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/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Transforms/Scalar.h"
74 #include "llvm/Support/CFG.h"
75 #include "llvm/Support/CommandLine.h"
76 #include "llvm/Support/Compiler.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/GetElementPtrTypeIterator.h"
79 #include "llvm/Support/InstIterator.h"
80 #include "llvm/Support/ManagedStatic.h"
81 #include "llvm/Support/MathExtras.h"
82 #include "llvm/Support/raw_ostream.h"
83 #include "llvm/ADT/Statistic.h"
84 #include "llvm/ADT/STLExtras.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant derived loop"),
105 static RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
107 char ScalarEvolution::ID = 0;
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
117 void SCEV::dump() const {
122 void SCEV::print(std::ostream &o) const {
123 raw_os_ostream OS(o);
127 bool SCEV::isZero() const {
128 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
129 return SC->getValue()->isZero();
134 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
135 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
137 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
142 const Type *SCEVCouldNotCompute::getType() const {
143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
147 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
148 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
152 SCEVHandle SCEVCouldNotCompute::
153 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
154 const SCEVHandle &Conc,
155 ScalarEvolution &SE) const {
159 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
160 OS << "***COULDNOTCOMPUTE***";
163 bool SCEVCouldNotCompute::classof(const SCEV *S) {
164 return S->getSCEVType() == scCouldNotCompute;
168 // SCEVConstants - Only allow the creation of one SCEVConstant for any
169 // particular value. Don't use a SCEVHandle here, or else the object will
171 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
174 SCEVConstant::~SCEVConstant() {
175 SCEVConstants->erase(V);
178 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
179 SCEVConstant *&R = (*SCEVConstants)[V];
180 if (R == 0) R = new SCEVConstant(V);
184 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
185 return getConstant(ConstantInt::get(Val));
188 const Type *SCEVConstant::getType() const { return V->getType(); }
190 void SCEVConstant::print(raw_ostream &OS) const {
191 WriteAsOperand(OS, V, false);
194 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
195 const SCEVHandle &op, const Type *ty)
196 : SCEV(SCEVTy), Op(op), Ty(ty) {}
198 SCEVCastExpr::~SCEVCastExpr() {}
200 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
201 return Op->dominates(BB, DT);
204 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
205 // particular input. Don't use a SCEVHandle here, or else the object will
207 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
208 SCEVTruncateExpr*> > SCEVTruncates;
210 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
211 : SCEVCastExpr(scTruncate, op, ty) {
212 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
213 (Ty->isInteger() || isa<PointerType>(Ty)) &&
214 "Cannot truncate non-integer value!");
217 SCEVTruncateExpr::~SCEVTruncateExpr() {
218 SCEVTruncates->erase(std::make_pair(Op, Ty));
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
226 // particular input. Don't use a SCEVHandle here, or else the object will never
228 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
229 SCEVZeroExtendExpr*> > SCEVZeroExtends;
231 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
232 : SCEVCastExpr(scZeroExtend, op, ty) {
233 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
234 (Ty->isInteger() || isa<PointerType>(Ty)) &&
235 "Cannot zero extend non-integer value!");
238 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
239 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
242 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
243 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
246 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
247 // particular input. Don't use a SCEVHandle here, or else the object will never
249 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
250 SCEVSignExtendExpr*> > SCEVSignExtends;
252 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
253 : SCEVCastExpr(scSignExtend, op, ty) {
254 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
255 (Ty->isInteger() || isa<PointerType>(Ty)) &&
256 "Cannot sign extend non-integer value!");
259 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
260 SCEVSignExtends->erase(std::make_pair(Op, Ty));
263 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
264 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
267 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
268 // particular input. Don't use a SCEVHandle here, or else the object will never
270 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
271 SCEVCommutativeExpr*> > SCEVCommExprs;
273 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
274 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
275 std::vector<SCEV*>(Operands.begin(),
279 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
280 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
281 const char *OpStr = getOperationStr();
282 OS << "(" << *Operands[0];
283 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
284 OS << OpStr << *Operands[i];
288 SCEVHandle SCEVCommutativeExpr::
289 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
290 const SCEVHandle &Conc,
291 ScalarEvolution &SE) const {
292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
294 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
295 if (H != getOperand(i)) {
296 std::vector<SCEVHandle> NewOps;
297 NewOps.reserve(getNumOperands());
298 for (unsigned j = 0; j != i; ++j)
299 NewOps.push_back(getOperand(j));
301 for (++i; i != e; ++i)
302 NewOps.push_back(getOperand(i)->
303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
305 if (isa<SCEVAddExpr>(this))
306 return SE.getAddExpr(NewOps);
307 else if (isa<SCEVMulExpr>(this))
308 return SE.getMulExpr(NewOps);
309 else if (isa<SCEVSMaxExpr>(this))
310 return SE.getSMaxExpr(NewOps);
311 else if (isa<SCEVUMaxExpr>(this))
312 return SE.getUMaxExpr(NewOps);
314 assert(0 && "Unknown commutative expr!");
320 bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
322 if (!getOperand(i)->dominates(BB, DT))
329 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
330 // input. Don't use a SCEVHandle here, or else the object will never be
332 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
333 SCEVUDivExpr*> > SCEVUDivs;
335 SCEVUDivExpr::~SCEVUDivExpr() {
336 SCEVUDivs->erase(std::make_pair(LHS, RHS));
339 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
343 void SCEVUDivExpr::print(raw_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 bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
364 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
365 if (!getOperand(i)->dominates(BB, DT))
372 SCEVHandle SCEVAddRecExpr::
373 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
374 const SCEVHandle &Conc,
375 ScalarEvolution &SE) const {
376 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
378 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
379 if (H != getOperand(i)) {
380 std::vector<SCEVHandle> NewOps;
381 NewOps.reserve(getNumOperands());
382 for (unsigned j = 0; j != i; ++j)
383 NewOps.push_back(getOperand(j));
385 for (++i; i != e; ++i)
386 NewOps.push_back(getOperand(i)->
387 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
389 return SE.getAddRecExpr(NewOps, L);
396 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
397 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
398 // contain L and if the start is invariant.
399 return !QueryLoop->contains(L->getHeader()) &&
400 getOperand(0)->isLoopInvariant(QueryLoop);
404 void SCEVAddRecExpr::print(raw_ostream &OS) const {
405 OS << "{" << *Operands[0];
406 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
407 OS << ",+," << *Operands[i];
408 OS << "}<" << L->getHeader()->getName() + ">";
411 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
412 // value. Don't use a SCEVHandle here, or else the object will never be
414 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
416 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
418 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
419 // All non-instruction values are loop invariant. All instructions are loop
420 // invariant if they are not contained in the specified loop.
421 if (Instruction *I = dyn_cast<Instruction>(V))
422 return !L->contains(I->getParent());
426 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
427 if (Instruction *I = dyn_cast<Instruction>(getValue()))
428 return DT->dominates(I->getParent(), BB);
432 const Type *SCEVUnknown::getType() const {
436 void SCEVUnknown::print(raw_ostream &OS) const {
437 WriteAsOperand(OS, V, false);
440 //===----------------------------------------------------------------------===//
442 //===----------------------------------------------------------------------===//
445 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
446 /// than the complexity of the RHS. This comparator is used to canonicalize
448 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
449 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
450 return LHS->getSCEVType() < RHS->getSCEVType();
455 /// GroupByComplexity - Given a list of SCEV objects, order them by their
456 /// complexity, and group objects of the same complexity together by value.
457 /// When this routine is finished, we know that any duplicates in the vector are
458 /// consecutive and that complexity is monotonically increasing.
460 /// Note that we go take special precautions to ensure that we get determinstic
461 /// results from this routine. In other words, we don't want the results of
462 /// this to depend on where the addresses of various SCEV objects happened to
465 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
466 if (Ops.size() < 2) return; // Noop
467 if (Ops.size() == 2) {
468 // This is the common case, which also happens to be trivially simple.
470 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
471 std::swap(Ops[0], Ops[1]);
475 // Do the rough sort by complexity.
476 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
478 // Now that we are sorted by complexity, group elements of the same
479 // complexity. Note that this is, at worst, N^2, but the vector is likely to
480 // be extremely short in practice. Note that we take this approach because we
481 // do not want to depend on the addresses of the objects we are grouping.
482 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
484 unsigned Complexity = S->getSCEVType();
486 // If there are any objects of the same complexity and same value as this
488 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
489 if (Ops[j] == S) { // Found a duplicate.
490 // Move it to immediately after i'th element.
491 std::swap(Ops[i+1], Ops[j]);
492 ++i; // no need to rescan it.
493 if (i == e-2) return; // Done!
501 //===----------------------------------------------------------------------===//
502 // Simple SCEV method implementations
503 //===----------------------------------------------------------------------===//
505 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
507 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
509 const Type* ResultTy) {
510 // Handle the simplest case efficiently.
512 return SE.getTruncateOrZeroExtend(It, ResultTy);
514 // We are using the following formula for BC(It, K):
516 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
518 // Suppose, W is the bitwidth of the return value. We must be prepared for
519 // overflow. Hence, we must assure that the result of our computation is
520 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
521 // safe in modular arithmetic.
523 // However, this code doesn't use exactly that formula; the formula it uses
524 // is something like the following, where T is the number of factors of 2 in
525 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
528 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
530 // This formula is trivially equivalent to the previous formula. However,
531 // this formula can be implemented much more efficiently. The trick is that
532 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
533 // arithmetic. To do exact division in modular arithmetic, all we have
534 // to do is multiply by the inverse. Therefore, this step can be done at
537 // The next issue is how to safely do the division by 2^T. The way this
538 // is done is by doing the multiplication step at a width of at least W + T
539 // bits. This way, the bottom W+T bits of the product are accurate. Then,
540 // when we perform the division by 2^T (which is equivalent to a right shift
541 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
542 // truncated out after the division by 2^T.
544 // In comparison to just directly using the first formula, this technique
545 // is much more efficient; using the first formula requires W * K bits,
546 // but this formula less than W + K bits. Also, the first formula requires
547 // a division step, whereas this formula only requires multiplies and shifts.
549 // It doesn't matter whether the subtraction step is done in the calculation
550 // width or the input iteration count's width; if the subtraction overflows,
551 // the result must be zero anyway. We prefer here to do it in the width of
552 // the induction variable because it helps a lot for certain cases; CodeGen
553 // isn't smart enough to ignore the overflow, which leads to much less
554 // efficient code if the width of the subtraction is wider than the native
557 // (It's possible to not widen at all by pulling out factors of 2 before
558 // the multiplication; for example, K=2 can be calculated as
559 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
560 // extra arithmetic, so it's not an obvious win, and it gets
561 // much more complicated for K > 3.)
563 // Protection from insane SCEVs; this bound is conservative,
564 // but it probably doesn't matter.
566 return SE.getCouldNotCompute();
568 unsigned W = SE.getTypeSizeInBits(ResultTy);
570 // Calculate K! / 2^T and T; we divide out the factors of two before
571 // multiplying for calculating K! / 2^T to avoid overflow.
572 // Other overflow doesn't matter because we only care about the bottom
573 // W bits of the result.
574 APInt OddFactorial(W, 1);
576 for (unsigned i = 3; i <= K; ++i) {
578 unsigned TwoFactors = Mult.countTrailingZeros();
580 Mult = Mult.lshr(TwoFactors);
581 OddFactorial *= Mult;
584 // We need at least W + T bits for the multiplication step
585 unsigned CalculationBits = W + T;
587 // Calcuate 2^T, at width T+W.
588 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
590 // Calculate the multiplicative inverse of K! / 2^T;
591 // this multiplication factor will perform the exact division by
593 APInt Mod = APInt::getSignedMinValue(W+1);
594 APInt MultiplyFactor = OddFactorial.zext(W+1);
595 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
596 MultiplyFactor = MultiplyFactor.trunc(W);
598 // Calculate the product, at width T+W
599 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
600 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
601 for (unsigned i = 1; i != K; ++i) {
602 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
603 Dividend = SE.getMulExpr(Dividend,
604 SE.getTruncateOrZeroExtend(S, CalculationTy));
608 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
610 // Truncate the result, and divide by K! / 2^T.
612 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
613 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
616 /// evaluateAtIteration - Return the value of this chain of recurrences at
617 /// the specified iteration number. We can evaluate this recurrence by
618 /// multiplying each element in the chain by the binomial coefficient
619 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
621 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
623 /// where BC(It, k) stands for binomial coefficient.
625 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
626 ScalarEvolution &SE) const {
627 SCEVHandle Result = getStart();
628 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
629 // The computation is correct in the face of overflow provided that the
630 // multiplication is performed _after_ the evaluation of the binomial
632 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
633 if (isa<SCEVCouldNotCompute>(Coeff))
636 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
641 //===----------------------------------------------------------------------===//
642 // SCEV Expression folder implementations
643 //===----------------------------------------------------------------------===//
645 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
647 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
648 "This is not a truncating conversion!");
649 assert(isSCEVable(Ty) &&
650 "This is not a conversion to a SCEVable type!");
651 Ty = getEffectiveSCEVType(Ty);
653 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
655 ConstantExpr::getTrunc(SC->getValue(), Ty));
657 // trunc(trunc(x)) --> trunc(x)
658 if (SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
659 return getTruncateExpr(ST->getOperand(), Ty);
661 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
662 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
663 return getTruncateOrSignExtend(SS->getOperand(), Ty);
665 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
666 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
667 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
669 // If the input value is a chrec scev made out of constants, truncate
670 // all of the constants.
671 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
672 std::vector<SCEVHandle> Operands;
673 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
674 // FIXME: This should allow truncation of other expression types!
675 if (isa<SCEVConstant>(AddRec->getOperand(i)))
676 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
679 if (Operands.size() == AddRec->getNumOperands())
680 return getAddRecExpr(Operands, AddRec->getLoop());
683 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
684 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
688 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
690 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
691 "This is not an extending conversion!");
692 assert(isSCEVable(Ty) &&
693 "This is not a conversion to a SCEVable type!");
694 Ty = getEffectiveSCEVType(Ty);
696 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
697 const Type *IntTy = getEffectiveSCEVType(Ty);
698 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
699 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
700 return getUnknown(C);
703 // zext(zext(x)) --> zext(x)
704 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
705 return getZeroExtendExpr(SZ->getOperand(), Ty);
707 // If the input value is a chrec scev, and we can prove that the value
708 // did not overflow the old, smaller, value, we can zero extend all of the
709 // operands (often constants). This allows analysis of something like
710 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
711 if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
712 if (AR->isAffine()) {
713 // Check whether the backedge-taken count is SCEVCouldNotCompute.
714 // Note that this serves two purposes: It filters out loops that are
715 // simply not analyzable, and it covers the case where this code is
716 // being called from within backedge-taken count analysis, such that
717 // attempting to ask for the backedge-taken count would likely result
718 // in infinite recursion. In the later case, the analysis code will
719 // cope with a conservative value, and it will take care to purge
720 // that value once it has finished.
721 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
722 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
723 // Manually compute the final value for AR, checking for
725 SCEVHandle Start = AR->getStart();
726 SCEVHandle Step = AR->getStepRecurrence(*this);
728 // Check whether the backedge-taken count can be losslessly casted to
729 // the addrec's type. The count is always unsigned.
730 SCEVHandle CastedMaxBECount =
731 getTruncateOrZeroExtend(MaxBECount, Start->getType());
733 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
735 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
736 // Check whether Start+Step*MaxBECount has no unsigned overflow.
738 getMulExpr(CastedMaxBECount,
739 getTruncateOrZeroExtend(Step, Start->getType()));
740 SCEVHandle Add = getAddExpr(Start, ZMul);
741 if (getZeroExtendExpr(Add, WideTy) ==
742 getAddExpr(getZeroExtendExpr(Start, WideTy),
743 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
744 getZeroExtendExpr(Step, WideTy))))
745 // Return the expression with the addrec on the outside.
746 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
747 getZeroExtendExpr(Step, Ty),
750 // Similar to above, only this time treat the step value as signed.
751 // This covers loops that count down.
753 getMulExpr(CastedMaxBECount,
754 getTruncateOrSignExtend(Step, Start->getType()));
755 Add = getAddExpr(Start, SMul);
756 if (getZeroExtendExpr(Add, WideTy) ==
757 getAddExpr(getZeroExtendExpr(Start, WideTy),
758 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
759 getSignExtendExpr(Step, WideTy))))
760 // Return the expression with the addrec on the outside.
761 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
762 getSignExtendExpr(Step, Ty),
768 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
769 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
773 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
775 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
776 "This is not an extending conversion!");
777 assert(isSCEVable(Ty) &&
778 "This is not a conversion to a SCEVable type!");
779 Ty = getEffectiveSCEVType(Ty);
781 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
782 const Type *IntTy = getEffectiveSCEVType(Ty);
783 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
784 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
785 return getUnknown(C);
788 // sext(sext(x)) --> sext(x)
789 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
790 return getSignExtendExpr(SS->getOperand(), Ty);
792 // If the input value is a chrec scev, and we can prove that the value
793 // did not overflow the old, smaller, value, we can sign extend all of the
794 // operands (often constants). This allows analysis of something like
795 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
796 if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
797 if (AR->isAffine()) {
798 // Check whether the backedge-taken count is SCEVCouldNotCompute.
799 // Note that this serves two purposes: It filters out loops that are
800 // simply not analyzable, and it covers the case where this code is
801 // being called from within backedge-taken count analysis, such that
802 // attempting to ask for the backedge-taken count would likely result
803 // in infinite recursion. In the later case, the analysis code will
804 // cope with a conservative value, and it will take care to purge
805 // that value once it has finished.
806 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
807 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
808 // Manually compute the final value for AR, checking for
810 SCEVHandle Start = AR->getStart();
811 SCEVHandle Step = AR->getStepRecurrence(*this);
813 // Check whether the backedge-taken count can be losslessly casted to
814 // the addrec's type. The count is always unsigned.
815 SCEVHandle CastedMaxBECount =
816 getTruncateOrZeroExtend(MaxBECount, Start->getType());
818 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
820 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
821 // Check whether Start+Step*MaxBECount has no signed overflow.
823 getMulExpr(CastedMaxBECount,
824 getTruncateOrSignExtend(Step, Start->getType()));
825 SCEVHandle Add = getAddExpr(Start, SMul);
826 if (getSignExtendExpr(Add, WideTy) ==
827 getAddExpr(getSignExtendExpr(Start, WideTy),
828 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
829 getSignExtendExpr(Step, WideTy))))
830 // Return the expression with the addrec on the outside.
831 return getAddRecExpr(getSignExtendExpr(Start, Ty),
832 getSignExtendExpr(Step, Ty),
838 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
839 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
843 // get - Get a canonical add expression, or something simpler if possible.
844 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
845 assert(!Ops.empty() && "Cannot get empty add!");
846 if (Ops.size() == 1) return Ops[0];
848 // Sort by complexity, this groups all similar expression types together.
849 GroupByComplexity(Ops);
851 // If there are any constants, fold them together.
853 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
855 assert(Idx < Ops.size());
856 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
857 // We found two constants, fold them together!
858 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
859 RHSC->getValue()->getValue());
860 Ops[0] = getConstant(Fold);
861 Ops.erase(Ops.begin()+1); // Erase the folded element
862 if (Ops.size() == 1) return Ops[0];
863 LHSC = cast<SCEVConstant>(Ops[0]);
866 // If we are left with a constant zero being added, strip it off.
867 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
868 Ops.erase(Ops.begin());
873 if (Ops.size() == 1) return Ops[0];
875 // Okay, check to see if the same value occurs in the operand list twice. If
876 // so, merge them together into an multiply expression. Since we sorted the
877 // list, these values are required to be adjacent.
878 const Type *Ty = Ops[0]->getType();
879 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
880 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
881 // Found a match, merge the two values into a multiply, and add any
882 // remaining values to the result.
883 SCEVHandle Two = getIntegerSCEV(2, Ty);
884 SCEVHandle Mul = getMulExpr(Ops[i], Two);
887 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
889 return getAddExpr(Ops);
892 // Now we know the first non-constant operand. Skip past any cast SCEVs.
893 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
896 // If there are add operands they would be next.
897 if (Idx < Ops.size()) {
898 bool DeletedAdd = false;
899 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
900 // If we have an add, expand the add operands onto the end of the operands
902 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
903 Ops.erase(Ops.begin()+Idx);
907 // If we deleted at least one add, we added operands to the end of the list,
908 // and they are not necessarily sorted. Recurse to resort and resimplify
909 // any operands we just aquired.
911 return getAddExpr(Ops);
914 // Skip over the add expression until we get to a multiply.
915 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
918 // If we are adding something to a multiply expression, make sure the
919 // something is not already an operand of the multiply. If so, merge it into
921 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
922 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
923 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
924 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
925 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
926 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
927 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
928 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
929 if (Mul->getNumOperands() != 2) {
930 // If the multiply has more than two operands, we must get the
932 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
933 MulOps.erase(MulOps.begin()+MulOp);
934 InnerMul = getMulExpr(MulOps);
936 SCEVHandle One = getIntegerSCEV(1, Ty);
937 SCEVHandle AddOne = getAddExpr(InnerMul, One);
938 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
939 if (Ops.size() == 2) return OuterMul;
941 Ops.erase(Ops.begin()+AddOp);
942 Ops.erase(Ops.begin()+Idx-1);
944 Ops.erase(Ops.begin()+Idx);
945 Ops.erase(Ops.begin()+AddOp-1);
947 Ops.push_back(OuterMul);
948 return getAddExpr(Ops);
951 // Check this multiply against other multiplies being added together.
952 for (unsigned OtherMulIdx = Idx+1;
953 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
955 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
956 // If MulOp occurs in OtherMul, we can fold the two multiplies
958 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
959 OMulOp != e; ++OMulOp)
960 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
961 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
962 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
963 if (Mul->getNumOperands() != 2) {
964 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
965 MulOps.erase(MulOps.begin()+MulOp);
966 InnerMul1 = getMulExpr(MulOps);
968 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
969 if (OtherMul->getNumOperands() != 2) {
970 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
972 MulOps.erase(MulOps.begin()+OMulOp);
973 InnerMul2 = getMulExpr(MulOps);
975 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
976 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
977 if (Ops.size() == 2) return OuterMul;
978 Ops.erase(Ops.begin()+Idx);
979 Ops.erase(Ops.begin()+OtherMulIdx-1);
980 Ops.push_back(OuterMul);
981 return getAddExpr(Ops);
987 // If there are any add recurrences in the operands list, see if any other
988 // added values are loop invariant. If so, we can fold them into the
990 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
993 // Scan over all recurrences, trying to fold loop invariants into them.
994 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
995 // Scan all of the other operands to this add and add them to the vector if
996 // they are loop invariant w.r.t. the recurrence.
997 std::vector<SCEVHandle> LIOps;
998 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
999 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1000 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1001 LIOps.push_back(Ops[i]);
1002 Ops.erase(Ops.begin()+i);
1006 // If we found some loop invariants, fold them into the recurrence.
1007 if (!LIOps.empty()) {
1008 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1009 LIOps.push_back(AddRec->getStart());
1011 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1012 AddRecOps[0] = getAddExpr(LIOps);
1014 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1015 // If all of the other operands were loop invariant, we are done.
1016 if (Ops.size() == 1) return NewRec;
1018 // Otherwise, add the folded AddRec by the non-liv parts.
1019 for (unsigned i = 0;; ++i)
1020 if (Ops[i] == AddRec) {
1024 return getAddExpr(Ops);
1027 // Okay, if there weren't any loop invariants to be folded, check to see if
1028 // there are multiple AddRec's with the same loop induction variable being
1029 // added together. If so, we can fold them.
1030 for (unsigned OtherIdx = Idx+1;
1031 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1032 if (OtherIdx != Idx) {
1033 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1034 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1035 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1036 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1037 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1038 if (i >= NewOps.size()) {
1039 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1040 OtherAddRec->op_end());
1043 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1045 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1047 if (Ops.size() == 2) return NewAddRec;
1049 Ops.erase(Ops.begin()+Idx);
1050 Ops.erase(Ops.begin()+OtherIdx-1);
1051 Ops.push_back(NewAddRec);
1052 return getAddExpr(Ops);
1056 // Otherwise couldn't fold anything into this recurrence. Move onto the
1060 // Okay, it looks like we really DO need an add expr. Check to see if we
1061 // already have one, otherwise create a new one.
1062 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1063 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1065 if (Result == 0) Result = new SCEVAddExpr(Ops);
1070 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1071 assert(!Ops.empty() && "Cannot get empty mul!");
1073 // Sort by complexity, this groups all similar expression types together.
1074 GroupByComplexity(Ops);
1076 // If there are any constants, fold them together.
1078 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1080 // C1*(C2+V) -> C1*C2 + C1*V
1081 if (Ops.size() == 2)
1082 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1083 if (Add->getNumOperands() == 2 &&
1084 isa<SCEVConstant>(Add->getOperand(0)))
1085 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1086 getMulExpr(LHSC, Add->getOperand(1)));
1090 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1091 // We found two constants, fold them together!
1092 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1093 RHSC->getValue()->getValue());
1094 Ops[0] = getConstant(Fold);
1095 Ops.erase(Ops.begin()+1); // Erase the folded element
1096 if (Ops.size() == 1) return Ops[0];
1097 LHSC = cast<SCEVConstant>(Ops[0]);
1100 // If we are left with a constant one being multiplied, strip it off.
1101 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1102 Ops.erase(Ops.begin());
1104 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1105 // If we have a multiply of zero, it will always be zero.
1110 // Skip over the add expression until we get to a multiply.
1111 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1114 if (Ops.size() == 1)
1117 // If there are mul operands inline them all into this expression.
1118 if (Idx < Ops.size()) {
1119 bool DeletedMul = false;
1120 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1121 // If we have an mul, expand the mul operands onto the end of the operands
1123 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1124 Ops.erase(Ops.begin()+Idx);
1128 // If we deleted at least one mul, we added operands to the end of the list,
1129 // and they are not necessarily sorted. Recurse to resort and resimplify
1130 // any operands we just aquired.
1132 return getMulExpr(Ops);
1135 // If there are any add recurrences in the operands list, see if any other
1136 // added values are loop invariant. If so, we can fold them into the
1138 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1141 // Scan over all recurrences, trying to fold loop invariants into them.
1142 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1143 // Scan all of the other operands to this mul and add them to the vector if
1144 // they are loop invariant w.r.t. the recurrence.
1145 std::vector<SCEVHandle> LIOps;
1146 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1147 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1148 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1149 LIOps.push_back(Ops[i]);
1150 Ops.erase(Ops.begin()+i);
1154 // If we found some loop invariants, fold them into the recurrence.
1155 if (!LIOps.empty()) {
1156 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1157 std::vector<SCEVHandle> NewOps;
1158 NewOps.reserve(AddRec->getNumOperands());
1159 if (LIOps.size() == 1) {
1160 SCEV *Scale = LIOps[0];
1161 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1162 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1164 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1165 std::vector<SCEVHandle> MulOps(LIOps);
1166 MulOps.push_back(AddRec->getOperand(i));
1167 NewOps.push_back(getMulExpr(MulOps));
1171 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1173 // If all of the other operands were loop invariant, we are done.
1174 if (Ops.size() == 1) return NewRec;
1176 // Otherwise, multiply the folded AddRec by the non-liv parts.
1177 for (unsigned i = 0;; ++i)
1178 if (Ops[i] == AddRec) {
1182 return getMulExpr(Ops);
1185 // Okay, if there weren't any loop invariants to be folded, check to see if
1186 // there are multiple AddRec's with the same loop induction variable being
1187 // multiplied together. If so, we can fold them.
1188 for (unsigned OtherIdx = Idx+1;
1189 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1190 if (OtherIdx != Idx) {
1191 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1192 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1193 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1194 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1195 SCEVHandle NewStart = getMulExpr(F->getStart(),
1197 SCEVHandle B = F->getStepRecurrence(*this);
1198 SCEVHandle D = G->getStepRecurrence(*this);
1199 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1202 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1204 if (Ops.size() == 2) return NewAddRec;
1206 Ops.erase(Ops.begin()+Idx);
1207 Ops.erase(Ops.begin()+OtherIdx-1);
1208 Ops.push_back(NewAddRec);
1209 return getMulExpr(Ops);
1213 // Otherwise couldn't fold anything into this recurrence. Move onto the
1217 // Okay, it looks like we really DO need an mul expr. Check to see if we
1218 // already have one, otherwise create a new one.
1219 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1220 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1223 Result = new SCEVMulExpr(Ops);
1227 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1228 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1229 if (RHSC->getValue()->equalsInt(1))
1230 return LHS; // X udiv 1 --> x
1232 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1233 Constant *LHSCV = LHSC->getValue();
1234 Constant *RHSCV = RHSC->getValue();
1235 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1239 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1241 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1242 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1247 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1248 /// specified loop. Simplify the expression as much as possible.
1249 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1250 const SCEVHandle &Step, const Loop *L) {
1251 std::vector<SCEVHandle> Operands;
1252 Operands.push_back(Start);
1253 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1254 if (StepChrec->getLoop() == L) {
1255 Operands.insert(Operands.end(), StepChrec->op_begin(),
1256 StepChrec->op_end());
1257 return getAddRecExpr(Operands, L);
1260 Operands.push_back(Step);
1261 return getAddRecExpr(Operands, L);
1264 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1265 /// specified loop. Simplify the expression as much as possible.
1266 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1268 if (Operands.size() == 1) return Operands[0];
1270 if (Operands.back()->isZero()) {
1271 Operands.pop_back();
1272 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1275 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1276 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1277 const Loop* NestedLoop = NestedAR->getLoop();
1278 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1279 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1280 NestedAR->op_end());
1281 SCEVHandle NestedARHandle(NestedAR);
1282 Operands[0] = NestedAR->getStart();
1283 NestedOperands[0] = getAddRecExpr(Operands, L);
1284 return getAddRecExpr(NestedOperands, NestedLoop);
1288 SCEVAddRecExpr *&Result =
1289 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1291 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1295 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1296 const SCEVHandle &RHS) {
1297 std::vector<SCEVHandle> Ops;
1300 return getSMaxExpr(Ops);
1303 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1304 assert(!Ops.empty() && "Cannot get empty smax!");
1305 if (Ops.size() == 1) return Ops[0];
1307 // Sort by complexity, this groups all similar expression types together.
1308 GroupByComplexity(Ops);
1310 // If there are any constants, fold them together.
1312 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1314 assert(Idx < Ops.size());
1315 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1316 // We found two constants, fold them together!
1317 ConstantInt *Fold = ConstantInt::get(
1318 APIntOps::smax(LHSC->getValue()->getValue(),
1319 RHSC->getValue()->getValue()));
1320 Ops[0] = getConstant(Fold);
1321 Ops.erase(Ops.begin()+1); // Erase the folded element
1322 if (Ops.size() == 1) return Ops[0];
1323 LHSC = cast<SCEVConstant>(Ops[0]);
1326 // If we are left with a constant -inf, strip it off.
1327 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1328 Ops.erase(Ops.begin());
1333 if (Ops.size() == 1) return Ops[0];
1335 // Find the first SMax
1336 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1339 // Check to see if one of the operands is an SMax. If so, expand its operands
1340 // onto our operand list, and recurse to simplify.
1341 if (Idx < Ops.size()) {
1342 bool DeletedSMax = false;
1343 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1344 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1345 Ops.erase(Ops.begin()+Idx);
1350 return getSMaxExpr(Ops);
1353 // Okay, check to see if the same value occurs in the operand list twice. If
1354 // so, delete one. Since we sorted the list, these values are required to
1356 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1357 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1358 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1362 if (Ops.size() == 1) return Ops[0];
1364 assert(!Ops.empty() && "Reduced smax down to nothing!");
1366 // Okay, it looks like we really DO need an smax expr. Check to see if we
1367 // already have one, otherwise create a new one.
1368 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1369 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1371 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1375 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1376 const SCEVHandle &RHS) {
1377 std::vector<SCEVHandle> Ops;
1380 return getUMaxExpr(Ops);
1383 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1384 assert(!Ops.empty() && "Cannot get empty umax!");
1385 if (Ops.size() == 1) return Ops[0];
1387 // Sort by complexity, this groups all similar expression types together.
1388 GroupByComplexity(Ops);
1390 // If there are any constants, fold them together.
1392 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1394 assert(Idx < Ops.size());
1395 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1396 // We found two constants, fold them together!
1397 ConstantInt *Fold = ConstantInt::get(
1398 APIntOps::umax(LHSC->getValue()->getValue(),
1399 RHSC->getValue()->getValue()));
1400 Ops[0] = getConstant(Fold);
1401 Ops.erase(Ops.begin()+1); // Erase the folded element
1402 if (Ops.size() == 1) return Ops[0];
1403 LHSC = cast<SCEVConstant>(Ops[0]);
1406 // If we are left with a constant zero, strip it off.
1407 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1408 Ops.erase(Ops.begin());
1413 if (Ops.size() == 1) return Ops[0];
1415 // Find the first UMax
1416 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1419 // Check to see if one of the operands is a UMax. If so, expand its operands
1420 // onto our operand list, and recurse to simplify.
1421 if (Idx < Ops.size()) {
1422 bool DeletedUMax = false;
1423 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1424 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1425 Ops.erase(Ops.begin()+Idx);
1430 return getUMaxExpr(Ops);
1433 // Okay, check to see if the same value occurs in the operand list twice. If
1434 // so, delete one. Since we sorted the list, these values are required to
1436 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1437 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1438 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1442 if (Ops.size() == 1) return Ops[0];
1444 assert(!Ops.empty() && "Reduced umax down to nothing!");
1446 // Okay, it looks like we really DO need a umax expr. Check to see if we
1447 // already have one, otherwise create a new one.
1448 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1449 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1451 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1455 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1456 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1457 return getConstant(CI);
1458 if (isa<ConstantPointerNull>(V))
1459 return getIntegerSCEV(0, V->getType());
1460 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1461 if (Result == 0) Result = new SCEVUnknown(V);
1465 //===----------------------------------------------------------------------===//
1466 // Basic SCEV Analysis and PHI Idiom Recognition Code
1469 /// isSCEVable - Test if values of the given type are analyzable within
1470 /// the SCEV framework. This primarily includes integer types, and it
1471 /// can optionally include pointer types if the ScalarEvolution class
1472 /// has access to target-specific information.
1473 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1474 // Integers are always SCEVable.
1475 if (Ty->isInteger())
1478 // Pointers are SCEVable if TargetData information is available
1479 // to provide pointer size information.
1480 if (isa<PointerType>(Ty))
1483 // Otherwise it's not SCEVable.
1487 /// getTypeSizeInBits - Return the size in bits of the specified type,
1488 /// for which isSCEVable must return true.
1489 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1490 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1492 // If we have a TargetData, use it!
1494 return TD->getTypeSizeInBits(Ty);
1496 // Otherwise, we support only integer types.
1497 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1498 return Ty->getPrimitiveSizeInBits();
1501 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1502 /// the given type and which represents how SCEV will treat the given
1503 /// type, for which isSCEVable must return true. For pointer types,
1504 /// this is the pointer-sized integer type.
1505 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1506 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1508 if (Ty->isInteger())
1511 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1512 return TD->getIntPtrType();
1515 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1516 return UnknownValue;
1519 // hasSCEV - Return true if the SCEV for this value has already been
1521 bool ScalarEvolution::hasSCEV(Value *V) const {
1522 return Scalars.count(V);
1525 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1526 /// expression and create a new one.
1527 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1528 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1530 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1531 if (I != Scalars.end()) return I->second;
1532 SCEVHandle S = createSCEV(V);
1533 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1537 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1538 /// specified signed integer value and return a SCEV for the constant.
1539 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1540 Ty = getEffectiveSCEVType(Ty);
1543 C = Constant::getNullValue(Ty);
1544 else if (Ty->isFloatingPoint())
1545 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1546 APFloat::IEEEdouble, Val));
1548 C = ConstantInt::get(Ty, Val);
1549 return getUnknown(C);
1552 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1554 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1555 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1556 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1558 const Type *Ty = V->getType();
1559 Ty = getEffectiveSCEVType(Ty);
1560 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1563 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1564 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1565 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1566 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1568 const Type *Ty = V->getType();
1569 Ty = getEffectiveSCEVType(Ty);
1570 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1571 return getMinusSCEV(AllOnes, V);
1574 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1576 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1577 const SCEVHandle &RHS) {
1579 return getAddExpr(LHS, getNegativeSCEV(RHS));
1582 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1583 /// input value to the specified type. If the type must be extended, it is zero
1586 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1588 const Type *SrcTy = V->getType();
1589 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1590 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1591 "Cannot truncate or zero extend with non-integer arguments!");
1592 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1593 return V; // No conversion
1594 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1595 return getTruncateExpr(V, Ty);
1596 return getZeroExtendExpr(V, Ty);
1599 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1600 /// input value to the specified type. If the type must be extended, it is sign
1603 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1605 const Type *SrcTy = V->getType();
1606 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1607 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1608 "Cannot truncate or zero extend with non-integer arguments!");
1609 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1610 return V; // No conversion
1611 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1612 return getTruncateExpr(V, Ty);
1613 return getSignExtendExpr(V, Ty);
1616 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1617 /// the specified instruction and replaces any references to the symbolic value
1618 /// SymName with the specified value. This is used during PHI resolution.
1619 void ScalarEvolution::
1620 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1621 const SCEVHandle &NewVal) {
1622 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1623 Scalars.find(SCEVCallbackVH(I, this));
1624 if (SI == Scalars.end()) return;
1627 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1628 if (NV == SI->second) return; // No change.
1630 SI->second = NV; // Update the scalars map!
1632 // Any instruction values that use this instruction might also need to be
1634 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1636 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1639 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1640 /// a loop header, making it a potential recurrence, or it doesn't.
1642 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1643 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1644 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1645 if (L->getHeader() == PN->getParent()) {
1646 // If it lives in the loop header, it has two incoming values, one
1647 // from outside the loop, and one from inside.
1648 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1649 unsigned BackEdge = IncomingEdge^1;
1651 // While we are analyzing this PHI node, handle its value symbolically.
1652 SCEVHandle SymbolicName = getUnknown(PN);
1653 assert(Scalars.find(PN) == Scalars.end() &&
1654 "PHI node already processed?");
1655 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1657 // Using this symbolic name for the PHI, analyze the value coming around
1659 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1661 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1662 // has a special value for the first iteration of the loop.
1664 // If the value coming around the backedge is an add with the symbolic
1665 // value we just inserted, then we found a simple induction variable!
1666 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1667 // If there is a single occurrence of the symbolic value, replace it
1668 // with a recurrence.
1669 unsigned FoundIndex = Add->getNumOperands();
1670 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1671 if (Add->getOperand(i) == SymbolicName)
1672 if (FoundIndex == e) {
1677 if (FoundIndex != Add->getNumOperands()) {
1678 // Create an add with everything but the specified operand.
1679 std::vector<SCEVHandle> Ops;
1680 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1681 if (i != FoundIndex)
1682 Ops.push_back(Add->getOperand(i));
1683 SCEVHandle Accum = getAddExpr(Ops);
1685 // This is not a valid addrec if the step amount is varying each
1686 // loop iteration, but is not itself an addrec in this loop.
1687 if (Accum->isLoopInvariant(L) ||
1688 (isa<SCEVAddRecExpr>(Accum) &&
1689 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1690 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1691 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1693 // Okay, for the entire analysis of this edge we assumed the PHI
1694 // to be symbolic. We now need to go back and update all of the
1695 // entries for the scalars that use the PHI (except for the PHI
1696 // itself) to use the new analyzed value instead of the "symbolic"
1698 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1702 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1703 // Otherwise, this could be a loop like this:
1704 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1705 // In this case, j = {1,+,1} and BEValue is j.
1706 // Because the other in-value of i (0) fits the evolution of BEValue
1707 // i really is an addrec evolution.
1708 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1709 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1711 // If StartVal = j.start - j.stride, we can use StartVal as the
1712 // initial step of the addrec evolution.
1713 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
1714 AddRec->getOperand(1))) {
1715 SCEVHandle PHISCEV =
1716 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1718 // Okay, for the entire analysis of this edge we assumed the PHI
1719 // to be symbolic. We now need to go back and update all of the
1720 // entries for the scalars that use the PHI (except for the PHI
1721 // itself) to use the new analyzed value instead of the "symbolic"
1723 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1729 return SymbolicName;
1732 // If it's not a loop phi, we can't handle it yet.
1733 return getUnknown(PN);
1736 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1737 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1738 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1739 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1740 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
1741 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1742 return C->getValue()->getValue().countTrailingZeros();
1744 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1745 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
1746 (uint32_t)SE.getTypeSizeInBits(T->getType()));
1748 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1749 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1750 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1751 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1754 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1755 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1756 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1757 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1760 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1761 // The result is the min of all operands results.
1762 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1763 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1764 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1768 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1769 // The result is the sum of all operands results.
1770 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1771 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
1772 for (unsigned i = 1, e = M->getNumOperands();
1773 SumOpRes != BitWidth && i != e; ++i)
1774 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
1779 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1780 // The result is the min of all operands results.
1781 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1782 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1783 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1787 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1788 // The result is the min of all operands results.
1789 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1790 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1791 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1795 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1796 // The result is the min of all operands results.
1797 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1798 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1799 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1803 // SCEVUDivExpr, SCEVUnknown
1807 /// createSCEV - We know that there is no SCEV for the specified value.
1808 /// Analyze the expression.
1810 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
1811 if (!isSCEVable(V->getType()))
1812 return getUnknown(V);
1814 unsigned Opcode = Instruction::UserOp1;
1815 if (Instruction *I = dyn_cast<Instruction>(V))
1816 Opcode = I->getOpcode();
1817 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1818 Opcode = CE->getOpcode();
1820 return getUnknown(V);
1822 User *U = cast<User>(V);
1824 case Instruction::Add:
1825 return getAddExpr(getSCEV(U->getOperand(0)),
1826 getSCEV(U->getOperand(1)));
1827 case Instruction::Mul:
1828 return getMulExpr(getSCEV(U->getOperand(0)),
1829 getSCEV(U->getOperand(1)));
1830 case Instruction::UDiv:
1831 return getUDivExpr(getSCEV(U->getOperand(0)),
1832 getSCEV(U->getOperand(1)));
1833 case Instruction::Sub:
1834 return getMinusSCEV(getSCEV(U->getOperand(0)),
1835 getSCEV(U->getOperand(1)));
1836 case Instruction::And:
1837 // For an expression like x&255 that merely masks off the high bits,
1838 // use zext(trunc(x)) as the SCEV expression.
1839 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1840 if (CI->isNullValue())
1841 return getSCEV(U->getOperand(1));
1842 if (CI->isAllOnesValue())
1843 return getSCEV(U->getOperand(0));
1844 const APInt &A = CI->getValue();
1845 unsigned Ones = A.countTrailingOnes();
1846 if (APIntOps::isMask(Ones, A))
1848 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
1849 IntegerType::get(Ones)),
1853 case Instruction::Or:
1854 // If the RHS of the Or is a constant, we may have something like:
1855 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1856 // optimizations will transparently handle this case.
1858 // In order for this transformation to be safe, the LHS must be of the
1859 // form X*(2^n) and the Or constant must be less than 2^n.
1860 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1861 SCEVHandle LHS = getSCEV(U->getOperand(0));
1862 const APInt &CIVal = CI->getValue();
1863 if (GetMinTrailingZeros(LHS, *this) >=
1864 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1865 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
1868 case Instruction::Xor:
1869 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1870 // If the RHS of the xor is a signbit, then this is just an add.
1871 // Instcombine turns add of signbit into xor as a strength reduction step.
1872 if (CI->getValue().isSignBit())
1873 return getAddExpr(getSCEV(U->getOperand(0)),
1874 getSCEV(U->getOperand(1)));
1876 // If the RHS of xor is -1, then this is a not operation.
1877 else if (CI->isAllOnesValue())
1878 return getNotSCEV(getSCEV(U->getOperand(0)));
1882 case Instruction::Shl:
1883 // Turn shift left of a constant amount into a multiply.
1884 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1885 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1886 Constant *X = ConstantInt::get(
1887 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1888 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1892 case Instruction::LShr:
1893 // Turn logical shift right of a constant into a unsigned divide.
1894 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1895 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1896 Constant *X = ConstantInt::get(
1897 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1898 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1902 case Instruction::AShr:
1903 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
1904 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
1905 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
1906 if (L->getOpcode() == Instruction::Shl &&
1907 L->getOperand(1) == U->getOperand(1)) {
1908 unsigned BitWidth = getTypeSizeInBits(U->getType());
1909 uint64_t Amt = BitWidth - CI->getZExtValue();
1910 if (Amt == BitWidth)
1911 return getSCEV(L->getOperand(0)); // shift by zero --> noop
1913 return getIntegerSCEV(0, U->getType()); // value is undefined
1915 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
1916 IntegerType::get(Amt)),
1921 case Instruction::Trunc:
1922 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1924 case Instruction::ZExt:
1925 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1927 case Instruction::SExt:
1928 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1930 case Instruction::BitCast:
1931 // BitCasts are no-op casts so we just eliminate the cast.
1932 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
1933 return getSCEV(U->getOperand(0));
1936 case Instruction::IntToPtr:
1937 if (!TD) break; // Without TD we can't analyze pointers.
1938 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1939 TD->getIntPtrType());
1941 case Instruction::PtrToInt:
1942 if (!TD) break; // Without TD we can't analyze pointers.
1943 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1946 case Instruction::GetElementPtr: {
1947 if (!TD) break; // Without TD we can't analyze pointers.
1948 const Type *IntPtrTy = TD->getIntPtrType();
1949 Value *Base = U->getOperand(0);
1950 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
1951 gep_type_iterator GTI = gep_type_begin(U);
1952 for (GetElementPtrInst::op_iterator I = next(U->op_begin()),
1956 // Compute the (potentially symbolic) offset in bytes for this index.
1957 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
1958 // For a struct, add the member offset.
1959 const StructLayout &SL = *TD->getStructLayout(STy);
1960 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
1961 uint64_t Offset = SL.getElementOffset(FieldNo);
1962 TotalOffset = getAddExpr(TotalOffset,
1963 getIntegerSCEV(Offset, IntPtrTy));
1965 // For an array, add the element offset, explicitly scaled.
1966 SCEVHandle LocalOffset = getSCEV(Index);
1967 if (!isa<PointerType>(LocalOffset->getType()))
1968 // Getelementptr indicies are signed.
1969 LocalOffset = getTruncateOrSignExtend(LocalOffset,
1972 getMulExpr(LocalOffset,
1973 getIntegerSCEV(TD->getTypePaddedSize(*GTI),
1975 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
1978 return getAddExpr(getSCEV(Base), TotalOffset);
1981 case Instruction::PHI:
1982 return createNodeForPHI(cast<PHINode>(U));
1984 case Instruction::Select:
1985 // This could be a smax or umax that was lowered earlier.
1986 // Try to recover it.
1987 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
1988 Value *LHS = ICI->getOperand(0);
1989 Value *RHS = ICI->getOperand(1);
1990 switch (ICI->getPredicate()) {
1991 case ICmpInst::ICMP_SLT:
1992 case ICmpInst::ICMP_SLE:
1993 std::swap(LHS, RHS);
1995 case ICmpInst::ICMP_SGT:
1996 case ICmpInst::ICMP_SGE:
1997 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1998 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1999 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2000 // ~smax(~x, ~y) == smin(x, y).
2001 return getNotSCEV(getSMaxExpr(
2002 getNotSCEV(getSCEV(LHS)),
2003 getNotSCEV(getSCEV(RHS))));
2005 case ICmpInst::ICMP_ULT:
2006 case ICmpInst::ICMP_ULE:
2007 std::swap(LHS, RHS);
2009 case ICmpInst::ICMP_UGT:
2010 case ICmpInst::ICMP_UGE:
2011 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2012 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2013 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2014 // ~umax(~x, ~y) == umin(x, y)
2015 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2016 getNotSCEV(getSCEV(RHS))));
2023 default: // We cannot analyze this expression.
2027 return getUnknown(V);
2032 //===----------------------------------------------------------------------===//
2033 // Iteration Count Computation Code
2036 /// getBackedgeTakenCount - If the specified loop has a predictable
2037 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2038 /// object. The backedge-taken count is the number of times the loop header
2039 /// will be branched to from within the loop. This is one less than the
2040 /// trip count of the loop, since it doesn't count the first iteration,
2041 /// when the header is branched to from outside the loop.
2043 /// Note that it is not valid to call this method on a loop without a
2044 /// loop-invariant backedge-taken count (see
2045 /// hasLoopInvariantBackedgeTakenCount).
2047 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2048 return getBackedgeTakenInfo(L).Exact;
2051 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2052 /// return the least SCEV value that is known never to be less than the
2053 /// actual backedge taken count.
2054 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2055 return getBackedgeTakenInfo(L).Max;
2058 const ScalarEvolution::BackedgeTakenInfo &
2059 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2060 // Initially insert a CouldNotCompute for this loop. If the insertion
2061 // succeeds, procede to actually compute a backedge-taken count and
2062 // update the value. The temporary CouldNotCompute value tells SCEV
2063 // code elsewhere that it shouldn't attempt to request a new
2064 // backedge-taken count, which could result in infinite recursion.
2065 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2066 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2068 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2069 if (ItCount.Exact != UnknownValue) {
2070 assert(ItCount.Exact->isLoopInvariant(L) &&
2071 ItCount.Max->isLoopInvariant(L) &&
2072 "Computed trip count isn't loop invariant for loop!");
2073 ++NumTripCountsComputed;
2075 // Update the value in the map.
2076 Pair.first->second = ItCount;
2077 } else if (isa<PHINode>(L->getHeader()->begin())) {
2078 // Only count loops that have phi nodes as not being computable.
2079 ++NumTripCountsNotComputed;
2082 // Now that we know more about the trip count for this loop, forget any
2083 // existing SCEV values for PHI nodes in this loop since they are only
2084 // conservative estimates made without the benefit
2085 // of trip count information.
2086 if (ItCount.hasAnyInfo())
2089 return Pair.first->second;
2092 /// forgetLoopBackedgeTakenCount - This method should be called by the
2093 /// client when it has changed a loop in a way that may effect
2094 /// ScalarEvolution's ability to compute a trip count, or if the loop
2096 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2097 BackedgeTakenCounts.erase(L);
2101 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2102 /// PHI nodes in the given loop. This is used when the trip count of
2103 /// the loop may have changed.
2104 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2105 for (BasicBlock::iterator I = L->getHeader()->begin();
2106 PHINode *PN = dyn_cast<PHINode>(I); ++I)
2110 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2111 /// of the specified loop will execute.
2112 ScalarEvolution::BackedgeTakenInfo
2113 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2114 // If the loop has a non-one exit block count, we can't analyze it.
2115 SmallVector<BasicBlock*, 8> ExitBlocks;
2116 L->getExitBlocks(ExitBlocks);
2117 if (ExitBlocks.size() != 1) return UnknownValue;
2119 // Okay, there is one exit block. Try to find the condition that causes the
2120 // loop to be exited.
2121 BasicBlock *ExitBlock = ExitBlocks[0];
2123 BasicBlock *ExitingBlock = 0;
2124 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2126 if (L->contains(*PI)) {
2127 if (ExitingBlock == 0)
2130 return UnknownValue; // More than one block exiting!
2132 assert(ExitingBlock && "No exits from loop, something is broken!");
2134 // Okay, we've computed the exiting block. See what condition causes us to
2137 // FIXME: we should be able to handle switch instructions (with a single exit)
2138 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2139 if (ExitBr == 0) return UnknownValue;
2140 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2142 // At this point, we know we have a conditional branch that determines whether
2143 // the loop is exited. However, we don't know if the branch is executed each
2144 // time through the loop. If not, then the execution count of the branch will
2145 // not be equal to the trip count of the loop.
2147 // Currently we check for this by checking to see if the Exit branch goes to
2148 // the loop header. If so, we know it will always execute the same number of
2149 // times as the loop. We also handle the case where the exit block *is* the
2150 // loop header. This is common for un-rotated loops. More extensive analysis
2151 // could be done to handle more cases here.
2152 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2153 ExitBr->getSuccessor(1) != L->getHeader() &&
2154 ExitBr->getParent() != L->getHeader())
2155 return UnknownValue;
2157 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2159 // If it's not an integer comparison then compute it the hard way.
2160 // Note that ICmpInst deals with pointer comparisons too so we must check
2161 // the type of the operand.
2162 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2163 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2164 ExitBr->getSuccessor(0) == ExitBlock);
2166 // If the condition was exit on true, convert the condition to exit on false
2167 ICmpInst::Predicate Cond;
2168 if (ExitBr->getSuccessor(1) == ExitBlock)
2169 Cond = ExitCond->getPredicate();
2171 Cond = ExitCond->getInversePredicate();
2173 // Handle common loops like: for (X = "string"; *X; ++X)
2174 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2175 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2177 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2178 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2181 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2182 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2184 // Try to evaluate any dependencies out of the loop.
2185 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2186 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2187 Tmp = getSCEVAtScope(RHS, L);
2188 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2190 // At this point, we would like to compute how many iterations of the
2191 // loop the predicate will return true for these inputs.
2192 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2193 // If there is a loop-invariant, force it into the RHS.
2194 std::swap(LHS, RHS);
2195 Cond = ICmpInst::getSwappedPredicate(Cond);
2198 // If we have a comparison of a chrec against a constant, try to use value
2199 // ranges to answer this query.
2200 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2201 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2202 if (AddRec->getLoop() == L) {
2203 // Form the comparison range using the constant of the correct type so
2204 // that the ConstantRange class knows to do a signed or unsigned
2206 ConstantInt *CompVal = RHSC->getValue();
2207 const Type *RealTy = ExitCond->getOperand(0)->getType();
2208 CompVal = dyn_cast<ConstantInt>(
2209 ConstantExpr::getBitCast(CompVal, RealTy));
2211 // Form the constant range.
2212 ConstantRange CompRange(
2213 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2215 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2216 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2221 case ICmpInst::ICMP_NE: { // while (X != Y)
2222 // Convert to: while (X-Y != 0)
2223 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2224 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2227 case ICmpInst::ICMP_EQ: {
2228 // Convert to: while (X-Y == 0) // while (X == Y)
2229 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2230 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2233 case ICmpInst::ICMP_SLT: {
2234 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2235 if (BTI.hasAnyInfo()) return BTI;
2238 case ICmpInst::ICMP_SGT: {
2239 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2240 getNotSCEV(RHS), L, true);
2241 if (BTI.hasAnyInfo()) return BTI;
2244 case ICmpInst::ICMP_ULT: {
2245 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2246 if (BTI.hasAnyInfo()) return BTI;
2249 case ICmpInst::ICMP_UGT: {
2250 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2251 getNotSCEV(RHS), L, false);
2252 if (BTI.hasAnyInfo()) return BTI;
2257 errs() << "ComputeBackedgeTakenCount ";
2258 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2259 errs() << "[unsigned] ";
2260 errs() << *LHS << " "
2261 << Instruction::getOpcodeName(Instruction::ICmp)
2262 << " " << *RHS << "\n";
2267 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2268 ExitBr->getSuccessor(0) == ExitBlock);
2271 static ConstantInt *
2272 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2273 ScalarEvolution &SE) {
2274 SCEVHandle InVal = SE.getConstant(C);
2275 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2276 assert(isa<SCEVConstant>(Val) &&
2277 "Evaluation of SCEV at constant didn't fold correctly?");
2278 return cast<SCEVConstant>(Val)->getValue();
2281 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2282 /// and a GEP expression (missing the pointer index) indexing into it, return
2283 /// the addressed element of the initializer or null if the index expression is
2286 GetAddressedElementFromGlobal(GlobalVariable *GV,
2287 const std::vector<ConstantInt*> &Indices) {
2288 Constant *Init = GV->getInitializer();
2289 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2290 uint64_t Idx = Indices[i]->getZExtValue();
2291 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2292 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2293 Init = cast<Constant>(CS->getOperand(Idx));
2294 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2295 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2296 Init = cast<Constant>(CA->getOperand(Idx));
2297 } else if (isa<ConstantAggregateZero>(Init)) {
2298 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2299 assert(Idx < STy->getNumElements() && "Bad struct index!");
2300 Init = Constant::getNullValue(STy->getElementType(Idx));
2301 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2302 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2303 Init = Constant::getNullValue(ATy->getElementType());
2305 assert(0 && "Unknown constant aggregate type!");
2309 return 0; // Unknown initializer type
2315 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2316 /// 'icmp op load X, cst', try to see if we can compute the backedge
2317 /// execution count.
2318 SCEVHandle ScalarEvolution::
2319 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2321 ICmpInst::Predicate predicate) {
2322 if (LI->isVolatile()) return UnknownValue;
2324 // Check to see if the loaded pointer is a getelementptr of a global.
2325 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2326 if (!GEP) return UnknownValue;
2328 // Make sure that it is really a constant global we are gepping, with an
2329 // initializer, and make sure the first IDX is really 0.
2330 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2331 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2332 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2333 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2334 return UnknownValue;
2336 // Okay, we allow one non-constant index into the GEP instruction.
2338 std::vector<ConstantInt*> Indexes;
2339 unsigned VarIdxNum = 0;
2340 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2341 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2342 Indexes.push_back(CI);
2343 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2344 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2345 VarIdx = GEP->getOperand(i);
2347 Indexes.push_back(0);
2350 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2351 // Check to see if X is a loop variant variable value now.
2352 SCEVHandle Idx = getSCEV(VarIdx);
2353 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2354 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2356 // We can only recognize very limited forms of loop index expressions, in
2357 // particular, only affine AddRec's like {C1,+,C2}.
2358 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2359 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2360 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2361 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2362 return UnknownValue;
2364 unsigned MaxSteps = MaxBruteForceIterations;
2365 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2366 ConstantInt *ItCst =
2367 ConstantInt::get(IdxExpr->getType(), IterationNum);
2368 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2370 // Form the GEP offset.
2371 Indexes[VarIdxNum] = Val;
2373 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2374 if (Result == 0) break; // Cannot compute!
2376 // Evaluate the condition for this iteration.
2377 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2378 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2379 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2381 errs() << "\n***\n*** Computed loop count " << *ItCst
2382 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2385 ++NumArrayLenItCounts;
2386 return getConstant(ItCst); // Found terminating iteration!
2389 return UnknownValue;
2393 /// CanConstantFold - Return true if we can constant fold an instruction of the
2394 /// specified type, assuming that all operands were constants.
2395 static bool CanConstantFold(const Instruction *I) {
2396 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2397 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2400 if (const CallInst *CI = dyn_cast<CallInst>(I))
2401 if (const Function *F = CI->getCalledFunction())
2402 return canConstantFoldCallTo(F);
2406 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2407 /// in the loop that V is derived from. We allow arbitrary operations along the
2408 /// way, but the operands of an operation must either be constants or a value
2409 /// derived from a constant PHI. If this expression does not fit with these
2410 /// constraints, return null.
2411 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2412 // If this is not an instruction, or if this is an instruction outside of the
2413 // loop, it can't be derived from a loop PHI.
2414 Instruction *I = dyn_cast<Instruction>(V);
2415 if (I == 0 || !L->contains(I->getParent())) return 0;
2417 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2418 if (L->getHeader() == I->getParent())
2421 // We don't currently keep track of the control flow needed to evaluate
2422 // PHIs, so we cannot handle PHIs inside of loops.
2426 // If we won't be able to constant fold this expression even if the operands
2427 // are constants, return early.
2428 if (!CanConstantFold(I)) return 0;
2430 // Otherwise, we can evaluate this instruction if all of its operands are
2431 // constant or derived from a PHI node themselves.
2433 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2434 if (!(isa<Constant>(I->getOperand(Op)) ||
2435 isa<GlobalValue>(I->getOperand(Op)))) {
2436 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2437 if (P == 0) return 0; // Not evolving from PHI
2441 return 0; // Evolving from multiple different PHIs.
2444 // This is a expression evolving from a constant PHI!
2448 /// EvaluateExpression - Given an expression that passes the
2449 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2450 /// in the loop has the value PHIVal. If we can't fold this expression for some
2451 /// reason, return null.
2452 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2453 if (isa<PHINode>(V)) return PHIVal;
2454 if (Constant *C = dyn_cast<Constant>(V)) return C;
2455 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2456 Instruction *I = cast<Instruction>(V);
2458 std::vector<Constant*> Operands;
2459 Operands.resize(I->getNumOperands());
2461 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2462 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2463 if (Operands[i] == 0) return 0;
2466 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2467 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2468 &Operands[0], Operands.size());
2470 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2471 &Operands[0], Operands.size());
2474 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2475 /// in the header of its containing loop, we know the loop executes a
2476 /// constant number of times, and the PHI node is just a recurrence
2477 /// involving constants, fold it.
2478 Constant *ScalarEvolution::
2479 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2480 std::map<PHINode*, Constant*>::iterator I =
2481 ConstantEvolutionLoopExitValue.find(PN);
2482 if (I != ConstantEvolutionLoopExitValue.end())
2485 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2486 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2488 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2490 // Since the loop is canonicalized, the PHI node must have two entries. One
2491 // entry must be a constant (coming in from outside of the loop), and the
2492 // second must be derived from the same PHI.
2493 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2494 Constant *StartCST =
2495 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2497 return RetVal = 0; // Must be a constant.
2499 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2500 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2502 return RetVal = 0; // Not derived from same PHI.
2504 // Execute the loop symbolically to determine the exit value.
2505 if (BEs.getActiveBits() >= 32)
2506 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2508 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2509 unsigned IterationNum = 0;
2510 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2511 if (IterationNum == NumIterations)
2512 return RetVal = PHIVal; // Got exit value!
2514 // Compute the value of the PHI node for the next iteration.
2515 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2516 if (NextPHI == PHIVal)
2517 return RetVal = NextPHI; // Stopped evolving!
2519 return 0; // Couldn't evaluate!
2524 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2525 /// constant number of times (the condition evolves only from constants),
2526 /// try to evaluate a few iterations of the loop until we get the exit
2527 /// condition gets a value of ExitWhen (true or false). If we cannot
2528 /// evaluate the trip count of the loop, return UnknownValue.
2529 SCEVHandle ScalarEvolution::
2530 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2531 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2532 if (PN == 0) return UnknownValue;
2534 // Since the loop is canonicalized, the PHI node must have two entries. One
2535 // entry must be a constant (coming in from outside of the loop), and the
2536 // second must be derived from the same PHI.
2537 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2538 Constant *StartCST =
2539 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2540 if (StartCST == 0) return UnknownValue; // Must be a constant.
2542 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2543 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2544 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2546 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2547 // the loop symbolically to determine when the condition gets a value of
2549 unsigned IterationNum = 0;
2550 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2551 for (Constant *PHIVal = StartCST;
2552 IterationNum != MaxIterations; ++IterationNum) {
2553 ConstantInt *CondVal =
2554 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2556 // Couldn't symbolically evaluate.
2557 if (!CondVal) return UnknownValue;
2559 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2560 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2561 ++NumBruteForceTripCountsComputed;
2562 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2565 // Compute the value of the PHI node for the next iteration.
2566 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2567 if (NextPHI == 0 || NextPHI == PHIVal)
2568 return UnknownValue; // Couldn't evaluate or not making progress...
2572 // Too many iterations were needed to evaluate.
2573 return UnknownValue;
2576 /// getSCEVAtScope - Compute the value of the specified expression within the
2577 /// indicated loop (which may be null to indicate in no loop). If the
2578 /// expression cannot be evaluated, return UnknownValue.
2579 SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) {
2580 // FIXME: this should be turned into a virtual method on SCEV!
2582 if (isa<SCEVConstant>(V)) return V;
2584 // If this instruction is evolved from a constant-evolving PHI, compute the
2585 // exit value from the loop without using SCEVs.
2586 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2587 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2588 const Loop *LI = (*this->LI)[I->getParent()];
2589 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2590 if (PHINode *PN = dyn_cast<PHINode>(I))
2591 if (PN->getParent() == LI->getHeader()) {
2592 // Okay, there is no closed form solution for the PHI node. Check
2593 // to see if the loop that contains it has a known backedge-taken
2594 // count. If so, we may be able to force computation of the exit
2596 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2597 if (SCEVConstant *BTCC =
2598 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2599 // Okay, we know how many times the containing loop executes. If
2600 // this is a constant evolving PHI node, get the final value at
2601 // the specified iteration number.
2602 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2603 BTCC->getValue()->getValue(),
2605 if (RV) return getUnknown(RV);
2609 // Okay, this is an expression that we cannot symbolically evaluate
2610 // into a SCEV. Check to see if it's possible to symbolically evaluate
2611 // the arguments into constants, and if so, try to constant propagate the
2612 // result. This is particularly useful for computing loop exit values.
2613 if (CanConstantFold(I)) {
2614 std::vector<Constant*> Operands;
2615 Operands.reserve(I->getNumOperands());
2616 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2617 Value *Op = I->getOperand(i);
2618 if (Constant *C = dyn_cast<Constant>(Op)) {
2619 Operands.push_back(C);
2621 // If any of the operands is non-constant and if they are
2622 // non-integer and non-pointer, don't even try to analyze them
2623 // with scev techniques.
2624 if (!isSCEVable(Op->getType()))
2627 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2628 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2629 Constant *C = SC->getValue();
2630 if (C->getType() != Op->getType())
2631 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2635 Operands.push_back(C);
2636 } else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2637 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2638 if (C->getType() != Op->getType())
2640 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2644 Operands.push_back(C);
2654 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2655 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2656 &Operands[0], Operands.size());
2658 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2659 &Operands[0], Operands.size());
2660 return getUnknown(C);
2664 // This is some other type of SCEVUnknown, just return it.
2668 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2669 // Avoid performing the look-up in the common case where the specified
2670 // expression has no loop-variant portions.
2671 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2672 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2673 if (OpAtScope != Comm->getOperand(i)) {
2674 if (OpAtScope == UnknownValue) return UnknownValue;
2675 // Okay, at least one of these operands is loop variant but might be
2676 // foldable. Build a new instance of the folded commutative expression.
2677 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2678 NewOps.push_back(OpAtScope);
2680 for (++i; i != e; ++i) {
2681 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2682 if (OpAtScope == UnknownValue) return UnknownValue;
2683 NewOps.push_back(OpAtScope);
2685 if (isa<SCEVAddExpr>(Comm))
2686 return getAddExpr(NewOps);
2687 if (isa<SCEVMulExpr>(Comm))
2688 return getMulExpr(NewOps);
2689 if (isa<SCEVSMaxExpr>(Comm))
2690 return getSMaxExpr(NewOps);
2691 if (isa<SCEVUMaxExpr>(Comm))
2692 return getUMaxExpr(NewOps);
2693 assert(0 && "Unknown commutative SCEV type!");
2696 // If we got here, all operands are loop invariant.
2700 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2701 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2702 if (LHS == UnknownValue) return LHS;
2703 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2704 if (RHS == UnknownValue) return RHS;
2705 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2706 return Div; // must be loop invariant
2707 return getUDivExpr(LHS, RHS);
2710 // If this is a loop recurrence for a loop that does not contain L, then we
2711 // are dealing with the final value computed by the loop.
2712 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2713 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2714 // To evaluate this recurrence, we need to know how many times the AddRec
2715 // loop iterates. Compute this now.
2716 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2717 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2719 // Then, evaluate the AddRec.
2720 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
2722 return UnknownValue;
2725 if (SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
2726 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2727 if (Op == UnknownValue) return Op;
2728 if (Op == Cast->getOperand())
2729 return Cast; // must be loop invariant
2730 return getZeroExtendExpr(Op, Cast->getType());
2733 if (SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
2734 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2735 if (Op == UnknownValue) return Op;
2736 if (Op == Cast->getOperand())
2737 return Cast; // must be loop invariant
2738 return getSignExtendExpr(Op, Cast->getType());
2741 if (SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
2742 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2743 if (Op == UnknownValue) return Op;
2744 if (Op == Cast->getOperand())
2745 return Cast; // must be loop invariant
2746 return getTruncateExpr(Op, Cast->getType());
2749 assert(0 && "Unknown SCEV type!");
2752 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2753 /// at the specified scope in the program. The L value specifies a loop
2754 /// nest to evaluate the expression at, where null is the top-level or a
2755 /// specified loop is immediately inside of the loop.
2757 /// This method can be used to compute the exit value for a variable defined
2758 /// in a loop by querying what the value will hold in the parent loop.
2760 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2761 /// object is returned.
2762 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
2763 return getSCEVAtScope(getSCEV(V), L);
2766 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2767 /// following equation:
2769 /// A * X = B (mod N)
2771 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2772 /// A and B isn't important.
2774 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2775 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2776 ScalarEvolution &SE) {
2777 uint32_t BW = A.getBitWidth();
2778 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2779 assert(A != 0 && "A must be non-zero.");
2783 // The gcd of A and N may have only one prime factor: 2. The number of
2784 // trailing zeros in A is its multiplicity
2785 uint32_t Mult2 = A.countTrailingZeros();
2788 // 2. Check if B is divisible by D.
2790 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2791 // is not less than multiplicity of this prime factor for D.
2792 if (B.countTrailingZeros() < Mult2)
2793 return SE.getCouldNotCompute();
2795 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2798 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2799 // bit width during computations.
2800 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2801 APInt Mod(BW + 1, 0);
2802 Mod.set(BW - Mult2); // Mod = N / D
2803 APInt I = AD.multiplicativeInverse(Mod);
2805 // 4. Compute the minimum unsigned root of the equation:
2806 // I * (B / D) mod (N / D)
2807 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2809 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2811 return SE.getConstant(Result.trunc(BW));
2814 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2815 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2816 /// might be the same) or two SCEVCouldNotCompute objects.
2818 static std::pair<SCEVHandle,SCEVHandle>
2819 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2820 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2821 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2822 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2823 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2825 // We currently can only solve this if the coefficients are constants.
2826 if (!LC || !MC || !NC) {
2827 SCEV *CNC = SE.getCouldNotCompute();
2828 return std::make_pair(CNC, CNC);
2831 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2832 const APInt &L = LC->getValue()->getValue();
2833 const APInt &M = MC->getValue()->getValue();
2834 const APInt &N = NC->getValue()->getValue();
2835 APInt Two(BitWidth, 2);
2836 APInt Four(BitWidth, 4);
2839 using namespace APIntOps;
2841 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2842 // The B coefficient is M-N/2
2846 // The A coefficient is N/2
2847 APInt A(N.sdiv(Two));
2849 // Compute the B^2-4ac term.
2852 SqrtTerm -= Four * (A * C);
2854 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2855 // integer value or else APInt::sqrt() will assert.
2856 APInt SqrtVal(SqrtTerm.sqrt());
2858 // Compute the two solutions for the quadratic formula.
2859 // The divisions must be performed as signed divisions.
2861 APInt TwoA( A << 1 );
2862 if (TwoA.isMinValue()) {
2863 SCEV *CNC = SE.getCouldNotCompute();
2864 return std::make_pair(CNC, CNC);
2867 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2868 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2870 return std::make_pair(SE.getConstant(Solution1),
2871 SE.getConstant(Solution2));
2872 } // end APIntOps namespace
2875 /// HowFarToZero - Return the number of times a backedge comparing the specified
2876 /// value to zero will execute. If not computable, return UnknownValue
2877 SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) {
2878 // If the value is a constant
2879 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2880 // If the value is already zero, the branch will execute zero times.
2881 if (C->getValue()->isZero()) return C;
2882 return UnknownValue; // Otherwise it will loop infinitely.
2885 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2886 if (!AddRec || AddRec->getLoop() != L)
2887 return UnknownValue;
2889 if (AddRec->isAffine()) {
2890 // If this is an affine expression, the execution count of this branch is
2891 // the minimum unsigned root of the following equation:
2893 // Start + Step*N = 0 (mod 2^BW)
2897 // Step*N = -Start (mod 2^BW)
2899 // where BW is the common bit width of Start and Step.
2901 // Get the initial value for the loop.
2902 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2903 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2905 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2907 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2908 // For now we handle only constant steps.
2910 // First, handle unitary steps.
2911 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2912 return getNegativeSCEV(Start); // N = -Start (as unsigned)
2913 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2914 return Start; // N = Start (as unsigned)
2916 // Then, try to solve the above equation provided that Start is constant.
2917 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2918 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2919 -StartC->getValue()->getValue(),
2922 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2923 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2924 // the quadratic equation to solve it.
2925 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
2927 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2928 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2931 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
2932 << " sol#2: " << *R2 << "\n";
2934 // Pick the smallest positive root value.
2935 if (ConstantInt *CB =
2936 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2937 R1->getValue(), R2->getValue()))) {
2938 if (CB->getZExtValue() == false)
2939 std::swap(R1, R2); // R1 is the minimum root now.
2941 // We can only use this value if the chrec ends up with an exact zero
2942 // value at this index. When solving for "X*X != 5", for example, we
2943 // should not accept a root of 2.
2944 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
2946 return R1; // We found a quadratic root!
2951 return UnknownValue;
2954 /// HowFarToNonZero - Return the number of times a backedge checking the
2955 /// specified value for nonzero will execute. If not computable, return
2957 SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) {
2958 // Loops that look like: while (X == 0) are very strange indeed. We don't
2959 // handle them yet except for the trivial case. This could be expanded in the
2960 // future as needed.
2962 // If the value is a constant, check to see if it is known to be non-zero
2963 // already. If so, the backedge will execute zero times.
2964 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2965 if (!C->getValue()->isNullValue())
2966 return getIntegerSCEV(0, C->getType());
2967 return UnknownValue; // Otherwise it will loop infinitely.
2970 // We could implement others, but I really doubt anyone writes loops like
2971 // this, and if they did, they would already be constant folded.
2972 return UnknownValue;
2975 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2976 /// (which may not be an immediate predecessor) which has exactly one
2977 /// successor from which BB is reachable, or null if no such block is
2981 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2982 // If the block has a unique predecessor, then there is no path from the
2983 // predecessor to the block that does not go through the direct edge
2984 // from the predecessor to the block.
2985 if (BasicBlock *Pred = BB->getSinglePredecessor())
2988 // A loop's header is defined to be a block that dominates the loop.
2989 // If the loop has a preheader, it must be a block that has exactly
2990 // one successor that can reach BB. This is slightly more strict
2991 // than necessary, but works if critical edges are split.
2992 if (Loop *L = LI->getLoopFor(BB))
2993 return L->getLoopPreheader();
2998 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
2999 /// a conditional between LHS and RHS. This is used to help avoid max
3000 /// expressions in loop trip counts.
3001 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3002 ICmpInst::Predicate Pred,
3003 SCEV *LHS, SCEV *RHS) {
3004 BasicBlock *Preheader = L->getLoopPreheader();
3005 BasicBlock *PreheaderDest = L->getHeader();
3007 // Starting at the preheader, climb up the predecessor chain, as long as
3008 // there are predecessors that can be found that have unique successors
3009 // leading to the original header.
3011 PreheaderDest = Preheader,
3012 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
3014 BranchInst *LoopEntryPredicate =
3015 dyn_cast<BranchInst>(Preheader->getTerminator());
3016 if (!LoopEntryPredicate ||
3017 LoopEntryPredicate->isUnconditional())
3020 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3023 // Now that we found a conditional branch that dominates the loop, check to
3024 // see if it is the comparison we are looking for.
3025 Value *PreCondLHS = ICI->getOperand(0);
3026 Value *PreCondRHS = ICI->getOperand(1);
3027 ICmpInst::Predicate Cond;
3028 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
3029 Cond = ICI->getPredicate();
3031 Cond = ICI->getInversePredicate();
3034 ; // An exact match.
3035 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3036 ; // The actual condition is beyond sufficient.
3038 // Check a few special cases.
3040 case ICmpInst::ICMP_UGT:
3041 if (Pred == ICmpInst::ICMP_ULT) {
3042 std::swap(PreCondLHS, PreCondRHS);
3043 Cond = ICmpInst::ICMP_ULT;
3047 case ICmpInst::ICMP_SGT:
3048 if (Pred == ICmpInst::ICMP_SLT) {
3049 std::swap(PreCondLHS, PreCondRHS);
3050 Cond = ICmpInst::ICMP_SLT;
3054 case ICmpInst::ICMP_NE:
3055 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3056 // so check for this case by checking if the NE is comparing against
3057 // a minimum or maximum constant.
3058 if (!ICmpInst::isTrueWhenEqual(Pred))
3059 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3060 const APInt &A = CI->getValue();
3062 case ICmpInst::ICMP_SLT:
3063 if (A.isMaxSignedValue()) break;
3065 case ICmpInst::ICMP_SGT:
3066 if (A.isMinSignedValue()) break;
3068 case ICmpInst::ICMP_ULT:
3069 if (A.isMaxValue()) break;
3071 case ICmpInst::ICMP_UGT:
3072 if (A.isMinValue()) break;
3077 Cond = ICmpInst::ICMP_NE;
3078 // NE is symmetric but the original comparison may not be. Swap
3079 // the operands if necessary so that they match below.
3080 if (isa<SCEVConstant>(LHS))
3081 std::swap(PreCondLHS, PreCondRHS);
3086 // We weren't able to reconcile the condition.
3090 if (!PreCondLHS->getType()->isInteger()) continue;
3092 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3093 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3094 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3095 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3096 RHS == getNotSCEV(PreCondLHSSCEV)))
3103 /// HowManyLessThans - Return the number of times a backedge containing the
3104 /// specified less-than comparison will execute. If not computable, return
3106 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3107 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
3108 // Only handle: "ADDREC < LoopInvariant".
3109 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3111 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3112 if (!AddRec || AddRec->getLoop() != L)
3113 return UnknownValue;
3115 if (AddRec->isAffine()) {
3116 // FORNOW: We only support unit strides.
3117 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3118 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3119 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3121 // TODO: handle non-constant strides.
3122 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3123 if (!CStep || CStep->isZero())
3124 return UnknownValue;
3125 if (CStep->getValue()->getValue() == 1) {
3126 // With unit stride, the iteration never steps past the limit value.
3127 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3128 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3129 // Test whether a positive iteration iteration can step past the limit
3130 // value and past the maximum value for its type in a single step.
3132 APInt Max = APInt::getSignedMaxValue(BitWidth);
3133 if ((Max - CStep->getValue()->getValue())
3134 .slt(CLimit->getValue()->getValue()))
3135 return UnknownValue;
3137 APInt Max = APInt::getMaxValue(BitWidth);
3138 if ((Max - CStep->getValue()->getValue())
3139 .ult(CLimit->getValue()->getValue()))
3140 return UnknownValue;
3143 // TODO: handle non-constant limit values below.
3144 return UnknownValue;
3146 // TODO: handle negative strides below.
3147 return UnknownValue;
3149 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3150 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3151 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3152 // treat m-n as signed nor unsigned due to overflow possibility.
3154 // First, we get the value of the LHS in the first iteration: n
3155 SCEVHandle Start = AddRec->getOperand(0);
3157 // Determine the minimum constant start value.
3158 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3159 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3160 APInt::getMinValue(BitWidth));
3162 // If we know that the condition is true in order to enter the loop,
3163 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3164 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3165 // division must round up.
3166 SCEVHandle End = RHS;
3167 if (!isLoopGuardedByCond(L,
3168 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3169 getMinusSCEV(Start, Step), RHS))
3170 End = isSigned ? getSMaxExpr(RHS, Start)
3171 : getUMaxExpr(RHS, Start);
3173 // Determine the maximum constant end value.
3174 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3175 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3176 APInt::getMaxValue(BitWidth));
3178 // Finally, we subtract these two values and divide, rounding up, to get
3179 // the number of times the backedge is executed.
3180 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3181 getAddExpr(Step, NegOne)),
3184 // The maximum backedge count is similar, except using the minimum start
3185 // value and the maximum end value.
3186 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3188 getAddExpr(Step, NegOne)),
3191 return BackedgeTakenInfo(BECount, MaxBECount);
3194 return UnknownValue;
3197 /// getNumIterationsInRange - Return the number of iterations of this loop that
3198 /// produce values in the specified constant range. Another way of looking at
3199 /// this is that it returns the first iteration number where the value is not in
3200 /// the condition, thus computing the exit count. If the iteration count can't
3201 /// be computed, an instance of SCEVCouldNotCompute is returned.
3202 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3203 ScalarEvolution &SE) const {
3204 if (Range.isFullSet()) // Infinite loop.
3205 return SE.getCouldNotCompute();
3207 // If the start is a non-zero constant, shift the range to simplify things.
3208 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3209 if (!SC->getValue()->isZero()) {
3210 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3211 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3212 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3213 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
3214 return ShiftedAddRec->getNumIterationsInRange(
3215 Range.subtract(SC->getValue()->getValue()), SE);
3216 // This is strange and shouldn't happen.
3217 return SE.getCouldNotCompute();
3220 // The only time we can solve this is when we have all constant indices.
3221 // Otherwise, we cannot determine the overflow conditions.
3222 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3223 if (!isa<SCEVConstant>(getOperand(i)))
3224 return SE.getCouldNotCompute();
3227 // Okay at this point we know that all elements of the chrec are constants and
3228 // that the start element is zero.
3230 // First check to see if the range contains zero. If not, the first
3232 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3233 if (!Range.contains(APInt(BitWidth, 0)))
3234 return SE.getConstant(ConstantInt::get(getType(),0));
3237 // If this is an affine expression then we have this situation:
3238 // Solve {0,+,A} in Range === Ax in Range
3240 // We know that zero is in the range. If A is positive then we know that
3241 // the upper value of the range must be the first possible exit value.
3242 // If A is negative then the lower of the range is the last possible loop
3243 // value. Also note that we already checked for a full range.
3244 APInt One(BitWidth,1);
3245 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3246 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3248 // The exit value should be (End+A)/A.
3249 APInt ExitVal = (End + A).udiv(A);
3250 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3252 // Evaluate at the exit value. If we really did fall out of the valid
3253 // range, then we computed our trip count, otherwise wrap around or other
3254 // things must have happened.
3255 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3256 if (Range.contains(Val->getValue()))
3257 return SE.getCouldNotCompute(); // Something strange happened
3259 // Ensure that the previous value is in the range. This is a sanity check.
3260 assert(Range.contains(
3261 EvaluateConstantChrecAtConstant(this,
3262 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3263 "Linear scev computation is off in a bad way!");
3264 return SE.getConstant(ExitValue);
3265 } else if (isQuadratic()) {
3266 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3267 // quadratic equation to solve it. To do this, we must frame our problem in
3268 // terms of figuring out when zero is crossed, instead of when
3269 // Range.getUpper() is crossed.
3270 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3271 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3272 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3274 // Next, solve the constructed addrec
3275 std::pair<SCEVHandle,SCEVHandle> Roots =
3276 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3277 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3278 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3280 // Pick the smallest positive root value.
3281 if (ConstantInt *CB =
3282 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3283 R1->getValue(), R2->getValue()))) {
3284 if (CB->getZExtValue() == false)
3285 std::swap(R1, R2); // R1 is the minimum root now.
3287 // Make sure the root is not off by one. The returned iteration should
3288 // not be in the range, but the previous one should be. When solving
3289 // for "X*X < 5", for example, we should not return a root of 2.
3290 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3293 if (Range.contains(R1Val->getValue())) {
3294 // The next iteration must be out of the range...
3295 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3297 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3298 if (!Range.contains(R1Val->getValue()))
3299 return SE.getConstant(NextVal);
3300 return SE.getCouldNotCompute(); // Something strange happened
3303 // If R1 was not in the range, then it is a good return value. Make
3304 // sure that R1-1 WAS in the range though, just in case.
3305 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3306 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3307 if (Range.contains(R1Val->getValue()))
3309 return SE.getCouldNotCompute(); // Something strange happened
3314 return SE.getCouldNotCompute();
3319 //===----------------------------------------------------------------------===//
3320 // SCEVCallbackVH Class Implementation
3321 //===----------------------------------------------------------------------===//
3323 void SCEVCallbackVH::deleted() {
3324 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3325 SE->Scalars.erase(getValPtr());
3326 // this now dangles!
3329 void SCEVCallbackVH::allUsesReplacedWith(Value *V) {
3330 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3331 SE->Scalars.erase(getValPtr());
3332 // this now dangles!
3335 SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3336 : CallbackVH(V), SE(se) {}
3338 //===----------------------------------------------------------------------===//
3339 // ScalarEvolution Class Implementation
3340 //===----------------------------------------------------------------------===//
3342 ScalarEvolution::ScalarEvolution()
3343 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3346 bool ScalarEvolution::runOnFunction(Function &F) {
3348 LI = &getAnalysis<LoopInfo>();
3349 TD = getAnalysisIfAvailable<TargetData>();
3353 void ScalarEvolution::releaseMemory() {
3355 BackedgeTakenCounts.clear();
3356 ConstantEvolutionLoopExitValue.clear();
3359 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3360 AU.setPreservesAll();
3361 AU.addRequiredTransitive<LoopInfo>();
3364 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3365 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3368 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3370 // Print all inner loops first
3371 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3372 PrintLoopInfo(OS, SE, *I);
3374 OS << "Loop " << L->getHeader()->getName() << ": ";
3376 SmallVector<BasicBlock*, 8> ExitBlocks;
3377 L->getExitBlocks(ExitBlocks);
3378 if (ExitBlocks.size() != 1)
3379 OS << "<multiple exits> ";
3381 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3382 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3384 OS << "Unpredictable backedge-taken count. ";
3390 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3391 // ScalarEvolution's implementaiton of the print method is to print
3392 // out SCEV values of all instructions that are interesting. Doing
3393 // this potentially causes it to create new SCEV objects though,
3394 // which technically conflicts with the const qualifier. This isn't
3395 // observable from outside the class though (the hasSCEV function
3396 // notwithstanding), so casting away the const isn't dangerous.
3397 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3399 OS << "Classifying expressions for: " << F->getName() << "\n";
3400 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3401 if (isSCEVable(I->getType())) {
3404 SCEVHandle SV = SE.getSCEV(&*I);
3408 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3410 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3411 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3412 OS << "<<Unknown>>";
3422 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3423 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3424 PrintLoopInfo(OS, &SE, *I);
3427 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3428 raw_os_ostream OS(o);