // PHI's incoming blocks are in a different loop, in which case doing so
3123 // risks breaking LCSSA form. Instcombine would normally zap these, but
3124 // it doesn't have DominatorTree information, so it may miss cases.
3125 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3126 if (LI->replacementPreservesLCSSAForm(PN, V))
3129 // If it's not a loop phi, we can't handle it yet.
3130 return getUnknown(PN);
3133 /// createNodeForGEP - Expand GEP instructions into add and multiply
3134 /// operations. This allows them to be analyzed by regular SCEV code.
3136 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3138 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3139 // Add expression, because the Instruction may be guarded by control flow
3140 // and the no-overflow bits may not be valid for the expression in any
3142 bool isInBounds = GEP->isInBounds();
3144 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3145 Value *Base = GEP->getOperand(0);
3146 // Don't attempt to analyze GEPs over unsized objects.
3147 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3148 return getUnknown(GEP);
3149 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3150 gep_type_iterator GTI = gep_type_begin(GEP);
3151 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3155 // Compute the (potentially symbolic) offset in bytes for this index.
3156 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3157 // For a struct, add the member offset.
3158 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3159 const SCEV *FieldOffset = getOffsetOfExpr(STy, IntPtrTy, FieldNo);
3161 // Add the field offset to the running total offset.
3162 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3164 // For an array, add the element offset, explicitly scaled.
3165 const SCEV *ElementSize = getSizeOfExpr(*GTI, IntPtrTy);
3166 const SCEV *IndexS = getSCEV(Index);
3167 // Getelementptr indices are signed.
3168 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3170 // Multiply the index by the element size to compute the element offset.
3171 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3172 isInBounds ? SCEV::FlagNSW :
3175 // Add the element offset to the running total offset.
3176 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3180 // Get the SCEV for the GEP base.
3181 const SCEV *BaseS = getSCEV(Base);
3183 // Add the total offset from all the GEP indices to the base.
3184 return getAddExpr(BaseS, TotalOffset,
3185 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3188 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3189 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3190 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3191 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3193 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3194 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3195 return C->getValue()->getValue().countTrailingZeros();
3197 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3198 return std::min(GetMinTrailingZeros(T->getOperand()),
3199 (uint32_t)getTypeSizeInBits(T->getType()));
3201 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3202 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3203 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3204 getTypeSizeInBits(E->getType()) : OpRes;
3207 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3208 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3209 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3210 getTypeSizeInBits(E->getType()) : OpRes;
3213 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3214 // The result is the min of all operands results.
3215 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3216 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3217 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3221 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3222 // The result is the sum of all operands results.
3223 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3224 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3225 for (unsigned i = 1, e = M->getNumOperands();
3226 SumOpRes != BitWidth && i != e; ++i)
3227 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3232 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3233 // The result is the min of all operands results.
3234 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3235 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3236 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3240 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3241 // The result is the min of all operands results.
3242 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3243 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3244 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3248 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3249 // The result is the min of all operands results.
3250 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3251 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3252 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3256 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3257 // For a SCEVUnknown, ask ValueTracking.
3258 unsigned BitWidth = getTypeSizeInBits(U->getType());
3259 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3260 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3261 return Zeros.countTrailingOnes();
3268 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3271 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3272 // See if we've computed this range already.
3273 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3274 if (I != UnsignedRanges.end())
3277 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3278 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3280 unsigned BitWidth = getTypeSizeInBits(S->getType());
3281 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3283 // If the value has known zeros, the maximum unsigned value will have those
3284 // known zeros as well.
3285 uint32_t TZ = GetMinTrailingZeros(S);
3287 ConservativeResult =
3288 ConstantRange(APInt::getMinValue(BitWidth),
3289 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3291 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3292 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3293 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3294 X = X.add(getUnsignedRange(Add->getOperand(i)));
3295 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3298 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3299 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3300 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3301 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3302 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3305 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3306 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3307 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3308 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3309 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3312 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3313 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3314 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3315 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3316 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3319 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3320 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3321 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3322 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3325 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3326 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3327 return setUnsignedRange(ZExt,
3328 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3331 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3332 ConstantRange X = getUnsignedRange(SExt->getOperand());
3333 return setUnsignedRange(SExt,
3334 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3337 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3338 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3339 return setUnsignedRange(Trunc,
3340 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3343 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3344 // If there's no unsigned wrap, the value will never be less than its
3346 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3347 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3348 if (!C->getValue()->isZero())
3349 ConservativeResult =
3350 ConservativeResult.intersectWith(
3351 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3353 // TODO: non-affine addrec
3354 if (AddRec->isAffine()) {
3355 Type *Ty = AddRec->getType();
3356 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3357 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3358 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3359 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3361 const SCEV *Start = AddRec->getStart();
3362 const SCEV *Step = AddRec->getStepRecurrence(*this);
3364 ConstantRange StartRange = getUnsignedRange(Start);
3365 ConstantRange StepRange = getSignedRange(Step);
3366 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3367 ConstantRange EndRange =
3368 StartRange.add(MaxBECountRange.multiply(StepRange));
3370 // Check for overflow. This must be done with ConstantRange arithmetic
3371 // because we could be called from within the ScalarEvolution overflow
3373 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3374 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3375 ConstantRange ExtMaxBECountRange =
3376 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3377 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3378 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3380 return setUnsignedRange(AddRec, ConservativeResult);
3382 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3383 EndRange.getUnsignedMin());
3384 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3385 EndRange.getUnsignedMax());
3386 if (Min.isMinValue() && Max.isMaxValue())
3387 return setUnsignedRange(AddRec, ConservativeResult);
3388 return setUnsignedRange(AddRec,
3389 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3393 return setUnsignedRange(AddRec, ConservativeResult);
3396 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3397 // For a SCEVUnknown, ask ValueTracking.
3398 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3399 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3400 if (Ones == ~Zeros + 1)
3401 return setUnsignedRange(U, ConservativeResult);
3402 return setUnsignedRange(U,
3403 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3406 return setUnsignedRange(S, ConservativeResult);
3409 /// getSignedRange - Determine the signed range for a particular SCEV.
3412 ScalarEvolution::getSignedRange(const SCEV *S) {
3413 // See if we've computed this range already.
3414 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3415 if (I != SignedRanges.end())
3418 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3419 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3421 unsigned BitWidth = getTypeSizeInBits(S->getType());
3422 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3424 // If the value has known zeros, the maximum signed value will have those
3425 // known zeros as well.
3426 uint32_t TZ = GetMinTrailingZeros(S);
3428 ConservativeResult =
3429 ConstantRange(APInt::getSignedMinValue(BitWidth),
3430 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3432 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3433 ConstantRange X = getSignedRange(Add->getOperand(0));
3434 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3435 X = X.add(getSignedRange(Add->getOperand(i)));
3436 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3439 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3440 ConstantRange X = getSignedRange(Mul->getOperand(0));
3441 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3442 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3443 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3446 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3447 ConstantRange X = getSignedRange(SMax->getOperand(0));
3448 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3449 X = X.smax(getSignedRange(SMax->getOperand(i)));
3450 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3453 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3454 ConstantRange X = getSignedRange(UMax->getOperand(0));
3455 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3456 X = X.umax(getSignedRange(UMax->getOperand(i)));
3457 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3460 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3461 ConstantRange X = getSignedRange(UDiv->getLHS());
3462 ConstantRange Y = getSignedRange(UDiv->getRHS());
3463 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3466 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3467 ConstantRange X = getSignedRange(ZExt->getOperand());
3468 return setSignedRange(ZExt,
3469 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3472 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3473 ConstantRange X = getSignedRange(SExt->getOperand());
3474 return setSignedRange(SExt,
3475 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3478 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3479 ConstantRange X = getSignedRange(Trunc->getOperand());
3480 return setSignedRange(Trunc,
3481 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3484 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3485 // If there's no signed wrap, and all the operands have the same sign or
3486 // zero, the value won't ever change sign.
3487 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3488 bool AllNonNeg = true;
3489 bool AllNonPos = true;
3490 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3491 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3492 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3495 ConservativeResult = ConservativeResult.intersectWith(
3496 ConstantRange(APInt(BitWidth, 0),
3497 APInt::getSignedMinValue(BitWidth)));
3499 ConservativeResult = ConservativeResult.intersectWith(
3500 ConstantRange(APInt::getSignedMinValue(BitWidth),
3501 APInt(BitWidth, 1)));
3504 // TODO: non-affine addrec
3505 if (AddRec->isAffine()) {
3506 Type *Ty = AddRec->getType();
3507 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3508 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3509 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3510 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3512 const SCEV *Start = AddRec->getStart();
3513 const SCEV *Step = AddRec->getStepRecurrence(*this);
3515 ConstantRange StartRange = getSignedRange(Start);
3516 ConstantRange StepRange = getSignedRange(Step);
3517 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3518 ConstantRange EndRange =
3519 StartRange.add(MaxBECountRange.multiply(StepRange));
3521 // Check for overflow. This must be done with ConstantRange arithmetic
3522 // because we could be called from within the ScalarEvolution overflow
3524 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3525 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3526 ConstantRange ExtMaxBECountRange =
3527 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3528 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3529 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3531 return setSignedRange(AddRec, ConservativeResult);
3533 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3534 EndRange.getSignedMin());
3535 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3536 EndRange.getSignedMax());
3537 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3538 return setSignedRange(AddRec, ConservativeResult);
3539 return setSignedRange(AddRec,
3540 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3544 return setSignedRange(AddRec, ConservativeResult);
3547 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3548 // For a SCEVUnknown, ask ValueTracking.
3549 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3550 return setSignedRange(U, ConservativeResult);
3551 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3553 return setSignedRange(U, ConservativeResult);
3554 return setSignedRange(U, ConservativeResult.intersectWith(
3555 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3556 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3559 return setSignedRange(S, ConservativeResult);
3562 /// createSCEV - We know that there is no SCEV for the specified value.
3563 /// Analyze the expression.
3565 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3566 if (!isSCEVable(V->getType()))
3567 return getUnknown(V);
3569 unsigned Opcode = Instruction::UserOp1;
3570 if (Instruction *I = dyn_cast<Instruction>(V)) {
3571 Opcode = I->getOpcode();
3573 // Don't attempt to analyze instructions in blocks that aren't
3574 // reachable. Such instructions don't matter, and they aren't required
3575 // to obey basic rules for definitions dominating uses which this
3576 // analysis depends on.
3577 if (!DT->isReachableFromEntry(I->getParent()))
3578 return getUnknown(V);
3579 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3580 Opcode = CE->getOpcode();
3581 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3582 return getConstant(CI);
3583 else if (isa<ConstantPointerNull>(V))
3584 return getConstant(V->getType(), 0);
3585 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3586 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3588 return getUnknown(V);
3590 Operator *U = cast<Operator>(V);
3592 case Instruction::Add: {
3593 // The simple thing to do would be to just call getSCEV on both operands
3594 // and call getAddExpr with the result. However if we're looking at a
3595 // bunch of things all added together, this can be quite inefficient,
3596 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3597 // Instead, gather up all the operands and make a single getAddExpr call.
3598 // LLVM IR canonical form means we need only traverse the left operands.
3600 // Don't apply this instruction's NSW or NUW flags to the new
3601 // expression. The instruction may be guarded by control flow that the
3602 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3603 // mapped to the same SCEV expression, and it would be incorrect to transfer
3604 // NSW/NUW semantics to those operations.
3605 SmallVector<const SCEV *, 4> AddOps;
3606 AddOps.push_back(getSCEV(U->getOperand(1)));
3607 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3608 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3609 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3611 U = cast<Operator>(Op);
3612 const SCEV *Op1 = getSCEV(U->getOperand(1));
3613 if (Opcode == Instruction::Sub)
3614 AddOps.push_back(getNegativeSCEV(Op1));
3616 AddOps.push_back(Op1);
3618 AddOps.push_back(getSCEV(U->getOperand(0)));
3619 return getAddExpr(AddOps);
3621 case Instruction::Mul: {
3622 // Don't transfer NSW/NUW for the same reason as AddExpr.
3623 SmallVector<const SCEV *, 4> MulOps;
3624 MulOps.push_back(getSCEV(U->getOperand(1)));
3625 for (Value *Op = U->getOperand(0);
3626 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3627 Op = U->getOperand(0)) {
3628 U = cast<Operator>(Op);
3629 MulOps.push_back(getSCEV(U->getOperand(1)));
3631 MulOps.push_back(getSCEV(U->getOperand(0)));
3632 return getMulExpr(MulOps);
3634 case Instruction::UDiv:
3635 return getUDivExpr(getSCEV(U->getOperand(0)),
3636 getSCEV(U->getOperand(1)));
3637 case Instruction::Sub:
3638 return getMinusSCEV(getSCEV(U->getOperand(0)),
3639 getSCEV(U->getOperand(1)));
3640 case Instruction::And:
3641 // For an expression like x&255 that merely masks off the high bits,
3642 // use zext(trunc(x)) as the SCEV expression.
3643 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3644 if (CI->isNullValue())
3645 return getSCEV(U->getOperand(1));
3646 if (CI->isAllOnesValue())
3647 return getSCEV(U->getOperand(0));
3648 const APInt &A = CI->getValue();
3650 // Instcombine's ShrinkDemandedConstant may strip bits out of
3651 // constants, obscuring what would otherwise be a low-bits mask.
3652 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3653 // knew about to reconstruct a low-bits mask value.
3654 unsigned LZ = A.countLeadingZeros();
3655 unsigned BitWidth = A.getBitWidth();
3656 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3657 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3659 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3661 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3663 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3664 IntegerType::get(getContext(), BitWidth - LZ)),
3669 case Instruction::Or:
3670 // If the RHS of the Or is a constant, we may have something like:
3671 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3672 // optimizations will transparently handle this case.
3674 // In order for this transformation to be safe, the LHS must be of the
3675 // form X*(2^n) and the Or constant must be less than 2^n.
3676 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3677 const SCEV *LHS = getSCEV(U->getOperand(0));
3678 const APInt &CIVal = CI->getValue();
3679 if (GetMinTrailingZeros(LHS) >=
3680 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3681 // Build a plain add SCEV.
3682 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3683 // If the LHS of the add was an addrec and it has no-wrap flags,
3684 // transfer the no-wrap flags, since an or won't introduce a wrap.
3685 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3686 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3687 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3688 OldAR->getNoWrapFlags());
3694 case Instruction::Xor:
3695 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3696 // If the RHS of the xor is a signbit, then this is just an add.
3697 // Instcombine turns add of signbit into xor as a strength reduction step.
3698 if (CI->getValue().isSignBit())
3699 return getAddExpr(getSCEV(U->getOperand(0)),
3700 getSCEV(U->getOperand(1)));
3702 // If the RHS of xor is -1, then this is a not operation.
3703 if (CI->isAllOnesValue())
3704 return getNotSCEV(getSCEV(U->getOperand(0)));
3706 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3707 // This is a variant of the check for xor with -1, and it handles
3708 // the case where instcombine has trimmed non-demanded bits out
3709 // of an xor with -1.
3710 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3711 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3712 if (BO->getOpcode() == Instruction::And &&
3713 LCI->getValue() == CI->getValue())
3714 if (const SCEVZeroExtendExpr *Z =
3715 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3716 Type *UTy = U->getType();
3717 const SCEV *Z0 = Z->getOperand();
3718 Type *Z0Ty = Z0->getType();
3719 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3721 // If C is a low-bits mask, the zero extend is serving to
3722 // mask off the high bits. Complement the operand and
3723 // re-apply the zext.
3724 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3725 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3727 // If C is a single bit, it may be in the sign-bit position
3728 // before the zero-extend. In this case, represent the xor
3729 // using an add, which is equivalent, and re-apply the zext.
3730 APInt Trunc = CI->getValue().trunc(Z0TySize);
3731 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3733 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3739 case Instruction::Shl:
3740 // Turn shift left of a constant amount into a multiply.
3741 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3742 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3744 // If the shift count is not less than the bitwidth, the result of
3745 // the shift is undefined. Don't try to analyze it, because the
3746 // resolution chosen here may differ from the resolution chosen in
3747 // other parts of the compiler.
3748 if (SA->getValue().uge(BitWidth))
3751 Constant *X = ConstantInt::get(getContext(),
3752 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3753 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3757 case Instruction::LShr:
3758 // Turn logical shift right of a constant into a unsigned divide.
3759 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3760 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3762 // If the shift count is not less than the bitwidth, the result of
3763 // the shift is undefined. Don't try to analyze it, because the
3764 // resolution chosen here may differ from the resolution chosen in
3765 // other parts of the compiler.
3766 if (SA->getValue().uge(BitWidth))
3769 Constant *X = ConstantInt::get(getContext(),
3770 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3771 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3775 case Instruction::AShr:
3776 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3777 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3778 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3779 if (L->getOpcode() == Instruction::Shl &&
3780 L->getOperand(1) == U->getOperand(1)) {
3781 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3783 // If the shift count is not less than the bitwidth, the result of
3784 // the shift is undefined. Don't try to analyze it, because the
3785 // resolution chosen here may differ from the resolution chosen in
3786 // other parts of the compiler.
3787 if (CI->getValue().uge(BitWidth))
3790 uint64_t Amt = BitWidth - CI->getZExtValue();
3791 if (Amt == BitWidth)
3792 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3794 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3795 IntegerType::get(getContext(),
3801 case Instruction::Trunc:
3802 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3804 case Instruction::ZExt:
3805 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3807 case Instruction::SExt:
3808 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3810 case Instruction::BitCast:
3811 // BitCasts are no-op casts so we just eliminate the cast.
3812 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3813 return getSCEV(U->getOperand(0));
3816 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3817 // lead to pointer expressions which cannot safely be expanded to GEPs,
3818 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3819 // simplifying integer expressions.
3821 case Instruction::GetElementPtr:
3822 return createNodeForGEP(cast<GEPOperator>(U));
3824 case Instruction::PHI:
3825 return createNodeForPHI(cast<PHINode>(U));
3827 case Instruction::Select:
3828 // This could be a smax or umax that was lowered earlier.
3829 // Try to recover it.
3830 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3831 Value *LHS = ICI->getOperand(0);
3832 Value *RHS = ICI->getOperand(1);
3833 switch (ICI->getPredicate()) {
3834 case ICmpInst::ICMP_SLT:
3835 case ICmpInst::ICMP_SLE:
3836 std::swap(LHS, RHS);
3838 case ICmpInst::ICMP_SGT:
3839 case ICmpInst::ICMP_SGE:
3840 // a >s b ? a+x : b+x -> smax(a, b)+x
3841 // a >s b ? b+x : a+x -> smin(a, b)+x
3842 if (LHS->getType() == U->getType()) {
3843 const SCEV *LS = getSCEV(LHS);
3844 const SCEV *RS = getSCEV(RHS);
3845 const SCEV *LA = getSCEV(U->getOperand(1));
3846 const SCEV *RA = getSCEV(U->getOperand(2));
3847 const SCEV *LDiff = getMinusSCEV(LA, LS);
3848 const SCEV *RDiff = getMinusSCEV(RA, RS);
3850 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3851 LDiff = getMinusSCEV(LA, RS);
3852 RDiff = getMinusSCEV(RA, LS);
3854 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3857 case ICmpInst::ICMP_ULT:
3858 case ICmpInst::ICMP_ULE:
3859 std::swap(LHS, RHS);
3861 case ICmpInst::ICMP_UGT:
3862 case ICmpInst::ICMP_UGE:
3863 // a >u b ? a+x : b+x -> umax(a, b)+x
3864 // a >u b ? b+x : a+x -> umin(a, b)+x
3865 if (LHS->getType() == U->getType()) {
3866 const SCEV *LS = getSCEV(LHS);
3867 const SCEV *RS = getSCEV(RHS);
3868 const SCEV *LA = getSCEV(U->getOperand(1));
3869 const SCEV *RA = getSCEV(U->getOperand(2));
3870 const SCEV *LDiff = getMinusSCEV(LA, LS);
3871 const SCEV *RDiff = getMinusSCEV(RA, RS);
3873 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3874 LDiff = getMinusSCEV(LA, RS);
3875 RDiff = getMinusSCEV(RA, LS);
3877 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3880 case ICmpInst::ICMP_NE:
3881 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3882 if (LHS->getType() == U->getType() &&
3883 isa<ConstantInt>(RHS) &&
3884 cast<ConstantInt>(RHS)->isZero()) {
3885 const SCEV *One = getConstant(LHS->getType(), 1);
3886 const SCEV *LS = getSCEV(LHS);
3887 const SCEV *LA = getSCEV(U->getOperand(1));
3888 const SCEV *RA = getSCEV(U->getOperand(2));
3889 const SCEV *LDiff = getMinusSCEV(LA, LS);
3890 const SCEV *RDiff = getMinusSCEV(RA, One);
3892 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3895 case ICmpInst::ICMP_EQ:
3896 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3897 if (LHS->getType() == U->getType() &&
3898 isa<ConstantInt>(RHS) &&
3899 cast<ConstantInt>(RHS)->isZero()) {
3900 const SCEV *One = getConstant(LHS->getType(), 1);
3901 const SCEV *LS = getSCEV(LHS);
3902 const SCEV *LA = getSCEV(U->getOperand(1));
3903 const SCEV *RA = getSCEV(U->getOperand(2));
3904 const SCEV *LDiff = getMinusSCEV(LA, One);
3905 const SCEV *RDiff = getMinusSCEV(RA, LS);
3907 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3915 default: // We cannot analyze this expression.
3919 return getUnknown(V);
3924 //===----------------------------------------------------------------------===//
3925 // Iteration Count Computation Code
3928 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3929 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3930 /// constant. Will also return 0 if the maximum trip count is very large (>=
3933 /// This "trip count" assumes that control exits via ExitingBlock. More
3934 /// precisely, it is the number of times that control may reach ExitingBlock
3935 /// before taking the branch. For loops with multiple exits, it may not be the
3936 /// number times that the loop header executes because the loop may exit
3937 /// prematurely via another branch.
3938 unsigned ScalarEvolution::
3939 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3940 const SCEVConstant *ExitCount =
3941 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3945 ConstantInt *ExitConst = ExitCount->getValue();
3947 // Guard against huge trip counts.
3948 if (ExitConst->getValue().getActiveBits() > 32)
3951 // In case of integer overflow, this returns 0, which is correct.
3952 return ((unsigned)ExitConst->getZExtValue()) + 1;
3955 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3956 /// trip count of this loop as a normal unsigned value, if possible. This
3957 /// means that the actual trip count is always a multiple of the returned
3958 /// value (don't forget the trip count could very well be zero as well!).
3960 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3961 /// multiple of a constant (which is also the case if the trip count is simply
3962 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3963 /// if the trip count is very large (>= 2^32).
3965 /// As explained in the comments for getSmallConstantTripCount, this assumes
3966 /// that control exits the loop via ExitingBlock.
3967 unsigned ScalarEvolution::
3968 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3969 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3970 if (ExitCount == getCouldNotCompute())
3973 // Get the trip count from the BE count by adding 1.
3974 const SCEV *TCMul = getAddExpr(ExitCount,
3975 getConstant(ExitCount->getType(), 1));
3976 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3977 // to factor simple cases.
3978 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3979 TCMul = Mul->getOperand(0);
3981 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3985 ConstantInt *Result = MulC->getValue();
3987 // Guard against huge trip counts (this requires checking
3988 // for zero to handle the case where the trip count == -1 and the
3990 if (!Result || Result->getValue().getActiveBits() > 32 ||
3991 Result->getValue().getActiveBits() == 0)
3994 return (unsigned)Result->getZExtValue();
3997 // getExitCount - Get the expression for the number of loop iterations for which
3998 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
3999 // SCEVCouldNotCompute.
4000 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4001 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4004 /// getBackedgeTakenCount - If the specified loop has a predictable
4005 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4006 /// object. The backedge-taken count is the number of times the loop header
4007 /// will be branched to from within the loop. This is one less than the
4008 /// trip count of the loop, since it doesn't count the first iteration,
4009 /// when the header is branched to from outside the loop.
4011 /// Note that it is not valid to call this method on a loop without a
4012 /// loop-invariant backedge-taken count (see
4013 /// hasLoopInvariantBackedgeTakenCount).
4015 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4016 return getBackedgeTakenInfo(L).getExact(this);
4019 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4020 /// return the least SCEV value that is known never to be less than the
4021 /// actual backedge taken count.
4022 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4023 return getBackedgeTakenInfo(L).getMax(this);
4026 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4027 /// onto the given Worklist.
4029 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4030 BasicBlock *Header = L->getHeader();
4032 // Push all Loop-header PHIs onto the Worklist stack.
4033 for (BasicBlock::iterator I = Header->begin();
4034 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4035 Worklist.push_back(PN);
4038 const ScalarEvolution::BackedgeTakenInfo &
4039 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4040 // Initially insert an invalid entry for this loop. If the insertion
4041 // succeeds, proceed to actually compute a backedge-taken count and
4042 // update the value. The temporary CouldNotCompute value tells SCEV
4043 // code elsewhere that it shouldn't attempt to request a new
4044 // backedge-taken count, which could result in infinite recursion.
4045 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4046 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4048 return Pair.first->second;
4050 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4051 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4052 // must be cleared in this scope.
4053 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4055 if (Result.getExact(this) != getCouldNotCompute()) {
4056 assert(isLoopInvariant(Result.getExact(this), L) &&
4057 isLoopInvariant(Result.getMax(this), L) &&
4058 "Computed backedge-taken count isn't loop invariant for loop!");
4059 ++NumTripCountsComputed;
4061 else if (Result.getMax(this) == getCouldNotCompute() &&
4062 isa<PHINode>(L->getHeader()->begin())) {
4063 // Only count loops that have phi nodes as not being computable.
4064 ++NumTripCountsNotComputed;
4067 // Now that we know more about the trip count for this loop, forget any
4068 // existing SCEV values for PHI nodes in this loop since they are only
4069 // conservative estimates made without the benefit of trip count
4070 // information. This is similar to the code in forgetLoop, except that
4071 // it handles SCEVUnknown PHI nodes specially.
4072 if (Result.hasAnyInfo()) {
4073 SmallVector<Instruction *, 16> Worklist;
4074 PushLoopPHIs(L, Worklist);
4076 SmallPtrSet<Instruction *, 8> Visited;
4077 while (!Worklist.empty()) {
4078 Instruction *I = Worklist.pop_back_val();
4079 if (!Visited.insert(I)) continue;
4081 ValueExprMapType::iterator It =
4082 ValueExprMap.find_as(static_cast<Value *>(I));
4083 if (It != ValueExprMap.end()) {
4084 const SCEV *Old = It->second;
4086 // SCEVUnknown for a PHI either means that it has an unrecognized
4087 // structure, or it's a PHI that's in the progress of being computed
4088 // by createNodeForPHI. In the former case, additional loop trip
4089 // count information isn't going to change anything. In the later
4090 // case, createNodeForPHI will perform the necessary updates on its
4091 // own when it gets to that point.
4092 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4093 forgetMemoizedResults(Old);
4094 ValueExprMap.erase(It);
4096 if (PHINode *PN = dyn_cast<PHINode>(I))
4097 ConstantEvolutionLoopExitValue.erase(PN);
4100 PushDefUseChildren(I, Worklist);
4104 // Re-lookup the insert position, since the call to
4105 // ComputeBackedgeTakenCount above could result in a
4106 // recusive call to getBackedgeTakenInfo (on a different
4107 // loop), which would invalidate the iterator computed
4109 return BackedgeTakenCounts.find(L)->second = Result;
4112 /// forgetLoop - This method should be called by the client when it has
4113 /// changed a loop in a way that may effect ScalarEvolution's ability to
4114 /// compute a trip count, or if the loop is deleted.
4115 void ScalarEvolution::forgetLoop(const Loop *L) {
4116 // Drop any stored trip count value.
4117 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4118 BackedgeTakenCounts.find(L);
4119 if (BTCPos != BackedgeTakenCounts.end()) {
4120 BTCPos->second.clear();
4121 BackedgeTakenCounts.erase(BTCPos);
4124 // Drop information about expressions based on loop-header PHIs.
4125 SmallVector<Instruction *, 16> Worklist;
4126 PushLoopPHIs(L, Worklist);
4128 SmallPtrSet<Instruction *, 8> Visited;
4129 while (!Worklist.empty()) {
4130 Instruction *I = Worklist.pop_back_val();
4131 if (!Visited.insert(I)) continue;
4133 ValueExprMapType::iterator It =
4134 ValueExprMap.find_as(static_cast<Value *>(I));
4135 if (It != ValueExprMap.end()) {
4136 forgetMemoizedResults(It->second);
4137 ValueExprMap.erase(It);
4138 if (PHINode *PN = dyn_cast<PHINode>(I))
4139 ConstantEvolutionLoopExitValue.erase(PN);
4142 PushDefUseChildren(I, Worklist);
4145 // Forget all contained loops too, to avoid dangling entries in the
4146 // ValuesAtScopes map.
4147 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4151 /// forgetValue - This method should be called by the client when it has
4152 /// changed a value in a way that may effect its value, or which may
4153 /// disconnect it from a def-use chain linking it to a loop.
4154 void ScalarEvolution::forgetValue(Value *V) {
4155 Instruction *I = dyn_cast<Instruction>(V);
4158 // Drop information about expressions based on loop-header PHIs.
4159 SmallVector<Instruction *, 16> Worklist;
4160 Worklist.push_back(I);
4162 SmallPtrSet<Instruction *, 8> Visited;
4163 while (!Worklist.empty()) {
4164 I = Worklist.pop_back_val();
4165 if (!Visited.insert(I)) continue;
4167 ValueExprMapType::iterator It =
4168 ValueExprMap.find_as(static_cast<Value *>(I));
4169 if (It != ValueExprMap.end()) {
4170 forgetMemoizedResults(It->second);
4171 ValueExprMap.erase(It);
4172 if (PHINode *PN = dyn_cast<PHINode>(I))
4173 ConstantEvolutionLoopExitValue.erase(PN);
4176 PushDefUseChildren(I, Worklist);
4180 /// getExact - Get the exact loop backedge taken count considering all loop
4181 /// exits. A computable result can only be return for loops with a single exit.
4182 /// Returning the minimum taken count among all exits is incorrect because one
4183 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4184 /// the limit of each loop test is never skipped. This is a valid assumption as
4185 /// long as the loop exits via that test. For precise results, it is the
4186 /// caller's responsibility to specify the relevant loop exit using
4187 /// getExact(ExitingBlock, SE).
4189 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4190 // If any exits were not computable, the loop is not computable.
4191 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4193 // We need exactly one computable exit.
4194 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4195 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4197 const SCEV *BECount = 0;
4198 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4199 ENT != 0; ENT = ENT->getNextExit()) {
4201 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4204 BECount = ENT->ExactNotTaken;
4205 else if (BECount != ENT->ExactNotTaken)
4206 return SE->getCouldNotCompute();
4208 assert(BECount && "Invalid not taken count for loop exit");
4212 /// getExact - Get the exact not taken count for this loop exit.
4214 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4215 ScalarEvolution *SE) const {
4216 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4217 ENT != 0; ENT = ENT->getNextExit()) {
4219 if (ENT->ExitingBlock == ExitingBlock)
4220 return ENT->ExactNotTaken;
4222 return SE->getCouldNotCompute();
4225 /// getMax - Get the max backedge taken count for the loop.
4227 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4228 return Max ? Max : SE->getCouldNotCompute();
4231 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4232 /// computable exit into a persistent ExitNotTakenInfo array.
4233 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4234 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4235 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4238 ExitNotTaken.setIncomplete();
4240 unsigned NumExits = ExitCounts.size();
4241 if (NumExits == 0) return;
4243 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4244 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4245 if (NumExits == 1) return;
4247 // Handle the rare case of multiple computable exits.
4248 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4250 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4251 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4252 PrevENT->setNextExit(ENT);
4253 ENT->ExitingBlock = ExitCounts[i].first;
4254 ENT->ExactNotTaken = ExitCounts[i].second;
4258 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4259 void ScalarEvolution::BackedgeTakenInfo::clear() {
4260 ExitNotTaken.ExitingBlock = 0;
4261 ExitNotTaken.ExactNotTaken = 0;
4262 delete[] ExitNotTaken.getNextExit();
4265 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4266 /// of the specified loop will execute.
4267 ScalarEvolution::BackedgeTakenInfo
4268 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4269 SmallVector<BasicBlock *, 8> ExitingBlocks;
4270 L->getExitingBlocks(ExitingBlocks);
4272 // Examine all exits and pick the most conservative values.
4273 const SCEV *MaxBECount = getCouldNotCompute();
4274 bool CouldComputeBECount = true;
4275 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4276 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4277 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4278 if (EL.Exact == getCouldNotCompute())
4279 // We couldn't compute an exact value for this exit, so
4280 // we won't be able to compute an exact value for the loop.
4281 CouldComputeBECount = false;
4283 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4285 if (MaxBECount == getCouldNotCompute())
4286 MaxBECount = EL.Max;
4287 else if (EL.Max != getCouldNotCompute()) {
4288 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4289 // skip some loop tests. Taking the max over the exits is sufficiently
4290 // conservative. TODO: We could do better taking into consideration
4291 // that (1) the loop has unit stride (2) the last loop test is
4292 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4293 // falls-through some constant times less then the other tests.
4294 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4298 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4301 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4302 /// loop will execute if it exits via the specified block.
4303 ScalarEvolution::ExitLimit
4304 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4306 // Okay, we've chosen an exiting block. See what condition causes us to
4307 // exit at this block.
4309 // FIXME: we should be able to handle switch instructions (with a single exit)
4310 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4311 if (ExitBr == 0) return getCouldNotCompute();
4312 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4314 // At this point, we know we have a conditional branch that determines whether
4315 // the loop is exited. However, we don't know if the branch is executed each
4316 // time through the loop. If not, then the execution count of the branch will
4317 // not be equal to the trip count of the loop.
4319 // Currently we check for this by checking to see if the Exit branch goes to
4320 // the loop header. If so, we know it will always execute the same number of
4321 // times as the loop. We also handle the case where the exit block *is* the
4322 // loop header. This is common for un-rotated loops.
4324 // If both of those tests fail, walk up the unique predecessor chain to the
4325 // header, stopping if there is an edge that doesn't exit the loop. If the
4326 // header is reached, the execution count of the branch will be equal to the
4327 // trip count of the loop.
4329 // More extensive analysis could be done to handle more cases here.
4331 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4332 ExitBr->getSuccessor(1) != L->getHeader() &&
4333 ExitBr->getParent() != L->getHeader()) {
4334 // The simple checks failed, try climbing the unique predecessor chain
4335 // up to the header.
4337 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4338 BasicBlock *Pred = BB->getUniquePredecessor();
4340 return getCouldNotCompute();
4341 TerminatorInst *PredTerm = Pred->getTerminator();
4342 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4343 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4346 // If the predecessor has a successor that isn't BB and isn't
4347 // outside the loop, assume the worst.
4348 if (L->contains(PredSucc))
4349 return getCouldNotCompute();
4351 if (Pred == L->getHeader()) {
4358 return getCouldNotCompute();
4361 // Proceed to the next level to examine the exit condition expression.
4362 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4363 ExitBr->getSuccessor(0),
4364 ExitBr->getSuccessor(1));
4367 /// ComputeExitLimitFromCond - Compute the number of times the
4368 /// backedge of the specified loop will execute if its exit condition
4369 /// were a conditional branch of ExitCond, TBB, and FBB.
4370 ScalarEvolution::ExitLimit
4371 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4375 // Check if the controlling expression for this loop is an And or Or.
4376 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4377 if (BO->getOpcode() == Instruction::And) {
4378 // Recurse on the operands of the and.
4379 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4380 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4381 const SCEV *BECount = getCouldNotCompute();
4382 const SCEV *MaxBECount = getCouldNotCompute();
4383 if (L->contains(TBB)) {
4384 // Both conditions must be true for the loop to continue executing.
4385 // Choose the less conservative count.
4386 if (EL0.Exact == getCouldNotCompute() ||
4387 EL1.Exact == getCouldNotCompute())
4388 BECount = getCouldNotCompute();
4390 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4391 if (EL0.Max == getCouldNotCompute())
4392 MaxBECount = EL1.Max;
4393 else if (EL1.Max == getCouldNotCompute())
4394 MaxBECount = EL0.Max;
4396 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4398 // Both conditions must be true at the same time for the loop to exit.
4399 // For now, be conservative.
4400 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4401 if (EL0.Max == EL1.Max)
4402 MaxBECount = EL0.Max;
4403 if (EL0.Exact == EL1.Exact)
4404 BECount = EL0.Exact;
4407 return ExitLimit(BECount, MaxBECount);
4409 if (BO->getOpcode() == Instruction::Or) {
4410 // Recurse on the operands of the or.
4411 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4412 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4413 const SCEV *BECount = getCouldNotCompute();
4414 const SCEV *MaxBECount = getCouldNotCompute();
4415 if (L->contains(FBB)) {
4416 // Both conditions must be false for the loop to continue executing.
4417 // Choose the less conservative count.
4418 if (EL0.Exact == getCouldNotCompute() ||
4419 EL1.Exact == getCouldNotCompute())
4420 BECount = getCouldNotCompute();
4422 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4423 if (EL0.Max == getCouldNotCompute())
4424 MaxBECount = EL1.Max;
4425 else if (EL1.Max == getCouldNotCompute())
4426 MaxBECount = EL0.Max;
4428 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4430 // Both conditions must be false at the same time for the loop to exit.
4431 // For now, be conservative.
4432 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4433 if (EL0.Max == EL1.Max)
4434 MaxBECount = EL0.Max;
4435 if (EL0.Exact == EL1.Exact)
4436 BECount = EL0.Exact;
4439 return ExitLimit(BECount, MaxBECount);
4443 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4444 // Proceed to the next level to examine the icmp.
4445 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4446 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4448 // Check for a constant condition. These are normally stripped out by
4449 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4450 // preserve the CFG and is temporarily leaving constant conditions
4452 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4453 if (L->contains(FBB) == !CI->getZExtValue())
4454 // The backedge is always taken.
4455 return getCouldNotCompute();
4457 // The backedge is never taken.
4458 return getConstant(CI->getType(), 0);
4461 // If it's not an integer or pointer comparison then compute it the hard way.
4462 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4465 /// ComputeExitLimitFromICmp - Compute the number of times the
4466 /// backedge of the specified loop will execute if its exit condition
4467 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4468 ScalarEvolution::ExitLimit
4469 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4474 // If the condition was exit on true, convert the condition to exit on false
4475 ICmpInst::Predicate Cond;
4476 if (!L->contains(FBB))
4477 Cond = ExitCond->getPredicate();
4479 Cond = ExitCond->getInversePredicate();
4481 // Handle common loops like: for (X = "string"; *X; ++X)
4482 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4483 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4485 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4486 if (ItCnt.hasAnyInfo())
4490 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4491 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4493 // Try to evaluate any dependencies out of the loop.
4494 LHS = getSCEVAtScope(LHS, L);
4495 RHS = getSCEVAtScope(RHS, L);
4497 // At this point, we would like to compute how many iterations of the
4498 // loop the predicate will return true for these inputs.
4499 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4500 // If there is a loop-invariant, force it into the RHS.
4501 std::swap(LHS, RHS);
4502 Cond = ICmpInst::getSwappedPredicate(Cond);
4505 // Simplify the operands before analyzing them.
4506 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4508 // If we have a comparison of a chrec against a constant, try to use value
4509 // ranges to answer this query.
4510 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4511 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4512 if (AddRec->getLoop() == L) {
4513 // Form the constant range.
4514 ConstantRange CompRange(
4515 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4517 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4518 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4522 case ICmpInst::ICMP_NE: { // while (X != Y)
4523 // Convert to: while (X-Y != 0)
4524 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4525 if (EL.hasAnyInfo()) return EL;
4528 case ICmpInst::ICMP_EQ: { // while (X == Y)
4529 // Convert to: while (X-Y == 0)
4530 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4531 if (EL.hasAnyInfo()) return EL;
4534 case ICmpInst::ICMP_SLT: {
4535 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4536 if (EL.hasAnyInfo()) return EL;
4539 case ICmpInst::ICMP_SGT: {
4540 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4541 getNotSCEV(RHS), L, true);
4542 if (EL.hasAnyInfo()) return EL;
4545 case ICmpInst::ICMP_ULT: {
4546 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4547 if (EL.hasAnyInfo()) return EL;
4550 case ICmpInst::ICMP_UGT: {
4551 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4552 getNotSCEV(RHS), L, false);
4553 if (EL.hasAnyInfo()) return EL;
4558 dbgs() << "ComputeBackedgeTakenCount ";
4559 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4560 dbgs() << "[unsigned] ";
4561 dbgs() << *LHS << " "
4562 << Instruction::getOpcodeName(Instruction::ICmp)
4563 << " " << *RHS << "\n";
4567 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4570 static ConstantInt *
4571 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4572 ScalarEvolution &SE) {
4573 const SCEV *InVal = SE.getConstant(C);
4574 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4575 assert(isa<SCEVConstant>(Val) &&
4576 "Evaluation of SCEV at constant didn't fold correctly?");
4577 return cast<SCEVConstant>(Val)->getValue();
4580 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4581 /// 'icmp op load X, cst', try to see if we can compute the backedge
4582 /// execution count.
4583 ScalarEvolution::ExitLimit
4584 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4588 ICmpInst::Predicate predicate) {
4590 if (LI->isVolatile()) return getCouldNotCompute();
4592 // Check to see if the loaded pointer is a getelementptr of a global.
4593 // TODO: Use SCEV instead of manually grubbing with GEPs.
4594 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4595 if (!GEP) return getCouldNotCompute();
4597 // Make sure that it is really a constant global we are gepping, with an
4598 // initializer, and make sure the first IDX is really 0.
4599 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4600 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4601 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4602 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4603 return getCouldNotCompute();
4605 // Okay, we allow one non-constant index into the GEP instruction.
4607 std::vector<Constant*> Indexes;
4608 unsigned VarIdxNum = 0;
4609 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4610 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4611 Indexes.push_back(CI);
4612 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4613 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4614 VarIdx = GEP->getOperand(i);
4616 Indexes.push_back(0);
4619 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4621 return getCouldNotCompute();
4623 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4624 // Check to see if X is a loop variant variable value now.
4625 const SCEV *Idx = getSCEV(VarIdx);
4626 Idx = getSCEVAtScope(Idx, L);
4628 // We can only recognize very limited forms of loop index expressions, in
4629 // particular, only affine AddRec's like {C1,+,C2}.
4630 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4631 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4632 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4633 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4634 return getCouldNotCompute();
4636 unsigned MaxSteps = MaxBruteForceIterations;
4637 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4638 ConstantInt *ItCst = ConstantInt::get(
4639 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4640 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4642 // Form the GEP offset.
4643 Indexes[VarIdxNum] = Val;
4645 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4647 if (Result == 0) break; // Cannot compute!
4649 // Evaluate the condition for this iteration.
4650 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4651 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4652 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4654 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4655 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4658 ++NumArrayLenItCounts;
4659 return getConstant(ItCst); // Found terminating iteration!
4662 return getCouldNotCompute();
4666 /// CanConstantFold - Return true if we can constant fold an instruction of the
4667 /// specified type, assuming that all operands were constants.
4668 static bool CanConstantFold(const Instruction *I) {
4669 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4670 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4674 if (const CallInst *CI = dyn_cast<CallInst>(I))
4675 if (const Function *F = CI->getCalledFunction())
4676 return canConstantFoldCallTo(F);
4680 /// Determine whether this instruction can constant evolve within this loop
4681 /// assuming its operands can all constant evolve.
4682 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4683 // An instruction outside of the loop can't be derived from a loop PHI.
4684 if (!L->contains(I)) return false;
4686 if (isa<PHINode>(I)) {
4687 if (L->getHeader() == I->getParent())
4690 // We don't currently keep track of the control flow needed to evaluate
4691 // PHIs, so we cannot handle PHIs inside of loops.
4695 // If we won't be able to constant fold this expression even if the operands
4696 // are constants, bail early.
4697 return CanConstantFold(I);
4700 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4701 /// recursing through each instruction operand until reaching a loop header phi.
4703 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4704 DenseMap<Instruction *, PHINode *> &PHIMap) {
4706 // Otherwise, we can evaluate this instruction if all of its operands are
4707 // constant or derived from a PHI node themselves.
4709 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4710 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4712 if (isa<Constant>(*OpI)) continue;
4714 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4715 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4717 PHINode *P = dyn_cast<PHINode>(OpInst);
4719 // If this operand is already visited, reuse the prior result.
4720 // We may have P != PHI if this is the deepest point at which the
4721 // inconsistent paths meet.
4722 P = PHIMap.lookup(OpInst);
4724 // Recurse and memoize the results, whether a phi is found or not.
4725 // This recursive call invalidates pointers into PHIMap.
4726 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4729 if (P == 0) return 0; // Not evolving from PHI
4730 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4733 // This is a expression evolving from a constant PHI!
4737 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4738 /// in the loop that V is derived from. We allow arbitrary operations along the
4739 /// way, but the operands of an operation must either be constants or a value
4740 /// derived from a constant PHI. If this expression does not fit with these
4741 /// constraints, return null.
4742 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4743 Instruction *I = dyn_cast<Instruction>(V);
4744 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4746 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4750 // Record non-constant instructions contained by the loop.
4751 DenseMap<Instruction *, PHINode *> PHIMap;
4752 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4755 /// EvaluateExpression - Given an expression that passes the
4756 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4757 /// in the loop has the value PHIVal. If we can't fold this expression for some
4758 /// reason, return null.
4759 static Constant *EvaluateExpression(Value *V, const Loop *L,
4760 DenseMap<Instruction *, Constant *> &Vals,
4761 const DataLayout *TD,
4762 const TargetLibraryInfo *TLI) {
4763 // Convenient constant check, but redundant for recursive calls.
4764 if (Constant *C = dyn_cast<Constant>(V)) return C;
4765 Instruction *I = dyn_cast<Instruction>(V);
4768 if (Constant *C = Vals.lookup(I)) return C;
4770 // An instruction inside the loop depends on a value outside the loop that we
4771 // weren't given a mapping for, or a value such as a call inside the loop.
4772 if (!canConstantEvolve(I, L)) return 0;
4774 // An unmapped PHI can be due to a branch or another loop inside this loop,
4775 // or due to this not being the initial iteration through a loop where we
4776 // couldn't compute the evolution of this particular PHI last time.
4777 if (isa<PHINode>(I)) return 0;
4779 std::vector<Constant*> Operands(I->getNumOperands());
4781 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4782 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4784 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4785 if (!Operands[i]) return 0;
4788 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4794 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4795 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4796 Operands[1], TD, TLI);
4797 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4798 if (!LI->isVolatile())
4799 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4801 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4805 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4806 /// in the header of its containing loop, we know the loop executes a
4807 /// constant number of times, and the PHI node is just a recurrence
4808 /// involving constants, fold it.
4810 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4813 DenseMap<PHINode*, Constant*>::const_iterator I =
4814 ConstantEvolutionLoopExitValue.find(PN);
4815 if (I != ConstantEvolutionLoopExitValue.end())
4818 if (BEs.ugt(MaxBruteForceIterations))
4819 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4821 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4823 DenseMap<Instruction *, Constant *> CurrentIterVals;
4824 BasicBlock *Header = L->getHeader();
4825 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4827 // Since the loop is canonicalized, the PHI node must have two entries. One
4828 // entry must be a constant (coming in from outside of the loop), and the
4829 // second must be derived from the same PHI.
4830 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4832 for (BasicBlock::iterator I = Header->begin();
4833 (PHI = dyn_cast<PHINode>(I)); ++I) {
4834 Constant *StartCST =
4835 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4836 if (StartCST == 0) continue;
4837 CurrentIterVals[PHI] = StartCST;
4839 if (!CurrentIterVals.count(PN))
4842 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4844 // Execute the loop symbolically to determine the exit value.
4845 if (BEs.getActiveBits() >= 32)
4846 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4848 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4849 unsigned IterationNum = 0;
4850 for (; ; ++IterationNum) {
4851 if (IterationNum == NumIterations)
4852 return RetVal = CurrentIterVals[PN]; // Got exit value!
4854 // Compute the value of the PHIs for the next iteration.
4855 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4856 DenseMap<Instruction *, Constant *> NextIterVals;
4857 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4860 return 0; // Couldn't evaluate!
4861 NextIterVals[PN] = NextPHI;
4863 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4865 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4866 // cease to be able to evaluate one of them or if they stop evolving,
4867 // because that doesn't necessarily prevent us from computing PN.
4868 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4869 for (DenseMap<Instruction *, Constant *>::const_iterator
4870 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4871 PHINode *PHI = dyn_cast<PHINode>(I->first);
4872 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4873 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4875 // We use two distinct loops because EvaluateExpression may invalidate any
4876 // iterators into CurrentIterVals.
4877 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4878 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4879 PHINode *PHI = I->first;
4880 Constant *&NextPHI = NextIterVals[PHI];
4881 if (!NextPHI) { // Not already computed.
4882 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4883 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4885 if (NextPHI != I->second)
4886 StoppedEvolving = false;
4889 // If all entries in CurrentIterVals == NextIterVals then we can stop
4890 // iterating, the loop can't continue to change.
4891 if (StoppedEvolving)
4892 return RetVal = CurrentIterVals[PN];
4894 CurrentIterVals.swap(NextIterVals);
4898 /// ComputeExitCountExhaustively - If the loop is known to execute a
4899 /// constant number of times (the condition evolves only from constants),
4900 /// try to evaluate a few iterations of the loop until we get the exit
4901 /// condition gets a value of ExitWhen (true or false). If we cannot
4902 /// evaluate the trip count of the loop, return getCouldNotCompute().
4903 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4906 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4907 if (PN == 0) return getCouldNotCompute();
4909 // If the loop is canonicalized, the PHI will have exactly two entries.
4910 // That's the only form we support here.
4911 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4913 DenseMap<Instruction *, Constant *> CurrentIterVals;
4914 BasicBlock *Header = L->getHeader();
4915 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4917 // One entry must be a constant (coming in from outside of the loop), and the
4918 // second must be derived from the same PHI.
4919 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4921 for (BasicBlock::iterator I = Header->begin();
4922 (PHI = dyn_cast<PHINode>(I)); ++I) {
4923 Constant *StartCST =
4924 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4925 if (StartCST == 0) continue;
4926 CurrentIterVals[PHI] = StartCST;
4928 if (!CurrentIterVals.count(PN))
4929 return getCouldNotCompute();
4931 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4932 // the loop symbolically to determine when the condition gets a value of
4935 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4936 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4937 ConstantInt *CondVal =
4938 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4941 // Couldn't symbolically evaluate.
4942 if (!CondVal) return getCouldNotCompute();
4944 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4945 ++NumBruteForceTripCountsComputed;
4946 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4949 // Update all the PHI nodes for the next iteration.
4950 DenseMap<Instruction *, Constant *> NextIterVals;
4952 // Create a list of which PHIs we need to compute. We want to do this before
4953 // calling EvaluateExpression on them because that may invalidate iterators
4954 // into CurrentIterVals.
4955 SmallVector<PHINode *, 8> PHIsToCompute;
4956 for (DenseMap<Instruction *, Constant *>::const_iterator
4957 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4958 PHINode *PHI = dyn_cast<PHINode>(I->first);
4959 if (!PHI || PHI->getParent() != Header) continue;
4960 PHIsToCompute.push_back(PHI);
4962 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4963 E = PHIsToCompute.end(); I != E; ++I) {
4965 Constant *&NextPHI = NextIterVals[PHI];
4966 if (NextPHI) continue; // Already computed!
4968 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4969 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4971 CurrentIterVals.swap(NextIterVals);
4974 // Too many iterations were needed to evaluate.
4975 return getCouldNotCompute();
4978 /// getSCEVAtScope - Return a SCEV expression for the specified value
4979 /// at the specified scope in the program. The L value specifies a loop
4980 /// nest to evaluate the expression at, where null is the top-level or a
4981 /// specified loop is immediately inside of the loop.
4983 /// This method can be used to compute the exit value for a variable defined
4984 /// in a loop by querying what the value will hold in the parent loop.
4986 /// In the case that a relevant loop exit value cannot be computed, the
4987 /// original value V is returned.
4988 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4989 // Check to see if we've folded this expression at this loop before.
4990 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4991 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4992 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4994 return Pair.first->second ? Pair.first->second : V;
4996 // Otherwise compute it.
4997 const SCEV *C = computeSCEVAtScope(V, L);
4998 ValuesAtScopes[V][L] = C;
5002 /// This builds up a Constant using the ConstantExpr interface. That way, we
5003 /// will return Constants for objects which aren't represented by a
5004 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5005 /// Returns NULL if the SCEV isn't representable as a Constant.
5006 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5007 switch (V->getSCEVType()) {
5008 default: // TODO: smax, umax.
5009 case scCouldNotCompute:
5013 return cast<SCEVConstant>(V)->getValue();
5015 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5016 case scSignExtend: {
5017 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5018 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5019 return ConstantExpr::getSExt(CastOp, SS->getType());
5022 case scZeroExtend: {
5023 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5024 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5025 return ConstantExpr::getZExt(CastOp, SZ->getType());
5029 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5030 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5031 return ConstantExpr::getTrunc(CastOp, ST->getType());
5035 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5036 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5037 if (C->getType()->isPointerTy())
5038 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5039 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5040 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5044 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5046 // The offsets have been converted to bytes. We can add bytes to an
5047 // i8* by GEP with the byte count in the first index.
5048 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5051 // Don't bother trying to sum two pointers. We probably can't
5052 // statically compute a load that results from it anyway.
5053 if (C2->getType()->isPointerTy())
5056 if (C->getType()->isPointerTy()) {
5057 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5058 C2 = ConstantExpr::getIntegerCast(
5059 C2, Type::getInt32Ty(C->getContext()), true);
5060 C = ConstantExpr::getGetElementPtr(C, C2);
5062 C = ConstantExpr::getAdd(C, C2);
5069 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5070 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5071 // Don't bother with pointers at all.
5072 if (C->getType()->isPointerTy()) return 0;
5073 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5074 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5075 if (!C2 || C2->getType()->isPointerTy()) return 0;
5076 C = ConstantExpr::getMul(C, C2);
5083 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5084 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5085 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5086 if (LHS->getType() == RHS->getType())
5087 return ConstantExpr::getUDiv(LHS, RHS);
5094 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5095 if (isa<SCEVConstant>(V)) return V;
5097 // If this instruction is evolved from a constant-evolving PHI, compute the
5098 // exit value from the loop without using SCEVs.
5099 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5100 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5101 const Loop *LI = (*this->LI)[I->getParent()];
5102 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5103 if (PHINode *PN = dyn_cast<PHINode>(I))
5104 if (PN->getParent() == LI->getHeader()) {
5105 // Okay, there is no closed form solution for the PHI node. Check
5106 // to see if the loop that contains it has a known backedge-taken
5107 // count. If so, we may be able to force computation of the exit
5109 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5110 if (const SCEVConstant *BTCC =
5111 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5112 // Okay, we know how many times the containing loop executes. If
5113 // this is a constant evolving PHI node, get the final value at
5114 // the specified iteration number.
5115 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5116 BTCC->getValue()->getValue(),
5118 if (RV) return getSCEV(RV);
5122 // Okay, this is an expression that we cannot symbolically evaluate
5123 // into a SCEV. Check to see if it's possible to symbolically evaluate
5124 // the arguments into constants, and if so, try to constant propagate the
5125 // result. This is particularly useful for computing loop exit values.
5126 if (CanConstantFold(I)) {
5127 SmallVector<Constant *, 4> Operands;
5128 bool MadeImprovement = false;
5129 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5130 Value *Op = I->getOperand(i);
5131 if (Constant *C = dyn_cast<Constant>(Op)) {
5132 Operands.push_back(C);
5136 // If any of the operands is non-constant and if they are
5137 // non-integer and non-pointer, don't even try to analyze them
5138 // with scev techniques.
5139 if (!isSCEVable(Op->getType()))
5142 const SCEV *OrigV = getSCEV(Op);
5143 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5144 MadeImprovement |= OrigV != OpV;
5146 Constant *C = BuildConstantFromSCEV(OpV);
5148 if (C->getType() != Op->getType())
5149 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5153 Operands.push_back(C);
5156 // Check to see if getSCEVAtScope actually made an improvement.
5157 if (MadeImprovement) {
5159 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5160 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5161 Operands[0], Operands[1], TD,
5163 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5164 if (!LI->isVolatile())
5165 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5167 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5175 // This is some other type of SCEVUnknown, just return it.
5179 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5180 // Avoid performing the look-up in the common case where the specified
5181 // expression has no loop-variant portions.
5182 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5183 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5184 if (OpAtScope != Comm->getOperand(i)) {
5185 // Okay, at least one of these operands is loop variant but might be
5186 // foldable. Build a new instance of the folded commutative expression.
5187 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5188 Comm->op_begin()+i);
5189 NewOps.push_back(OpAtScope);
5191 for (++i; i != e; ++i) {
5192 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5193 NewOps.push_back(OpAtScope);
5195 if (isa<SCEVAddExpr>(Comm))
5196 return getAddExpr(NewOps);
5197 if (isa<SCEVMulExpr>(Comm))
5198 return getMulExpr(NewOps);
5199 if (isa<SCEVSMaxExpr>(Comm))
5200 return getSMaxExpr(NewOps);
5201 if (isa<SCEVUMaxExpr>(Comm))
5202 return getUMaxExpr(NewOps);
5203 llvm_unreachable("Unknown commutative SCEV type!");
5206 // If we got here, all operands are loop invariant.
5210 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5211 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5212 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5213 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5214 return Div; // must be loop invariant
5215 return getUDivExpr(LHS, RHS);
5218 // If this is a loop recurrence for a loop that does not contain L, then we
5219 // are dealing with the final value computed by the loop.
5220 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5221 // First, attempt to evaluate each operand.
5222 // Avoid performing the look-up in the common case where the specified
5223 // expression has no loop-variant portions.
5224 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5225 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5226 if (OpAtScope == AddRec->getOperand(i))
5229 // Okay, at least one of these operands is loop variant but might be
5230 // foldable. Build a new instance of the folded commutative expression.
5231 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5232 AddRec->op_begin()+i);
5233 NewOps.push_back(OpAtScope);
5234 for (++i; i != e; ++i)
5235 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5237 const SCEV *FoldedRec =
5238 getAddRecExpr(NewOps, AddRec->getLoop(),
5239 AddRec->getNoWrapFlags(SCEV::FlagNW));
5240 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5241 // The addrec may be folded to a nonrecurrence, for example, if the
5242 // induction variable is multiplied by zero after constant folding. Go
5243 // ahead and return the folded value.
5249 // If the scope is outside the addrec's loop, evaluate it by using the
5250 // loop exit value of the addrec.
5251 if (!AddRec->getLoop()->contains(L)) {
5252 // To evaluate this recurrence, we need to know how many times the AddRec
5253 // loop iterates. Compute this now.
5254 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5255 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5257 // Then, evaluate the AddRec.
5258 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5264 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5265 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5266 if (Op == Cast->getOperand())
5267 return Cast; // must be loop invariant
5268 return getZeroExtendExpr(Op, Cast->getType());
5271 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5272 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5273 if (Op == Cast->getOperand())
5274 return Cast; // must be loop invariant
5275 return getSignExtendExpr(Op, Cast->getType());
5278 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5279 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5280 if (Op == Cast->getOperand())
5281 return Cast; // must be loop invariant
5282 return getTruncateExpr(Op, Cast->getType());
5285 llvm_unreachable("Unknown SCEV type!");
5288 /// getSCEVAtScope - This is a convenience function which does
5289 /// getSCEVAtScope(getSCEV(V), L).
5290 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5291 return getSCEVAtScope(getSCEV(V), L);
5294 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5295 /// following equation:
5297 /// A * X = B (mod N)
5299 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5300 /// A and B isn't important.
5302 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5303 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5304 ScalarEvolution &SE) {
5305 uint32_t BW = A.getBitWidth();
5306 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5307 assert(A != 0 && "A must be non-zero.");
5311 // The gcd of A and N may have only one prime factor: 2. The number of
5312 // trailing zeros in A is its multiplicity
5313 uint32_t Mult2 = A.countTrailingZeros();
5316 // 2. Check if B is divisible by D.
5318 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5319 // is not less than multiplicity of this prime factor for D.
5320 if (B.countTrailingZeros() < Mult2)
5321 return SE.getCouldNotCompute();
5323 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5326 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5327 // bit width during computations.
5328 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5329 APInt Mod(BW + 1, 0);
5330 Mod.setBit(BW - Mult2); // Mod = N / D
5331 APInt I = AD.multiplicativeInverse(Mod);
5333 // 4. Compute the minimum unsigned root of the equation:
5334 // I * (B / D) mod (N / D)
5335 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5337 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5339 return SE.getConstant(Result.trunc(BW));
5342 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5343 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5344 /// might be the same) or two SCEVCouldNotCompute objects.
5346 static std::pair<const SCEV *,const SCEV *>
5347 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5348 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5349 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5350 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5351 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5353 // We currently can only solve this if the coefficients are constants.
5354 if (!LC || !MC || !NC) {
5355 const SCEV *CNC = SE.getCouldNotCompute();
5356 return std::make_pair(CNC, CNC);
5359 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5360 const APInt &L = LC->getValue()->getValue();
5361 const APInt &M = MC->getValue()->getValue();
5362 const APInt &N = NC->getValue()->getValue();
5363 APInt Two(BitWidth, 2);
5364 APInt Four(BitWidth, 4);
5367 using namespace APIntOps;
5369 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5370 // The B coefficient is M-N/2
5374 // The A coefficient is N/2
5375 APInt A(N.sdiv(Two));
5377 // Compute the B^2-4ac term.
5380 SqrtTerm -= Four * (A * C);
5382 if (SqrtTerm.isNegative()) {
5383 // The loop is provably infinite.
5384 const SCEV *CNC = SE.getCouldNotCompute();
5385 return std::make_pair(CNC, CNC);
5388 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5389 // integer value or else APInt::sqrt() will assert.
5390 APInt SqrtVal(SqrtTerm.sqrt());
5392 // Compute the two solutions for the quadratic formula.
5393 // The divisions must be performed as signed divisions.
5396 if (TwoA.isMinValue()) {
5397 const SCEV *CNC = SE.getCouldNotCompute();
5398 return std::make_pair(CNC, CNC);
5401 LLVMContext &Context = SE.getContext();
5403 ConstantInt *Solution1 =
5404 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5405 ConstantInt *Solution2 =
5406 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5408 return std::make_pair(SE.getConstant(Solution1),
5409 SE.getConstant(Solution2));
5410 } // end APIntOps namespace
5413 /// HowFarToZero - Return the number of times a backedge comparing the specified
5414 /// value to zero will execute. If not computable, return CouldNotCompute.
5416 /// This is only used for loops with a "x != y" exit test. The exit condition is
5417 /// now expressed as a single expression, V = x-y. So the exit test is
5418 /// effectively V != 0. We know and take advantage of the fact that this
5419 /// expression only being used in a comparison by zero context.
5420 ScalarEvolution::ExitLimit
5421 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5422 // If the value is a constant
5423 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5424 // If the value is already zero, the branch will execute zero times.
5425 if (C->getValue()->isZero()) return C;
5426 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5429 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5430 if (!AddRec || AddRec->getLoop() != L)
5431 return getCouldNotCompute();
5433 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5434 // the quadratic equation to solve it.
5435 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5436 std::pair<const SCEV *,const SCEV *> Roots =
5437 SolveQuadraticEquation(AddRec, *this);
5438 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5439 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5442 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5443 << " sol#2: " << *R2 << "\n";
5445 // Pick the smallest positive root value.
5446 if (ConstantInt *CB =
5447 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5450 if (CB->getZExtValue() == false)
5451 std::swap(R1, R2); // R1 is the minimum root now.
5453 // We can only use this value if the chrec ends up with an exact zero
5454 // value at this index. When solving for "X*X != 5", for example, we
5455 // should not accept a root of 2.
5456 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5458 return R1; // We found a quadratic root!
5461 return getCouldNotCompute();
5464 // Otherwise we can only handle this if it is affine.
5465 if (!AddRec->isAffine())
5466 return getCouldNotCompute();
5468 // If this is an affine expression, the execution count of this branch is
5469 // the minimum unsigned root of the following equation:
5471 // Start + Step*N = 0 (mod 2^BW)
5475 // Step*N = -Start (mod 2^BW)
5477 // where BW is the common bit width of Start and Step.
5479 // Get the initial value for the loop.
5480 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5481 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5483 // For now we handle only constant steps.
5485 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5486 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5487 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5488 // We have not yet seen any such cases.
5489 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5490 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5491 return getCouldNotCompute();
5493 // For positive steps (counting up until unsigned overflow):
5494 // N = -Start/Step (as unsigned)
5495 // For negative steps (counting down to zero):
5497 // First compute the unsigned distance from zero in the direction of Step.
5498 bool CountDown = StepC->getValue()->getValue().isNegative();
5499 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5501 // Handle unitary steps, which cannot wraparound.
5502 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5503 // N = Distance (as unsigned)
5504 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5505 ConstantRange CR = getUnsignedRange(Start);
5506 const SCEV *MaxBECount;
5507 if (!CountDown && CR.getUnsignedMin().isMinValue())
5508 // When counting up, the worst starting value is 1, not 0.
5509 MaxBECount = CR.getUnsignedMax().isMinValue()
5510 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5511 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5513 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5514 : -CR.getUnsignedMin());
5515 return ExitLimit(Distance, MaxBECount);
5518 // If the recurrence is known not to wraparound, unsigned divide computes the
5519 // back edge count. We know that the value will either become zero (and thus
5520 // the loop terminates), that the loop will terminate through some other exit
5521 // condition first, or that the loop has undefined behavior. This means
5522 // we can't "miss" the exit value, even with nonunit stride.
5524 // FIXME: Prove that loops always exhibits *acceptable* undefined
5525 // behavior. Loops must exhibit defined behavior until a wrapped value is
5526 // actually used. So the trip count computed by udiv could be smaller than the
5527 // number of well-defined iterations.
5528 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5529 // FIXME: We really want an "isexact" bit for udiv.
5530 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5532 // Then, try to solve the above equation provided that Start is constant.
5533 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5534 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5535 -StartC->getValue()->getValue(),
5537 return getCouldNotCompute();
5540 /// HowFarToNonZero - Return the number of times a backedge checking the
5541 /// specified value for nonzero will execute. If not computable, return
5543 ScalarEvolution::ExitLimit
5544 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5545 // Loops that look like: while (X == 0) are very strange indeed. We don't
5546 // handle them yet except for the trivial case. This could be expanded in the
5547 // future as needed.
5549 // If the value is a constant, check to see if it is known to be non-zero
5550 // already. If so, the backedge will execute zero times.
5551 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5552 if (!C->getValue()->isNullValue())
5553 return getConstant(C->getType(), 0);
5554 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5557 // We could implement others, but I really doubt anyone writes loops like
5558 // this, and if they did, they would already be constant folded.
5559 return getCouldNotCompute();
5562 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5563 /// (which may not be an immediate predecessor) which has exactly one
5564 /// successor from which BB is reachable, or null if no such block is
5567 std::pair<BasicBlock *, BasicBlock *>
5568 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5569 // If the block has a unique predecessor, then there is no path from the
5570 // predecessor to the block that does not go through the direct edge
5571 // from the predecessor to the block.
5572 if (BasicBlock *Pred = BB->getSinglePredecessor())
5573 return std::make_pair(Pred, BB);
5575 // A loop's header is defined to be a block that dominates the loop.
5576 // If the header has a unique predecessor outside the loop, it must be
5577 // a block that has exactly one successor that can reach the loop.
5578 if (Loop *L = LI->getLoopFor(BB))
5579 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5581 return std::pair<BasicBlock *, BasicBlock *>();
5584 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5585 /// testing whether two expressions are equal, however for the purposes of
5586 /// looking for a condition guarding a loop, it can be useful to be a little
5587 /// more general, since a front-end may have replicated the controlling
5590 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5591 // Quick check to see if they are the same SCEV.
5592 if (A == B) return true;
5594 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5595 // two different instructions with the same value. Check for this case.
5596 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5597 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5598 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5599 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5600 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5603 // Otherwise assume they may have a different value.
5607 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5608 /// predicate Pred. Return true iff any changes were made.
5610 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5611 const SCEV *&LHS, const SCEV *&RHS,
5613 bool Changed = false;
5615 // If we hit the max recursion limit bail out.
5619 // Canonicalize a constant to the right side.
5620 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5621 // Check for both operands constant.
5622 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5623 if (ConstantExpr::getICmp(Pred,
5625 RHSC->getValue())->isNullValue())
5626 goto trivially_false;
5628 goto trivially_true;
5630 // Otherwise swap the operands to put the constant on the right.
5631 std::swap(LHS, RHS);
5632 Pred = ICmpInst::getSwappedPredicate(Pred);
5636 // If we're comparing an addrec with a value which is loop-invariant in the
5637 // addrec's loop, put the addrec on the left. Also make a dominance check,
5638 // as both operands could be addrecs loop-invariant in each other's loop.
5639 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5640 const Loop *L = AR->getLoop();
5641 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5642 std::swap(LHS, RHS);
5643 Pred = ICmpInst::getSwappedPredicate(Pred);
5648 // If there's a constant operand, canonicalize comparisons with boundary
5649 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5650 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5651 const APInt &RA = RC->getValue()->getValue();
5653 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5654 case ICmpInst::ICMP_EQ:
5655 case ICmpInst::ICMP_NE:
5656 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5658 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5659 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5660 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5661 ME->getOperand(0)->isAllOnesValue()) {
5662 RHS = AE->getOperand(1);
5663 LHS = ME->getOperand(1);
5667 case ICmpInst::ICMP_UGE:
5668 if ((RA - 1).isMinValue()) {
5669 Pred = ICmpInst::ICMP_NE;
5670 RHS = getConstant(RA - 1);
5674 if (RA.isMaxValue()) {
5675 Pred = ICmpInst::ICMP_EQ;
5679 if (RA.isMinValue()) goto trivially_true;
5681 Pred = ICmpInst::ICMP_UGT;
5682 RHS = getConstant(RA - 1);
5685 case ICmpInst::ICMP_ULE:
5686 if ((RA + 1).isMaxValue()) {
5687 Pred = ICmpInst::ICMP_NE;
5688 RHS = getConstant(RA + 1);
5692 if (RA.isMinValue()) {
5693 Pred = ICmpInst::ICMP_EQ;
5697 if (RA.isMaxValue()) goto trivially_true;
5699 Pred = ICmpInst::ICMP_ULT;
5700 RHS = getConstant(RA + 1);
5703 case ICmpInst::ICMP_SGE:
5704 if ((RA - 1).isMinSignedValue()) {
5705 Pred = ICmpInst::ICMP_NE;
5706 RHS = getConstant(RA - 1);
5710 if (RA.isMaxSignedValue()) {
5711 Pred = ICmpInst::ICMP_EQ;
5715 if (RA.isMinSignedValue()) goto trivially_true;
5717 Pred = ICmpInst::ICMP_SGT;
5718 RHS = getConstant(RA - 1);
5721 case ICmpInst::ICMP_SLE:
5722 if ((RA + 1).isMaxSignedValue()) {
5723 Pred = ICmpInst::ICMP_NE;
5724 RHS = getConstant(RA + 1);
5728 if (RA.isMinSignedValue()) {
5729 Pred = ICmpInst::ICMP_EQ;
5733 if (RA.isMaxSignedValue()) goto trivially_true;
5735 Pred = ICmpInst::ICMP_SLT;
5736 RHS = getConstant(RA + 1);
5739 case ICmpInst::ICMP_UGT:
5740 if (RA.isMinValue()) {
5741 Pred = ICmpInst::ICMP_NE;
5745 if ((RA + 1).isMaxValue()) {
5746 Pred = ICmpInst::ICMP_EQ;
5747 RHS = getConstant(RA + 1);
5751 if (RA.isMaxValue()) goto trivially_false;
5753 case ICmpInst::ICMP_ULT:
5754 if (RA.isMaxValue()) {
5755 Pred = ICmpInst::ICMP_NE;
5759 if ((RA - 1).isMinValue()) {
5760 Pred = ICmpInst::ICMP_EQ;
5761 RHS = getConstant(RA - 1);
5765 if (RA.isMinValue()) goto trivially_false;
5767 case ICmpInst::ICMP_SGT:
5768 if (RA.isMinSignedValue()) {
5769 Pred = ICmpInst::ICMP_NE;
5773 if ((RA + 1).isMaxSignedValue()) {
5774 Pred = ICmpInst::ICMP_EQ;
5775 RHS = getConstant(RA + 1);
5779 if (RA.isMaxSignedValue()) goto trivially_false;
5781 case ICmpInst::ICMP_SLT:
5782 if (RA.isMaxSignedValue()) {
5783 Pred = ICmpInst::ICMP_NE;
5787 if ((RA - 1).isMinSignedValue()) {
5788 Pred = ICmpInst::ICMP_EQ;
5789 RHS = getConstant(RA - 1);
5793 if (RA.isMinSignedValue()) goto trivially_false;
5798 // Check for obvious equality.
5799 if (HasSameValue(LHS, RHS)) {
5800 if (ICmpInst::isTrueWhenEqual(Pred))
5801 goto trivially_true;
5802 if (ICmpInst::isFalseWhenEqual(Pred))
5803 goto trivially_false;
5806 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5807 // adding or subtracting 1 from one of the operands.
5809 case ICmpInst::ICMP_SLE:
5810 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5811 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5813 Pred = ICmpInst::ICMP_SLT;
5815 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5816 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5818 Pred = ICmpInst::ICMP_SLT;
5822 case ICmpInst::ICMP_SGE:
5823 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5824 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5826 Pred = ICmpInst::ICMP_SGT;
5828 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5829 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5831 Pred = ICmpInst::ICMP_SGT;
5835 case ICmpInst::ICMP_ULE:
5836 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5837 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5839 Pred = ICmpInst::ICMP_ULT;
5841 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5842 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5844 Pred = ICmpInst::ICMP_ULT;
5848 case ICmpInst::ICMP_UGE:
5849 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5850 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5852 Pred = ICmpInst::ICMP_UGT;
5854 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5855 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5857 Pred = ICmpInst::ICMP_UGT;
5865 // TODO: More simplifications are possible here.
5867 // Recursively simplify until we either hit a recursion limit or nothing
5870 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5876 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5877 Pred = ICmpInst::ICMP_EQ;
5882 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5883 Pred = ICmpInst::ICMP_NE;
5887 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5888 return getSignedRange(S).getSignedMax().isNegative();
5891 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5892 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5895 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5896 return !getSignedRange(S).getSignedMin().isNegative();
5899 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5900 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5903 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5904 return isKnownNegative(S) || isKnownPositive(S);
5907 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5908 const SCEV *LHS, const SCEV *RHS) {
5909 // Canonicalize the inputs first.
5910 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5912 // If LHS or RHS is an addrec, check to see if the condition is true in
5913 // every iteration of the loop.
5914 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5915 if (isLoopEntryGuardedByCond(
5916 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5917 isLoopBackedgeGuardedByCond(
5918 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5920 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5921 if (isLoopEntryGuardedByCond(
5922 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5923 isLoopBackedgeGuardedByCond(
5924 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5927 // Otherwise see what can be done with known constant ranges.
5928 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5932 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5933 const SCEV *LHS, const SCEV *RHS) {
5934 if (HasSameValue(LHS, RHS))
5935 return ICmpInst::isTrueWhenEqual(Pred);
5937 // This code is split out from isKnownPredicate because it is called from
5938 // within isLoopEntryGuardedByCond.
5941 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5942 case ICmpInst::ICMP_SGT:
5943 Pred = ICmpInst::ICMP_SLT;
5944 std::swap(LHS, RHS);
5945 case ICmpInst::ICMP_SLT: {
5946 ConstantRange LHSRange = getSignedRange(LHS);
5947 ConstantRange RHSRange = getSignedRange(RHS);
5948 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5950 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5954 case ICmpInst::ICMP_SGE:
5955 Pred = ICmpInst::ICMP_SLE;
5956 std::swap(LHS, RHS);
5957 case ICmpInst::ICMP_SLE: {
5958 ConstantRange LHSRange = getSignedRange(LHS);
5959 ConstantRange RHSRange = getSignedRange(RHS);
5960 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5962 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5966 case ICmpInst::ICMP_UGT:
5967 Pred = ICmpInst::ICMP_ULT;
5968 std::swap(LHS, RHS);
5969 case ICmpInst::ICMP_ULT: {
5970 ConstantRange LHSRange = getUnsignedRange(LHS);
5971 ConstantRange RHSRange = getUnsignedRange(RHS);
5972 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5974 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5978 case ICmpInst::ICMP_UGE:
5979 Pred = ICmpInst::ICMP_ULE;
5980 std::swap(LHS, RHS);
5981 case ICmpInst::ICMP_ULE: {
5982 ConstantRange LHSRange = getUnsignedRange(LHS);
5983 ConstantRange RHSRange = getUnsignedRange(RHS);
5984 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5986 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5990 case ICmpInst::ICMP_NE: {
5991 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5993 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5996 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5997 if (isKnownNonZero(Diff))
6001 case ICmpInst::ICMP_EQ:
6002 // The check at the top of the function catches the case where
6003 // the values are known to be equal.
6009 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6010 /// protected by a conditional between LHS and RHS. This is used to
6011 /// to eliminate casts.
6013 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6014 ICmpInst::Predicate Pred,
6015 const SCEV *LHS, const SCEV *RHS) {
6016 // Interpret a null as meaning no loop, where there is obviously no guard
6017 // (interprocedural conditions notwithstanding).
6018 if (!L) return true;
6020 BasicBlock *Latch = L->getLoopLatch();
6024 BranchInst *LoopContinuePredicate =
6025 dyn_cast<BranchInst>(Latch->getTerminator());
6026 if (!LoopContinuePredicate ||
6027 LoopContinuePredicate->isUnconditional())
6030 return isImpliedCond(Pred, LHS, RHS,
6031 LoopContinuePredicate->getCondition(),
6032 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6035 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6036 /// by a conditional between LHS and RHS. This is used to help avoid max
6037 /// expressions in loop trip counts, and to eliminate casts.
6039 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6040 ICmpInst::Predicate Pred,
6041 const SCEV *LHS, const SCEV *RHS) {
6042 // Interpret a null as meaning no loop, where there is obviously no guard
6043 // (interprocedural conditions notwithstanding).
6044 if (!L) return false;
6046 // Starting at the loop predecessor, climb up the predecessor chain, as long
6047 // as there are predecessors that can be found that have unique successors
6048 // leading to the original header.
6049 for (std::pair<BasicBlock *, BasicBlock *>
6050 Pair(L->getLoopPredecessor(), L->getHeader());
6052 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6054 BranchInst *LoopEntryPredicate =
6055 dyn_cast<BranchInst>(Pair.first->getTerminator());
6056 if (!LoopEntryPredicate ||
6057 LoopEntryPredicate->isUnconditional())
6060 if (isImpliedCond(Pred, LHS, RHS,
6061 LoopEntryPredicate->getCondition(),
6062 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6069 /// RAII wrapper to prevent recursive application of isImpliedCond.
6070 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6071 /// currently evaluating isImpliedCond.
6072 struct MarkPendingLoopPredicate {
6074 DenseSet<Value*> &LoopPreds;
6077 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6078 : Cond(C), LoopPreds(LP) {
6079 Pending = !LoopPreds.insert(Cond).second;
6081 ~MarkPendingLoopPredicate() {
6083 LoopPreds.erase(Cond);
6087 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6088 /// and RHS is true whenever the given Cond value evaluates to true.
6089 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6090 const SCEV *LHS, const SCEV *RHS,
6091 Value *FoundCondValue,
6093 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6097 // Recursively handle And and Or conditions.
6098 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6099 if (BO->getOpcode() == Instruction::And) {
6101 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6102 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6103 } else if (BO->getOpcode() == Instruction::Or) {
6105 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6106 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6110 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6111 if (!ICI) return false;
6113 // Bail if the ICmp's operands' types are wider than the needed type
6114 // before attempting to call getSCEV on them. This avoids infinite
6115 // recursion, since the analysis of widening casts can require loop
6116 // exit condition information for overflow checking, which would
6118 if (getTypeSizeInBits(LHS->getType()) <
6119 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6122 // Now that we found a conditional branch that dominates the loop, check to
6123 // see if it is the comparison we are looking for.
6124 ICmpInst::Predicate FoundPred;
6126 FoundPred = ICI->getInversePredicate();
6128 FoundPred = ICI->getPredicate();
6130 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6131 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6133 // Balance the types. The case where FoundLHS' type is wider than
6134 // LHS' type is checked for above.
6135 if (getTypeSizeInBits(LHS->getType()) >
6136 getTypeSizeInBits(FoundLHS->getType())) {
6137 if (CmpInst::isSigned(Pred)) {
6138 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6139 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6141 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6142 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6146 // Canonicalize the query to match the way instcombine will have
6147 // canonicalized the comparison.
6148 if (SimplifyICmpOperands(Pred, LHS, RHS))
6150 return CmpInst::isTrueWhenEqual(Pred);
6151 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6152 if (FoundLHS == FoundRHS)
6153 return CmpInst::isFalseWhenEqual(Pred);
6155 // Check to see if we can make the LHS or RHS match.
6156 if (LHS == FoundRHS || RHS == FoundLHS) {
6157 if (isa<SCEVConstant>(RHS)) {
6158 std::swap(FoundLHS, FoundRHS);
6159 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6161 std::swap(LHS, RHS);
6162 Pred = ICmpInst::getSwappedPredicate(Pred);
6166 // Check whether the found predicate is the same as the desired predicate.
6167 if (FoundPred == Pred)
6168 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6170 // Check whether swapping the found predicate makes it the same as the
6171 // desired predicate.
6172 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6173 if (isa<SCEVConstant>(RHS))
6174 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6176 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6177 RHS, LHS, FoundLHS, FoundRHS);
6180 // Check whether the actual condition is beyond sufficient.
6181 if (FoundPred == ICmpInst::ICMP_EQ)
6182 if (ICmpInst::isTrueWhenEqual(Pred))
6183 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6185 if (Pred == ICmpInst::ICMP_NE)
6186 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6187 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6190 // Otherwise assume the worst.
6194 /// isImpliedCondOperands - Test whether the condition described by Pred,
6195 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6196 /// and FoundRHS is true.
6197 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6198 const SCEV *LHS, const SCEV *RHS,
6199 const SCEV *FoundLHS,
6200 const SCEV *FoundRHS) {
6201 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6202 FoundLHS, FoundRHS) ||
6203 // ~x < ~y --> x > y
6204 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6205 getNotSCEV(FoundRHS),
6206 getNotSCEV(FoundLHS));
6209 /// isImpliedCondOperandsHelper - Test whether the condition described by
6210 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6211 /// FoundLHS, and FoundRHS is true.
6213 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6214 const SCEV *LHS, const SCEV *RHS,
6215 const SCEV *FoundLHS,
6216 const SCEV *FoundRHS) {
6218 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6219 case ICmpInst::ICMP_EQ:
6220 case ICmpInst::ICMP_NE:
6221 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6224 case ICmpInst::ICMP_SLT:
6225 case ICmpInst::ICMP_SLE:
6226 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6227 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6230 case ICmpInst::ICMP_SGT:
6231 case ICmpInst::ICMP_SGE:
6232 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6233 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6236 case ICmpInst::ICMP_ULT:
6237 case ICmpInst::ICMP_ULE:
6238 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6239 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6242 case ICmpInst::ICMP_UGT:
6243 case ICmpInst::ICMP_UGE:
6244 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6245 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6253 /// getBECount - Subtract the end and start values and divide by the step,
6254 /// rounding up, to get the number of times the backedge is executed. Return
6255 /// CouldNotCompute if an intermediate computation overflows.
6256 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6260 assert(!isKnownNegative(Step) &&
6261 "This code doesn't handle negative strides yet!");
6263 Type *Ty = Start->getType();
6265 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6266 // here because SCEV may not be able to determine that the unsigned division
6267 // after rounding is zero.
6269 return getConstant(Ty, 0);
6271 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6272 const SCEV *Diff = getMinusSCEV(End, Start);
6273 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6275 // Add an adjustment to the difference between End and Start so that
6276 // the division will effectively round up.
6277 const SCEV *Add = getAddExpr(Diff, RoundUp);
6280 // Check Add for unsigned overflow.
6281 // TODO: More sophisticated things could be done here.
6282 Type *WideTy = IntegerType::get(getContext(),
6283 getTypeSizeInBits(Ty) + 1);
6284 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6285 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6286 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6287 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6288 return getCouldNotCompute();
6291 return getUDivExpr(Add, Step);
6294 /// HowManyLessThans - Return the number of times a backedge containing the
6295 /// specified less-than comparison will execute. If not computable, return
6296 /// CouldNotCompute.
6297 ScalarEvolution::ExitLimit
6298 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6299 const Loop *L, bool isSigned) {
6300 // Only handle: "ADDREC < LoopInvariant".
6301 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6303 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6304 if (!AddRec || AddRec->getLoop() != L)
6305 return getCouldNotCompute();
6307 // Check to see if we have a flag which makes analysis easy.
6308 bool NoWrap = isSigned ?
6309 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6310 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6312 if (AddRec->isAffine()) {
6313 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6314 const SCEV *Step = AddRec->getStepRecurrence(*this);
6317 return getCouldNotCompute();
6318 if (Step->isOne()) {
6319 // With unit stride, the iteration never steps past the limit value.
6320 } else if (isKnownPositive(Step)) {
6321 // Test whether a positive iteration can step past the limit
6322 // value and past the maximum value for its type in a single step.
6323 // Note that it's not sufficient to check NoWrap here, because even
6324 // though the value after a wrap is undefined, it's not undefined
6325 // behavior, so if wrap does occur, the loop could either terminate or
6326 // loop infinitely, but in either case, the loop is guaranteed to
6327 // iterate at least until the iteration where the wrapping occurs.
6328 const SCEV *One = getConstant(Step->getType(), 1);
6330 APInt Max = APInt::getSignedMaxValue(BitWidth);
6331 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6332 .slt(getSignedRange(RHS).getSignedMax()))
6333 return getCouldNotCompute();
6335 APInt Max = APInt::getMaxValue(BitWidth);
6336 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6337 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6338 return getCouldNotCompute();
6341 // TODO: Handle negative strides here and below.
6342 return getCouldNotCompute();
6344 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6345 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6346 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6347 // treat m-n as signed nor unsigned due to overflow possibility.
6349 // First, we get the value of the LHS in the first iteration: n
6350 const SCEV *Start = AddRec->getOperand(0);
6352 // Determine the minimum constant start value.
6353 const SCEV *MinStart = getConstant(isSigned ?
6354 getSignedRange(Start).getSignedMin() :
6355 getUnsignedRange(Start).getUnsignedMin());
6357 // If we know that the condition is true in order to enter the loop,
6358 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6359 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6360 // the division must round up.
6361 const SCEV *End = RHS;
6362 if (!isLoopEntryGuardedByCond(L,
6363 isSigned ? ICmpInst::ICMP_SLT :
6365 getMinusSCEV(Start, Step), RHS))
6366 End = isSigned ? getSMaxExpr(RHS, Start)
6367 : getUMaxExpr(RHS, Start);
6369 // Determine the maximum constant end value.
6370 const SCEV *MaxEnd = getConstant(isSigned ?
6371 getSignedRange(End).getSignedMax() :
6372 getUnsignedRange(End).getUnsignedMax());
6374 // If MaxEnd is within a step of the maximum integer value in its type,
6375 // adjust it down to the minimum value which would produce the same effect.
6376 // This allows the subsequent ceiling division of (N+(step-1))/step to
6377 // compute the correct value.
6378 const SCEV *StepMinusOne = getMinusSCEV(Step,
6379 getConstant(Step->getType(), 1));
6382 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6385 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6388 // Finally, we subtract these two values and divide, rounding up, to get
6389 // the number of times the backedge is executed.
6390 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6392 // The maximum backedge count is similar, except using the minimum start
6393 // value and the maximum end value.
6394 // If we already have an exact constant BECount, use it instead.
6395 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6396 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6398 // If the stride is nonconstant, and NoWrap == true, then
6399 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6400 // exact BECount and invalid MaxBECount, which should be avoided to catch
6401 // more optimization opportunities.
6402 if (isa<SCEVCouldNotCompute>(MaxBECount))
6403 MaxBECount = BECount;
6405 return ExitLimit(BECount, MaxBECount);
6408 return getCouldNotCompute();
6411 /// getNumIterationsInRange - Return the number of iterations of this loop that
6412 /// produce values in the specified constant range. Another way of looking at
6413 /// this is that it returns the first iteration number where the value is not in
6414 /// the condition, thus computing the exit count. If the iteration count can't
6415 /// be computed, an instance of SCEVCouldNotCompute is returned.
6416 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6417 ScalarEvolution &SE) const {
6418 if (Range.isFullSet()) // Infinite loop.
6419 return SE.getCouldNotCompute();
6421 // If the start is a non-zero constant, shift the range to simplify things.
6422 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6423 if (!SC->getValue()->isZero()) {
6424 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6425 Operands[0] = SE.getConstant(SC->getType(), 0);
6426 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6427 getNoWrapFlags(FlagNW));
6428 if (const SCEVAddRecExpr *ShiftedAddRec =
6429 dyn_cast<SCEVAddRecExpr>(Shifted))
6430 return ShiftedAddRec->getNumIterationsInRange(
6431 Range.subtract(SC->getValue()->getValue()), SE);
6432 // This is strange and shouldn't happen.
6433 return SE.getCouldNotCompute();
6436 // The only time we can solve this is when we have all constant indices.
6437 // Otherwise, we cannot determine the overflow conditions.
6438 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6439 if (!isa<SCEVConstant>(getOperand(i)))
6440 return SE.getCouldNotCompute();
6443 // Okay at this point we know that all elements of the chrec are constants and
6444 // that the start element is zero.
6446 // First check to see if the range contains zero. If not, the first
6448 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6449 if (!Range.contains(APInt(BitWidth, 0)))
6450 return SE.getConstant(getType(), 0);
6453 // If this is an affine expression then we have this situation:
6454 // Solve {0,+,A} in Range === Ax in Range
6456 // We know that zero is in the range. If A is positive then we know that
6457 // the upper value of the range must be the first possible exit value.
6458 // If A is negative then the lower of the range is the last possible loop
6459 // value. Also note that we already checked for a full range.
6460 APInt One(BitWidth,1);
6461 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6462 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6464 // The exit value should be (End+A)/A.
6465 APInt ExitVal = (End + A).udiv(A);
6466 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6468 // Evaluate at the exit value. If we really did fall out of the valid
6469 // range, then we computed our trip count, otherwise wrap around or other
6470 // things must have happened.
6471 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6472 if (Range.contains(Val->getValue()))
6473 return SE.getCouldNotCompute(); // Something strange happened
6475 // Ensure that the previous value is in the range. This is a sanity check.
6476 assert(Range.contains(
6477 EvaluateConstantChrecAtConstant(this,
6478 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6479 "Linear scev computation is off in a bad way!");
6480 return SE.getConstant(ExitValue);
6481 } else if (isQuadratic()) {
6482 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6483 // quadratic equation to solve it. To do this, we must frame our problem in
6484 // terms of figuring out when zero is crossed, instead of when
6485 // Range.getUpper() is crossed.
6486 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6487 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6488 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6489 // getNoWrapFlags(FlagNW)
6492 // Next, solve the constructed addrec
6493 std::pair<const SCEV *,const SCEV *> Roots =
6494 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6495 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6496 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6498 // Pick the smallest positive root value.
6499 if (ConstantInt *CB =
6500 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6501 R1->getValue(), R2->getValue()))) {
6502 if (CB->getZExtValue() == false)
6503 std::swap(R1, R2); // R1 is the minimum root now.
6505 // Make sure the root is not off by one. The returned iteration should
6506 // not be in the range, but the previous one should be. When solving
6507 // for "X*X < 5", for example, we should not return a root of 2.
6508 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6511 if (Range.contains(R1Val->getValue())) {
6512 // The next iteration must be out of the range...
6513 ConstantInt *NextVal =
6514 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6516 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6517 if (!Range.contains(R1Val->getValue()))
6518 return SE.getConstant(NextVal);
6519 return SE.getCouldNotCompute(); // Something strange happened
6522 // If R1 was not in the range, then it is a good return value. Make
6523 // sure that R1-1 WAS in the range though, just in case.
6524 ConstantInt *NextVal =
6525 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6526 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6527 if (Range.contains(R1Val->getValue()))
6529 return SE.getCouldNotCompute(); // Something strange happened
6534 return SE.getCouldNotCompute();
6539 //===----------------------------------------------------------------------===//
6540 // SCEVCallbackVH Class Implementation
6541 //===----------------------------------------------------------------------===//
6543 void ScalarEvolution::SCEVCallbackVH::deleted() {
6544 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6545 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6546 SE->ConstantEvolutionLoopExitValue.erase(PN);
6547 SE->ValueExprMap.erase(getValPtr());
6548 // this now dangles!
6551 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6552 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6554 // Forget all the expressions associated with users of the old value,
6555 // so that future queries will recompute the expressions using the new
6557 Value *Old = getValPtr();
6558 SmallVector<User *, 16> Worklist;
6559 SmallPtrSet<User *, 8> Visited;
6560 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6562 Worklist.push_back(*UI);
6563 while (!Worklist.empty()) {
6564 User *U = Worklist.pop_back_val();
6565 // Deleting the Old value will cause this to dangle. Postpone
6566 // that until everything else is done.
6569 if (!Visited.insert(U))
6571 if (PHINode *PN = dyn_cast<PHINode>(U))
6572 SE->ConstantEvolutionLoopExitValue.erase(PN);
6573 SE->ValueExprMap.erase(U);
6574 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6576 Worklist.push_back(*UI);
6578 // Delete the Old value.
6579 if (PHINode *PN = dyn_cast<PHINode>(Old))
6580 SE->ConstantEvolutionLoopExitValue.erase(PN);
6581 SE->ValueExprMap.erase(Old);
6582 // this now dangles!
6585 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6586 : CallbackVH(V), SE(se) {}
6588 //===----------------------------------------------------------------------===//
6589 // ScalarEvolution Class Implementation
6590 //===----------------------------------------------------------------------===//
6592 ScalarEvolution::ScalarEvolution()
6593 : FunctionPass(ID), FirstUnknown(0) {
6594 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6597 bool ScalarEvolution::runOnFunction(Function &F) {
6599 LI = &getAnalysis<LoopInfo>();
6600 TD = getAnalysisIfAvailable<DataLayout>();
6601 TLI = &getAnalysis<TargetLibraryInfo>();
6602 DT = &getAnalysis<DominatorTree>();
6606 void ScalarEvolution::releaseMemory() {
6607 // Iterate through all the SCEVUnknown instances and call their
6608 // destructors, so that they release their references to their values.
6609 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6613 ValueExprMap.clear();
6615 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6616 // that a loop had multiple computable exits.
6617 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6618 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6623 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6625 BackedgeTakenCounts.clear();
6626 ConstantEvolutionLoopExitValue.clear();
6627 ValuesAtScopes.clear();
6628 LoopDispositions.clear();
6629 BlockDispositions.clear();
6630 UnsignedRanges.clear();
6631 SignedRanges.clear();
6632 UniqueSCEVs.clear();
6633 SCEVAllocator.Reset();
6636 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6637 AU.setPreservesAll();
6638 AU.addRequiredTransitive<LoopInfo>();
6639 AU.addRequiredTransitive<DominatorTree>();
6640 AU.addRequired<TargetLibraryInfo>();
6643 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6644 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6647 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6649 // Print all inner loops first
6650 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6651 PrintLoopInfo(OS, SE, *I);
6654 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6657 SmallVector<BasicBlock *, 8> ExitBlocks;
6658 L->getExitBlocks(ExitBlocks);
6659 if (ExitBlocks.size() != 1)
6660 OS << "<multiple exits> ";
6662 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6663 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6665 OS << "Unpredictable backedge-taken count. ";
6670 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6673 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6674 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6676 OS << "Unpredictable max backedge-taken count. ";
6682 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6683 // ScalarEvolution's implementation of the print method is to print
6684 // out SCEV values of all instructions that are interesting. Doing
6685 // this potentially causes it to create new SCEV objects though,
6686 // which technically conflicts with the const qualifier. This isn't
6687 // observable from outside the class though, so casting away the
6688 // const isn't dangerous.
6689 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6691 OS << "Classifying expressions for: ";
6692 WriteAsOperand(OS, F, /*PrintType=*/false);
6694 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6695 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6698 const SCEV *SV = SE.getSCEV(&*I);
6701 const Loop *L = LI->getLoopFor((*I).getParent());
6703 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6710 OS << "\t\t" "Exits: ";
6711 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6712 if (!SE.isLoopInvariant(ExitValue, L)) {
6713 OS << "<<Unknown>>";
6722 OS << "Determining loop execution counts for: ";
6723 WriteAsOperand(OS, F, /*PrintType=*/false);
6725 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6726 PrintLoopInfo(OS, &SE, *I);
6729 ScalarEvolution::LoopDisposition
6730 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6731 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6732 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6733 Values.insert(std::make_pair(L, LoopVariant));
6735 return Pair.first->second;
6737 LoopDisposition D = computeLoopDisposition(S, L);
6738 return LoopDispositions[S][L] = D;
6741 ScalarEvolution::LoopDisposition
6742 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6743 switch (S->getSCEVType()) {
6745 return LoopInvariant;
6749 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6750 case scAddRecExpr: {
6751 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6753 // If L is the addrec's loop, it's computable.
6754 if (AR->getLoop() == L)
6755 return LoopComputable;
6757 // Add recurrences are never invariant in the function-body (null loop).
6761 // This recurrence is variant w.r.t. L if L contains AR's loop.
6762 if (L->contains(AR->getLoop()))
6765 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6766 if (AR->getLoop()->contains(L))
6767 return LoopInvariant;
6769 // This recurrence is variant w.r.t. L if any of its operands
6771 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6773 if (!isLoopInvariant(*I, L))
6776 // Otherwise it's loop-invariant.
6777 return LoopInvariant;
6783 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6784 bool HasVarying = false;
6785 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6787 LoopDisposition D = getLoopDisposition(*I, L);
6788 if (D == LoopVariant)
6790 if (D == LoopComputable)
6793 return HasVarying ? LoopComputable : LoopInvariant;
6796 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6797 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6798 if (LD == LoopVariant)
6800 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6801 if (RD == LoopVariant)
6803 return (LD == LoopInvariant && RD == LoopInvariant) ?
6804 LoopInvariant : LoopComputable;
6807 // All non-instruction values are loop invariant. All instructions are loop
6808 // invariant if they are not contained in the specified loop.
6809 // Instructions are never considered invariant in the function body
6810 // (null loop) because they are defined within the "loop".
6811 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6812 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6813 return LoopInvariant;
6814 case scCouldNotCompute:
6815 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6816 default: llvm_unreachable("Unknown SCEV kind!");
6820 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6821 return getLoopDisposition(S, L) == LoopInvariant;
6824 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6825 return getLoopDisposition(S, L) == LoopComputable;
6828 ScalarEvolution::BlockDisposition
6829 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6830 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6831 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6832 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6834 return Pair.first->second;
6836 BlockDisposition D = computeBlockDisposition(S, BB);
6837 return BlockDispositions[S][BB] = D;
6840 ScalarEvolution::BlockDisposition
6841 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6842 switch (S->getSCEVType()) {
6844 return ProperlyDominatesBlock;
6848 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6849 case scAddRecExpr: {
6850 // This uses a "dominates" query instead of "properly dominates" query
6851 // to test for proper dominance too, because the instruction which
6852 // produces the addrec's value is a PHI, and a PHI effectively properly
6853 // dominates its entire containing block.
6854 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6855 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6856 return DoesNotDominateBlock;
6858 // FALL THROUGH into SCEVNAryExpr handling.
6863 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6865 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6867 BlockDisposition D = getBlockDisposition(*I, BB);
6868 if (D == DoesNotDominateBlock)
6869 return DoesNotDominateBlock;
6870 if (D == DominatesBlock)
6873 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6876 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6877 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6878 BlockDisposition LD = getBlockDisposition(LHS, BB);
6879 if (LD == DoesNotDominateBlock)
6880 return DoesNotDominateBlock;
6881 BlockDisposition RD = getBlockDisposition(RHS, BB);
6882 if (RD == DoesNotDominateBlock)
6883 return DoesNotDominateBlock;
6884 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6885 ProperlyDominatesBlock : DominatesBlock;
6888 if (Instruction *I =
6889 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6890 if (I->getParent() == BB)
6891 return DominatesBlock;
6892 if (DT->properlyDominates(I->getParent(), BB))
6893 return ProperlyDominatesBlock;
6894 return DoesNotDominateBlock;
6896 return ProperlyDominatesBlock;
6897 case scCouldNotCompute:
6898 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6900 llvm_unreachable("Unknown SCEV kind!");
6904 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6905 return getBlockDisposition(S, BB) >= DominatesBlock;
6908 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6909 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6913 // Search for a SCEV expression node within an expression tree.
6914 // Implements SCEVTraversal::Visitor.
6919 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
6921 bool follow(const SCEV *S) {
6922 IsFound |= (S == Node);
6925 bool isDone() const { return IsFound; }
6929 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6930 SCEVSearch Search(Op);
6931 visitAll(S, Search);
6932 return Search.IsFound;
6935 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6936 ValuesAtScopes.erase(S);
6937 LoopDispositions.erase(S);
6938 BlockDispositions.erase(S);
6939 UnsignedRanges.erase(S);
6940 SignedRanges.erase(S);
6943 typedef DenseMap<const Loop *, std::string> VerifyMap;
6944 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
6946 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
6947 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
6948 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
6950 std::string &S = Map[L];
6952 raw_string_ostream OS(S);
6953 SE.getBackedgeTakenCount(L)->print(OS);
6958 void ScalarEvolution::verifyAnalysis() const {
6962 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6964 // Gather stringified backedge taken counts for all loops using SCEV's caches.
6965 // FIXME: It would be much better to store actual values instead of strings,
6966 // but SCEV pointers will change if we drop the caches.
6967 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
6968 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
6969 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
6971 // Gather stringified backedge taken counts for all loops without using
6974 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
6975 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
6977 // Now compare whether they're the same with and without caches. This allows
6978 // verifying that no pass changed the cache.
6979 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
6980 "New loops suddenly appeared!");
6982 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
6983 OldE = BackedgeDumpsOld.end(),
6984 NewI = BackedgeDumpsNew.begin();
6985 OldI != OldE; ++OldI, ++NewI) {
6986 assert(OldI->first == NewI->first && "Loop order changed!");
6988 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
6990 // FIXME: We currently ignore SCEV changes towards CouldNotCompute. This
6991 // means that a pass is buggy or SCEV has to learn a new pattern but is
6992 // usually not harmful.
6993 if (OldI->second != NewI->second &&
6994 OldI->second.find("undef") == std::string::npos &&
6995 NewI->second != "***COULDNOTCOMPUTE***") {
6996 dbgs() << "SCEVValidator: SCEV for Loop '"
6997 << OldI->first->getHeader()->getName()
6998 << "' from '" << OldI->second << "' to '" << NewI->second << "'!";
7003 // TODO: Verify more things.