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 /// deleteValueFromRecords - This method should be called by the
1470 /// client before it removes an instruction from the program, to make sure
1471 /// that no dangling references are left around.
1472 void ScalarEvolution::deleteValueFromRecords(Value *V) {
1473 SmallVector<Value *, 16> Worklist;
1475 if (Scalars.erase(V)) {
1476 if (PHINode *PN = dyn_cast<PHINode>(V))
1477 ConstantEvolutionLoopExitValue.erase(PN);
1478 Worklist.push_back(V);
1481 while (!Worklist.empty()) {
1482 Value *VV = Worklist.back();
1483 Worklist.pop_back();
1485 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1487 Instruction *Inst = cast<Instruction>(*UI);
1488 if (Scalars.erase(Inst)) {
1489 if (PHINode *PN = dyn_cast<PHINode>(VV))
1490 ConstantEvolutionLoopExitValue.erase(PN);
1491 Worklist.push_back(Inst);
1497 /// isSCEVable - Test if values of the given type are analyzable within
1498 /// the SCEV framework. This primarily includes integer types, and it
1499 /// can optionally include pointer types if the ScalarEvolution class
1500 /// has access to target-specific information.
1501 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1502 // Integers are always SCEVable.
1503 if (Ty->isInteger())
1506 // Pointers are SCEVable if TargetData information is available
1507 // to provide pointer size information.
1508 if (isa<PointerType>(Ty))
1511 // Otherwise it's not SCEVable.
1515 /// getTypeSizeInBits - Return the size in bits of the specified type,
1516 /// for which isSCEVable must return true.
1517 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1518 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1520 // If we have a TargetData, use it!
1522 return TD->getTypeSizeInBits(Ty);
1524 // Otherwise, we support only integer types.
1525 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1526 return Ty->getPrimitiveSizeInBits();
1529 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1530 /// the given type and which represents how SCEV will treat the given
1531 /// type, for which isSCEVable must return true. For pointer types,
1532 /// this is the pointer-sized integer type.
1533 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1534 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1536 if (Ty->isInteger())
1539 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1540 return TD->getIntPtrType();
1543 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1544 return UnknownValue;
1547 // hasSCEV - Return true if the SCEV for this value has already been
1549 bool ScalarEvolution::hasSCEV(Value *V) const {
1550 return Scalars.count(V);
1553 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1554 /// expression and create a new one.
1555 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1556 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1558 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1559 if (I != Scalars.end()) return I->second;
1560 SCEVHandle S = createSCEV(V);
1561 Scalars.insert(std::make_pair(V, S));
1565 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1566 /// specified signed integer value and return a SCEV for the constant.
1567 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1568 Ty = getEffectiveSCEVType(Ty);
1571 C = Constant::getNullValue(Ty);
1572 else if (Ty->isFloatingPoint())
1573 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1574 APFloat::IEEEdouble, Val));
1576 C = ConstantInt::get(Ty, Val);
1577 return getUnknown(C);
1580 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1582 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1583 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1584 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1586 const Type *Ty = V->getType();
1587 Ty = getEffectiveSCEVType(Ty);
1588 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1591 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1592 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1593 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1594 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1596 const Type *Ty = V->getType();
1597 Ty = getEffectiveSCEVType(Ty);
1598 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1599 return getMinusSCEV(AllOnes, V);
1602 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1604 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1605 const SCEVHandle &RHS) {
1607 return getAddExpr(LHS, getNegativeSCEV(RHS));
1610 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1611 /// input value to the specified type. If the type must be extended, it is zero
1614 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1616 const Type *SrcTy = V->getType();
1617 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1618 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1619 "Cannot truncate or zero extend with non-integer arguments!");
1620 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1621 return V; // No conversion
1622 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1623 return getTruncateExpr(V, Ty);
1624 return getZeroExtendExpr(V, Ty);
1627 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1628 /// input value to the specified type. If the type must be extended, it is sign
1631 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1633 const Type *SrcTy = V->getType();
1634 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1635 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1636 "Cannot truncate or zero extend with non-integer arguments!");
1637 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1638 return V; // No conversion
1639 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1640 return getTruncateExpr(V, Ty);
1641 return getSignExtendExpr(V, Ty);
1644 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1645 /// the specified instruction and replaces any references to the symbolic value
1646 /// SymName with the specified value. This is used during PHI resolution.
1647 void ScalarEvolution::
1648 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1649 const SCEVHandle &NewVal) {
1650 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1651 if (SI == Scalars.end()) return;
1654 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1655 if (NV == SI->second) return; // No change.
1657 SI->second = NV; // Update the scalars map!
1659 // Any instruction values that use this instruction might also need to be
1661 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1663 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1666 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1667 /// a loop header, making it a potential recurrence, or it doesn't.
1669 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1670 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1671 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1672 if (L->getHeader() == PN->getParent()) {
1673 // If it lives in the loop header, it has two incoming values, one
1674 // from outside the loop, and one from inside.
1675 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1676 unsigned BackEdge = IncomingEdge^1;
1678 // While we are analyzing this PHI node, handle its value symbolically.
1679 SCEVHandle SymbolicName = getUnknown(PN);
1680 assert(Scalars.find(PN) == Scalars.end() &&
1681 "PHI node already processed?");
1682 Scalars.insert(std::make_pair(PN, SymbolicName));
1684 // Using this symbolic name for the PHI, analyze the value coming around
1686 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1688 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1689 // has a special value for the first iteration of the loop.
1691 // If the value coming around the backedge is an add with the symbolic
1692 // value we just inserted, then we found a simple induction variable!
1693 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1694 // If there is a single occurrence of the symbolic value, replace it
1695 // with a recurrence.
1696 unsigned FoundIndex = Add->getNumOperands();
1697 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1698 if (Add->getOperand(i) == SymbolicName)
1699 if (FoundIndex == e) {
1704 if (FoundIndex != Add->getNumOperands()) {
1705 // Create an add with everything but the specified operand.
1706 std::vector<SCEVHandle> Ops;
1707 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1708 if (i != FoundIndex)
1709 Ops.push_back(Add->getOperand(i));
1710 SCEVHandle Accum = getAddExpr(Ops);
1712 // This is not a valid addrec if the step amount is varying each
1713 // loop iteration, but is not itself an addrec in this loop.
1714 if (Accum->isLoopInvariant(L) ||
1715 (isa<SCEVAddRecExpr>(Accum) &&
1716 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1717 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1718 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1720 // Okay, for the entire analysis of this edge we assumed the PHI
1721 // to be symbolic. We now need to go back and update all of the
1722 // entries for the scalars that use the PHI (except for the PHI
1723 // itself) to use the new analyzed value instead of the "symbolic"
1725 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1729 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1730 // Otherwise, this could be a loop like this:
1731 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1732 // In this case, j = {1,+,1} and BEValue is j.
1733 // Because the other in-value of i (0) fits the evolution of BEValue
1734 // i really is an addrec evolution.
1735 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1736 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1738 // If StartVal = j.start - j.stride, we can use StartVal as the
1739 // initial step of the addrec evolution.
1740 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
1741 AddRec->getOperand(1))) {
1742 SCEVHandle PHISCEV =
1743 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1745 // Okay, for the entire analysis of this edge we assumed the PHI
1746 // to be symbolic. We now need to go back and update all of the
1747 // entries for the scalars that use the PHI (except for the PHI
1748 // itself) to use the new analyzed value instead of the "symbolic"
1750 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1756 return SymbolicName;
1759 // If it's not a loop phi, we can't handle it yet.
1760 return getUnknown(PN);
1763 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1764 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1765 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1766 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1767 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
1768 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1769 return C->getValue()->getValue().countTrailingZeros();
1771 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1772 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
1773 (uint32_t)SE.getTypeSizeInBits(T->getType()));
1775 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1776 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1777 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1778 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1781 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1782 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1783 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1784 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1787 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1788 // The result is the min of all operands results.
1789 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1790 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1791 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1795 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1796 // The result is the sum of all operands results.
1797 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1798 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
1799 for (unsigned i = 1, e = M->getNumOperands();
1800 SumOpRes != BitWidth && i != e; ++i)
1801 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
1806 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1807 // The result is the min of all operands results.
1808 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1809 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1810 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1814 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1815 // The result is the min of all operands results.
1816 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1817 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1818 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1822 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1823 // The result is the min of all operands results.
1824 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1825 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1826 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1830 // SCEVUDivExpr, SCEVUnknown
1834 /// createSCEV - We know that there is no SCEV for the specified value.
1835 /// Analyze the expression.
1837 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
1838 if (!isSCEVable(V->getType()))
1839 return getUnknown(V);
1841 unsigned Opcode = Instruction::UserOp1;
1842 if (Instruction *I = dyn_cast<Instruction>(V))
1843 Opcode = I->getOpcode();
1844 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1845 Opcode = CE->getOpcode();
1847 return getUnknown(V);
1849 User *U = cast<User>(V);
1851 case Instruction::Add:
1852 return getAddExpr(getSCEV(U->getOperand(0)),
1853 getSCEV(U->getOperand(1)));
1854 case Instruction::Mul:
1855 return getMulExpr(getSCEV(U->getOperand(0)),
1856 getSCEV(U->getOperand(1)));
1857 case Instruction::UDiv:
1858 return getUDivExpr(getSCEV(U->getOperand(0)),
1859 getSCEV(U->getOperand(1)));
1860 case Instruction::Sub:
1861 return getMinusSCEV(getSCEV(U->getOperand(0)),
1862 getSCEV(U->getOperand(1)));
1863 case Instruction::And:
1864 // For an expression like x&255 that merely masks off the high bits,
1865 // use zext(trunc(x)) as the SCEV expression.
1866 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1867 if (CI->isNullValue())
1868 return getSCEV(U->getOperand(1));
1869 if (CI->isAllOnesValue())
1870 return getSCEV(U->getOperand(0));
1871 const APInt &A = CI->getValue();
1872 unsigned Ones = A.countTrailingOnes();
1873 if (APIntOps::isMask(Ones, A))
1875 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
1876 IntegerType::get(Ones)),
1880 case Instruction::Or:
1881 // If the RHS of the Or is a constant, we may have something like:
1882 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1883 // optimizations will transparently handle this case.
1885 // In order for this transformation to be safe, the LHS must be of the
1886 // form X*(2^n) and the Or constant must be less than 2^n.
1887 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1888 SCEVHandle LHS = getSCEV(U->getOperand(0));
1889 const APInt &CIVal = CI->getValue();
1890 if (GetMinTrailingZeros(LHS, *this) >=
1891 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1892 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
1895 case Instruction::Xor:
1896 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1897 // If the RHS of the xor is a signbit, then this is just an add.
1898 // Instcombine turns add of signbit into xor as a strength reduction step.
1899 if (CI->getValue().isSignBit())
1900 return getAddExpr(getSCEV(U->getOperand(0)),
1901 getSCEV(U->getOperand(1)));
1903 // If the RHS of xor is -1, then this is a not operation.
1904 else if (CI->isAllOnesValue())
1905 return getNotSCEV(getSCEV(U->getOperand(0)));
1909 case Instruction::Shl:
1910 // Turn shift left of a constant amount into a multiply.
1911 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1912 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1913 Constant *X = ConstantInt::get(
1914 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1915 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1919 case Instruction::LShr:
1920 // Turn logical shift right of a constant into a unsigned divide.
1921 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1922 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1923 Constant *X = ConstantInt::get(
1924 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1925 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1929 case Instruction::AShr:
1930 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
1931 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
1932 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
1933 if (L->getOpcode() == Instruction::Shl &&
1934 L->getOperand(1) == U->getOperand(1)) {
1935 unsigned BitWidth = getTypeSizeInBits(U->getType());
1936 uint64_t Amt = BitWidth - CI->getZExtValue();
1937 if (Amt == BitWidth)
1938 return getSCEV(L->getOperand(0)); // shift by zero --> noop
1940 return getIntegerSCEV(0, U->getType()); // value is undefined
1942 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
1943 IntegerType::get(Amt)),
1948 case Instruction::Trunc:
1949 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1951 case Instruction::ZExt:
1952 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1954 case Instruction::SExt:
1955 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1957 case Instruction::BitCast:
1958 // BitCasts are no-op casts so we just eliminate the cast.
1959 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
1960 return getSCEV(U->getOperand(0));
1963 case Instruction::IntToPtr:
1964 if (!TD) break; // Without TD we can't analyze pointers.
1965 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1966 TD->getIntPtrType());
1968 case Instruction::PtrToInt:
1969 if (!TD) break; // Without TD we can't analyze pointers.
1970 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1973 case Instruction::GetElementPtr: {
1974 if (!TD) break; // Without TD we can't analyze pointers.
1975 const Type *IntPtrTy = TD->getIntPtrType();
1976 Value *Base = U->getOperand(0);
1977 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
1978 gep_type_iterator GTI = gep_type_begin(U);
1979 for (GetElementPtrInst::op_iterator I = next(U->op_begin()),
1983 // Compute the (potentially symbolic) offset in bytes for this index.
1984 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
1985 // For a struct, add the member offset.
1986 const StructLayout &SL = *TD->getStructLayout(STy);
1987 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
1988 uint64_t Offset = SL.getElementOffset(FieldNo);
1989 TotalOffset = getAddExpr(TotalOffset,
1990 getIntegerSCEV(Offset, IntPtrTy));
1992 // For an array, add the element offset, explicitly scaled.
1993 SCEVHandle LocalOffset = getSCEV(Index);
1994 if (!isa<PointerType>(LocalOffset->getType()))
1995 // Getelementptr indicies are signed.
1996 LocalOffset = getTruncateOrSignExtend(LocalOffset,
1999 getMulExpr(LocalOffset,
2000 getIntegerSCEV(TD->getTypePaddedSize(*GTI),
2002 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2005 return getAddExpr(getSCEV(Base), TotalOffset);
2008 case Instruction::PHI:
2009 return createNodeForPHI(cast<PHINode>(U));
2011 case Instruction::Select:
2012 // This could be a smax or umax that was lowered earlier.
2013 // Try to recover it.
2014 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2015 Value *LHS = ICI->getOperand(0);
2016 Value *RHS = ICI->getOperand(1);
2017 switch (ICI->getPredicate()) {
2018 case ICmpInst::ICMP_SLT:
2019 case ICmpInst::ICMP_SLE:
2020 std::swap(LHS, RHS);
2022 case ICmpInst::ICMP_SGT:
2023 case ICmpInst::ICMP_SGE:
2024 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2025 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2026 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2027 // ~smax(~x, ~y) == smin(x, y).
2028 return getNotSCEV(getSMaxExpr(
2029 getNotSCEV(getSCEV(LHS)),
2030 getNotSCEV(getSCEV(RHS))));
2032 case ICmpInst::ICMP_ULT:
2033 case ICmpInst::ICMP_ULE:
2034 std::swap(LHS, RHS);
2036 case ICmpInst::ICMP_UGT:
2037 case ICmpInst::ICMP_UGE:
2038 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2039 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2040 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2041 // ~umax(~x, ~y) == umin(x, y)
2042 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2043 getNotSCEV(getSCEV(RHS))));
2050 default: // We cannot analyze this expression.
2054 return getUnknown(V);
2059 //===----------------------------------------------------------------------===//
2060 // Iteration Count Computation Code
2063 /// getBackedgeTakenCount - If the specified loop has a predictable
2064 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2065 /// object. The backedge-taken count is the number of times the loop header
2066 /// will be branched to from within the loop. This is one less than the
2067 /// trip count of the loop, since it doesn't count the first iteration,
2068 /// when the header is branched to from outside the loop.
2070 /// Note that it is not valid to call this method on a loop without a
2071 /// loop-invariant backedge-taken count (see
2072 /// hasLoopInvariantBackedgeTakenCount).
2074 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2075 return getBackedgeTakenInfo(L).Exact;
2078 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2079 /// return the least SCEV value that is known never to be less than the
2080 /// actual backedge taken count.
2081 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2082 return getBackedgeTakenInfo(L).Max;
2085 const ScalarEvolution::BackedgeTakenInfo &
2086 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2087 // Initially insert a CouldNotCompute for this loop. If the insertion
2088 // succeeds, procede to actually compute a backedge-taken count and
2089 // update the value. The temporary CouldNotCompute value tells SCEV
2090 // code elsewhere that it shouldn't attempt to request a new
2091 // backedge-taken count, which could result in infinite recursion.
2092 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2093 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2095 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2096 if (ItCount.Exact != UnknownValue) {
2097 assert(ItCount.Exact->isLoopInvariant(L) &&
2098 ItCount.Max->isLoopInvariant(L) &&
2099 "Computed trip count isn't loop invariant for loop!");
2100 ++NumTripCountsComputed;
2102 // Update the value in the map.
2103 Pair.first->second = ItCount;
2104 } else if (isa<PHINode>(L->getHeader()->begin())) {
2105 // Only count loops that have phi nodes as not being computable.
2106 ++NumTripCountsNotComputed;
2109 // Now that we know more about the trip count for this loop, forget any
2110 // existing SCEV values for PHI nodes in this loop since they are only
2111 // conservative estimates made without the benefit
2112 // of trip count information.
2113 if (ItCount.hasAnyInfo())
2116 return Pair.first->second;
2119 /// forgetLoopBackedgeTakenCount - This method should be called by the
2120 /// client when it has changed a loop in a way that may effect
2121 /// ScalarEvolution's ability to compute a trip count, or if the loop
2123 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2124 BackedgeTakenCounts.erase(L);
2128 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2129 /// PHI nodes in the given loop. This is used when the trip count of
2130 /// the loop may have changed.
2131 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2132 for (BasicBlock::iterator I = L->getHeader()->begin();
2133 PHINode *PN = dyn_cast<PHINode>(I); ++I)
2134 deleteValueFromRecords(PN);
2137 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2138 /// of the specified loop will execute.
2139 ScalarEvolution::BackedgeTakenInfo
2140 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2141 // If the loop has a non-one exit block count, we can't analyze it.
2142 SmallVector<BasicBlock*, 8> ExitBlocks;
2143 L->getExitBlocks(ExitBlocks);
2144 if (ExitBlocks.size() != 1) return UnknownValue;
2146 // Okay, there is one exit block. Try to find the condition that causes the
2147 // loop to be exited.
2148 BasicBlock *ExitBlock = ExitBlocks[0];
2150 BasicBlock *ExitingBlock = 0;
2151 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2153 if (L->contains(*PI)) {
2154 if (ExitingBlock == 0)
2157 return UnknownValue; // More than one block exiting!
2159 assert(ExitingBlock && "No exits from loop, something is broken!");
2161 // Okay, we've computed the exiting block. See what condition causes us to
2164 // FIXME: we should be able to handle switch instructions (with a single exit)
2165 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2166 if (ExitBr == 0) return UnknownValue;
2167 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2169 // At this point, we know we have a conditional branch that determines whether
2170 // the loop is exited. However, we don't know if the branch is executed each
2171 // time through the loop. If not, then the execution count of the branch will
2172 // not be equal to the trip count of the loop.
2174 // Currently we check for this by checking to see if the Exit branch goes to
2175 // the loop header. If so, we know it will always execute the same number of
2176 // times as the loop. We also handle the case where the exit block *is* the
2177 // loop header. This is common for un-rotated loops. More extensive analysis
2178 // could be done to handle more cases here.
2179 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2180 ExitBr->getSuccessor(1) != L->getHeader() &&
2181 ExitBr->getParent() != L->getHeader())
2182 return UnknownValue;
2184 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2186 // If it's not an integer comparison then compute it the hard way.
2187 // Note that ICmpInst deals with pointer comparisons too so we must check
2188 // the type of the operand.
2189 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2190 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2191 ExitBr->getSuccessor(0) == ExitBlock);
2193 // If the condition was exit on true, convert the condition to exit on false
2194 ICmpInst::Predicate Cond;
2195 if (ExitBr->getSuccessor(1) == ExitBlock)
2196 Cond = ExitCond->getPredicate();
2198 Cond = ExitCond->getInversePredicate();
2200 // Handle common loops like: for (X = "string"; *X; ++X)
2201 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2202 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2204 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2205 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2208 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2209 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2211 // Try to evaluate any dependencies out of the loop.
2212 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2213 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2214 Tmp = getSCEVAtScope(RHS, L);
2215 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2217 // At this point, we would like to compute how many iterations of the
2218 // loop the predicate will return true for these inputs.
2219 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2220 // If there is a loop-invariant, force it into the RHS.
2221 std::swap(LHS, RHS);
2222 Cond = ICmpInst::getSwappedPredicate(Cond);
2225 // If we have a comparison of a chrec against a constant, try to use value
2226 // ranges to answer this query.
2227 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2228 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2229 if (AddRec->getLoop() == L) {
2230 // Form the comparison range using the constant of the correct type so
2231 // that the ConstantRange class knows to do a signed or unsigned
2233 ConstantInt *CompVal = RHSC->getValue();
2234 const Type *RealTy = ExitCond->getOperand(0)->getType();
2235 CompVal = dyn_cast<ConstantInt>(
2236 ConstantExpr::getBitCast(CompVal, RealTy));
2238 // Form the constant range.
2239 ConstantRange CompRange(
2240 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2242 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2243 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2248 case ICmpInst::ICMP_NE: { // while (X != Y)
2249 // Convert to: while (X-Y != 0)
2250 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2251 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2254 case ICmpInst::ICMP_EQ: {
2255 // Convert to: while (X-Y == 0) // while (X == Y)
2256 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2257 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2260 case ICmpInst::ICMP_SLT: {
2261 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2262 if (BTI.hasAnyInfo()) return BTI;
2265 case ICmpInst::ICMP_SGT: {
2266 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2267 getNotSCEV(RHS), L, true);
2268 if (BTI.hasAnyInfo()) return BTI;
2271 case ICmpInst::ICMP_ULT: {
2272 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2273 if (BTI.hasAnyInfo()) return BTI;
2276 case ICmpInst::ICMP_UGT: {
2277 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2278 getNotSCEV(RHS), L, false);
2279 if (BTI.hasAnyInfo()) return BTI;
2284 errs() << "ComputeBackedgeTakenCount ";
2285 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2286 errs() << "[unsigned] ";
2287 errs() << *LHS << " "
2288 << Instruction::getOpcodeName(Instruction::ICmp)
2289 << " " << *RHS << "\n";
2294 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2295 ExitBr->getSuccessor(0) == ExitBlock);
2298 static ConstantInt *
2299 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2300 ScalarEvolution &SE) {
2301 SCEVHandle InVal = SE.getConstant(C);
2302 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2303 assert(isa<SCEVConstant>(Val) &&
2304 "Evaluation of SCEV at constant didn't fold correctly?");
2305 return cast<SCEVConstant>(Val)->getValue();
2308 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2309 /// and a GEP expression (missing the pointer index) indexing into it, return
2310 /// the addressed element of the initializer or null if the index expression is
2313 GetAddressedElementFromGlobal(GlobalVariable *GV,
2314 const std::vector<ConstantInt*> &Indices) {
2315 Constant *Init = GV->getInitializer();
2316 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2317 uint64_t Idx = Indices[i]->getZExtValue();
2318 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2319 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2320 Init = cast<Constant>(CS->getOperand(Idx));
2321 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2322 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2323 Init = cast<Constant>(CA->getOperand(Idx));
2324 } else if (isa<ConstantAggregateZero>(Init)) {
2325 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2326 assert(Idx < STy->getNumElements() && "Bad struct index!");
2327 Init = Constant::getNullValue(STy->getElementType(Idx));
2328 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2329 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2330 Init = Constant::getNullValue(ATy->getElementType());
2332 assert(0 && "Unknown constant aggregate type!");
2336 return 0; // Unknown initializer type
2342 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2343 /// 'icmp op load X, cst', try to see if we can compute the backedge
2344 /// execution count.
2345 SCEVHandle ScalarEvolution::
2346 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2348 ICmpInst::Predicate predicate) {
2349 if (LI->isVolatile()) return UnknownValue;
2351 // Check to see if the loaded pointer is a getelementptr of a global.
2352 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2353 if (!GEP) return UnknownValue;
2355 // Make sure that it is really a constant global we are gepping, with an
2356 // initializer, and make sure the first IDX is really 0.
2357 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2358 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2359 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2360 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2361 return UnknownValue;
2363 // Okay, we allow one non-constant index into the GEP instruction.
2365 std::vector<ConstantInt*> Indexes;
2366 unsigned VarIdxNum = 0;
2367 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2368 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2369 Indexes.push_back(CI);
2370 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2371 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2372 VarIdx = GEP->getOperand(i);
2374 Indexes.push_back(0);
2377 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2378 // Check to see if X is a loop variant variable value now.
2379 SCEVHandle Idx = getSCEV(VarIdx);
2380 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2381 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2383 // We can only recognize very limited forms of loop index expressions, in
2384 // particular, only affine AddRec's like {C1,+,C2}.
2385 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2386 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2387 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2388 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2389 return UnknownValue;
2391 unsigned MaxSteps = MaxBruteForceIterations;
2392 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2393 ConstantInt *ItCst =
2394 ConstantInt::get(IdxExpr->getType(), IterationNum);
2395 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2397 // Form the GEP offset.
2398 Indexes[VarIdxNum] = Val;
2400 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2401 if (Result == 0) break; // Cannot compute!
2403 // Evaluate the condition for this iteration.
2404 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2405 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2406 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2408 errs() << "\n***\n*** Computed loop count " << *ItCst
2409 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2412 ++NumArrayLenItCounts;
2413 return getConstant(ItCst); // Found terminating iteration!
2416 return UnknownValue;
2420 /// CanConstantFold - Return true if we can constant fold an instruction of the
2421 /// specified type, assuming that all operands were constants.
2422 static bool CanConstantFold(const Instruction *I) {
2423 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2424 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2427 if (const CallInst *CI = dyn_cast<CallInst>(I))
2428 if (const Function *F = CI->getCalledFunction())
2429 return canConstantFoldCallTo(F);
2433 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2434 /// in the loop that V is derived from. We allow arbitrary operations along the
2435 /// way, but the operands of an operation must either be constants or a value
2436 /// derived from a constant PHI. If this expression does not fit with these
2437 /// constraints, return null.
2438 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2439 // If this is not an instruction, or if this is an instruction outside of the
2440 // loop, it can't be derived from a loop PHI.
2441 Instruction *I = dyn_cast<Instruction>(V);
2442 if (I == 0 || !L->contains(I->getParent())) return 0;
2444 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2445 if (L->getHeader() == I->getParent())
2448 // We don't currently keep track of the control flow needed to evaluate
2449 // PHIs, so we cannot handle PHIs inside of loops.
2453 // If we won't be able to constant fold this expression even if the operands
2454 // are constants, return early.
2455 if (!CanConstantFold(I)) return 0;
2457 // Otherwise, we can evaluate this instruction if all of its operands are
2458 // constant or derived from a PHI node themselves.
2460 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2461 if (!(isa<Constant>(I->getOperand(Op)) ||
2462 isa<GlobalValue>(I->getOperand(Op)))) {
2463 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2464 if (P == 0) return 0; // Not evolving from PHI
2468 return 0; // Evolving from multiple different PHIs.
2471 // This is a expression evolving from a constant PHI!
2475 /// EvaluateExpression - Given an expression that passes the
2476 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2477 /// in the loop has the value PHIVal. If we can't fold this expression for some
2478 /// reason, return null.
2479 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2480 if (isa<PHINode>(V)) return PHIVal;
2481 if (Constant *C = dyn_cast<Constant>(V)) return C;
2482 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2483 Instruction *I = cast<Instruction>(V);
2485 std::vector<Constant*> Operands;
2486 Operands.resize(I->getNumOperands());
2488 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2489 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2490 if (Operands[i] == 0) return 0;
2493 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2494 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2495 &Operands[0], Operands.size());
2497 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2498 &Operands[0], Operands.size());
2501 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2502 /// in the header of its containing loop, we know the loop executes a
2503 /// constant number of times, and the PHI node is just a recurrence
2504 /// involving constants, fold it.
2505 Constant *ScalarEvolution::
2506 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2507 std::map<PHINode*, Constant*>::iterator I =
2508 ConstantEvolutionLoopExitValue.find(PN);
2509 if (I != ConstantEvolutionLoopExitValue.end())
2512 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2513 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2515 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2517 // Since the loop is canonicalized, the PHI node must have two entries. One
2518 // entry must be a constant (coming in from outside of the loop), and the
2519 // second must be derived from the same PHI.
2520 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2521 Constant *StartCST =
2522 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2524 return RetVal = 0; // Must be a constant.
2526 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2527 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2529 return RetVal = 0; // Not derived from same PHI.
2531 // Execute the loop symbolically to determine the exit value.
2532 if (BEs.getActiveBits() >= 32)
2533 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2535 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2536 unsigned IterationNum = 0;
2537 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2538 if (IterationNum == NumIterations)
2539 return RetVal = PHIVal; // Got exit value!
2541 // Compute the value of the PHI node for the next iteration.
2542 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2543 if (NextPHI == PHIVal)
2544 return RetVal = NextPHI; // Stopped evolving!
2546 return 0; // Couldn't evaluate!
2551 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2552 /// constant number of times (the condition evolves only from constants),
2553 /// try to evaluate a few iterations of the loop until we get the exit
2554 /// condition gets a value of ExitWhen (true or false). If we cannot
2555 /// evaluate the trip count of the loop, return UnknownValue.
2556 SCEVHandle ScalarEvolution::
2557 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2558 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2559 if (PN == 0) return UnknownValue;
2561 // Since the loop is canonicalized, the PHI node must have two entries. One
2562 // entry must be a constant (coming in from outside of the loop), and the
2563 // second must be derived from the same PHI.
2564 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2565 Constant *StartCST =
2566 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2567 if (StartCST == 0) return UnknownValue; // Must be a constant.
2569 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2570 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2571 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2573 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2574 // the loop symbolically to determine when the condition gets a value of
2576 unsigned IterationNum = 0;
2577 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2578 for (Constant *PHIVal = StartCST;
2579 IterationNum != MaxIterations; ++IterationNum) {
2580 ConstantInt *CondVal =
2581 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2583 // Couldn't symbolically evaluate.
2584 if (!CondVal) return UnknownValue;
2586 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2587 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2588 ++NumBruteForceTripCountsComputed;
2589 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2592 // Compute the value of the PHI node for the next iteration.
2593 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2594 if (NextPHI == 0 || NextPHI == PHIVal)
2595 return UnknownValue; // Couldn't evaluate or not making progress...
2599 // Too many iterations were needed to evaluate.
2600 return UnknownValue;
2603 /// getSCEVAtScope - Compute the value of the specified expression within the
2604 /// indicated loop (which may be null to indicate in no loop). If the
2605 /// expression cannot be evaluated, return UnknownValue.
2606 SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) {
2607 // FIXME: this should be turned into a virtual method on SCEV!
2609 if (isa<SCEVConstant>(V)) return V;
2611 // If this instruction is evolved from a constant-evolving PHI, compute the
2612 // exit value from the loop without using SCEVs.
2613 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2614 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2615 const Loop *LI = (*this->LI)[I->getParent()];
2616 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2617 if (PHINode *PN = dyn_cast<PHINode>(I))
2618 if (PN->getParent() == LI->getHeader()) {
2619 // Okay, there is no closed form solution for the PHI node. Check
2620 // to see if the loop that contains it has a known backedge-taken
2621 // count. If so, we may be able to force computation of the exit
2623 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2624 if (SCEVConstant *BTCC =
2625 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2626 // Okay, we know how many times the containing loop executes. If
2627 // this is a constant evolving PHI node, get the final value at
2628 // the specified iteration number.
2629 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2630 BTCC->getValue()->getValue(),
2632 if (RV) return getUnknown(RV);
2636 // Okay, this is an expression that we cannot symbolically evaluate
2637 // into a SCEV. Check to see if it's possible to symbolically evaluate
2638 // the arguments into constants, and if so, try to constant propagate the
2639 // result. This is particularly useful for computing loop exit values.
2640 if (CanConstantFold(I)) {
2641 std::vector<Constant*> Operands;
2642 Operands.reserve(I->getNumOperands());
2643 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2644 Value *Op = I->getOperand(i);
2645 if (Constant *C = dyn_cast<Constant>(Op)) {
2646 Operands.push_back(C);
2648 // If any of the operands is non-constant and if they are
2649 // non-integer and non-pointer, don't even try to analyze them
2650 // with scev techniques.
2651 if (!isSCEVable(Op->getType()))
2654 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2655 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2656 Constant *C = SC->getValue();
2657 if (C->getType() != Op->getType())
2658 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2662 Operands.push_back(C);
2663 } else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2664 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2665 if (C->getType() != Op->getType())
2667 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2671 Operands.push_back(C);
2681 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2682 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2683 &Operands[0], Operands.size());
2685 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2686 &Operands[0], Operands.size());
2687 return getUnknown(C);
2691 // This is some other type of SCEVUnknown, just return it.
2695 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2696 // Avoid performing the look-up in the common case where the specified
2697 // expression has no loop-variant portions.
2698 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2699 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2700 if (OpAtScope != Comm->getOperand(i)) {
2701 if (OpAtScope == UnknownValue) return UnknownValue;
2702 // Okay, at least one of these operands is loop variant but might be
2703 // foldable. Build a new instance of the folded commutative expression.
2704 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2705 NewOps.push_back(OpAtScope);
2707 for (++i; i != e; ++i) {
2708 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2709 if (OpAtScope == UnknownValue) return UnknownValue;
2710 NewOps.push_back(OpAtScope);
2712 if (isa<SCEVAddExpr>(Comm))
2713 return getAddExpr(NewOps);
2714 if (isa<SCEVMulExpr>(Comm))
2715 return getMulExpr(NewOps);
2716 if (isa<SCEVSMaxExpr>(Comm))
2717 return getSMaxExpr(NewOps);
2718 if (isa<SCEVUMaxExpr>(Comm))
2719 return getUMaxExpr(NewOps);
2720 assert(0 && "Unknown commutative SCEV type!");
2723 // If we got here, all operands are loop invariant.
2727 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2728 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2729 if (LHS == UnknownValue) return LHS;
2730 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2731 if (RHS == UnknownValue) return RHS;
2732 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2733 return Div; // must be loop invariant
2734 return getUDivExpr(LHS, RHS);
2737 // If this is a loop recurrence for a loop that does not contain L, then we
2738 // are dealing with the final value computed by the loop.
2739 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2740 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2741 // To evaluate this recurrence, we need to know how many times the AddRec
2742 // loop iterates. Compute this now.
2743 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2744 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2746 // Then, evaluate the AddRec.
2747 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
2749 return UnknownValue;
2752 if (SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
2753 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2754 if (Op == UnknownValue) return Op;
2755 if (Op == Cast->getOperand())
2756 return Cast; // must be loop invariant
2757 return getZeroExtendExpr(Op, Cast->getType());
2760 if (SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
2761 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2762 if (Op == UnknownValue) return Op;
2763 if (Op == Cast->getOperand())
2764 return Cast; // must be loop invariant
2765 return getSignExtendExpr(Op, Cast->getType());
2768 if (SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
2769 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2770 if (Op == UnknownValue) return Op;
2771 if (Op == Cast->getOperand())
2772 return Cast; // must be loop invariant
2773 return getTruncateExpr(Op, Cast->getType());
2776 assert(0 && "Unknown SCEV type!");
2779 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2780 /// at the specified scope in the program. The L value specifies a loop
2781 /// nest to evaluate the expression at, where null is the top-level or a
2782 /// specified loop is immediately inside of the loop.
2784 /// This method can be used to compute the exit value for a variable defined
2785 /// in a loop by querying what the value will hold in the parent loop.
2787 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2788 /// object is returned.
2789 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
2790 return getSCEVAtScope(getSCEV(V), L);
2793 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2794 /// following equation:
2796 /// A * X = B (mod N)
2798 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2799 /// A and B isn't important.
2801 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2802 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2803 ScalarEvolution &SE) {
2804 uint32_t BW = A.getBitWidth();
2805 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2806 assert(A != 0 && "A must be non-zero.");
2810 // The gcd of A and N may have only one prime factor: 2. The number of
2811 // trailing zeros in A is its multiplicity
2812 uint32_t Mult2 = A.countTrailingZeros();
2815 // 2. Check if B is divisible by D.
2817 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2818 // is not less than multiplicity of this prime factor for D.
2819 if (B.countTrailingZeros() < Mult2)
2820 return SE.getCouldNotCompute();
2822 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2825 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2826 // bit width during computations.
2827 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2828 APInt Mod(BW + 1, 0);
2829 Mod.set(BW - Mult2); // Mod = N / D
2830 APInt I = AD.multiplicativeInverse(Mod);
2832 // 4. Compute the minimum unsigned root of the equation:
2833 // I * (B / D) mod (N / D)
2834 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2836 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2838 return SE.getConstant(Result.trunc(BW));
2841 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2842 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2843 /// might be the same) or two SCEVCouldNotCompute objects.
2845 static std::pair<SCEVHandle,SCEVHandle>
2846 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2847 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2848 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2849 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2850 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2852 // We currently can only solve this if the coefficients are constants.
2853 if (!LC || !MC || !NC) {
2854 SCEV *CNC = SE.getCouldNotCompute();
2855 return std::make_pair(CNC, CNC);
2858 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2859 const APInt &L = LC->getValue()->getValue();
2860 const APInt &M = MC->getValue()->getValue();
2861 const APInt &N = NC->getValue()->getValue();
2862 APInt Two(BitWidth, 2);
2863 APInt Four(BitWidth, 4);
2866 using namespace APIntOps;
2868 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2869 // The B coefficient is M-N/2
2873 // The A coefficient is N/2
2874 APInt A(N.sdiv(Two));
2876 // Compute the B^2-4ac term.
2879 SqrtTerm -= Four * (A * C);
2881 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2882 // integer value or else APInt::sqrt() will assert.
2883 APInt SqrtVal(SqrtTerm.sqrt());
2885 // Compute the two solutions for the quadratic formula.
2886 // The divisions must be performed as signed divisions.
2888 APInt TwoA( A << 1 );
2889 if (TwoA.isMinValue()) {
2890 SCEV *CNC = SE.getCouldNotCompute();
2891 return std::make_pair(CNC, CNC);
2894 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2895 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2897 return std::make_pair(SE.getConstant(Solution1),
2898 SE.getConstant(Solution2));
2899 } // end APIntOps namespace
2902 /// HowFarToZero - Return the number of times a backedge comparing the specified
2903 /// value to zero will execute. If not computable, return UnknownValue
2904 SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) {
2905 // If the value is a constant
2906 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2907 // If the value is already zero, the branch will execute zero times.
2908 if (C->getValue()->isZero()) return C;
2909 return UnknownValue; // Otherwise it will loop infinitely.
2912 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2913 if (!AddRec || AddRec->getLoop() != L)
2914 return UnknownValue;
2916 if (AddRec->isAffine()) {
2917 // If this is an affine expression, the execution count of this branch is
2918 // the minimum unsigned root of the following equation:
2920 // Start + Step*N = 0 (mod 2^BW)
2924 // Step*N = -Start (mod 2^BW)
2926 // where BW is the common bit width of Start and Step.
2928 // Get the initial value for the loop.
2929 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2930 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2932 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2934 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2935 // For now we handle only constant steps.
2937 // First, handle unitary steps.
2938 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2939 return getNegativeSCEV(Start); // N = -Start (as unsigned)
2940 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2941 return Start; // N = Start (as unsigned)
2943 // Then, try to solve the above equation provided that Start is constant.
2944 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2945 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2946 -StartC->getValue()->getValue(),
2949 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2950 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2951 // the quadratic equation to solve it.
2952 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
2954 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2955 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2958 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
2959 << " sol#2: " << *R2 << "\n";
2961 // Pick the smallest positive root value.
2962 if (ConstantInt *CB =
2963 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2964 R1->getValue(), R2->getValue()))) {
2965 if (CB->getZExtValue() == false)
2966 std::swap(R1, R2); // R1 is the minimum root now.
2968 // We can only use this value if the chrec ends up with an exact zero
2969 // value at this index. When solving for "X*X != 5", for example, we
2970 // should not accept a root of 2.
2971 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
2973 return R1; // We found a quadratic root!
2978 return UnknownValue;
2981 /// HowFarToNonZero - Return the number of times a backedge checking the
2982 /// specified value for nonzero will execute. If not computable, return
2984 SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) {
2985 // Loops that look like: while (X == 0) are very strange indeed. We don't
2986 // handle them yet except for the trivial case. This could be expanded in the
2987 // future as needed.
2989 // If the value is a constant, check to see if it is known to be non-zero
2990 // already. If so, the backedge will execute zero times.
2991 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2992 if (!C->getValue()->isNullValue())
2993 return getIntegerSCEV(0, C->getType());
2994 return UnknownValue; // Otherwise it will loop infinitely.
2997 // We could implement others, but I really doubt anyone writes loops like
2998 // this, and if they did, they would already be constant folded.
2999 return UnknownValue;
3002 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3003 /// (which may not be an immediate predecessor) which has exactly one
3004 /// successor from which BB is reachable, or null if no such block is
3008 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3009 // If the block has a unique predecessor, then there is no path from the
3010 // predecessor to the block that does not go through the direct edge
3011 // from the predecessor to the block.
3012 if (BasicBlock *Pred = BB->getSinglePredecessor())
3015 // A loop's header is defined to be a block that dominates the loop.
3016 // If the loop has a preheader, it must be a block that has exactly
3017 // one successor that can reach BB. This is slightly more strict
3018 // than necessary, but works if critical edges are split.
3019 if (Loop *L = LI->getLoopFor(BB))
3020 return L->getLoopPreheader();
3025 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3026 /// a conditional between LHS and RHS. This is used to help avoid max
3027 /// expressions in loop trip counts.
3028 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3029 ICmpInst::Predicate Pred,
3030 SCEV *LHS, SCEV *RHS) {
3031 BasicBlock *Preheader = L->getLoopPreheader();
3032 BasicBlock *PreheaderDest = L->getHeader();
3034 // Starting at the preheader, climb up the predecessor chain, as long as
3035 // there are predecessors that can be found that have unique successors
3036 // leading to the original header.
3038 PreheaderDest = Preheader,
3039 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
3041 BranchInst *LoopEntryPredicate =
3042 dyn_cast<BranchInst>(Preheader->getTerminator());
3043 if (!LoopEntryPredicate ||
3044 LoopEntryPredicate->isUnconditional())
3047 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3050 // Now that we found a conditional branch that dominates the loop, check to
3051 // see if it is the comparison we are looking for.
3052 Value *PreCondLHS = ICI->getOperand(0);
3053 Value *PreCondRHS = ICI->getOperand(1);
3054 ICmpInst::Predicate Cond;
3055 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
3056 Cond = ICI->getPredicate();
3058 Cond = ICI->getInversePredicate();
3061 ; // An exact match.
3062 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3063 ; // The actual condition is beyond sufficient.
3065 // Check a few special cases.
3067 case ICmpInst::ICMP_UGT:
3068 if (Pred == ICmpInst::ICMP_ULT) {
3069 std::swap(PreCondLHS, PreCondRHS);
3070 Cond = ICmpInst::ICMP_ULT;
3074 case ICmpInst::ICMP_SGT:
3075 if (Pred == ICmpInst::ICMP_SLT) {
3076 std::swap(PreCondLHS, PreCondRHS);
3077 Cond = ICmpInst::ICMP_SLT;
3081 case ICmpInst::ICMP_NE:
3082 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3083 // so check for this case by checking if the NE is comparing against
3084 // a minimum or maximum constant.
3085 if (!ICmpInst::isTrueWhenEqual(Pred))
3086 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3087 const APInt &A = CI->getValue();
3089 case ICmpInst::ICMP_SLT:
3090 if (A.isMaxSignedValue()) break;
3092 case ICmpInst::ICMP_SGT:
3093 if (A.isMinSignedValue()) break;
3095 case ICmpInst::ICMP_ULT:
3096 if (A.isMaxValue()) break;
3098 case ICmpInst::ICMP_UGT:
3099 if (A.isMinValue()) break;
3104 Cond = ICmpInst::ICMP_NE;
3105 // NE is symmetric but the original comparison may not be. Swap
3106 // the operands if necessary so that they match below.
3107 if (isa<SCEVConstant>(LHS))
3108 std::swap(PreCondLHS, PreCondRHS);
3113 // We weren't able to reconcile the condition.
3117 if (!PreCondLHS->getType()->isInteger()) continue;
3119 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3120 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3121 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3122 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3123 RHS == getNotSCEV(PreCondLHSSCEV)))
3130 /// HowManyLessThans - Return the number of times a backedge containing the
3131 /// specified less-than comparison will execute. If not computable, return
3133 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3134 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
3135 // Only handle: "ADDREC < LoopInvariant".
3136 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3138 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3139 if (!AddRec || AddRec->getLoop() != L)
3140 return UnknownValue;
3142 if (AddRec->isAffine()) {
3143 // FORNOW: We only support unit strides.
3144 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3145 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3146 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3148 // TODO: handle non-constant strides.
3149 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3150 if (!CStep || CStep->isZero())
3151 return UnknownValue;
3152 if (CStep->getValue()->getValue() == 1) {
3153 // With unit stride, the iteration never steps past the limit value.
3154 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3155 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3156 // Test whether a positive iteration iteration can step past the limit
3157 // value and past the maximum value for its type in a single step.
3159 APInt Max = APInt::getSignedMaxValue(BitWidth);
3160 if ((Max - CStep->getValue()->getValue())
3161 .slt(CLimit->getValue()->getValue()))
3162 return UnknownValue;
3164 APInt Max = APInt::getMaxValue(BitWidth);
3165 if ((Max - CStep->getValue()->getValue())
3166 .ult(CLimit->getValue()->getValue()))
3167 return UnknownValue;
3170 // TODO: handle non-constant limit values below.
3171 return UnknownValue;
3173 // TODO: handle negative strides below.
3174 return UnknownValue;
3176 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3177 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3178 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3179 // treat m-n as signed nor unsigned due to overflow possibility.
3181 // First, we get the value of the LHS in the first iteration: n
3182 SCEVHandle Start = AddRec->getOperand(0);
3184 // Determine the minimum constant start value.
3185 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3186 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3187 APInt::getMinValue(BitWidth));
3189 // If we know that the condition is true in order to enter the loop,
3190 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3191 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3192 // division must round up.
3193 SCEVHandle End = RHS;
3194 if (!isLoopGuardedByCond(L,
3195 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3196 getMinusSCEV(Start, Step), RHS))
3197 End = isSigned ? getSMaxExpr(RHS, Start)
3198 : getUMaxExpr(RHS, Start);
3200 // Determine the maximum constant end value.
3201 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3202 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3203 APInt::getMaxValue(BitWidth));
3205 // Finally, we subtract these two values and divide, rounding up, to get
3206 // the number of times the backedge is executed.
3207 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3208 getAddExpr(Step, NegOne)),
3211 // The maximum backedge count is similar, except using the minimum start
3212 // value and the maximum end value.
3213 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3215 getAddExpr(Step, NegOne)),
3218 return BackedgeTakenInfo(BECount, MaxBECount);
3221 return UnknownValue;
3224 /// getNumIterationsInRange - Return the number of iterations of this loop that
3225 /// produce values in the specified constant range. Another way of looking at
3226 /// this is that it returns the first iteration number where the value is not in
3227 /// the condition, thus computing the exit count. If the iteration count can't
3228 /// be computed, an instance of SCEVCouldNotCompute is returned.
3229 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3230 ScalarEvolution &SE) const {
3231 if (Range.isFullSet()) // Infinite loop.
3232 return SE.getCouldNotCompute();
3234 // If the start is a non-zero constant, shift the range to simplify things.
3235 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3236 if (!SC->getValue()->isZero()) {
3237 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3238 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3239 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3240 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
3241 return ShiftedAddRec->getNumIterationsInRange(
3242 Range.subtract(SC->getValue()->getValue()), SE);
3243 // This is strange and shouldn't happen.
3244 return SE.getCouldNotCompute();
3247 // The only time we can solve this is when we have all constant indices.
3248 // Otherwise, we cannot determine the overflow conditions.
3249 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3250 if (!isa<SCEVConstant>(getOperand(i)))
3251 return SE.getCouldNotCompute();
3254 // Okay at this point we know that all elements of the chrec are constants and
3255 // that the start element is zero.
3257 // First check to see if the range contains zero. If not, the first
3259 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3260 if (!Range.contains(APInt(BitWidth, 0)))
3261 return SE.getConstant(ConstantInt::get(getType(),0));
3264 // If this is an affine expression then we have this situation:
3265 // Solve {0,+,A} in Range === Ax in Range
3267 // We know that zero is in the range. If A is positive then we know that
3268 // the upper value of the range must be the first possible exit value.
3269 // If A is negative then the lower of the range is the last possible loop
3270 // value. Also note that we already checked for a full range.
3271 APInt One(BitWidth,1);
3272 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3273 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3275 // The exit value should be (End+A)/A.
3276 APInt ExitVal = (End + A).udiv(A);
3277 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3279 // Evaluate at the exit value. If we really did fall out of the valid
3280 // range, then we computed our trip count, otherwise wrap around or other
3281 // things must have happened.
3282 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3283 if (Range.contains(Val->getValue()))
3284 return SE.getCouldNotCompute(); // Something strange happened
3286 // Ensure that the previous value is in the range. This is a sanity check.
3287 assert(Range.contains(
3288 EvaluateConstantChrecAtConstant(this,
3289 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3290 "Linear scev computation is off in a bad way!");
3291 return SE.getConstant(ExitValue);
3292 } else if (isQuadratic()) {
3293 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3294 // quadratic equation to solve it. To do this, we must frame our problem in
3295 // terms of figuring out when zero is crossed, instead of when
3296 // Range.getUpper() is crossed.
3297 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3298 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3299 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3301 // Next, solve the constructed addrec
3302 std::pair<SCEVHandle,SCEVHandle> Roots =
3303 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3304 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3305 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3307 // Pick the smallest positive root value.
3308 if (ConstantInt *CB =
3309 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3310 R1->getValue(), R2->getValue()))) {
3311 if (CB->getZExtValue() == false)
3312 std::swap(R1, R2); // R1 is the minimum root now.
3314 // Make sure the root is not off by one. The returned iteration should
3315 // not be in the range, but the previous one should be. When solving
3316 // for "X*X < 5", for example, we should not return a root of 2.
3317 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3320 if (Range.contains(R1Val->getValue())) {
3321 // The next iteration must be out of the range...
3322 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3324 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3325 if (!Range.contains(R1Val->getValue()))
3326 return SE.getConstant(NextVal);
3327 return SE.getCouldNotCompute(); // Something strange happened
3330 // If R1 was not in the range, then it is a good return value. Make
3331 // sure that R1-1 WAS in the range though, just in case.
3332 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3333 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3334 if (Range.contains(R1Val->getValue()))
3336 return SE.getCouldNotCompute(); // Something strange happened
3341 return SE.getCouldNotCompute();
3346 //===----------------------------------------------------------------------===//
3347 // ScalarEvolution Class Implementation
3348 //===----------------------------------------------------------------------===//
3350 ScalarEvolution::ScalarEvolution()
3351 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3354 bool ScalarEvolution::runOnFunction(Function &F) {
3356 LI = &getAnalysis<LoopInfo>();
3357 TD = getAnalysisIfAvailable<TargetData>();
3361 void ScalarEvolution::releaseMemory() {
3363 BackedgeTakenCounts.clear();
3364 ConstantEvolutionLoopExitValue.clear();
3367 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3368 AU.setPreservesAll();
3369 AU.addRequiredTransitive<LoopInfo>();
3372 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3373 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3376 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3378 // Print all inner loops first
3379 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3380 PrintLoopInfo(OS, SE, *I);
3382 OS << "Loop " << L->getHeader()->getName() << ": ";
3384 SmallVector<BasicBlock*, 8> ExitBlocks;
3385 L->getExitBlocks(ExitBlocks);
3386 if (ExitBlocks.size() != 1)
3387 OS << "<multiple exits> ";
3389 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3390 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3392 OS << "Unpredictable backedge-taken count. ";
3398 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3399 // ScalarEvolution's implementaiton of the print method is to print
3400 // out SCEV values of all instructions that are interesting. Doing
3401 // this potentially causes it to create new SCEV objects though,
3402 // which technically conflicts with the const qualifier. This isn't
3403 // observable from outside the class though (the hasSCEV function
3404 // notwithstanding), so casting away the const isn't dangerous.
3405 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3407 OS << "Classifying expressions for: " << F->getName() << "\n";
3408 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3409 if (isSCEVable(I->getType())) {
3412 SCEVHandle SV = SE.getSCEV(&*I);
3416 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3418 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3419 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3420 OS << "<<Unknown>>";
3430 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3431 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3432 PrintLoopInfo(OS, &SE, *I);
3435 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3436 raw_os_ostream OS(o);