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. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Assembly/Writer.h"
71 #include "llvm/Transforms/Scalar.h"
72 #include "llvm/Support/CFG.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/InstIterator.h"
77 #include "llvm/Support/ManagedStatic.h"
78 #include "llvm/Support/MathExtras.h"
79 #include "llvm/Support/Streams.h"
80 #include "llvm/ADT/Statistic.h"
86 STATISTIC(NumBruteForceEvaluations,
87 "Number of brute force evaluations needed to "
88 "calculate high-order polynomial exit values");
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant derived loop"),
105 RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis");
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
118 void SCEV::dump() const {
122 /// getValueRange - Return the tightest constant bounds that this value is
123 /// known to have. This method is only valid on integer SCEV objects.
124 ConstantRange SCEV::getValueRange() const {
125 const Type *Ty = getType();
126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
127 // Default to a full range if no better information is available.
128 return ConstantRange(getBitWidth());
131 uint32_t SCEV::getBitWidth() const {
132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
133 return ITy->getBitWidth();
138 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
140 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 const Type *SCEVCouldNotCompute::getType() const {
146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
155 SCEVHandle SCEVCouldNotCompute::
156 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
157 const SCEVHandle &Conc,
158 ScalarEvolution &SE) const {
162 void SCEVCouldNotCompute::print(std::ostream &OS) const {
163 OS << "***COULDNOTCOMPUTE***";
166 bool SCEVCouldNotCompute::classof(const SCEV *S) {
167 return S->getSCEVType() == scCouldNotCompute;
171 // SCEVConstants - Only allow the creation of one SCEVConstant for any
172 // particular value. Don't use a SCEVHandle here, or else the object will
174 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
177 SCEVConstant::~SCEVConstant() {
178 SCEVConstants->erase(V);
181 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
182 SCEVConstant *&R = (*SCEVConstants)[V];
183 if (R == 0) R = new SCEVConstant(V);
187 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
188 return getConstant(ConstantInt::get(Val));
191 ConstantRange SCEVConstant::getValueRange() const {
192 return ConstantRange(V->getValue());
195 const Type *SCEVConstant::getType() const { return V->getType(); }
197 void SCEVConstant::print(std::ostream &OS) const {
198 WriteAsOperand(OS, V, false);
201 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
202 // particular input. Don't use a SCEVHandle here, or else the object will
204 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
205 SCEVTruncateExpr*> > SCEVTruncates;
207 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
208 : SCEV(scTruncate), Op(op), Ty(ty) {
209 assert(Op->getType()->isInteger() && Ty->isInteger() &&
210 "Cannot truncate non-integer value!");
211 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
212 && "This is not a truncating conversion!");
215 SCEVTruncateExpr::~SCEVTruncateExpr() {
216 SCEVTruncates->erase(std::make_pair(Op, Ty));
219 ConstantRange SCEVTruncateExpr::getValueRange() const {
220 return getOperand()->getValueRange().truncate(getBitWidth());
223 void SCEVTruncateExpr::print(std::ostream &OS) const {
224 OS << "(truncate " << *Op << " to " << *Ty << ")";
227 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
228 // particular input. Don't use a SCEVHandle here, or else the object will never
230 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
231 SCEVZeroExtendExpr*> > SCEVZeroExtends;
233 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
234 : SCEV(scZeroExtend), Op(op), Ty(ty) {
235 assert(Op->getType()->isInteger() && Ty->isInteger() &&
236 "Cannot zero extend non-integer value!");
237 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
238 && "This is not an extending conversion!");
241 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
242 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
245 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
246 return getOperand()->getValueRange().zeroExtend(getBitWidth());
249 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
250 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
253 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
254 // particular input. Don't use a SCEVHandle here, or else the object will never
256 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
257 SCEVSignExtendExpr*> > SCEVSignExtends;
259 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
260 : SCEV(scSignExtend), Op(op), Ty(ty) {
261 assert(Op->getType()->isInteger() && Ty->isInteger() &&
262 "Cannot sign extend non-integer value!");
263 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
264 && "This is not an extending conversion!");
267 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
268 SCEVSignExtends->erase(std::make_pair(Op, Ty));
271 ConstantRange SCEVSignExtendExpr::getValueRange() const {
272 return getOperand()->getValueRange().signExtend(getBitWidth());
275 void SCEVSignExtendExpr::print(std::ostream &OS) const {
276 OS << "(signextend " << *Op << " to " << *Ty << ")";
279 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
280 // particular input. Don't use a SCEVHandle here, or else the object will never
282 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
283 SCEVCommutativeExpr*> > SCEVCommExprs;
285 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
286 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
287 std::vector<SCEV*>(Operands.begin(),
291 void SCEVCommutativeExpr::print(std::ostream &OS) const {
292 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
293 const char *OpStr = getOperationStr();
294 OS << "(" << *Operands[0];
295 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
296 OS << OpStr << *Operands[i];
300 SCEVHandle SCEVCommutativeExpr::
301 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
302 const SCEVHandle &Conc,
303 ScalarEvolution &SE) const {
304 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
306 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
307 if (H != getOperand(i)) {
308 std::vector<SCEVHandle> NewOps;
309 NewOps.reserve(getNumOperands());
310 for (unsigned j = 0; j != i; ++j)
311 NewOps.push_back(getOperand(j));
313 for (++i; i != e; ++i)
314 NewOps.push_back(getOperand(i)->
315 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
317 if (isa<SCEVAddExpr>(this))
318 return SE.getAddExpr(NewOps);
319 else if (isa<SCEVMulExpr>(this))
320 return SE.getMulExpr(NewOps);
321 else if (isa<SCEVSMaxExpr>(this))
322 return SE.getSMaxExpr(NewOps);
323 else if (isa<SCEVUMaxExpr>(this))
324 return SE.getUMaxExpr(NewOps);
326 assert(0 && "Unknown commutative expr!");
333 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
334 // input. Don't use a SCEVHandle here, or else the object will never be
336 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
337 SCEVUDivExpr*> > SCEVUDivs;
339 SCEVUDivExpr::~SCEVUDivExpr() {
340 SCEVUDivs->erase(std::make_pair(LHS, RHS));
343 void SCEVUDivExpr::print(std::ostream &OS) const {
344 OS << "(" << *LHS << " /u " << *RHS << ")";
347 const Type *SCEVUDivExpr::getType() const {
348 return LHS->getType();
351 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
352 // particular input. Don't use a SCEVHandle here, or else the object will never
354 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
355 SCEVAddRecExpr*> > SCEVAddRecExprs;
357 SCEVAddRecExpr::~SCEVAddRecExpr() {
358 SCEVAddRecExprs->erase(std::make_pair(L,
359 std::vector<SCEV*>(Operands.begin(),
363 SCEVHandle SCEVAddRecExpr::
364 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
365 const SCEVHandle &Conc,
366 ScalarEvolution &SE) const {
367 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
369 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
370 if (H != getOperand(i)) {
371 std::vector<SCEVHandle> NewOps;
372 NewOps.reserve(getNumOperands());
373 for (unsigned j = 0; j != i; ++j)
374 NewOps.push_back(getOperand(j));
376 for (++i; i != e; ++i)
377 NewOps.push_back(getOperand(i)->
378 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
380 return SE.getAddRecExpr(NewOps, L);
387 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
388 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
389 // contain L and if the start is invariant.
390 return !QueryLoop->contains(L->getHeader()) &&
391 getOperand(0)->isLoopInvariant(QueryLoop);
395 void SCEVAddRecExpr::print(std::ostream &OS) const {
396 OS << "{" << *Operands[0];
397 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
398 OS << ",+," << *Operands[i];
399 OS << "}<" << L->getHeader()->getName() + ">";
402 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
403 // value. Don't use a SCEVHandle here, or else the object will never be
405 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
407 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
409 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
410 // All non-instruction values are loop invariant. All instructions are loop
411 // invariant if they are not contained in the specified loop.
412 if (Instruction *I = dyn_cast<Instruction>(V))
413 return !L->contains(I->getParent());
417 const Type *SCEVUnknown::getType() const {
421 void SCEVUnknown::print(std::ostream &OS) const {
422 WriteAsOperand(OS, V, false);
425 //===----------------------------------------------------------------------===//
427 //===----------------------------------------------------------------------===//
430 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
431 /// than the complexity of the RHS. This comparator is used to canonicalize
433 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
434 bool operator()(SCEV *LHS, SCEV *RHS) {
435 return LHS->getSCEVType() < RHS->getSCEVType();
440 /// GroupByComplexity - Given a list of SCEV objects, order them by their
441 /// complexity, and group objects of the same complexity together by value.
442 /// When this routine is finished, we know that any duplicates in the vector are
443 /// consecutive and that complexity is monotonically increasing.
445 /// Note that we go take special precautions to ensure that we get determinstic
446 /// results from this routine. In other words, we don't want the results of
447 /// this to depend on where the addresses of various SCEV objects happened to
450 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
451 if (Ops.size() < 2) return; // Noop
452 if (Ops.size() == 2) {
453 // This is the common case, which also happens to be trivially simple.
455 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
456 std::swap(Ops[0], Ops[1]);
460 // Do the rough sort by complexity.
461 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
463 // Now that we are sorted by complexity, group elements of the same
464 // complexity. Note that this is, at worst, N^2, but the vector is likely to
465 // be extremely short in practice. Note that we take this approach because we
466 // do not want to depend on the addresses of the objects we are grouping.
467 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
469 unsigned Complexity = S->getSCEVType();
471 // If there are any objects of the same complexity and same value as this
473 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
474 if (Ops[j] == S) { // Found a duplicate.
475 // Move it to immediately after i'th element.
476 std::swap(Ops[i+1], Ops[j]);
477 ++i; // no need to rescan it.
478 if (i == e-2) return; // Done!
486 //===----------------------------------------------------------------------===//
487 // Simple SCEV method implementations
488 //===----------------------------------------------------------------------===//
490 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
491 /// specified signed integer value and return a SCEV for the constant.
492 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
495 C = Constant::getNullValue(Ty);
496 else if (Ty->isFloatingPoint())
497 C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
498 APFloat::IEEEdouble, Val));
500 C = ConstantInt::get(Ty, Val);
501 return getUnknown(C);
504 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
505 /// input value to the specified type. If the type must be extended, it is zero
507 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty,
508 ScalarEvolution &SE) {
509 const Type *SrcTy = V->getType();
510 assert(SrcTy->isInteger() && Ty->isInteger() &&
511 "Cannot truncate or zero extend with non-integer arguments!");
512 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
513 return V; // No conversion
514 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
515 return SE.getTruncateExpr(V, Ty);
516 return SE.getZeroExtendExpr(V, Ty);
519 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
521 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
522 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
523 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
525 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType())));
528 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
529 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
530 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
531 return getUnknown(ConstantExpr::getNot(VC->getValue()));
533 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType()));
534 return getMinusSCEV(AllOnes, V);
537 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
539 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
540 const SCEVHandle &RHS) {
542 return getAddExpr(LHS, getNegativeSCEV(RHS));
546 /// BinomialCoefficient - Compute BC(It, K). The result is of the same type as
547 /// It. Assume, K > 0.
548 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
549 ScalarEvolution &SE) {
550 // We are using the following formula for BC(It, K):
552 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
554 // Suppose, W is the bitwidth of It (and of the return value as well). We
555 // must be prepared for overflow. Hence, we must assure that the result of
556 // our computation is equal to the accurate one modulo 2^W. Unfortunately,
557 // division isn't safe in modular arithmetic. This means we must perform the
558 // whole computation accurately and then truncate the result to W bits.
560 // The dividend of the formula is a multiplication of K integers of bitwidth
561 // W. K*W bits suffice to compute it accurately.
563 // FIXME: We assume the divisor can be accurately computed using 16-bit
564 // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In
565 // future we may use APInt to use the minimum number of bits necessary to
566 // compute it accurately.
568 // It is safe to use unsigned division here: the dividend is nonnegative and
569 // the divisor is positive.
571 // Handle the simplest case efficiently.
575 assert(K < 9 && "We cannot handle such long AddRecs yet.");
577 // FIXME: A temporary hack to remove in future. Arbitrary precision integers
578 // aren't supported by the code generator yet. For the dividend, the bitwidth
579 // we use is the smallest power of 2 greater or equal to K*W and less or equal
580 // to 64. Note that setting the upper bound for bitwidth may still lead to
581 // miscompilation in some cases.
582 unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth());
583 if (DividendBits > 64)
585 #if 0 // Waiting for the APInt support in the code generator...
586 unsigned DividendBits = K * It->getBitWidth();
589 const IntegerType *DividendTy = IntegerType::get(DividendBits);
590 const SCEVHandle ExIt = SE.getZeroExtendExpr(It, DividendTy);
592 // The final number of bits we need to perform the division is the maximum of
593 // dividend and divisor bitwidths.
594 const IntegerType *DivisionTy =
595 IntegerType::get(std::max(DividendBits, 16U));
597 // Compute K! We know K >= 2 here.
599 for (unsigned i = 3; i <= K; ++i)
601 APInt Divisor(DivisionTy->getBitWidth(), F);
603 // Handle this case efficiently, it is common to have constant iteration
604 // counts while computing loop exit values.
605 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) {
606 const APInt& N = SC->getValue()->getValue();
607 APInt Dividend(N.getBitWidth(), 1);
610 if (DividendTy != DivisionTy)
611 Dividend = Dividend.zext(DivisionTy->getBitWidth());
612 return SE.getConstant(Dividend.udiv(Divisor).trunc(It->getBitWidth()));
615 SCEVHandle Dividend = ExIt;
616 for (unsigned i = 1; i != K; ++i)
618 SE.getMulExpr(Dividend,
619 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy)));
620 if (DividendTy != DivisionTy)
621 Dividend = SE.getZeroExtendExpr(Dividend, DivisionTy);
623 SE.getTruncateExpr(SE.getUDivExpr(Dividend, SE.getConstant(Divisor)),
627 /// evaluateAtIteration - Return the value of this chain of recurrences at
628 /// the specified iteration number. We can evaluate this recurrence by
629 /// multiplying each element in the chain by the binomial coefficient
630 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
632 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
634 /// where BC(It, k) stands for binomial coefficient.
636 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
637 ScalarEvolution &SE) const {
638 SCEVHandle Result = getStart();
639 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
640 // The computation is correct in the face of overflow provided that the
641 // multiplication is performed _after_ the evaluation of the binomial
643 SCEVHandle Val = SE.getMulExpr(getOperand(i),
644 BinomialCoefficient(It, i, SE));
645 Result = SE.getAddExpr(Result, Val);
650 //===----------------------------------------------------------------------===//
651 // SCEV Expression folder implementations
652 //===----------------------------------------------------------------------===//
654 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
655 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
657 ConstantExpr::getTrunc(SC->getValue(), Ty));
659 // If the input value is a chrec scev made out of constants, truncate
660 // all of the constants.
661 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
662 std::vector<SCEVHandle> Operands;
663 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
664 // FIXME: This should allow truncation of other expression types!
665 if (isa<SCEVConstant>(AddRec->getOperand(i)))
666 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
669 if (Operands.size() == AddRec->getNumOperands())
670 return getAddRecExpr(Operands, AddRec->getLoop());
673 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
674 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
678 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) {
679 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
681 ConstantExpr::getZExt(SC->getValue(), Ty));
683 // FIXME: If the input value is a chrec scev, and we can prove that the value
684 // did not overflow the old, smaller, value, we can zero extend all of the
685 // operands (often constants). This would allow analysis of something like
686 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
688 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
689 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
693 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
694 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
696 ConstantExpr::getSExt(SC->getValue(), Ty));
698 // FIXME: If the input value is a chrec scev, and we can prove that the value
699 // did not overflow the old, smaller, value, we can sign extend all of the
700 // operands (often constants). This would allow analysis of something like
701 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
703 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
704 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
708 // get - Get a canonical add expression, or something simpler if possible.
709 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
710 assert(!Ops.empty() && "Cannot get empty add!");
711 if (Ops.size() == 1) return Ops[0];
713 // Sort by complexity, this groups all similar expression types together.
714 GroupByComplexity(Ops);
716 // If there are any constants, fold them together.
718 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
720 assert(Idx < Ops.size());
721 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
722 // We found two constants, fold them together!
723 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
724 RHSC->getValue()->getValue());
725 Ops[0] = getConstant(Fold);
726 Ops.erase(Ops.begin()+1); // Erase the folded element
727 if (Ops.size() == 1) return Ops[0];
728 LHSC = cast<SCEVConstant>(Ops[0]);
731 // If we are left with a constant zero being added, strip it off.
732 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
733 Ops.erase(Ops.begin());
738 if (Ops.size() == 1) return Ops[0];
740 // Okay, check to see if the same value occurs in the operand list twice. If
741 // so, merge them together into an multiply expression. Since we sorted the
742 // list, these values are required to be adjacent.
743 const Type *Ty = Ops[0]->getType();
744 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
745 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
746 // Found a match, merge the two values into a multiply, and add any
747 // remaining values to the result.
748 SCEVHandle Two = getIntegerSCEV(2, Ty);
749 SCEVHandle Mul = getMulExpr(Ops[i], Two);
752 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
754 return getAddExpr(Ops);
757 // Now we know the first non-constant operand. Skip past any cast SCEVs.
758 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
761 // If there are add operands they would be next.
762 if (Idx < Ops.size()) {
763 bool DeletedAdd = false;
764 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
765 // If we have an add, expand the add operands onto the end of the operands
767 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
768 Ops.erase(Ops.begin()+Idx);
772 // If we deleted at least one add, we added operands to the end of the list,
773 // and they are not necessarily sorted. Recurse to resort and resimplify
774 // any operands we just aquired.
776 return getAddExpr(Ops);
779 // Skip over the add expression until we get to a multiply.
780 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
783 // If we are adding something to a multiply expression, make sure the
784 // something is not already an operand of the multiply. If so, merge it into
786 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
787 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
788 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
789 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
790 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
791 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
792 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
793 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
794 if (Mul->getNumOperands() != 2) {
795 // If the multiply has more than two operands, we must get the
797 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
798 MulOps.erase(MulOps.begin()+MulOp);
799 InnerMul = getMulExpr(MulOps);
801 SCEVHandle One = getIntegerSCEV(1, Ty);
802 SCEVHandle AddOne = getAddExpr(InnerMul, One);
803 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
804 if (Ops.size() == 2) return OuterMul;
806 Ops.erase(Ops.begin()+AddOp);
807 Ops.erase(Ops.begin()+Idx-1);
809 Ops.erase(Ops.begin()+Idx);
810 Ops.erase(Ops.begin()+AddOp-1);
812 Ops.push_back(OuterMul);
813 return getAddExpr(Ops);
816 // Check this multiply against other multiplies being added together.
817 for (unsigned OtherMulIdx = Idx+1;
818 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
820 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
821 // If MulOp occurs in OtherMul, we can fold the two multiplies
823 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
824 OMulOp != e; ++OMulOp)
825 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
826 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
827 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
828 if (Mul->getNumOperands() != 2) {
829 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
830 MulOps.erase(MulOps.begin()+MulOp);
831 InnerMul1 = getMulExpr(MulOps);
833 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
834 if (OtherMul->getNumOperands() != 2) {
835 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
837 MulOps.erase(MulOps.begin()+OMulOp);
838 InnerMul2 = getMulExpr(MulOps);
840 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
841 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
842 if (Ops.size() == 2) return OuterMul;
843 Ops.erase(Ops.begin()+Idx);
844 Ops.erase(Ops.begin()+OtherMulIdx-1);
845 Ops.push_back(OuterMul);
846 return getAddExpr(Ops);
852 // If there are any add recurrences in the operands list, see if any other
853 // added values are loop invariant. If so, we can fold them into the
855 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
858 // Scan over all recurrences, trying to fold loop invariants into them.
859 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
860 // Scan all of the other operands to this add and add them to the vector if
861 // they are loop invariant w.r.t. the recurrence.
862 std::vector<SCEVHandle> LIOps;
863 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
864 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
865 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
866 LIOps.push_back(Ops[i]);
867 Ops.erase(Ops.begin()+i);
871 // If we found some loop invariants, fold them into the recurrence.
872 if (!LIOps.empty()) {
873 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
874 LIOps.push_back(AddRec->getStart());
876 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
877 AddRecOps[0] = getAddExpr(LIOps);
879 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
880 // If all of the other operands were loop invariant, we are done.
881 if (Ops.size() == 1) return NewRec;
883 // Otherwise, add the folded AddRec by the non-liv parts.
884 for (unsigned i = 0;; ++i)
885 if (Ops[i] == AddRec) {
889 return getAddExpr(Ops);
892 // Okay, if there weren't any loop invariants to be folded, check to see if
893 // there are multiple AddRec's with the same loop induction variable being
894 // added together. If so, we can fold them.
895 for (unsigned OtherIdx = Idx+1;
896 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
897 if (OtherIdx != Idx) {
898 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
899 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
900 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
901 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
902 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
903 if (i >= NewOps.size()) {
904 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
905 OtherAddRec->op_end());
908 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
910 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
912 if (Ops.size() == 2) return NewAddRec;
914 Ops.erase(Ops.begin()+Idx);
915 Ops.erase(Ops.begin()+OtherIdx-1);
916 Ops.push_back(NewAddRec);
917 return getAddExpr(Ops);
921 // Otherwise couldn't fold anything into this recurrence. Move onto the
925 // Okay, it looks like we really DO need an add expr. Check to see if we
926 // already have one, otherwise create a new one.
927 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
928 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
930 if (Result == 0) Result = new SCEVAddExpr(Ops);
935 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
936 assert(!Ops.empty() && "Cannot get empty mul!");
938 // Sort by complexity, this groups all similar expression types together.
939 GroupByComplexity(Ops);
941 // If there are any constants, fold them together.
943 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
945 // C1*(C2+V) -> C1*C2 + C1*V
947 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
948 if (Add->getNumOperands() == 2 &&
949 isa<SCEVConstant>(Add->getOperand(0)))
950 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
951 getMulExpr(LHSC, Add->getOperand(1)));
955 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
956 // We found two constants, fold them together!
957 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
958 RHSC->getValue()->getValue());
959 Ops[0] = getConstant(Fold);
960 Ops.erase(Ops.begin()+1); // Erase the folded element
961 if (Ops.size() == 1) return Ops[0];
962 LHSC = cast<SCEVConstant>(Ops[0]);
965 // If we are left with a constant one being multiplied, strip it off.
966 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
967 Ops.erase(Ops.begin());
969 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
970 // If we have a multiply of zero, it will always be zero.
975 // Skip over the add expression until we get to a multiply.
976 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
982 // If there are mul operands inline them all into this expression.
983 if (Idx < Ops.size()) {
984 bool DeletedMul = false;
985 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
986 // If we have an mul, expand the mul operands onto the end of the operands
988 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
989 Ops.erase(Ops.begin()+Idx);
993 // If we deleted at least one mul, we added operands to the end of the list,
994 // and they are not necessarily sorted. Recurse to resort and resimplify
995 // any operands we just aquired.
997 return getMulExpr(Ops);
1000 // If there are any add recurrences in the operands list, see if any other
1001 // added values are loop invariant. If so, we can fold them into the
1003 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1006 // Scan over all recurrences, trying to fold loop invariants into them.
1007 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1008 // Scan all of the other operands to this mul and add them to the vector if
1009 // they are loop invariant w.r.t. the recurrence.
1010 std::vector<SCEVHandle> LIOps;
1011 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1012 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1013 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1014 LIOps.push_back(Ops[i]);
1015 Ops.erase(Ops.begin()+i);
1019 // If we found some loop invariants, fold them into the recurrence.
1020 if (!LIOps.empty()) {
1021 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
1022 std::vector<SCEVHandle> NewOps;
1023 NewOps.reserve(AddRec->getNumOperands());
1024 if (LIOps.size() == 1) {
1025 SCEV *Scale = LIOps[0];
1026 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1027 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1029 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1030 std::vector<SCEVHandle> MulOps(LIOps);
1031 MulOps.push_back(AddRec->getOperand(i));
1032 NewOps.push_back(getMulExpr(MulOps));
1036 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1038 // If all of the other operands were loop invariant, we are done.
1039 if (Ops.size() == 1) return NewRec;
1041 // Otherwise, multiply the folded AddRec by the non-liv parts.
1042 for (unsigned i = 0;; ++i)
1043 if (Ops[i] == AddRec) {
1047 return getMulExpr(Ops);
1050 // Okay, if there weren't any loop invariants to be folded, check to see if
1051 // there are multiple AddRec's with the same loop induction variable being
1052 // multiplied together. If so, we can fold them.
1053 for (unsigned OtherIdx = Idx+1;
1054 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1055 if (OtherIdx != Idx) {
1056 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1057 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1058 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1059 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1060 SCEVHandle NewStart = getMulExpr(F->getStart(),
1062 SCEVHandle B = F->getStepRecurrence(*this);
1063 SCEVHandle D = G->getStepRecurrence(*this);
1064 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1067 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1069 if (Ops.size() == 2) return NewAddRec;
1071 Ops.erase(Ops.begin()+Idx);
1072 Ops.erase(Ops.begin()+OtherIdx-1);
1073 Ops.push_back(NewAddRec);
1074 return getMulExpr(Ops);
1078 // Otherwise couldn't fold anything into this recurrence. Move onto the
1082 // Okay, it looks like we really DO need an mul expr. Check to see if we
1083 // already have one, otherwise create a new one.
1084 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1085 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1088 Result = new SCEVMulExpr(Ops);
1092 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1093 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1094 if (RHSC->getValue()->equalsInt(1))
1095 return LHS; // X udiv 1 --> x
1097 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1098 Constant *LHSCV = LHSC->getValue();
1099 Constant *RHSCV = RHSC->getValue();
1100 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1104 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1106 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1107 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1112 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1113 /// specified loop. Simplify the expression as much as possible.
1114 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1115 const SCEVHandle &Step, const Loop *L) {
1116 std::vector<SCEVHandle> Operands;
1117 Operands.push_back(Start);
1118 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1119 if (StepChrec->getLoop() == L) {
1120 Operands.insert(Operands.end(), StepChrec->op_begin(),
1121 StepChrec->op_end());
1122 return getAddRecExpr(Operands, L);
1125 Operands.push_back(Step);
1126 return getAddRecExpr(Operands, L);
1129 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1130 /// specified loop. Simplify the expression as much as possible.
1131 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1133 if (Operands.size() == 1) return Operands[0];
1135 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1136 if (StepC->getValue()->isZero()) {
1137 Operands.pop_back();
1138 return getAddRecExpr(Operands, L); // { X,+,0 } --> X
1141 SCEVAddRecExpr *&Result =
1142 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1144 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1148 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1149 const SCEVHandle &RHS) {
1150 std::vector<SCEVHandle> Ops;
1153 return getSMaxExpr(Ops);
1156 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1157 assert(!Ops.empty() && "Cannot get empty smax!");
1158 if (Ops.size() == 1) return Ops[0];
1160 // Sort by complexity, this groups all similar expression types together.
1161 GroupByComplexity(Ops);
1163 // If there are any constants, fold them together.
1165 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1167 assert(Idx < Ops.size());
1168 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1169 // We found two constants, fold them together!
1170 ConstantInt *Fold = ConstantInt::get(
1171 APIntOps::smax(LHSC->getValue()->getValue(),
1172 RHSC->getValue()->getValue()));
1173 Ops[0] = getConstant(Fold);
1174 Ops.erase(Ops.begin()+1); // Erase the folded element
1175 if (Ops.size() == 1) return Ops[0];
1176 LHSC = cast<SCEVConstant>(Ops[0]);
1179 // If we are left with a constant -inf, strip it off.
1180 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1181 Ops.erase(Ops.begin());
1186 if (Ops.size() == 1) return Ops[0];
1188 // Find the first SMax
1189 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1192 // Check to see if one of the operands is an SMax. If so, expand its operands
1193 // onto our operand list, and recurse to simplify.
1194 if (Idx < Ops.size()) {
1195 bool DeletedSMax = false;
1196 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1197 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1198 Ops.erase(Ops.begin()+Idx);
1203 return getSMaxExpr(Ops);
1206 // Okay, check to see if the same value occurs in the operand list twice. If
1207 // so, delete one. Since we sorted the list, these values are required to
1209 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1210 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1211 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1215 if (Ops.size() == 1) return Ops[0];
1217 assert(!Ops.empty() && "Reduced smax down to nothing!");
1219 // Okay, it looks like we really DO need an smax expr. Check to see if we
1220 // already have one, otherwise create a new one.
1221 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1222 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1224 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1228 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1229 const SCEVHandle &RHS) {
1230 std::vector<SCEVHandle> Ops;
1233 return getUMaxExpr(Ops);
1236 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1237 assert(!Ops.empty() && "Cannot get empty umax!");
1238 if (Ops.size() == 1) return Ops[0];
1240 // Sort by complexity, this groups all similar expression types together.
1241 GroupByComplexity(Ops);
1243 // If there are any constants, fold them together.
1245 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1247 assert(Idx < Ops.size());
1248 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1249 // We found two constants, fold them together!
1250 ConstantInt *Fold = ConstantInt::get(
1251 APIntOps::umax(LHSC->getValue()->getValue(),
1252 RHSC->getValue()->getValue()));
1253 Ops[0] = getConstant(Fold);
1254 Ops.erase(Ops.begin()+1); // Erase the folded element
1255 if (Ops.size() == 1) return Ops[0];
1256 LHSC = cast<SCEVConstant>(Ops[0]);
1259 // If we are left with a constant zero, strip it off.
1260 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1261 Ops.erase(Ops.begin());
1266 if (Ops.size() == 1) return Ops[0];
1268 // Find the first UMax
1269 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1272 // Check to see if one of the operands is a UMax. If so, expand its operands
1273 // onto our operand list, and recurse to simplify.
1274 if (Idx < Ops.size()) {
1275 bool DeletedUMax = false;
1276 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1277 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1278 Ops.erase(Ops.begin()+Idx);
1283 return getUMaxExpr(Ops);
1286 // Okay, check to see if the same value occurs in the operand list twice. If
1287 // so, delete one. Since we sorted the list, these values are required to
1289 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1290 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1291 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1295 if (Ops.size() == 1) return Ops[0];
1297 assert(!Ops.empty() && "Reduced umax down to nothing!");
1299 // Okay, it looks like we really DO need a umax expr. Check to see if we
1300 // already have one, otherwise create a new one.
1301 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1302 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1304 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1308 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1309 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1310 return getConstant(CI);
1311 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1312 if (Result == 0) Result = new SCEVUnknown(V);
1317 //===----------------------------------------------------------------------===//
1318 // ScalarEvolutionsImpl Definition and Implementation
1319 //===----------------------------------------------------------------------===//
1321 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1325 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1326 /// SE - A reference to the public ScalarEvolution object.
1327 ScalarEvolution &SE;
1329 /// F - The function we are analyzing.
1333 /// LI - The loop information for the function we are currently analyzing.
1337 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1339 SCEVHandle UnknownValue;
1341 /// Scalars - This is a cache of the scalars we have analyzed so far.
1343 std::map<Value*, SCEVHandle> Scalars;
1345 /// IterationCounts - Cache the iteration count of the loops for this
1346 /// function as they are computed.
1347 std::map<const Loop*, SCEVHandle> IterationCounts;
1349 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1350 /// the PHI instructions that we attempt to compute constant evolutions for.
1351 /// This allows us to avoid potentially expensive recomputation of these
1352 /// properties. An instruction maps to null if we are unable to compute its
1354 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1357 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li)
1358 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1360 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1361 /// expression and create a new one.
1362 SCEVHandle getSCEV(Value *V);
1364 /// hasSCEV - Return true if the SCEV for this value has already been
1366 bool hasSCEV(Value *V) const {
1367 return Scalars.count(V);
1370 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1371 /// the specified value.
1372 void setSCEV(Value *V, const SCEVHandle &H) {
1373 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1374 assert(isNew && "This entry already existed!");
1378 /// getSCEVAtScope - Compute the value of the specified expression within
1379 /// the indicated loop (which may be null to indicate in no loop). If the
1380 /// expression cannot be evaluated, return UnknownValue itself.
1381 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1384 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1385 /// an analyzable loop-invariant iteration count.
1386 bool hasLoopInvariantIterationCount(const Loop *L);
1388 /// getIterationCount - If the specified loop has a predictable iteration
1389 /// count, return it. Note that it is not valid to call this method on a
1390 /// loop without a loop-invariant iteration count.
1391 SCEVHandle getIterationCount(const Loop *L);
1393 /// deleteValueFromRecords - This method should be called by the
1394 /// client before it removes a value from the program, to make sure
1395 /// that no dangling references are left around.
1396 void deleteValueFromRecords(Value *V);
1399 /// createSCEV - We know that there is no SCEV for the specified value.
1400 /// Analyze the expression.
1401 SCEVHandle createSCEV(Value *V);
1403 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1405 SCEVHandle createNodeForPHI(PHINode *PN);
1407 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1408 /// for the specified instruction and replaces any references to the
1409 /// symbolic value SymName with the specified value. This is used during
1411 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1412 const SCEVHandle &SymName,
1413 const SCEVHandle &NewVal);
1415 /// ComputeIterationCount - Compute the number of times the specified loop
1417 SCEVHandle ComputeIterationCount(const Loop *L);
1419 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1420 /// 'icmp op load X, cst', try to see if we can compute the trip count.
1421 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1424 ICmpInst::Predicate p);
1426 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1427 /// constant number of times (the condition evolves only from constants),
1428 /// try to evaluate a few iterations of the loop until we get the exit
1429 /// condition gets a value of ExitWhen (true or false). If we cannot
1430 /// evaluate the trip count of the loop, return UnknownValue.
1431 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1434 /// HowFarToZero - Return the number of times a backedge comparing the
1435 /// specified value to zero will execute. If not computable, return
1437 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1439 /// HowFarToNonZero - Return the number of times a backedge checking the
1440 /// specified value for nonzero will execute. If not computable, return
1442 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1444 /// HowManyLessThans - Return the number of times a backedge containing the
1445 /// specified less-than comparison will execute. If not computable, return
1446 /// UnknownValue. isSigned specifies whether the less-than is signed.
1447 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1450 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1451 /// in the header of its containing loop, we know the loop executes a
1452 /// constant number of times, and the PHI node is just a recurrence
1453 /// involving constants, fold it.
1454 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1459 //===----------------------------------------------------------------------===//
1460 // Basic SCEV Analysis and PHI Idiom Recognition Code
1463 /// deleteValueFromRecords - This method should be called by the
1464 /// client before it removes an instruction from the program, to make sure
1465 /// that no dangling references are left around.
1466 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1467 SmallVector<Value *, 16> Worklist;
1469 if (Scalars.erase(V)) {
1470 if (PHINode *PN = dyn_cast<PHINode>(V))
1471 ConstantEvolutionLoopExitValue.erase(PN);
1472 Worklist.push_back(V);
1475 while (!Worklist.empty()) {
1476 Value *VV = Worklist.back();
1477 Worklist.pop_back();
1479 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1481 Instruction *Inst = cast<Instruction>(*UI);
1482 if (Scalars.erase(Inst)) {
1483 if (PHINode *PN = dyn_cast<PHINode>(VV))
1484 ConstantEvolutionLoopExitValue.erase(PN);
1485 Worklist.push_back(Inst);
1492 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1493 /// expression and create a new one.
1494 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1495 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1497 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1498 if (I != Scalars.end()) return I->second;
1499 SCEVHandle S = createSCEV(V);
1500 Scalars.insert(std::make_pair(V, S));
1504 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1505 /// the specified instruction and replaces any references to the symbolic value
1506 /// SymName with the specified value. This is used during PHI resolution.
1507 void ScalarEvolutionsImpl::
1508 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1509 const SCEVHandle &NewVal) {
1510 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1511 if (SI == Scalars.end()) return;
1514 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
1515 if (NV == SI->second) return; // No change.
1517 SI->second = NV; // Update the scalars map!
1519 // Any instruction values that use this instruction might also need to be
1521 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1523 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1526 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1527 /// a loop header, making it a potential recurrence, or it doesn't.
1529 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1530 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1531 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1532 if (L->getHeader() == PN->getParent()) {
1533 // If it lives in the loop header, it has two incoming values, one
1534 // from outside the loop, and one from inside.
1535 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1536 unsigned BackEdge = IncomingEdge^1;
1538 // While we are analyzing this PHI node, handle its value symbolically.
1539 SCEVHandle SymbolicName = SE.getUnknown(PN);
1540 assert(Scalars.find(PN) == Scalars.end() &&
1541 "PHI node already processed?");
1542 Scalars.insert(std::make_pair(PN, SymbolicName));
1544 // Using this symbolic name for the PHI, analyze the value coming around
1546 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1548 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1549 // has a special value for the first iteration of the loop.
1551 // If the value coming around the backedge is an add with the symbolic
1552 // value we just inserted, then we found a simple induction variable!
1553 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1554 // If there is a single occurrence of the symbolic value, replace it
1555 // with a recurrence.
1556 unsigned FoundIndex = Add->getNumOperands();
1557 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1558 if (Add->getOperand(i) == SymbolicName)
1559 if (FoundIndex == e) {
1564 if (FoundIndex != Add->getNumOperands()) {
1565 // Create an add with everything but the specified operand.
1566 std::vector<SCEVHandle> Ops;
1567 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1568 if (i != FoundIndex)
1569 Ops.push_back(Add->getOperand(i));
1570 SCEVHandle Accum = SE.getAddExpr(Ops);
1572 // This is not a valid addrec if the step amount is varying each
1573 // loop iteration, but is not itself an addrec in this loop.
1574 if (Accum->isLoopInvariant(L) ||
1575 (isa<SCEVAddRecExpr>(Accum) &&
1576 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1577 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1578 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L);
1580 // Okay, for the entire analysis of this edge we assumed the PHI
1581 // to be symbolic. We now need to go back and update all of the
1582 // entries for the scalars that use the PHI (except for the PHI
1583 // itself) to use the new analyzed value instead of the "symbolic"
1585 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1589 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1590 // Otherwise, this could be a loop like this:
1591 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1592 // In this case, j = {1,+,1} and BEValue is j.
1593 // Because the other in-value of i (0) fits the evolution of BEValue
1594 // i really is an addrec evolution.
1595 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1596 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1598 // If StartVal = j.start - j.stride, we can use StartVal as the
1599 // initial step of the addrec evolution.
1600 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
1601 AddRec->getOperand(1))) {
1602 SCEVHandle PHISCEV =
1603 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1605 // Okay, for the entire analysis of this edge we assumed the PHI
1606 // to be symbolic. We now need to go back and update all of the
1607 // entries for the scalars that use the PHI (except for the PHI
1608 // itself) to use the new analyzed value instead of the "symbolic"
1610 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1616 return SymbolicName;
1619 // If it's not a loop phi, we can't handle it yet.
1620 return SE.getUnknown(PN);
1623 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1624 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1625 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1626 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1627 static uint32_t GetMinTrailingZeros(SCEVHandle S) {
1628 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1629 return C->getValue()->getValue().countTrailingZeros();
1631 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1632 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
1634 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1635 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1636 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1639 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1640 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1641 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1644 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1645 // The result is the min of all operands results.
1646 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1647 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1648 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1652 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1653 // The result is the sum of all operands results.
1654 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
1655 uint32_t BitWidth = M->getBitWidth();
1656 for (unsigned i = 1, e = M->getNumOperands();
1657 SumOpRes != BitWidth && i != e; ++i)
1658 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
1663 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1664 // The result is the min of all operands results.
1665 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1666 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1667 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1671 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1672 // The result is the min of all operands results.
1673 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1674 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1675 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1679 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1680 // The result is the min of all operands results.
1681 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1682 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1683 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1687 // SCEVUDivExpr, SCEVUnknown
1691 /// createSCEV - We know that there is no SCEV for the specified value.
1692 /// Analyze the expression.
1694 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1695 if (!isa<IntegerType>(V->getType()))
1696 return SE.getUnknown(V);
1698 if (Instruction *I = dyn_cast<Instruction>(V)) {
1699 switch (I->getOpcode()) {
1700 case Instruction::Add:
1701 return SE.getAddExpr(getSCEV(I->getOperand(0)),
1702 getSCEV(I->getOperand(1)));
1703 case Instruction::Mul:
1704 return SE.getMulExpr(getSCEV(I->getOperand(0)),
1705 getSCEV(I->getOperand(1)));
1706 case Instruction::UDiv:
1707 return SE.getUDivExpr(getSCEV(I->getOperand(0)),
1708 getSCEV(I->getOperand(1)));
1709 case Instruction::Sub:
1710 return SE.getMinusSCEV(getSCEV(I->getOperand(0)),
1711 getSCEV(I->getOperand(1)));
1712 case Instruction::Or:
1713 // If the RHS of the Or is a constant, we may have something like:
1714 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1715 // optimizations will transparently handle this case.
1717 // In order for this transformation to be safe, the LHS must be of the
1718 // form X*(2^n) and the Or constant must be less than 2^n.
1719 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1720 SCEVHandle LHS = getSCEV(I->getOperand(0));
1721 const APInt &CIVal = CI->getValue();
1722 if (GetMinTrailingZeros(LHS) >=
1723 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1724 return SE.getAddExpr(LHS, getSCEV(I->getOperand(1)));
1727 case Instruction::Xor:
1728 // If the RHS of the xor is a signbit, then this is just an add.
1729 // Instcombine turns add of signbit into xor as a strength reduction step.
1730 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1731 if (CI->getValue().isSignBit())
1732 return SE.getAddExpr(getSCEV(I->getOperand(0)),
1733 getSCEV(I->getOperand(1)));
1734 else if (CI->isAllOnesValue())
1735 return SE.getNotSCEV(getSCEV(I->getOperand(0)));
1739 case Instruction::Shl:
1740 // Turn shift left of a constant amount into a multiply.
1741 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1742 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1743 Constant *X = ConstantInt::get(
1744 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1745 return SE.getMulExpr(getSCEV(I->getOperand(0)), getSCEV(X));
1749 case Instruction::Trunc:
1750 return SE.getTruncateExpr(getSCEV(I->getOperand(0)), I->getType());
1752 case Instruction::ZExt:
1753 return SE.getZeroExtendExpr(getSCEV(I->getOperand(0)), I->getType());
1755 case Instruction::SExt:
1756 return SE.getSignExtendExpr(getSCEV(I->getOperand(0)), I->getType());
1758 case Instruction::BitCast:
1759 // BitCasts are no-op casts so we just eliminate the cast.
1760 if (I->getType()->isInteger() &&
1761 I->getOperand(0)->getType()->isInteger())
1762 return getSCEV(I->getOperand(0));
1765 case Instruction::PHI:
1766 return createNodeForPHI(cast<PHINode>(I));
1768 case Instruction::Select:
1769 // This could be a smax or umax that was lowered earlier.
1770 // Try to recover it.
1771 if (ICmpInst *ICI = dyn_cast<ICmpInst>(I->getOperand(0))) {
1772 Value *LHS = ICI->getOperand(0);
1773 Value *RHS = ICI->getOperand(1);
1774 switch (ICI->getPredicate()) {
1775 case ICmpInst::ICMP_SLT:
1776 case ICmpInst::ICMP_SLE:
1777 std::swap(LHS, RHS);
1779 case ICmpInst::ICMP_SGT:
1780 case ICmpInst::ICMP_SGE:
1781 if (LHS == I->getOperand(1) && RHS == I->getOperand(2))
1782 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1783 else if (LHS == I->getOperand(2) && RHS == I->getOperand(1))
1784 // -smax(-x, -y) == smin(x, y).
1785 return SE.getNegativeSCEV(SE.getSMaxExpr(
1786 SE.getNegativeSCEV(getSCEV(LHS)),
1787 SE.getNegativeSCEV(getSCEV(RHS))));
1789 case ICmpInst::ICMP_ULT:
1790 case ICmpInst::ICMP_ULE:
1791 std::swap(LHS, RHS);
1793 case ICmpInst::ICMP_UGT:
1794 case ICmpInst::ICMP_UGE:
1795 if (LHS == I->getOperand(1) && RHS == I->getOperand(2))
1796 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
1797 else if (LHS == I->getOperand(2) && RHS == I->getOperand(1))
1798 // ~umax(~x, ~y) == umin(x, y)
1799 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
1800 SE.getNotSCEV(getSCEV(RHS))));
1807 default: // We cannot analyze this expression.
1812 return SE.getUnknown(V);
1817 //===----------------------------------------------------------------------===//
1818 // Iteration Count Computation Code
1821 /// getIterationCount - If the specified loop has a predictable iteration
1822 /// count, return it. Note that it is not valid to call this method on a
1823 /// loop without a loop-invariant iteration count.
1824 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1825 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1826 if (I == IterationCounts.end()) {
1827 SCEVHandle ItCount = ComputeIterationCount(L);
1828 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1829 if (ItCount != UnknownValue) {
1830 assert(ItCount->isLoopInvariant(L) &&
1831 "Computed trip count isn't loop invariant for loop!");
1832 ++NumTripCountsComputed;
1833 } else if (isa<PHINode>(L->getHeader()->begin())) {
1834 // Only count loops that have phi nodes as not being computable.
1835 ++NumTripCountsNotComputed;
1841 /// ComputeIterationCount - Compute the number of times the specified loop
1843 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1844 // If the loop has a non-one exit block count, we can't analyze it.
1845 SmallVector<BasicBlock*, 8> ExitBlocks;
1846 L->getExitBlocks(ExitBlocks);
1847 if (ExitBlocks.size() != 1) return UnknownValue;
1849 // Okay, there is one exit block. Try to find the condition that causes the
1850 // loop to be exited.
1851 BasicBlock *ExitBlock = ExitBlocks[0];
1853 BasicBlock *ExitingBlock = 0;
1854 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1856 if (L->contains(*PI)) {
1857 if (ExitingBlock == 0)
1860 return UnknownValue; // More than one block exiting!
1862 assert(ExitingBlock && "No exits from loop, something is broken!");
1864 // Okay, we've computed the exiting block. See what condition causes us to
1867 // FIXME: we should be able to handle switch instructions (with a single exit)
1868 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1869 if (ExitBr == 0) return UnknownValue;
1870 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1872 // At this point, we know we have a conditional branch that determines whether
1873 // the loop is exited. However, we don't know if the branch is executed each
1874 // time through the loop. If not, then the execution count of the branch will
1875 // not be equal to the trip count of the loop.
1877 // Currently we check for this by checking to see if the Exit branch goes to
1878 // the loop header. If so, we know it will always execute the same number of
1879 // times as the loop. We also handle the case where the exit block *is* the
1880 // loop header. This is common for un-rotated loops. More extensive analysis
1881 // could be done to handle more cases here.
1882 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1883 ExitBr->getSuccessor(1) != L->getHeader() &&
1884 ExitBr->getParent() != L->getHeader())
1885 return UnknownValue;
1887 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1889 // If its not an integer comparison then compute it the hard way.
1890 // Note that ICmpInst deals with pointer comparisons too so we must check
1891 // the type of the operand.
1892 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1893 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1894 ExitBr->getSuccessor(0) == ExitBlock);
1896 // If the condition was exit on true, convert the condition to exit on false
1897 ICmpInst::Predicate Cond;
1898 if (ExitBr->getSuccessor(1) == ExitBlock)
1899 Cond = ExitCond->getPredicate();
1901 Cond = ExitCond->getInversePredicate();
1903 // Handle common loops like: for (X = "string"; *X; ++X)
1904 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1905 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1907 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1908 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1911 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1912 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1914 // Try to evaluate any dependencies out of the loop.
1915 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1916 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1917 Tmp = getSCEVAtScope(RHS, L);
1918 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1920 // At this point, we would like to compute how many iterations of the
1921 // loop the predicate will return true for these inputs.
1922 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
1923 // If there is a loop-invariant, force it into the RHS.
1924 std::swap(LHS, RHS);
1925 Cond = ICmpInst::getSwappedPredicate(Cond);
1928 // FIXME: think about handling pointer comparisons! i.e.:
1929 // while (P != P+100) ++P;
1931 // If we have a comparison of a chrec against a constant, try to use value
1932 // ranges to answer this query.
1933 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1934 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1935 if (AddRec->getLoop() == L) {
1936 // Form the comparison range using the constant of the correct type so
1937 // that the ConstantRange class knows to do a signed or unsigned
1939 ConstantInt *CompVal = RHSC->getValue();
1940 const Type *RealTy = ExitCond->getOperand(0)->getType();
1941 CompVal = dyn_cast<ConstantInt>(
1942 ConstantExpr::getBitCast(CompVal, RealTy));
1944 // Form the constant range.
1945 ConstantRange CompRange(
1946 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
1948 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
1949 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1954 case ICmpInst::ICMP_NE: { // while (X != Y)
1955 // Convert to: while (X-Y != 0)
1956 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
1957 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1960 case ICmpInst::ICMP_EQ: {
1961 // Convert to: while (X-Y == 0) // while (X == Y)
1962 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
1963 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1966 case ICmpInst::ICMP_SLT: {
1967 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
1968 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1971 case ICmpInst::ICMP_SGT: {
1972 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS),
1973 SE.getNegativeSCEV(RHS), L, true);
1974 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1977 case ICmpInst::ICMP_ULT: {
1978 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
1979 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1982 case ICmpInst::ICMP_UGT: {
1983 SCEVHandle TC = HowManyLessThans(SE.getNegativeSCEV(LHS),
1984 SE.getNegativeSCEV(RHS), L, false);
1985 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1990 cerr << "ComputeIterationCount ";
1991 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1992 cerr << "[unsigned] ";
1994 << Instruction::getOpcodeName(Instruction::ICmp)
1995 << " " << *RHS << "\n";
1999 return ComputeIterationCountExhaustively(L, ExitCond,
2000 ExitBr->getSuccessor(0) == ExitBlock);
2003 static ConstantInt *
2004 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2005 ScalarEvolution &SE) {
2006 SCEVHandle InVal = SE.getConstant(C);
2007 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2008 assert(isa<SCEVConstant>(Val) &&
2009 "Evaluation of SCEV at constant didn't fold correctly?");
2010 return cast<SCEVConstant>(Val)->getValue();
2013 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2014 /// and a GEP expression (missing the pointer index) indexing into it, return
2015 /// the addressed element of the initializer or null if the index expression is
2018 GetAddressedElementFromGlobal(GlobalVariable *GV,
2019 const std::vector<ConstantInt*> &Indices) {
2020 Constant *Init = GV->getInitializer();
2021 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2022 uint64_t Idx = Indices[i]->getZExtValue();
2023 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2024 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2025 Init = cast<Constant>(CS->getOperand(Idx));
2026 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2027 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2028 Init = cast<Constant>(CA->getOperand(Idx));
2029 } else if (isa<ConstantAggregateZero>(Init)) {
2030 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2031 assert(Idx < STy->getNumElements() && "Bad struct index!");
2032 Init = Constant::getNullValue(STy->getElementType(Idx));
2033 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2034 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2035 Init = Constant::getNullValue(ATy->getElementType());
2037 assert(0 && "Unknown constant aggregate type!");
2041 return 0; // Unknown initializer type
2047 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
2048 /// 'icmp op load X, cst', try to se if we can compute the trip count.
2049 SCEVHandle ScalarEvolutionsImpl::
2050 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
2052 ICmpInst::Predicate predicate) {
2053 if (LI->isVolatile()) return UnknownValue;
2055 // Check to see if the loaded pointer is a getelementptr of a global.
2056 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2057 if (!GEP) return UnknownValue;
2059 // Make sure that it is really a constant global we are gepping, with an
2060 // initializer, and make sure the first IDX is really 0.
2061 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2062 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2063 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2064 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2065 return UnknownValue;
2067 // Okay, we allow one non-constant index into the GEP instruction.
2069 std::vector<ConstantInt*> Indexes;
2070 unsigned VarIdxNum = 0;
2071 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2072 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2073 Indexes.push_back(CI);
2074 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2075 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2076 VarIdx = GEP->getOperand(i);
2078 Indexes.push_back(0);
2081 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2082 // Check to see if X is a loop variant variable value now.
2083 SCEVHandle Idx = getSCEV(VarIdx);
2084 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2085 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2087 // We can only recognize very limited forms of loop index expressions, in
2088 // particular, only affine AddRec's like {C1,+,C2}.
2089 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2090 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2091 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2092 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2093 return UnknownValue;
2095 unsigned MaxSteps = MaxBruteForceIterations;
2096 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2097 ConstantInt *ItCst =
2098 ConstantInt::get(IdxExpr->getType(), IterationNum);
2099 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
2101 // Form the GEP offset.
2102 Indexes[VarIdxNum] = Val;
2104 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2105 if (Result == 0) break; // Cannot compute!
2107 // Evaluate the condition for this iteration.
2108 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2109 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2110 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2112 cerr << "\n***\n*** Computed loop count " << *ItCst
2113 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2116 ++NumArrayLenItCounts;
2117 return SE.getConstant(ItCst); // Found terminating iteration!
2120 return UnknownValue;
2124 /// CanConstantFold - Return true if we can constant fold an instruction of the
2125 /// specified type, assuming that all operands were constants.
2126 static bool CanConstantFold(const Instruction *I) {
2127 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2128 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2131 if (const CallInst *CI = dyn_cast<CallInst>(I))
2132 if (const Function *F = CI->getCalledFunction())
2133 return canConstantFoldCallTo(F);
2137 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2138 /// in the loop that V is derived from. We allow arbitrary operations along the
2139 /// way, but the operands of an operation must either be constants or a value
2140 /// derived from a constant PHI. If this expression does not fit with these
2141 /// constraints, return null.
2142 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2143 // If this is not an instruction, or if this is an instruction outside of the
2144 // loop, it can't be derived from a loop PHI.
2145 Instruction *I = dyn_cast<Instruction>(V);
2146 if (I == 0 || !L->contains(I->getParent())) return 0;
2148 if (PHINode *PN = dyn_cast<PHINode>(I))
2149 if (L->getHeader() == I->getParent())
2152 // We don't currently keep track of the control flow needed to evaluate
2153 // PHIs, so we cannot handle PHIs inside of loops.
2156 // If we won't be able to constant fold this expression even if the operands
2157 // are constants, return early.
2158 if (!CanConstantFold(I)) return 0;
2160 // Otherwise, we can evaluate this instruction if all of its operands are
2161 // constant or derived from a PHI node themselves.
2163 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2164 if (!(isa<Constant>(I->getOperand(Op)) ||
2165 isa<GlobalValue>(I->getOperand(Op)))) {
2166 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2167 if (P == 0) return 0; // Not evolving from PHI
2171 return 0; // Evolving from multiple different PHIs.
2174 // This is a expression evolving from a constant PHI!
2178 /// EvaluateExpression - Given an expression that passes the
2179 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2180 /// in the loop has the value PHIVal. If we can't fold this expression for some
2181 /// reason, return null.
2182 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2183 if (isa<PHINode>(V)) return PHIVal;
2184 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
2186 if (Constant *C = dyn_cast<Constant>(V)) return C;
2187 Instruction *I = cast<Instruction>(V);
2189 std::vector<Constant*> Operands;
2190 Operands.resize(I->getNumOperands());
2192 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2193 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2194 if (Operands[i] == 0) return 0;
2197 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2198 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2199 &Operands[0], Operands.size());
2201 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2202 &Operands[0], Operands.size());
2205 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2206 /// in the header of its containing loop, we know the loop executes a
2207 /// constant number of times, and the PHI node is just a recurrence
2208 /// involving constants, fold it.
2209 Constant *ScalarEvolutionsImpl::
2210 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
2211 std::map<PHINode*, Constant*>::iterator I =
2212 ConstantEvolutionLoopExitValue.find(PN);
2213 if (I != ConstantEvolutionLoopExitValue.end())
2216 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
2217 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2219 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2221 // Since the loop is canonicalized, the PHI node must have two entries. One
2222 // entry must be a constant (coming in from outside of the loop), and the
2223 // second must be derived from the same PHI.
2224 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2225 Constant *StartCST =
2226 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2228 return RetVal = 0; // Must be a constant.
2230 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2231 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2233 return RetVal = 0; // Not derived from same PHI.
2235 // Execute the loop symbolically to determine the exit value.
2236 if (Its.getActiveBits() >= 32)
2237 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2239 unsigned NumIterations = Its.getZExtValue(); // must be in range
2240 unsigned IterationNum = 0;
2241 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2242 if (IterationNum == NumIterations)
2243 return RetVal = PHIVal; // Got exit value!
2245 // Compute the value of the PHI node for the next iteration.
2246 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2247 if (NextPHI == PHIVal)
2248 return RetVal = NextPHI; // Stopped evolving!
2250 return 0; // Couldn't evaluate!
2255 /// ComputeIterationCountExhaustively - If the trip is known to execute a
2256 /// constant number of times (the condition evolves only from constants),
2257 /// try to evaluate a few iterations of the loop until we get the exit
2258 /// condition gets a value of ExitWhen (true or false). If we cannot
2259 /// evaluate the trip count of the loop, return UnknownValue.
2260 SCEVHandle ScalarEvolutionsImpl::
2261 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2262 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2263 if (PN == 0) return UnknownValue;
2265 // Since the loop is canonicalized, the PHI node must have two entries. One
2266 // entry must be a constant (coming in from outside of the loop), and the
2267 // second must be derived from the same PHI.
2268 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2269 Constant *StartCST =
2270 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2271 if (StartCST == 0) return UnknownValue; // Must be a constant.
2273 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2274 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2275 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2277 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2278 // the loop symbolically to determine when the condition gets a value of
2280 unsigned IterationNum = 0;
2281 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2282 for (Constant *PHIVal = StartCST;
2283 IterationNum != MaxIterations; ++IterationNum) {
2284 ConstantInt *CondVal =
2285 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2287 // Couldn't symbolically evaluate.
2288 if (!CondVal) return UnknownValue;
2290 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2291 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2292 ++NumBruteForceTripCountsComputed;
2293 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2296 // Compute the value of the PHI node for the next iteration.
2297 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2298 if (NextPHI == 0 || NextPHI == PHIVal)
2299 return UnknownValue; // Couldn't evaluate or not making progress...
2303 // Too many iterations were needed to evaluate.
2304 return UnknownValue;
2307 /// getSCEVAtScope - Compute the value of the specified expression within the
2308 /// indicated loop (which may be null to indicate in no loop). If the
2309 /// expression cannot be evaluated, return UnknownValue.
2310 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2311 // FIXME: this should be turned into a virtual method on SCEV!
2313 if (isa<SCEVConstant>(V)) return V;
2315 // If this instruction is evolved from a constant-evolving PHI, compute the
2316 // exit value from the loop without using SCEVs.
2317 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2318 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2319 const Loop *LI = this->LI[I->getParent()];
2320 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2321 if (PHINode *PN = dyn_cast<PHINode>(I))
2322 if (PN->getParent() == LI->getHeader()) {
2323 // Okay, there is no closed form solution for the PHI node. Check
2324 // to see if the loop that contains it has a known iteration count.
2325 // If so, we may be able to force computation of the exit value.
2326 SCEVHandle IterationCount = getIterationCount(LI);
2327 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
2328 // Okay, we know how many times the containing loop executes. If
2329 // this is a constant evolving PHI node, get the final value at
2330 // the specified iteration number.
2331 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2332 ICC->getValue()->getValue(),
2334 if (RV) return SE.getUnknown(RV);
2338 // Okay, this is an expression that we cannot symbolically evaluate
2339 // into a SCEV. Check to see if it's possible to symbolically evaluate
2340 // the arguments into constants, and if so, try to constant propagate the
2341 // result. This is particularly useful for computing loop exit values.
2342 if (CanConstantFold(I)) {
2343 std::vector<Constant*> Operands;
2344 Operands.reserve(I->getNumOperands());
2345 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2346 Value *Op = I->getOperand(i);
2347 if (Constant *C = dyn_cast<Constant>(Op)) {
2348 Operands.push_back(C);
2350 // If any of the operands is non-constant and if they are
2351 // non-integer, don't even try to analyze them with scev techniques.
2352 if (!isa<IntegerType>(Op->getType()))
2355 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2356 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2357 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2360 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2361 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2362 Operands.push_back(ConstantExpr::getIntegerCast(C,
2374 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2375 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2376 &Operands[0], Operands.size());
2378 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2379 &Operands[0], Operands.size());
2380 return SE.getUnknown(C);
2384 // This is some other type of SCEVUnknown, just return it.
2388 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2389 // Avoid performing the look-up in the common case where the specified
2390 // expression has no loop-variant portions.
2391 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2392 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2393 if (OpAtScope != Comm->getOperand(i)) {
2394 if (OpAtScope == UnknownValue) return UnknownValue;
2395 // Okay, at least one of these operands is loop variant but might be
2396 // foldable. Build a new instance of the folded commutative expression.
2397 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2398 NewOps.push_back(OpAtScope);
2400 for (++i; i != e; ++i) {
2401 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2402 if (OpAtScope == UnknownValue) return UnknownValue;
2403 NewOps.push_back(OpAtScope);
2405 if (isa<SCEVAddExpr>(Comm))
2406 return SE.getAddExpr(NewOps);
2407 if (isa<SCEVMulExpr>(Comm))
2408 return SE.getMulExpr(NewOps);
2409 if (isa<SCEVSMaxExpr>(Comm))
2410 return SE.getSMaxExpr(NewOps);
2411 if (isa<SCEVUMaxExpr>(Comm))
2412 return SE.getUMaxExpr(NewOps);
2413 assert(0 && "Unknown commutative SCEV type!");
2416 // If we got here, all operands are loop invariant.
2420 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2421 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2422 if (LHS == UnknownValue) return LHS;
2423 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2424 if (RHS == UnknownValue) return RHS;
2425 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2426 return Div; // must be loop invariant
2427 return SE.getUDivExpr(LHS, RHS);
2430 // If this is a loop recurrence for a loop that does not contain L, then we
2431 // are dealing with the final value computed by the loop.
2432 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2433 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2434 // To evaluate this recurrence, we need to know how many times the AddRec
2435 // loop iterates. Compute this now.
2436 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2437 if (IterationCount == UnknownValue) return UnknownValue;
2438 IterationCount = getTruncateOrZeroExtend(IterationCount,
2439 AddRec->getType(), SE);
2441 // If the value is affine, simplify the expression evaluation to just
2442 // Start + Step*IterationCount.
2443 if (AddRec->isAffine())
2444 return SE.getAddExpr(AddRec->getStart(),
2445 SE.getMulExpr(IterationCount,
2446 AddRec->getOperand(1)));
2448 // Otherwise, evaluate it the hard way.
2449 return AddRec->evaluateAtIteration(IterationCount, SE);
2451 return UnknownValue;
2454 //assert(0 && "Unknown SCEV type!");
2455 return UnknownValue;
2459 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2460 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2461 /// might be the same) or two SCEVCouldNotCompute objects.
2463 static std::pair<SCEVHandle,SCEVHandle>
2464 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2465 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2466 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2467 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2468 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2470 // We currently can only solve this if the coefficients are constants.
2471 if (!LC || !MC || !NC) {
2472 SCEV *CNC = new SCEVCouldNotCompute();
2473 return std::make_pair(CNC, CNC);
2476 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2477 const APInt &L = LC->getValue()->getValue();
2478 const APInt &M = MC->getValue()->getValue();
2479 const APInt &N = NC->getValue()->getValue();
2480 APInt Two(BitWidth, 2);
2481 APInt Four(BitWidth, 4);
2484 using namespace APIntOps;
2486 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2487 // The B coefficient is M-N/2
2491 // The A coefficient is N/2
2492 APInt A(N.sdiv(Two));
2494 // Compute the B^2-4ac term.
2497 SqrtTerm -= Four * (A * C);
2499 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2500 // integer value or else APInt::sqrt() will assert.
2501 APInt SqrtVal(SqrtTerm.sqrt());
2503 // Compute the two solutions for the quadratic formula.
2504 // The divisions must be performed as signed divisions.
2506 APInt TwoA( A << 1 );
2507 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2508 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2510 return std::make_pair(SE.getConstant(Solution1),
2511 SE.getConstant(Solution2));
2512 } // end APIntOps namespace
2515 /// HowFarToZero - Return the number of times a backedge comparing the specified
2516 /// value to zero will execute. If not computable, return UnknownValue
2517 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2518 // If the value is a constant
2519 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2520 // If the value is already zero, the branch will execute zero times.
2521 if (C->getValue()->isZero()) return C;
2522 return UnknownValue; // Otherwise it will loop infinitely.
2525 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2526 if (!AddRec || AddRec->getLoop() != L)
2527 return UnknownValue;
2529 if (AddRec->isAffine()) {
2530 // If this is an affine expression the execution count of this branch is
2533 // (0 - Start/Step) iff Start % Step == 0
2535 // Get the initial value for the loop.
2536 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2537 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2538 SCEVHandle Step = AddRec->getOperand(1);
2540 Step = getSCEVAtScope(Step, L->getParentLoop());
2542 // Figure out if Start % Step == 0.
2543 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2544 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2545 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2546 return SE.getNegativeSCEV(Start); // 0 - Start/1 == -Start
2547 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2548 return Start; // 0 - Start/-1 == Start
2550 // Check to see if Start is divisible by SC with no remainder.
2551 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2552 ConstantInt *StartCC = StartC->getValue();
2553 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2554 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2555 if (Rem->isNullValue()) {
2556 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2557 return SE.getUnknown(Result);
2561 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2562 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2563 // the quadratic equation to solve it.
2564 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
2565 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2566 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2569 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2570 << " sol#2: " << *R2 << "\n";
2572 // Pick the smallest positive root value.
2573 if (ConstantInt *CB =
2574 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2575 R1->getValue(), R2->getValue()))) {
2576 if (CB->getZExtValue() == false)
2577 std::swap(R1, R2); // R1 is the minimum root now.
2579 // We can only use this value if the chrec ends up with an exact zero
2580 // value at this index. When solving for "X*X != 5", for example, we
2581 // should not accept a root of 2.
2582 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
2583 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2584 if (EvalVal->getValue()->isZero())
2585 return R1; // We found a quadratic root!
2590 return UnknownValue;
2593 /// HowFarToNonZero - Return the number of times a backedge checking the
2594 /// specified value for nonzero will execute. If not computable, return
2596 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2597 // Loops that look like: while (X == 0) are very strange indeed. We don't
2598 // handle them yet except for the trivial case. This could be expanded in the
2599 // future as needed.
2601 // If the value is a constant, check to see if it is known to be non-zero
2602 // already. If so, the backedge will execute zero times.
2603 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2604 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2606 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2607 if (NonZero == ConstantInt::getTrue())
2608 return getSCEV(Zero);
2609 return UnknownValue; // Otherwise it will loop infinitely.
2612 // We could implement others, but I really doubt anyone writes loops like
2613 // this, and if they did, they would already be constant folded.
2614 return UnknownValue;
2617 /// HowManyLessThans - Return the number of times a backedge containing the
2618 /// specified less-than comparison will execute. If not computable, return
2620 SCEVHandle ScalarEvolutionsImpl::
2621 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
2622 // Only handle: "ADDREC < LoopInvariant".
2623 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2625 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2626 if (!AddRec || AddRec->getLoop() != L)
2627 return UnknownValue;
2629 if (AddRec->isAffine()) {
2630 // FORNOW: We only support unit strides.
2631 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
2632 if (AddRec->getOperand(1) != One)
2633 return UnknownValue;
2635 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
2636 // m. So, we count the number of iterations in which {n,+,1} < m is true.
2637 // Note that we cannot simply return max(m-n,0) because it's not safe to
2638 // treat m-n as signed nor unsigned due to overflow possibility.
2640 // First, we get the value of the LHS in the first iteration: n
2641 SCEVHandle Start = AddRec->getOperand(0);
2643 // Then, we get the value of the LHS in the first iteration in which the
2644 // above condition doesn't hold. This equals to max(m,n).
2645 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
2646 : SE.getUMaxExpr(RHS, Start);
2648 // Finally, we subtract these two values to get the number of times the
2649 // backedge is executed: max(m,n)-n.
2650 return SE.getMinusSCEV(End, Start);
2653 return UnknownValue;
2656 /// getNumIterationsInRange - Return the number of iterations of this loop that
2657 /// produce values in the specified constant range. Another way of looking at
2658 /// this is that it returns the first iteration number where the value is not in
2659 /// the condition, thus computing the exit count. If the iteration count can't
2660 /// be computed, an instance of SCEVCouldNotCompute is returned.
2661 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2662 ScalarEvolution &SE) const {
2663 if (Range.isFullSet()) // Infinite loop.
2664 return new SCEVCouldNotCompute();
2666 // If the start is a non-zero constant, shift the range to simplify things.
2667 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2668 if (!SC->getValue()->isZero()) {
2669 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2670 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
2671 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
2672 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2673 return ShiftedAddRec->getNumIterationsInRange(
2674 Range.subtract(SC->getValue()->getValue()), SE);
2675 // This is strange and shouldn't happen.
2676 return new SCEVCouldNotCompute();
2679 // The only time we can solve this is when we have all constant indices.
2680 // Otherwise, we cannot determine the overflow conditions.
2681 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2682 if (!isa<SCEVConstant>(getOperand(i)))
2683 return new SCEVCouldNotCompute();
2686 // Okay at this point we know that all elements of the chrec are constants and
2687 // that the start element is zero.
2689 // First check to see if the range contains zero. If not, the first
2691 if (!Range.contains(APInt(getBitWidth(),0)))
2692 return SE.getConstant(ConstantInt::get(getType(),0));
2695 // If this is an affine expression then we have this situation:
2696 // Solve {0,+,A} in Range === Ax in Range
2698 // We know that zero is in the range. If A is positive then we know that
2699 // the upper value of the range must be the first possible exit value.
2700 // If A is negative then the lower of the range is the last possible loop
2701 // value. Also note that we already checked for a full range.
2702 APInt One(getBitWidth(),1);
2703 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2704 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
2706 // The exit value should be (End+A)/A.
2707 APInt ExitVal = (End + A).udiv(A);
2708 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
2710 // Evaluate at the exit value. If we really did fall out of the valid
2711 // range, then we computed our trip count, otherwise wrap around or other
2712 // things must have happened.
2713 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
2714 if (Range.contains(Val->getValue()))
2715 return new SCEVCouldNotCompute(); // Something strange happened
2717 // Ensure that the previous value is in the range. This is a sanity check.
2718 assert(Range.contains(
2719 EvaluateConstantChrecAtConstant(this,
2720 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
2721 "Linear scev computation is off in a bad way!");
2722 return SE.getConstant(ExitValue);
2723 } else if (isQuadratic()) {
2724 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2725 // quadratic equation to solve it. To do this, we must frame our problem in
2726 // terms of figuring out when zero is crossed, instead of when
2727 // Range.getUpper() is crossed.
2728 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2729 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
2730 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
2732 // Next, solve the constructed addrec
2733 std::pair<SCEVHandle,SCEVHandle> Roots =
2734 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
2735 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2736 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2738 // Pick the smallest positive root value.
2739 if (ConstantInt *CB =
2740 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2741 R1->getValue(), R2->getValue()))) {
2742 if (CB->getZExtValue() == false)
2743 std::swap(R1, R2); // R1 is the minimum root now.
2745 // Make sure the root is not off by one. The returned iteration should
2746 // not be in the range, but the previous one should be. When solving
2747 // for "X*X < 5", for example, we should not return a root of 2.
2748 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2751 if (Range.contains(R1Val->getValue())) {
2752 // The next iteration must be out of the range...
2753 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
2755 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
2756 if (!Range.contains(R1Val->getValue()))
2757 return SE.getConstant(NextVal);
2758 return new SCEVCouldNotCompute(); // Something strange happened
2761 // If R1 was not in the range, then it is a good return value. Make
2762 // sure that R1-1 WAS in the range though, just in case.
2763 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
2764 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
2765 if (Range.contains(R1Val->getValue()))
2767 return new SCEVCouldNotCompute(); // Something strange happened
2772 // Fallback, if this is a general polynomial, figure out the progression
2773 // through brute force: evaluate until we find an iteration that fails the
2774 // test. This is likely to be slow, but getting an accurate trip count is
2775 // incredibly important, we will be able to simplify the exit test a lot, and
2776 // we are almost guaranteed to get a trip count in this case.
2777 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2778 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2780 ++NumBruteForceEvaluations;
2781 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE);
2782 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2783 return new SCEVCouldNotCompute();
2785 // Check to see if we found the value!
2786 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
2787 return SE.getConstant(TestVal);
2789 // Increment to test the next index.
2790 TestVal = ConstantInt::get(TestVal->getValue()+1);
2791 } while (TestVal != EndVal);
2793 return new SCEVCouldNotCompute();
2798 //===----------------------------------------------------------------------===//
2799 // ScalarEvolution Class Implementation
2800 //===----------------------------------------------------------------------===//
2802 bool ScalarEvolution::runOnFunction(Function &F) {
2803 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
2807 void ScalarEvolution::releaseMemory() {
2808 delete (ScalarEvolutionsImpl*)Impl;
2812 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2813 AU.setPreservesAll();
2814 AU.addRequiredTransitive<LoopInfo>();
2817 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2818 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2821 /// hasSCEV - Return true if the SCEV for this value has already been
2823 bool ScalarEvolution::hasSCEV(Value *V) const {
2824 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2828 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2829 /// the specified value.
2830 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2831 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2835 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2836 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2839 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2840 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2843 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2844 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2847 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
2848 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
2851 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2853 // Print all inner loops first
2854 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2855 PrintLoopInfo(OS, SE, *I);
2857 OS << "Loop " << L->getHeader()->getName() << ": ";
2859 SmallVector<BasicBlock*, 8> ExitBlocks;
2860 L->getExitBlocks(ExitBlocks);
2861 if (ExitBlocks.size() != 1)
2862 OS << "<multiple exits> ";
2864 if (SE->hasLoopInvariantIterationCount(L)) {
2865 OS << *SE->getIterationCount(L) << " iterations! ";
2867 OS << "Unpredictable iteration count. ";
2873 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2874 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2875 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2877 OS << "Classifying expressions for: " << F.getName() << "\n";
2878 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2879 if (I->getType()->isInteger()) {
2882 SCEVHandle SV = getSCEV(&*I);
2886 if ((*I).getType()->isInteger()) {
2887 ConstantRange Bounds = SV->getValueRange();
2888 if (!Bounds.isFullSet())
2889 OS << "Bounds: " << Bounds << " ";
2892 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2894 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2895 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2896 OS << "<<Unknown>>";
2906 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2907 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2908 PrintLoopInfo(OS, this, *I);