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) {}
136 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
137 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
141 const Type *SCEVCouldNotCompute::getType() const {
142 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
146 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
147 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
151 SCEVHandle SCEVCouldNotCompute::
152 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
153 const SCEVHandle &Conc,
154 ScalarEvolution &SE) const {
158 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
159 OS << "***COULDNOTCOMPUTE***";
162 bool SCEVCouldNotCompute::classof(const SCEV *S) {
163 return S->getSCEVType() == scCouldNotCompute;
167 // SCEVConstants - Only allow the creation of one SCEVConstant for any
168 // particular value. Don't use a SCEVHandle here, or else the object will
170 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
173 SCEVConstant::~SCEVConstant() {
174 SCEVConstants->erase(V);
177 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
178 SCEVConstant *&R = (*SCEVConstants)[V];
179 if (R == 0) R = new SCEVConstant(V);
183 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
184 return getConstant(ConstantInt::get(Val));
187 const Type *SCEVConstant::getType() const { return V->getType(); }
189 void SCEVConstant::print(raw_ostream &OS) const {
190 WriteAsOperand(OS, V, false);
193 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
194 // particular input. Don't use a SCEVHandle here, or else the object will
196 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
197 SCEVTruncateExpr*> > SCEVTruncates;
199 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
200 : SCEV(scTruncate), Op(op), Ty(ty) {
201 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
202 (Ty->isInteger() || isa<PointerType>(Ty)) &&
203 "Cannot truncate non-integer value!");
206 SCEVTruncateExpr::~SCEVTruncateExpr() {
207 SCEVTruncates->erase(std::make_pair(Op, Ty));
210 bool SCEVTruncateExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
211 return Op->dominates(BB, DT);
214 void SCEVTruncateExpr::print(raw_ostream &OS) const {
215 OS << "(truncate " << *Op << " to " << *Ty << ")";
218 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
219 // particular input. Don't use a SCEVHandle here, or else the object will never
221 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
222 SCEVZeroExtendExpr*> > SCEVZeroExtends;
224 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
225 : SCEV(scZeroExtend), Op(op), Ty(ty) {
226 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
227 (Ty->isInteger() || isa<PointerType>(Ty)) &&
228 "Cannot zero extend non-integer value!");
231 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
232 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
235 bool SCEVZeroExtendExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
236 return Op->dominates(BB, DT);
239 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
240 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
243 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
244 // particular input. Don't use a SCEVHandle here, or else the object will never
246 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
247 SCEVSignExtendExpr*> > SCEVSignExtends;
249 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
250 : SCEV(scSignExtend), Op(op), Ty(ty) {
251 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
252 (Ty->isInteger() || isa<PointerType>(Ty)) &&
253 "Cannot sign extend non-integer value!");
256 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
257 SCEVSignExtends->erase(std::make_pair(Op, Ty));
260 bool SCEVSignExtendExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
261 return Op->dominates(BB, DT);
264 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
265 OS << "(signextend " << *Op << " to " << *Ty << ")";
268 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
269 // particular input. Don't use a SCEVHandle here, or else the object will never
271 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
272 SCEVCommutativeExpr*> > SCEVCommExprs;
274 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
275 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
276 std::vector<SCEV*>(Operands.begin(),
280 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
281 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
282 const char *OpStr = getOperationStr();
283 OS << "(" << *Operands[0];
284 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
285 OS << OpStr << *Operands[i];
289 SCEVHandle SCEVCommutativeExpr::
290 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
291 const SCEVHandle &Conc,
292 ScalarEvolution &SE) const {
293 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
295 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
296 if (H != getOperand(i)) {
297 std::vector<SCEVHandle> NewOps;
298 NewOps.reserve(getNumOperands());
299 for (unsigned j = 0; j != i; ++j)
300 NewOps.push_back(getOperand(j));
302 for (++i; i != e; ++i)
303 NewOps.push_back(getOperand(i)->
304 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
306 if (isa<SCEVAddExpr>(this))
307 return SE.getAddExpr(NewOps);
308 else if (isa<SCEVMulExpr>(this))
309 return SE.getMulExpr(NewOps);
310 else if (isa<SCEVSMaxExpr>(this))
311 return SE.getSMaxExpr(NewOps);
312 else if (isa<SCEVUMaxExpr>(this))
313 return SE.getUMaxExpr(NewOps);
315 assert(0 && "Unknown commutative expr!");
321 bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323 if (!getOperand(i)->dominates(BB, DT))
330 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
331 // input. Don't use a SCEVHandle here, or else the object will never be
333 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
334 SCEVUDivExpr*> > SCEVUDivs;
336 SCEVUDivExpr::~SCEVUDivExpr() {
337 SCEVUDivs->erase(std::make_pair(LHS, RHS));
340 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
341 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
344 void SCEVUDivExpr::print(raw_ostream &OS) const {
345 OS << "(" << *LHS << " /u " << *RHS << ")";
348 const Type *SCEVUDivExpr::getType() const {
349 return LHS->getType();
352 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
353 // particular input. Don't use a SCEVHandle here, or else the object will never
355 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
356 SCEVAddRecExpr*> > SCEVAddRecExprs;
358 SCEVAddRecExpr::~SCEVAddRecExpr() {
359 SCEVAddRecExprs->erase(std::make_pair(L,
360 std::vector<SCEV*>(Operands.begin(),
364 bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
365 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
366 if (!getOperand(i)->dominates(BB, DT))
373 SCEVHandle SCEVAddRecExpr::
374 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
375 const SCEVHandle &Conc,
376 ScalarEvolution &SE) const {
377 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
379 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
380 if (H != getOperand(i)) {
381 std::vector<SCEVHandle> NewOps;
382 NewOps.reserve(getNumOperands());
383 for (unsigned j = 0; j != i; ++j)
384 NewOps.push_back(getOperand(j));
386 for (++i; i != e; ++i)
387 NewOps.push_back(getOperand(i)->
388 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
390 return SE.getAddRecExpr(NewOps, L);
397 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
398 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
399 // contain L and if the start is invariant.
400 return !QueryLoop->contains(L->getHeader()) &&
401 getOperand(0)->isLoopInvariant(QueryLoop);
405 void SCEVAddRecExpr::print(raw_ostream &OS) const {
406 OS << "{" << *Operands[0];
407 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
408 OS << ",+," << *Operands[i];
409 OS << "}<" << L->getHeader()->getName() + ">";
412 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
413 // value. Don't use a SCEVHandle here, or else the object will never be
415 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
417 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
419 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
420 // All non-instruction values are loop invariant. All instructions are loop
421 // invariant if they are not contained in the specified loop.
422 if (Instruction *I = dyn_cast<Instruction>(V))
423 return !L->contains(I->getParent());
427 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
428 if (Instruction *I = dyn_cast<Instruction>(getValue()))
429 return DT->dominates(I->getParent(), BB);
433 const Type *SCEVUnknown::getType() const {
437 void SCEVUnknown::print(raw_ostream &OS) const {
438 if (isa<PointerType>(V->getType()))
439 OS << "(ptrtoint " << *V->getType() << " ";
440 WriteAsOperand(OS, V, false);
441 if (isa<PointerType>(V->getType()))
445 //===----------------------------------------------------------------------===//
447 //===----------------------------------------------------------------------===//
450 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
451 /// than the complexity of the RHS. This comparator is used to canonicalize
453 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
454 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
455 return LHS->getSCEVType() < RHS->getSCEVType();
460 /// GroupByComplexity - Given a list of SCEV objects, order them by their
461 /// complexity, and group objects of the same complexity together by value.
462 /// When this routine is finished, we know that any duplicates in the vector are
463 /// consecutive and that complexity is monotonically increasing.
465 /// Note that we go take special precautions to ensure that we get determinstic
466 /// results from this routine. In other words, we don't want the results of
467 /// this to depend on where the addresses of various SCEV objects happened to
470 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
471 if (Ops.size() < 2) return; // Noop
472 if (Ops.size() == 2) {
473 // This is the common case, which also happens to be trivially simple.
475 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
476 std::swap(Ops[0], Ops[1]);
480 // Do the rough sort by complexity.
481 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
483 // Now that we are sorted by complexity, group elements of the same
484 // complexity. Note that this is, at worst, N^2, but the vector is likely to
485 // be extremely short in practice. Note that we take this approach because we
486 // do not want to depend on the addresses of the objects we are grouping.
487 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
489 unsigned Complexity = S->getSCEVType();
491 // If there are any objects of the same complexity and same value as this
493 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
494 if (Ops[j] == S) { // Found a duplicate.
495 // Move it to immediately after i'th element.
496 std::swap(Ops[i+1], Ops[j]);
497 ++i; // no need to rescan it.
498 if (i == e-2) return; // Done!
506 //===----------------------------------------------------------------------===//
507 // Simple SCEV method implementations
508 //===----------------------------------------------------------------------===//
510 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
512 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
514 const Type* ResultTy) {
515 // Handle the simplest case efficiently.
517 return SE.getTruncateOrZeroExtend(It, ResultTy);
519 // We are using the following formula for BC(It, K):
521 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
523 // Suppose, W is the bitwidth of the return value. We must be prepared for
524 // overflow. Hence, we must assure that the result of our computation is
525 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
526 // safe in modular arithmetic.
528 // However, this code doesn't use exactly that formula; the formula it uses
529 // is something like the following, where T is the number of factors of 2 in
530 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
533 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
535 // This formula is trivially equivalent to the previous formula. However,
536 // this formula can be implemented much more efficiently. The trick is that
537 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
538 // arithmetic. To do exact division in modular arithmetic, all we have
539 // to do is multiply by the inverse. Therefore, this step can be done at
542 // The next issue is how to safely do the division by 2^T. The way this
543 // is done is by doing the multiplication step at a width of at least W + T
544 // bits. This way, the bottom W+T bits of the product are accurate. Then,
545 // when we perform the division by 2^T (which is equivalent to a right shift
546 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
547 // truncated out after the division by 2^T.
549 // In comparison to just directly using the first formula, this technique
550 // is much more efficient; using the first formula requires W * K bits,
551 // but this formula less than W + K bits. Also, the first formula requires
552 // a division step, whereas this formula only requires multiplies and shifts.
554 // It doesn't matter whether the subtraction step is done in the calculation
555 // width or the input iteration count's width; if the subtraction overflows,
556 // the result must be zero anyway. We prefer here to do it in the width of
557 // the induction variable because it helps a lot for certain cases; CodeGen
558 // isn't smart enough to ignore the overflow, which leads to much less
559 // efficient code if the width of the subtraction is wider than the native
562 // (It's possible to not widen at all by pulling out factors of 2 before
563 // the multiplication; for example, K=2 can be calculated as
564 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
565 // extra arithmetic, so it's not an obvious win, and it gets
566 // much more complicated for K > 3.)
568 // Protection from insane SCEVs; this bound is conservative,
569 // but it probably doesn't matter.
571 return SE.getCouldNotCompute();
573 unsigned W = SE.getTypeSizeInBits(ResultTy);
575 // Calculate K! / 2^T and T; we divide out the factors of two before
576 // multiplying for calculating K! / 2^T to avoid overflow.
577 // Other overflow doesn't matter because we only care about the bottom
578 // W bits of the result.
579 APInt OddFactorial(W, 1);
581 for (unsigned i = 3; i <= K; ++i) {
583 unsigned TwoFactors = Mult.countTrailingZeros();
585 Mult = Mult.lshr(TwoFactors);
586 OddFactorial *= Mult;
589 // We need at least W + T bits for the multiplication step
590 unsigned CalculationBits = W + T;
592 // Calcuate 2^T, at width T+W.
593 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
595 // Calculate the multiplicative inverse of K! / 2^T;
596 // this multiplication factor will perform the exact division by
598 APInt Mod = APInt::getSignedMinValue(W+1);
599 APInt MultiplyFactor = OddFactorial.zext(W+1);
600 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
601 MultiplyFactor = MultiplyFactor.trunc(W);
603 // Calculate the product, at width T+W
604 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
605 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
606 for (unsigned i = 1; i != K; ++i) {
607 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
608 Dividend = SE.getMulExpr(Dividend,
609 SE.getTruncateOrZeroExtend(S, CalculationTy));
613 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
615 // Truncate the result, and divide by K! / 2^T.
617 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
618 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
621 /// evaluateAtIteration - Return the value of this chain of recurrences at
622 /// the specified iteration number. We can evaluate this recurrence by
623 /// multiplying each element in the chain by the binomial coefficient
624 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
626 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
628 /// where BC(It, k) stands for binomial coefficient.
630 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
631 ScalarEvolution &SE) const {
632 SCEVHandle Result = getStart();
633 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
634 // The computation is correct in the face of overflow provided that the
635 // multiplication is performed _after_ the evaluation of the binomial
637 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
638 if (isa<SCEVCouldNotCompute>(Coeff))
641 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
646 //===----------------------------------------------------------------------===//
647 // SCEV Expression folder implementations
648 //===----------------------------------------------------------------------===//
650 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
651 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
652 "This is not a truncating conversion!");
654 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
656 ConstantExpr::getTrunc(SC->getValue(), Ty));
658 // If the input value is a chrec scev made out of constants, truncate
659 // all of the constants.
660 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
661 std::vector<SCEVHandle> Operands;
662 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
663 // FIXME: This should allow truncation of other expression types!
664 if (isa<SCEVConstant>(AddRec->getOperand(i)))
665 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
668 if (Operands.size() == AddRec->getNumOperands())
669 return getAddRecExpr(Operands, AddRec->getLoop());
672 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
673 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
677 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
679 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
680 "This is not an extending conversion!");
682 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
683 const Type *IntTy = getEffectiveSCEVType(Ty);
684 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
685 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
686 return getUnknown(C);
689 // FIXME: If the input value is a chrec scev, and we can prove that the value
690 // did not overflow the old, smaller, value, we can zero extend all of the
691 // operands (often constants). This would allow analysis of something like
692 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
694 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
695 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
699 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
700 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
701 "This is not an extending conversion!");
703 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
704 const Type *IntTy = getEffectiveSCEVType(Ty);
705 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
706 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
707 return getUnknown(C);
710 // FIXME: If the input value is a chrec scev, and we can prove that the value
711 // did not overflow the old, smaller, value, we can sign extend all of the
712 // operands (often constants). This would allow analysis of something like
713 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
715 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
716 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
720 // get - Get a canonical add expression, or something simpler if possible.
721 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
722 assert(!Ops.empty() && "Cannot get empty add!");
723 if (Ops.size() == 1) return Ops[0];
725 // Sort by complexity, this groups all similar expression types together.
726 GroupByComplexity(Ops);
728 // If there are any constants, fold them together.
730 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
732 assert(Idx < Ops.size());
733 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
734 // We found two constants, fold them together!
735 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
736 RHSC->getValue()->getValue());
737 Ops[0] = getConstant(Fold);
738 Ops.erase(Ops.begin()+1); // Erase the folded element
739 if (Ops.size() == 1) return Ops[0];
740 LHSC = cast<SCEVConstant>(Ops[0]);
743 // If we are left with a constant zero being added, strip it off.
744 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
745 Ops.erase(Ops.begin());
750 if (Ops.size() == 1) return Ops[0];
752 // Okay, check to see if the same value occurs in the operand list twice. If
753 // so, merge them together into an multiply expression. Since we sorted the
754 // list, these values are required to be adjacent.
755 const Type *Ty = Ops[0]->getType();
756 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
757 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
758 // Found a match, merge the two values into a multiply, and add any
759 // remaining values to the result.
760 SCEVHandle Two = getIntegerSCEV(2, Ty);
761 SCEVHandle Mul = getMulExpr(Ops[i], Two);
764 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
766 return getAddExpr(Ops);
769 // Now we know the first non-constant operand. Skip past any cast SCEVs.
770 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
773 // If there are add operands they would be next.
774 if (Idx < Ops.size()) {
775 bool DeletedAdd = false;
776 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
777 // If we have an add, expand the add operands onto the end of the operands
779 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
780 Ops.erase(Ops.begin()+Idx);
784 // If we deleted at least one add, we added operands to the end of the list,
785 // and they are not necessarily sorted. Recurse to resort and resimplify
786 // any operands we just aquired.
788 return getAddExpr(Ops);
791 // Skip over the add expression until we get to a multiply.
792 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
795 // If we are adding something to a multiply expression, make sure the
796 // something is not already an operand of the multiply. If so, merge it into
798 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
799 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
800 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
801 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
802 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
803 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
804 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
805 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
806 if (Mul->getNumOperands() != 2) {
807 // If the multiply has more than two operands, we must get the
809 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
810 MulOps.erase(MulOps.begin()+MulOp);
811 InnerMul = getMulExpr(MulOps);
813 SCEVHandle One = getIntegerSCEV(1, Ty);
814 SCEVHandle AddOne = getAddExpr(InnerMul, One);
815 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
816 if (Ops.size() == 2) return OuterMul;
818 Ops.erase(Ops.begin()+AddOp);
819 Ops.erase(Ops.begin()+Idx-1);
821 Ops.erase(Ops.begin()+Idx);
822 Ops.erase(Ops.begin()+AddOp-1);
824 Ops.push_back(OuterMul);
825 return getAddExpr(Ops);
828 // Check this multiply against other multiplies being added together.
829 for (unsigned OtherMulIdx = Idx+1;
830 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
832 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
833 // If MulOp occurs in OtherMul, we can fold the two multiplies
835 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
836 OMulOp != e; ++OMulOp)
837 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
838 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
839 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
840 if (Mul->getNumOperands() != 2) {
841 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
842 MulOps.erase(MulOps.begin()+MulOp);
843 InnerMul1 = getMulExpr(MulOps);
845 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
846 if (OtherMul->getNumOperands() != 2) {
847 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
849 MulOps.erase(MulOps.begin()+OMulOp);
850 InnerMul2 = getMulExpr(MulOps);
852 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
853 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
854 if (Ops.size() == 2) return OuterMul;
855 Ops.erase(Ops.begin()+Idx);
856 Ops.erase(Ops.begin()+OtherMulIdx-1);
857 Ops.push_back(OuterMul);
858 return getAddExpr(Ops);
864 // If there are any add recurrences in the operands list, see if any other
865 // added values are loop invariant. If so, we can fold them into the
867 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
870 // Scan over all recurrences, trying to fold loop invariants into them.
871 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
872 // Scan all of the other operands to this add and add them to the vector if
873 // they are loop invariant w.r.t. the recurrence.
874 std::vector<SCEVHandle> LIOps;
875 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
876 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
877 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
878 LIOps.push_back(Ops[i]);
879 Ops.erase(Ops.begin()+i);
883 // If we found some loop invariants, fold them into the recurrence.
884 if (!LIOps.empty()) {
885 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
886 LIOps.push_back(AddRec->getStart());
888 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
889 AddRecOps[0] = getAddExpr(LIOps);
891 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
892 // If all of the other operands were loop invariant, we are done.
893 if (Ops.size() == 1) return NewRec;
895 // Otherwise, add the folded AddRec by the non-liv parts.
896 for (unsigned i = 0;; ++i)
897 if (Ops[i] == AddRec) {
901 return getAddExpr(Ops);
904 // Okay, if there weren't any loop invariants to be folded, check to see if
905 // there are multiple AddRec's with the same loop induction variable being
906 // added together. If so, we can fold them.
907 for (unsigned OtherIdx = Idx+1;
908 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
909 if (OtherIdx != Idx) {
910 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
911 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
912 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
913 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
914 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
915 if (i >= NewOps.size()) {
916 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
917 OtherAddRec->op_end());
920 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
922 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
924 if (Ops.size() == 2) return NewAddRec;
926 Ops.erase(Ops.begin()+Idx);
927 Ops.erase(Ops.begin()+OtherIdx-1);
928 Ops.push_back(NewAddRec);
929 return getAddExpr(Ops);
933 // Otherwise couldn't fold anything into this recurrence. Move onto the
937 // Okay, it looks like we really DO need an add expr. Check to see if we
938 // already have one, otherwise create a new one.
939 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
940 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
942 if (Result == 0) Result = new SCEVAddExpr(Ops);
947 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
948 assert(!Ops.empty() && "Cannot get empty mul!");
950 // Sort by complexity, this groups all similar expression types together.
951 GroupByComplexity(Ops);
953 // If there are any constants, fold them together.
955 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
957 // C1*(C2+V) -> C1*C2 + C1*V
959 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
960 if (Add->getNumOperands() == 2 &&
961 isa<SCEVConstant>(Add->getOperand(0)))
962 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
963 getMulExpr(LHSC, Add->getOperand(1)));
967 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
968 // We found two constants, fold them together!
969 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
970 RHSC->getValue()->getValue());
971 Ops[0] = getConstant(Fold);
972 Ops.erase(Ops.begin()+1); // Erase the folded element
973 if (Ops.size() == 1) return Ops[0];
974 LHSC = cast<SCEVConstant>(Ops[0]);
977 // If we are left with a constant one being multiplied, strip it off.
978 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
979 Ops.erase(Ops.begin());
981 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
982 // If we have a multiply of zero, it will always be zero.
987 // Skip over the add expression until we get to a multiply.
988 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
994 // If there are mul operands inline them all into this expression.
995 if (Idx < Ops.size()) {
996 bool DeletedMul = false;
997 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
998 // If we have an mul, expand the mul operands onto the end of the operands
1000 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1001 Ops.erase(Ops.begin()+Idx);
1005 // If we deleted at least one mul, we added operands to the end of the list,
1006 // and they are not necessarily sorted. Recurse to resort and resimplify
1007 // any operands we just aquired.
1009 return getMulExpr(Ops);
1012 // If there are any add recurrences in the operands list, see if any other
1013 // added values are loop invariant. If so, we can fold them into the
1015 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1018 // Scan over all recurrences, trying to fold loop invariants into them.
1019 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1020 // Scan all of the other operands to this mul and add them to the vector if
1021 // they are loop invariant w.r.t. the recurrence.
1022 std::vector<SCEVHandle> LIOps;
1023 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1024 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1025 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1026 LIOps.push_back(Ops[i]);
1027 Ops.erase(Ops.begin()+i);
1031 // If we found some loop invariants, fold them into the recurrence.
1032 if (!LIOps.empty()) {
1033 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1034 std::vector<SCEVHandle> NewOps;
1035 NewOps.reserve(AddRec->getNumOperands());
1036 if (LIOps.size() == 1) {
1037 SCEV *Scale = LIOps[0];
1038 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1039 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1041 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1042 std::vector<SCEVHandle> MulOps(LIOps);
1043 MulOps.push_back(AddRec->getOperand(i));
1044 NewOps.push_back(getMulExpr(MulOps));
1048 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1050 // If all of the other operands were loop invariant, we are done.
1051 if (Ops.size() == 1) return NewRec;
1053 // Otherwise, multiply the folded AddRec by the non-liv parts.
1054 for (unsigned i = 0;; ++i)
1055 if (Ops[i] == AddRec) {
1059 return getMulExpr(Ops);
1062 // Okay, if there weren't any loop invariants to be folded, check to see if
1063 // there are multiple AddRec's with the same loop induction variable being
1064 // multiplied together. If so, we can fold them.
1065 for (unsigned OtherIdx = Idx+1;
1066 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1067 if (OtherIdx != Idx) {
1068 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1069 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1070 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1071 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1072 SCEVHandle NewStart = getMulExpr(F->getStart(),
1074 SCEVHandle B = F->getStepRecurrence(*this);
1075 SCEVHandle D = G->getStepRecurrence(*this);
1076 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1079 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1081 if (Ops.size() == 2) return NewAddRec;
1083 Ops.erase(Ops.begin()+Idx);
1084 Ops.erase(Ops.begin()+OtherIdx-1);
1085 Ops.push_back(NewAddRec);
1086 return getMulExpr(Ops);
1090 // Otherwise couldn't fold anything into this recurrence. Move onto the
1094 // Okay, it looks like we really DO need an mul expr. Check to see if we
1095 // already have one, otherwise create a new one.
1096 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1097 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1100 Result = new SCEVMulExpr(Ops);
1104 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1105 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1106 if (RHSC->getValue()->equalsInt(1))
1107 return LHS; // X udiv 1 --> x
1109 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1110 Constant *LHSCV = LHSC->getValue();
1111 Constant *RHSCV = RHSC->getValue();
1112 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1116 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1118 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1119 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1124 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1125 /// specified loop. Simplify the expression as much as possible.
1126 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1127 const SCEVHandle &Step, const Loop *L) {
1128 std::vector<SCEVHandle> Operands;
1129 Operands.push_back(Start);
1130 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1131 if (StepChrec->getLoop() == L) {
1132 Operands.insert(Operands.end(), StepChrec->op_begin(),
1133 StepChrec->op_end());
1134 return getAddRecExpr(Operands, L);
1137 Operands.push_back(Step);
1138 return getAddRecExpr(Operands, L);
1141 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1142 /// specified loop. Simplify the expression as much as possible.
1143 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1145 if (Operands.size() == 1) return Operands[0];
1147 if (Operands.back()->isZero()) {
1148 Operands.pop_back();
1149 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1152 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1153 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1154 const Loop* NestedLoop = NestedAR->getLoop();
1155 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1156 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1157 NestedAR->op_end());
1158 SCEVHandle NestedARHandle(NestedAR);
1159 Operands[0] = NestedAR->getStart();
1160 NestedOperands[0] = getAddRecExpr(Operands, L);
1161 return getAddRecExpr(NestedOperands, NestedLoop);
1165 SCEVAddRecExpr *&Result =
1166 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1168 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1172 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1173 const SCEVHandle &RHS) {
1174 std::vector<SCEVHandle> Ops;
1177 return getSMaxExpr(Ops);
1180 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1181 assert(!Ops.empty() && "Cannot get empty smax!");
1182 if (Ops.size() == 1) return Ops[0];
1184 // Sort by complexity, this groups all similar expression types together.
1185 GroupByComplexity(Ops);
1187 // If there are any constants, fold them together.
1189 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1191 assert(Idx < Ops.size());
1192 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1193 // We found two constants, fold them together!
1194 ConstantInt *Fold = ConstantInt::get(
1195 APIntOps::smax(LHSC->getValue()->getValue(),
1196 RHSC->getValue()->getValue()));
1197 Ops[0] = getConstant(Fold);
1198 Ops.erase(Ops.begin()+1); // Erase the folded element
1199 if (Ops.size() == 1) return Ops[0];
1200 LHSC = cast<SCEVConstant>(Ops[0]);
1203 // If we are left with a constant -inf, strip it off.
1204 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1205 Ops.erase(Ops.begin());
1210 if (Ops.size() == 1) return Ops[0];
1212 // Find the first SMax
1213 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1216 // Check to see if one of the operands is an SMax. If so, expand its operands
1217 // onto our operand list, and recurse to simplify.
1218 if (Idx < Ops.size()) {
1219 bool DeletedSMax = false;
1220 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1221 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1222 Ops.erase(Ops.begin()+Idx);
1227 return getSMaxExpr(Ops);
1230 // Okay, check to see if the same value occurs in the operand list twice. If
1231 // so, delete one. Since we sorted the list, these values are required to
1233 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1234 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1235 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1239 if (Ops.size() == 1) return Ops[0];
1241 assert(!Ops.empty() && "Reduced smax down to nothing!");
1243 // Okay, it looks like we really DO need an smax expr. Check to see if we
1244 // already have one, otherwise create a new one.
1245 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1246 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1248 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1252 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1253 const SCEVHandle &RHS) {
1254 std::vector<SCEVHandle> Ops;
1257 return getUMaxExpr(Ops);
1260 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1261 assert(!Ops.empty() && "Cannot get empty umax!");
1262 if (Ops.size() == 1) return Ops[0];
1264 // Sort by complexity, this groups all similar expression types together.
1265 GroupByComplexity(Ops);
1267 // If there are any constants, fold them together.
1269 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1271 assert(Idx < Ops.size());
1272 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1273 // We found two constants, fold them together!
1274 ConstantInt *Fold = ConstantInt::get(
1275 APIntOps::umax(LHSC->getValue()->getValue(),
1276 RHSC->getValue()->getValue()));
1277 Ops[0] = getConstant(Fold);
1278 Ops.erase(Ops.begin()+1); // Erase the folded element
1279 if (Ops.size() == 1) return Ops[0];
1280 LHSC = cast<SCEVConstant>(Ops[0]);
1283 // If we are left with a constant zero, strip it off.
1284 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1285 Ops.erase(Ops.begin());
1290 if (Ops.size() == 1) return Ops[0];
1292 // Find the first UMax
1293 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1296 // Check to see if one of the operands is a UMax. If so, expand its operands
1297 // onto our operand list, and recurse to simplify.
1298 if (Idx < Ops.size()) {
1299 bool DeletedUMax = false;
1300 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1301 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1302 Ops.erase(Ops.begin()+Idx);
1307 return getUMaxExpr(Ops);
1310 // Okay, check to see if the same value occurs in the operand list twice. If
1311 // so, delete one. Since we sorted the list, these values are required to
1313 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1314 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1315 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1319 if (Ops.size() == 1) return Ops[0];
1321 assert(!Ops.empty() && "Reduced umax down to nothing!");
1323 // Okay, it looks like we really DO need a umax expr. Check to see if we
1324 // already have one, otherwise create a new one.
1325 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1326 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1328 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1332 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1333 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1334 return getConstant(CI);
1335 if (isa<ConstantPointerNull>(V))
1336 return getIntegerSCEV(0, V->getType());
1337 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1338 if (Result == 0) Result = new SCEVUnknown(V);
1342 //===----------------------------------------------------------------------===//
1343 // ScalarEvolutionsImpl Definition and Implementation
1344 //===----------------------------------------------------------------------===//
1346 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1350 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1351 /// SE - A reference to the public ScalarEvolution object.
1352 ScalarEvolution &SE;
1354 /// F - The function we are analyzing.
1358 /// LI - The loop information for the function we are currently analyzing.
1362 /// TD - The target data information for the target we are targetting.
1366 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1368 SCEVHandle UnknownValue;
1370 /// Scalars - This is a cache of the scalars we have analyzed so far.
1372 std::map<Value*, SCEVHandle> Scalars;
1374 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
1375 /// this function as they are computed.
1376 std::map<const Loop*, SCEVHandle> BackedgeTakenCounts;
1378 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1379 /// the PHI instructions that we attempt to compute constant evolutions for.
1380 /// This allows us to avoid potentially expensive recomputation of these
1381 /// properties. An instruction maps to null if we are unable to compute its
1383 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1386 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li,
1388 : SE(se), F(f), LI(li), TD(td), UnknownValue(new SCEVCouldNotCompute()) {}
1390 /// isSCEVable - Test if values of the given type are analyzable within
1391 /// the SCEV framework. This primarily includes integer types, and it
1392 /// can optionally include pointer types if the ScalarEvolution class
1393 /// has access to target-specific information.
1394 bool isSCEVable(const Type *Ty) const;
1396 /// getTypeSizeInBits - Return the size in bits of the specified type,
1397 /// for which isSCEVable must return true.
1398 uint64_t getTypeSizeInBits(const Type *Ty) const;
1400 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1401 /// the given type and which represents how SCEV will treat the given
1402 /// type, for which isSCEVable must return true. For pointer types,
1403 /// this is the pointer-sized integer type.
1404 const Type *getEffectiveSCEVType(const Type *Ty) const;
1406 SCEVHandle getCouldNotCompute();
1408 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1409 /// specified signed integer value and return a SCEV for the constant.
1410 SCEVHandle getIntegerSCEV(int Val, const Type *Ty);
1412 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1414 SCEVHandle getNegativeSCEV(const SCEVHandle &V);
1416 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1418 SCEVHandle getNotSCEV(const SCEVHandle &V);
1420 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1422 SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS);
1424 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
1425 /// of the input value to the specified type. If the type must be extended,
1426 /// it is zero extended.
1427 SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty);
1429 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
1430 /// of the input value to the specified type. If the type must be extended,
1431 /// it is sign extended.
1432 SCEVHandle getTruncateOrSignExtend(const SCEVHandle &V, const Type *Ty);
1434 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1435 /// expression and create a new one.
1436 SCEVHandle getSCEV(Value *V);
1438 /// hasSCEV - Return true if the SCEV for this value has already been
1440 bool hasSCEV(Value *V) const {
1441 return Scalars.count(V);
1444 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1445 /// the specified value.
1446 void setSCEV(Value *V, const SCEVHandle &H) {
1447 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1448 assert(isNew && "This entry already existed!");
1453 /// getSCEVAtScope - Compute the value of the specified expression within
1454 /// the indicated loop (which may be null to indicate in no loop). If the
1455 /// expression cannot be evaluated, return UnknownValue itself.
1456 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1459 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
1460 /// a conditional between LHS and RHS.
1461 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
1462 SCEV *LHS, SCEV *RHS);
1464 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
1465 /// has an analyzable loop-invariant backedge-taken count.
1466 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
1468 /// forgetLoopBackedgeTakenCount - This method should be called by the
1469 /// client when it has changed a loop in a way that may effect
1470 /// ScalarEvolution's ability to compute a trip count, or if the loop
1472 void forgetLoopBackedgeTakenCount(const Loop *L);
1474 /// getBackedgeTakenCount - If the specified loop has a predictable
1475 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
1476 /// object. The backedge-taken count is the number of times the loop header
1477 /// will be branched to from within the loop. This is one less than the
1478 /// trip count of the loop, since it doesn't count the first iteration,
1479 /// when the header is branched to from outside the loop.
1481 /// Note that it is not valid to call this method on a loop without a
1482 /// loop-invariant backedge-taken count (see
1483 /// hasLoopInvariantBackedgeTakenCount).
1485 SCEVHandle getBackedgeTakenCount(const Loop *L);
1487 /// deleteValueFromRecords - This method should be called by the
1488 /// client before it removes a value from the program, to make sure
1489 /// that no dangling references are left around.
1490 void deleteValueFromRecords(Value *V);
1493 /// createSCEV - We know that there is no SCEV for the specified value.
1494 /// Analyze the expression.
1495 SCEVHandle createSCEV(Value *V);
1497 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1499 SCEVHandle createNodeForPHI(PHINode *PN);
1501 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1502 /// for the specified instruction and replaces any references to the
1503 /// symbolic value SymName with the specified value. This is used during
1505 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1506 const SCEVHandle &SymName,
1507 const SCEVHandle &NewVal);
1509 /// ComputeBackedgeTakenCount - Compute the number of times the specified
1510 /// loop will iterate.
1511 SCEVHandle ComputeBackedgeTakenCount(const Loop *L);
1513 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
1514 /// of 'icmp op load X, cst', try to see if we can compute the trip count.
1516 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
1519 ICmpInst::Predicate p);
1521 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute
1522 /// a constant number of times (the condition evolves only from constants),
1523 /// try to evaluate a few iterations of the loop until we get the exit
1524 /// condition gets a value of ExitWhen (true or false). If we cannot
1525 /// evaluate the trip count of the loop, return UnknownValue.
1526 SCEVHandle ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond,
1529 /// HowFarToZero - Return the number of times a backedge comparing the
1530 /// specified value to zero will execute. If not computable, return
1532 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1534 /// HowFarToNonZero - Return the number of times a backedge checking the
1535 /// specified value for nonzero will execute. If not computable, return
1537 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1539 /// HowManyLessThans - Return the number of times a backedge containing the
1540 /// specified less-than comparison will execute. If not computable, return
1541 /// UnknownValue. isSigned specifies whether the less-than is signed.
1542 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1545 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
1546 /// (which may not be an immediate predecessor) which has exactly one
1547 /// successor from which BB is reachable, or null if no such block is
1549 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1551 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1552 /// in the header of its containing loop, we know the loop executes a
1553 /// constant number of times, and the PHI node is just a recurrence
1554 /// involving constants, fold it.
1555 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
1560 //===----------------------------------------------------------------------===//
1561 // Basic SCEV Analysis and PHI Idiom Recognition Code
1564 /// deleteValueFromRecords - This method should be called by the
1565 /// client before it removes an instruction from the program, to make sure
1566 /// that no dangling references are left around.
1567 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1568 SmallVector<Value *, 16> Worklist;
1570 if (Scalars.erase(V)) {
1571 if (PHINode *PN = dyn_cast<PHINode>(V))
1572 ConstantEvolutionLoopExitValue.erase(PN);
1573 Worklist.push_back(V);
1576 while (!Worklist.empty()) {
1577 Value *VV = Worklist.back();
1578 Worklist.pop_back();
1580 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1582 Instruction *Inst = cast<Instruction>(*UI);
1583 if (Scalars.erase(Inst)) {
1584 if (PHINode *PN = dyn_cast<PHINode>(VV))
1585 ConstantEvolutionLoopExitValue.erase(PN);
1586 Worklist.push_back(Inst);
1592 /// isSCEVable - Test if values of the given type are analyzable within
1593 /// the SCEV framework. This primarily includes integer types, and it
1594 /// can optionally include pointer types if the ScalarEvolution class
1595 /// has access to target-specific information.
1596 bool ScalarEvolutionsImpl::isSCEVable(const Type *Ty) const {
1597 // Integers are always SCEVable.
1598 if (Ty->isInteger())
1601 // Pointers are SCEVable if TargetData information is available
1602 // to provide pointer size information.
1603 if (isa<PointerType>(Ty))
1606 // Otherwise it's not SCEVable.
1610 /// getTypeSizeInBits - Return the size in bits of the specified type,
1611 /// for which isSCEVable must return true.
1612 uint64_t ScalarEvolutionsImpl::getTypeSizeInBits(const Type *Ty) const {
1613 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1615 // If we have a TargetData, use it!
1617 return TD->getTypeSizeInBits(Ty);
1619 // Otherwise, we support only integer types.
1620 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1621 return Ty->getPrimitiveSizeInBits();
1624 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1625 /// the given type and which represents how SCEV will treat the given
1626 /// type, for which isSCEVable must return true. For pointer types,
1627 /// this is the pointer-sized integer type.
1628 const Type *ScalarEvolutionsImpl::getEffectiveSCEVType(const Type *Ty) const {
1629 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1631 if (Ty->isInteger())
1634 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1635 return TD->getIntPtrType();
1638 SCEVHandle ScalarEvolutionsImpl::getCouldNotCompute() {
1639 return UnknownValue;
1642 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1643 /// expression and create a new one.
1644 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1645 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1647 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1648 if (I != Scalars.end()) return I->second;
1649 SCEVHandle S = createSCEV(V);
1650 Scalars.insert(std::make_pair(V, S));
1654 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1655 /// specified signed integer value and return a SCEV for the constant.
1656 SCEVHandle ScalarEvolutionsImpl::getIntegerSCEV(int Val, const Type *Ty) {
1657 Ty = SE.getEffectiveSCEVType(Ty);
1660 C = Constant::getNullValue(Ty);
1661 else if (Ty->isFloatingPoint())
1662 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1663 APFloat::IEEEdouble, Val));
1665 C = ConstantInt::get(Ty, Val);
1666 return SE.getUnknown(C);
1669 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1671 SCEVHandle ScalarEvolutionsImpl::getNegativeSCEV(const SCEVHandle &V) {
1672 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1673 return SE.getUnknown(ConstantExpr::getNeg(VC->getValue()));
1675 const Type *Ty = V->getType();
1676 Ty = SE.getEffectiveSCEVType(Ty);
1677 return SE.getMulExpr(V, SE.getConstant(ConstantInt::getAllOnesValue(Ty)));
1680 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1681 SCEVHandle ScalarEvolutionsImpl::getNotSCEV(const SCEVHandle &V) {
1682 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1683 return SE.getUnknown(ConstantExpr::getNot(VC->getValue()));
1685 const Type *Ty = V->getType();
1686 Ty = SE.getEffectiveSCEVType(Ty);
1687 SCEVHandle AllOnes = SE.getConstant(ConstantInt::getAllOnesValue(Ty));
1688 return getMinusSCEV(AllOnes, V);
1691 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1693 SCEVHandle ScalarEvolutionsImpl::getMinusSCEV(const SCEVHandle &LHS,
1694 const SCEVHandle &RHS) {
1696 return SE.getAddExpr(LHS, SE.getNegativeSCEV(RHS));
1699 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1700 /// input value to the specified type. If the type must be extended, it is zero
1703 ScalarEvolutionsImpl::getTruncateOrZeroExtend(const SCEVHandle &V,
1705 const Type *SrcTy = V->getType();
1706 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1707 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1708 "Cannot truncate or zero extend with non-integer arguments!");
1709 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1710 return V; // No conversion
1711 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1712 return SE.getTruncateExpr(V, Ty);
1713 return SE.getZeroExtendExpr(V, Ty);
1716 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1717 /// input value to the specified type. If the type must be extended, it is sign
1720 ScalarEvolutionsImpl::getTruncateOrSignExtend(const SCEVHandle &V,
1722 const Type *SrcTy = V->getType();
1723 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1724 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1725 "Cannot truncate or zero extend with non-integer arguments!");
1726 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1727 return V; // No conversion
1728 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1729 return SE.getTruncateExpr(V, Ty);
1730 return SE.getSignExtendExpr(V, Ty);
1733 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1734 /// the specified instruction and replaces any references to the symbolic value
1735 /// SymName with the specified value. This is used during PHI resolution.
1736 void ScalarEvolutionsImpl::
1737 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1738 const SCEVHandle &NewVal) {
1739 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1740 if (SI == Scalars.end()) return;
1743 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
1744 if (NV == SI->second) return; // No change.
1746 SI->second = NV; // Update the scalars map!
1748 // Any instruction values that use this instruction might also need to be
1750 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1752 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1755 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1756 /// a loop header, making it a potential recurrence, or it doesn't.
1758 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1759 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1760 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1761 if (L->getHeader() == PN->getParent()) {
1762 // If it lives in the loop header, it has two incoming values, one
1763 // from outside the loop, and one from inside.
1764 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1765 unsigned BackEdge = IncomingEdge^1;
1767 // While we are analyzing this PHI node, handle its value symbolically.
1768 SCEVHandle SymbolicName = SE.getUnknown(PN);
1769 assert(Scalars.find(PN) == Scalars.end() &&
1770 "PHI node already processed?");
1771 Scalars.insert(std::make_pair(PN, SymbolicName));
1773 // Using this symbolic name for the PHI, analyze the value coming around
1775 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1777 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1778 // has a special value for the first iteration of the loop.
1780 // If the value coming around the backedge is an add with the symbolic
1781 // value we just inserted, then we found a simple induction variable!
1782 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1783 // If there is a single occurrence of the symbolic value, replace it
1784 // with a recurrence.
1785 unsigned FoundIndex = Add->getNumOperands();
1786 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1787 if (Add->getOperand(i) == SymbolicName)
1788 if (FoundIndex == e) {
1793 if (FoundIndex != Add->getNumOperands()) {
1794 // Create an add with everything but the specified operand.
1795 std::vector<SCEVHandle> Ops;
1796 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1797 if (i != FoundIndex)
1798 Ops.push_back(Add->getOperand(i));
1799 SCEVHandle Accum = SE.getAddExpr(Ops);
1801 // This is not a valid addrec if the step amount is varying each
1802 // loop iteration, but is not itself an addrec in this loop.
1803 if (Accum->isLoopInvariant(L) ||
1804 (isa<SCEVAddRecExpr>(Accum) &&
1805 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1806 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1807 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L);
1809 // Okay, for the entire analysis of this edge we assumed the PHI
1810 // to be symbolic. We now need to go back and update all of the
1811 // entries for the scalars that use the PHI (except for the PHI
1812 // itself) to use the new analyzed value instead of the "symbolic"
1814 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1818 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1819 // Otherwise, this could be a loop like this:
1820 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1821 // In this case, j = {1,+,1} and BEValue is j.
1822 // Because the other in-value of i (0) fits the evolution of BEValue
1823 // i really is an addrec evolution.
1824 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1825 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1827 // If StartVal = j.start - j.stride, we can use StartVal as the
1828 // initial step of the addrec evolution.
1829 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
1830 AddRec->getOperand(1))) {
1831 SCEVHandle PHISCEV =
1832 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1834 // Okay, for the entire analysis of this edge we assumed the PHI
1835 // to be symbolic. We now need to go back and update all of the
1836 // entries for the scalars that use the PHI (except for the PHI
1837 // itself) to use the new analyzed value instead of the "symbolic"
1839 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1845 return SymbolicName;
1848 // If it's not a loop phi, we can't handle it yet.
1849 return SE.getUnknown(PN);
1852 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1853 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1854 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1855 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1856 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
1857 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1858 return C->getValue()->getValue().countTrailingZeros();
1860 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1861 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
1862 (uint32_t)SE.getTypeSizeInBits(T->getType()));
1864 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1865 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1866 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1867 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1870 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1871 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1872 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1873 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1876 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1877 // The result is the min of all operands results.
1878 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1879 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1880 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1884 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1885 // The result is the sum of all operands results.
1886 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1887 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
1888 for (unsigned i = 1, e = M->getNumOperands();
1889 SumOpRes != BitWidth && i != e; ++i)
1890 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
1895 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1896 // The result is the min of all operands results.
1897 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1898 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1899 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1903 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1904 // The result is the min of all operands results.
1905 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1906 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1907 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1911 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1912 // The result is the min of all operands results.
1913 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1914 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1915 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1919 // SCEVUDivExpr, SCEVUnknown
1923 /// createSCEV - We know that there is no SCEV for the specified value.
1924 /// Analyze the expression.
1926 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1927 if (!isSCEVable(V->getType()))
1928 return SE.getUnknown(V);
1930 unsigned Opcode = Instruction::UserOp1;
1931 if (Instruction *I = dyn_cast<Instruction>(V))
1932 Opcode = I->getOpcode();
1933 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1934 Opcode = CE->getOpcode();
1936 return SE.getUnknown(V);
1938 User *U = cast<User>(V);
1940 case Instruction::Add:
1941 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1942 getSCEV(U->getOperand(1)));
1943 case Instruction::Mul:
1944 return SE.getMulExpr(getSCEV(U->getOperand(0)),
1945 getSCEV(U->getOperand(1)));
1946 case Instruction::UDiv:
1947 return SE.getUDivExpr(getSCEV(U->getOperand(0)),
1948 getSCEV(U->getOperand(1)));
1949 case Instruction::Sub:
1950 return SE.getMinusSCEV(getSCEV(U->getOperand(0)),
1951 getSCEV(U->getOperand(1)));
1952 case Instruction::Or:
1953 // If the RHS of the Or is a constant, we may have something like:
1954 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1955 // optimizations will transparently handle this case.
1957 // In order for this transformation to be safe, the LHS must be of the
1958 // form X*(2^n) and the Or constant must be less than 2^n.
1959 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1960 SCEVHandle LHS = getSCEV(U->getOperand(0));
1961 const APInt &CIVal = CI->getValue();
1962 if (GetMinTrailingZeros(LHS, SE) >=
1963 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1964 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1)));
1967 case Instruction::Xor:
1968 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1969 // If the RHS of the xor is a signbit, then this is just an add.
1970 // Instcombine turns add of signbit into xor as a strength reduction step.
1971 if (CI->getValue().isSignBit())
1972 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1973 getSCEV(U->getOperand(1)));
1975 // If the RHS of xor is -1, then this is a not operation.
1976 else if (CI->isAllOnesValue())
1977 return SE.getNotSCEV(getSCEV(U->getOperand(0)));
1981 case Instruction::Shl:
1982 // Turn shift left of a constant amount into a multiply.
1983 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1984 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1985 Constant *X = ConstantInt::get(
1986 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1987 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1991 case Instruction::LShr:
1992 // Turn logical shift right of a constant into a unsigned divide.
1993 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1994 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1995 Constant *X = ConstantInt::get(
1996 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1997 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2001 case Instruction::Trunc:
2002 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2004 case Instruction::ZExt:
2005 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2007 case Instruction::SExt:
2008 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2010 case Instruction::BitCast:
2011 // BitCasts are no-op casts so we just eliminate the cast.
2012 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2013 return getSCEV(U->getOperand(0));
2016 case Instruction::IntToPtr:
2017 if (!TD) break; // Without TD we can't analyze pointers.
2018 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2019 TD->getIntPtrType());
2021 case Instruction::PtrToInt:
2022 if (!TD) break; // Without TD we can't analyze pointers.
2023 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2026 case Instruction::GetElementPtr: {
2027 if (!TD) break; // Without TD we can't analyze pointers.
2028 const Type *IntPtrTy = TD->getIntPtrType();
2029 Value *Base = U->getOperand(0);
2030 SCEVHandle TotalOffset = SE.getIntegerSCEV(0, IntPtrTy);
2031 gep_type_iterator GTI = gep_type_begin(U);
2032 for (GetElementPtrInst::op_iterator I = next(U->op_begin()),
2036 // Compute the (potentially symbolic) offset in bytes for this index.
2037 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2038 // For a struct, add the member offset.
2039 const StructLayout &SL = *TD->getStructLayout(STy);
2040 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2041 uint64_t Offset = SL.getElementOffset(FieldNo);
2042 TotalOffset = SE.getAddExpr(TotalOffset,
2043 SE.getIntegerSCEV(Offset, IntPtrTy));
2045 // For an array, add the element offset, explicitly scaled.
2046 SCEVHandle LocalOffset = getSCEV(Index);
2047 if (!isa<PointerType>(LocalOffset->getType()))
2048 // Getelementptr indicies are signed.
2049 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2052 SE.getMulExpr(LocalOffset,
2053 SE.getIntegerSCEV(TD->getTypePaddedSize(*GTI),
2055 TotalOffset = SE.getAddExpr(TotalOffset, LocalOffset);
2058 return SE.getAddExpr(getSCEV(Base), TotalOffset);
2061 case Instruction::PHI:
2062 return createNodeForPHI(cast<PHINode>(U));
2064 case Instruction::Select:
2065 // This could be a smax or umax that was lowered earlier.
2066 // Try to recover it.
2067 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2068 Value *LHS = ICI->getOperand(0);
2069 Value *RHS = ICI->getOperand(1);
2070 switch (ICI->getPredicate()) {
2071 case ICmpInst::ICMP_SLT:
2072 case ICmpInst::ICMP_SLE:
2073 std::swap(LHS, RHS);
2075 case ICmpInst::ICMP_SGT:
2076 case ICmpInst::ICMP_SGE:
2077 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2078 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2079 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2080 // ~smax(~x, ~y) == smin(x, y).
2081 return SE.getNotSCEV(SE.getSMaxExpr(
2082 SE.getNotSCEV(getSCEV(LHS)),
2083 SE.getNotSCEV(getSCEV(RHS))));
2085 case ICmpInst::ICMP_ULT:
2086 case ICmpInst::ICMP_ULE:
2087 std::swap(LHS, RHS);
2089 case ICmpInst::ICMP_UGT:
2090 case ICmpInst::ICMP_UGE:
2091 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2092 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2093 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2094 // ~umax(~x, ~y) == umin(x, y)
2095 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
2096 SE.getNotSCEV(getSCEV(RHS))));
2103 default: // We cannot analyze this expression.
2107 return SE.getUnknown(V);
2112 //===----------------------------------------------------------------------===//
2113 // Iteration Count Computation Code
2116 /// getBackedgeTakenCount - If the specified loop has a predictable
2117 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2118 /// object. The backedge-taken count is the number of times the loop header
2119 /// will be branched to from within the loop. This is one less than the
2120 /// trip count of the loop, since it doesn't count the first iteration,
2121 /// when the header is branched to from outside the loop.
2123 /// Note that it is not valid to call this method on a loop without a
2124 /// loop-invariant backedge-taken count (see
2125 /// hasLoopInvariantBackedgeTakenCount).
2127 SCEVHandle ScalarEvolutionsImpl::getBackedgeTakenCount(const Loop *L) {
2128 std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L);
2129 if (I == BackedgeTakenCounts.end()) {
2130 SCEVHandle ItCount = ComputeBackedgeTakenCount(L);
2131 I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first;
2132 if (ItCount != UnknownValue) {
2133 assert(ItCount->isLoopInvariant(L) &&
2134 "Computed trip count isn't loop invariant for loop!");
2135 ++NumTripCountsComputed;
2136 } else if (isa<PHINode>(L->getHeader()->begin())) {
2137 // Only count loops that have phi nodes as not being computable.
2138 ++NumTripCountsNotComputed;
2144 /// forgetLoopBackedgeTakenCount - This method should be called by the
2145 /// client when it has changed a loop in a way that may effect
2146 /// ScalarEvolution's ability to compute a trip count, or if the loop
2148 void ScalarEvolutionsImpl::forgetLoopBackedgeTakenCount(const Loop *L) {
2149 BackedgeTakenCounts.erase(L);
2152 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2153 /// of the specified loop will execute.
2154 SCEVHandle ScalarEvolutionsImpl::ComputeBackedgeTakenCount(const Loop *L) {
2155 // If the loop has a non-one exit block count, we can't analyze it.
2156 SmallVector<BasicBlock*, 8> ExitBlocks;
2157 L->getExitBlocks(ExitBlocks);
2158 if (ExitBlocks.size() != 1) return UnknownValue;
2160 // Okay, there is one exit block. Try to find the condition that causes the
2161 // loop to be exited.
2162 BasicBlock *ExitBlock = ExitBlocks[0];
2164 BasicBlock *ExitingBlock = 0;
2165 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2167 if (L->contains(*PI)) {
2168 if (ExitingBlock == 0)
2171 return UnknownValue; // More than one block exiting!
2173 assert(ExitingBlock && "No exits from loop, something is broken!");
2175 // Okay, we've computed the exiting block. See what condition causes us to
2178 // FIXME: we should be able to handle switch instructions (with a single exit)
2179 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2180 if (ExitBr == 0) return UnknownValue;
2181 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2183 // At this point, we know we have a conditional branch that determines whether
2184 // the loop is exited. However, we don't know if the branch is executed each
2185 // time through the loop. If not, then the execution count of the branch will
2186 // not be equal to the trip count of the loop.
2188 // Currently we check for this by checking to see if the Exit branch goes to
2189 // the loop header. If so, we know it will always execute the same number of
2190 // times as the loop. We also handle the case where the exit block *is* the
2191 // loop header. This is common for un-rotated loops. More extensive analysis
2192 // could be done to handle more cases here.
2193 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2194 ExitBr->getSuccessor(1) != L->getHeader() &&
2195 ExitBr->getParent() != L->getHeader())
2196 return UnknownValue;
2198 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2200 // If it's not an integer comparison then compute it the hard way.
2201 // Note that ICmpInst deals with pointer comparisons too so we must check
2202 // the type of the operand.
2203 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2204 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2205 ExitBr->getSuccessor(0) == ExitBlock);
2207 // If the condition was exit on true, convert the condition to exit on false
2208 ICmpInst::Predicate Cond;
2209 if (ExitBr->getSuccessor(1) == ExitBlock)
2210 Cond = ExitCond->getPredicate();
2212 Cond = ExitCond->getInversePredicate();
2214 // Handle common loops like: for (X = "string"; *X; ++X)
2215 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2216 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2218 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2219 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2222 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2223 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2225 // Try to evaluate any dependencies out of the loop.
2226 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2227 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2228 Tmp = getSCEVAtScope(RHS, L);
2229 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2231 // At this point, we would like to compute how many iterations of the
2232 // loop the predicate will return true for these inputs.
2233 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2234 // If there is a loop-invariant, force it into the RHS.
2235 std::swap(LHS, RHS);
2236 Cond = ICmpInst::getSwappedPredicate(Cond);
2239 // FIXME: think about handling pointer comparisons! i.e.:
2240 // while (P != P+100) ++P;
2242 // If we have a comparison of a chrec against a constant, try to use value
2243 // ranges to answer this query.
2244 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2245 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2246 if (AddRec->getLoop() == L) {
2247 // Form the comparison range using the constant of the correct type so
2248 // that the ConstantRange class knows to do a signed or unsigned
2250 ConstantInt *CompVal = RHSC->getValue();
2251 const Type *RealTy = ExitCond->getOperand(0)->getType();
2252 CompVal = dyn_cast<ConstantInt>(
2253 ConstantExpr::getBitCast(CompVal, RealTy));
2255 // Form the constant range.
2256 ConstantRange CompRange(
2257 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2259 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
2260 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2265 case ICmpInst::ICMP_NE: { // while (X != Y)
2266 // Convert to: while (X-Y != 0)
2267 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
2268 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2271 case ICmpInst::ICMP_EQ: {
2272 // Convert to: while (X-Y == 0) // while (X == Y)
2273 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
2274 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2277 case ICmpInst::ICMP_SLT: {
2278 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
2279 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2282 case ICmpInst::ICMP_SGT: {
2283 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2284 SE.getNotSCEV(RHS), L, true);
2285 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2288 case ICmpInst::ICMP_ULT: {
2289 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
2290 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2293 case ICmpInst::ICMP_UGT: {
2294 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2295 SE.getNotSCEV(RHS), L, false);
2296 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2301 errs() << "ComputeBackedgeTakenCount ";
2302 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2303 errs() << "[unsigned] ";
2304 errs() << *LHS << " "
2305 << Instruction::getOpcodeName(Instruction::ICmp)
2306 << " " << *RHS << "\n";
2311 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2312 ExitBr->getSuccessor(0) == ExitBlock);
2315 static ConstantInt *
2316 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2317 ScalarEvolution &SE) {
2318 SCEVHandle InVal = SE.getConstant(C);
2319 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2320 assert(isa<SCEVConstant>(Val) &&
2321 "Evaluation of SCEV at constant didn't fold correctly?");
2322 return cast<SCEVConstant>(Val)->getValue();
2325 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2326 /// and a GEP expression (missing the pointer index) indexing into it, return
2327 /// the addressed element of the initializer or null if the index expression is
2330 GetAddressedElementFromGlobal(GlobalVariable *GV,
2331 const std::vector<ConstantInt*> &Indices) {
2332 Constant *Init = GV->getInitializer();
2333 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2334 uint64_t Idx = Indices[i]->getZExtValue();
2335 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2336 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2337 Init = cast<Constant>(CS->getOperand(Idx));
2338 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2339 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2340 Init = cast<Constant>(CA->getOperand(Idx));
2341 } else if (isa<ConstantAggregateZero>(Init)) {
2342 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2343 assert(Idx < STy->getNumElements() && "Bad struct index!");
2344 Init = Constant::getNullValue(STy->getElementType(Idx));
2345 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2346 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2347 Init = Constant::getNullValue(ATy->getElementType());
2349 assert(0 && "Unknown constant aggregate type!");
2353 return 0; // Unknown initializer type
2359 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2360 /// 'icmp op load X, cst', try to see if we can compute the backedge
2361 /// execution count.
2362 SCEVHandle ScalarEvolutionsImpl::
2363 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2365 ICmpInst::Predicate predicate) {
2366 if (LI->isVolatile()) return UnknownValue;
2368 // Check to see if the loaded pointer is a getelementptr of a global.
2369 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2370 if (!GEP) return UnknownValue;
2372 // Make sure that it is really a constant global we are gepping, with an
2373 // initializer, and make sure the first IDX is really 0.
2374 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2375 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2376 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2377 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2378 return UnknownValue;
2380 // Okay, we allow one non-constant index into the GEP instruction.
2382 std::vector<ConstantInt*> Indexes;
2383 unsigned VarIdxNum = 0;
2384 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2385 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2386 Indexes.push_back(CI);
2387 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2388 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2389 VarIdx = GEP->getOperand(i);
2391 Indexes.push_back(0);
2394 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2395 // Check to see if X is a loop variant variable value now.
2396 SCEVHandle Idx = getSCEV(VarIdx);
2397 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2398 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2400 // We can only recognize very limited forms of loop index expressions, in
2401 // particular, only affine AddRec's like {C1,+,C2}.
2402 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2403 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2404 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2405 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2406 return UnknownValue;
2408 unsigned MaxSteps = MaxBruteForceIterations;
2409 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2410 ConstantInt *ItCst =
2411 ConstantInt::get(IdxExpr->getType(), IterationNum);
2412 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
2414 // Form the GEP offset.
2415 Indexes[VarIdxNum] = Val;
2417 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2418 if (Result == 0) break; // Cannot compute!
2420 // Evaluate the condition for this iteration.
2421 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2422 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2423 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2425 errs() << "\n***\n*** Computed loop count " << *ItCst
2426 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2429 ++NumArrayLenItCounts;
2430 return SE.getConstant(ItCst); // Found terminating iteration!
2433 return UnknownValue;
2437 /// CanConstantFold - Return true if we can constant fold an instruction of the
2438 /// specified type, assuming that all operands were constants.
2439 static bool CanConstantFold(const Instruction *I) {
2440 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2441 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2444 if (const CallInst *CI = dyn_cast<CallInst>(I))
2445 if (const Function *F = CI->getCalledFunction())
2446 return canConstantFoldCallTo(F);
2450 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2451 /// in the loop that V is derived from. We allow arbitrary operations along the
2452 /// way, but the operands of an operation must either be constants or a value
2453 /// derived from a constant PHI. If this expression does not fit with these
2454 /// constraints, return null.
2455 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2456 // If this is not an instruction, or if this is an instruction outside of the
2457 // loop, it can't be derived from a loop PHI.
2458 Instruction *I = dyn_cast<Instruction>(V);
2459 if (I == 0 || !L->contains(I->getParent())) return 0;
2461 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2462 if (L->getHeader() == I->getParent())
2465 // We don't currently keep track of the control flow needed to evaluate
2466 // PHIs, so we cannot handle PHIs inside of loops.
2470 // If we won't be able to constant fold this expression even if the operands
2471 // are constants, return early.
2472 if (!CanConstantFold(I)) return 0;
2474 // Otherwise, we can evaluate this instruction if all of its operands are
2475 // constant or derived from a PHI node themselves.
2477 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2478 if (!(isa<Constant>(I->getOperand(Op)) ||
2479 isa<GlobalValue>(I->getOperand(Op)))) {
2480 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2481 if (P == 0) return 0; // Not evolving from PHI
2485 return 0; // Evolving from multiple different PHIs.
2488 // This is a expression evolving from a constant PHI!
2492 /// EvaluateExpression - Given an expression that passes the
2493 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2494 /// in the loop has the value PHIVal. If we can't fold this expression for some
2495 /// reason, return null.
2496 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2497 if (isa<PHINode>(V)) return PHIVal;
2498 if (Constant *C = dyn_cast<Constant>(V)) return C;
2499 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2500 Instruction *I = cast<Instruction>(V);
2502 std::vector<Constant*> Operands;
2503 Operands.resize(I->getNumOperands());
2505 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2506 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2507 if (Operands[i] == 0) return 0;
2510 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2511 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2512 &Operands[0], Operands.size());
2514 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2515 &Operands[0], Operands.size());
2518 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2519 /// in the header of its containing loop, we know the loop executes a
2520 /// constant number of times, and the PHI node is just a recurrence
2521 /// involving constants, fold it.
2522 Constant *ScalarEvolutionsImpl::
2523 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2524 std::map<PHINode*, Constant*>::iterator I =
2525 ConstantEvolutionLoopExitValue.find(PN);
2526 if (I != ConstantEvolutionLoopExitValue.end())
2529 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2530 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2532 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2534 // Since the loop is canonicalized, the PHI node must have two entries. One
2535 // entry must be a constant (coming in from outside of the loop), and the
2536 // second must be derived from the same PHI.
2537 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2538 Constant *StartCST =
2539 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2541 return RetVal = 0; // Must be a constant.
2543 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2544 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2546 return RetVal = 0; // Not derived from same PHI.
2548 // Execute the loop symbolically to determine the exit value.
2549 if (BEs.getActiveBits() >= 32)
2550 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2552 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2553 unsigned IterationNum = 0;
2554 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2555 if (IterationNum == NumIterations)
2556 return RetVal = PHIVal; // Got exit value!
2558 // Compute the value of the PHI node for the next iteration.
2559 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2560 if (NextPHI == PHIVal)
2561 return RetVal = NextPHI; // Stopped evolving!
2563 return 0; // Couldn't evaluate!
2568 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2569 /// constant number of times (the condition evolves only from constants),
2570 /// try to evaluate a few iterations of the loop until we get the exit
2571 /// condition gets a value of ExitWhen (true or false). If we cannot
2572 /// evaluate the trip count of the loop, return UnknownValue.
2573 SCEVHandle ScalarEvolutionsImpl::
2574 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2575 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2576 if (PN == 0) return UnknownValue;
2578 // Since the loop is canonicalized, the PHI node must have two entries. One
2579 // entry must be a constant (coming in from outside of the loop), and the
2580 // second must be derived from the same PHI.
2581 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2582 Constant *StartCST =
2583 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2584 if (StartCST == 0) return UnknownValue; // Must be a constant.
2586 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2587 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2588 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2590 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2591 // the loop symbolically to determine when the condition gets a value of
2593 unsigned IterationNum = 0;
2594 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2595 for (Constant *PHIVal = StartCST;
2596 IterationNum != MaxIterations; ++IterationNum) {
2597 ConstantInt *CondVal =
2598 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2600 // Couldn't symbolically evaluate.
2601 if (!CondVal) return UnknownValue;
2603 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2604 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2605 ++NumBruteForceTripCountsComputed;
2606 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2609 // Compute the value of the PHI node for the next iteration.
2610 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2611 if (NextPHI == 0 || NextPHI == PHIVal)
2612 return UnknownValue; // Couldn't evaluate or not making progress...
2616 // Too many iterations were needed to evaluate.
2617 return UnknownValue;
2620 /// getSCEVAtScope - Compute the value of the specified expression within the
2621 /// indicated loop (which may be null to indicate in no loop). If the
2622 /// expression cannot be evaluated, return UnknownValue.
2623 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2624 // FIXME: this should be turned into a virtual method on SCEV!
2626 if (isa<SCEVConstant>(V)) return V;
2628 // If this instruction is evolved from a constant-evolving PHI, compute the
2629 // exit value from the loop without using SCEVs.
2630 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2631 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2632 const Loop *LI = this->LI[I->getParent()];
2633 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2634 if (PHINode *PN = dyn_cast<PHINode>(I))
2635 if (PN->getParent() == LI->getHeader()) {
2636 // Okay, there is no closed form solution for the PHI node. Check
2637 // to see if the loop that contains it has a known backedge-taken
2638 // count. If so, we may be able to force computation of the exit
2640 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2641 if (SCEVConstant *BTCC =
2642 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2643 // Okay, we know how many times the containing loop executes. If
2644 // this is a constant evolving PHI node, get the final value at
2645 // the specified iteration number.
2646 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2647 BTCC->getValue()->getValue(),
2649 if (RV) return SE.getUnknown(RV);
2653 // Okay, this is an expression that we cannot symbolically evaluate
2654 // into a SCEV. Check to see if it's possible to symbolically evaluate
2655 // the arguments into constants, and if so, try to constant propagate the
2656 // result. This is particularly useful for computing loop exit values.
2657 if (CanConstantFold(I)) {
2658 std::vector<Constant*> Operands;
2659 Operands.reserve(I->getNumOperands());
2660 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2661 Value *Op = I->getOperand(i);
2662 if (Constant *C = dyn_cast<Constant>(Op)) {
2663 Operands.push_back(C);
2665 // If any of the operands is non-constant and if they are
2666 // non-integer and non-pointer, don't even try to analyze them
2667 // with scev techniques.
2668 if (!isa<IntegerType>(Op->getType()) &&
2669 !isa<PointerType>(Op->getType()))
2672 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2673 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2674 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2677 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2678 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2679 Operands.push_back(ConstantExpr::getIntegerCast(C,
2691 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2692 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2693 &Operands[0], Operands.size());
2695 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2696 &Operands[0], Operands.size());
2697 return SE.getUnknown(C);
2701 // This is some other type of SCEVUnknown, just return it.
2705 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2706 // Avoid performing the look-up in the common case where the specified
2707 // expression has no loop-variant portions.
2708 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2709 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2710 if (OpAtScope != Comm->getOperand(i)) {
2711 if (OpAtScope == UnknownValue) return UnknownValue;
2712 // Okay, at least one of these operands is loop variant but might be
2713 // foldable. Build a new instance of the folded commutative expression.
2714 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2715 NewOps.push_back(OpAtScope);
2717 for (++i; i != e; ++i) {
2718 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2719 if (OpAtScope == UnknownValue) return UnknownValue;
2720 NewOps.push_back(OpAtScope);
2722 if (isa<SCEVAddExpr>(Comm))
2723 return SE.getAddExpr(NewOps);
2724 if (isa<SCEVMulExpr>(Comm))
2725 return SE.getMulExpr(NewOps);
2726 if (isa<SCEVSMaxExpr>(Comm))
2727 return SE.getSMaxExpr(NewOps);
2728 if (isa<SCEVUMaxExpr>(Comm))
2729 return SE.getUMaxExpr(NewOps);
2730 assert(0 && "Unknown commutative SCEV type!");
2733 // If we got here, all operands are loop invariant.
2737 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2738 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2739 if (LHS == UnknownValue) return LHS;
2740 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2741 if (RHS == UnknownValue) return RHS;
2742 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2743 return Div; // must be loop invariant
2744 return SE.getUDivExpr(LHS, RHS);
2747 // If this is a loop recurrence for a loop that does not contain L, then we
2748 // are dealing with the final value computed by the loop.
2749 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2750 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2751 // To evaluate this recurrence, we need to know how many times the AddRec
2752 // loop iterates. Compute this now.
2753 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2754 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2756 // Then, evaluate the AddRec.
2757 return AddRec->evaluateAtIteration(BackedgeTakenCount, SE);
2759 return UnknownValue;
2762 //assert(0 && "Unknown SCEV type!");
2763 return UnknownValue;
2766 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2767 /// following equation:
2769 /// A * X = B (mod N)
2771 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2772 /// A and B isn't important.
2774 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2775 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2776 ScalarEvolution &SE) {
2777 uint32_t BW = A.getBitWidth();
2778 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2779 assert(A != 0 && "A must be non-zero.");
2783 // The gcd of A and N may have only one prime factor: 2. The number of
2784 // trailing zeros in A is its multiplicity
2785 uint32_t Mult2 = A.countTrailingZeros();
2788 // 2. Check if B is divisible by D.
2790 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2791 // is not less than multiplicity of this prime factor for D.
2792 if (B.countTrailingZeros() < Mult2)
2793 return SE.getCouldNotCompute();
2795 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2798 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2799 // bit width during computations.
2800 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2801 APInt Mod(BW + 1, 0);
2802 Mod.set(BW - Mult2); // Mod = N / D
2803 APInt I = AD.multiplicativeInverse(Mod);
2805 // 4. Compute the minimum unsigned root of the equation:
2806 // I * (B / D) mod (N / D)
2807 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2809 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2811 return SE.getConstant(Result.trunc(BW));
2814 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2815 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2816 /// might be the same) or two SCEVCouldNotCompute objects.
2818 static std::pair<SCEVHandle,SCEVHandle>
2819 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2820 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2821 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2822 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2823 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2825 // We currently can only solve this if the coefficients are constants.
2826 if (!LC || !MC || !NC) {
2827 SCEV *CNC = SE.getCouldNotCompute();
2828 return std::make_pair(CNC, CNC);
2831 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2832 const APInt &L = LC->getValue()->getValue();
2833 const APInt &M = MC->getValue()->getValue();
2834 const APInt &N = NC->getValue()->getValue();
2835 APInt Two(BitWidth, 2);
2836 APInt Four(BitWidth, 4);
2839 using namespace APIntOps;
2841 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2842 // The B coefficient is M-N/2
2846 // The A coefficient is N/2
2847 APInt A(N.sdiv(Two));
2849 // Compute the B^2-4ac term.
2852 SqrtTerm -= Four * (A * C);
2854 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2855 // integer value or else APInt::sqrt() will assert.
2856 APInt SqrtVal(SqrtTerm.sqrt());
2858 // Compute the two solutions for the quadratic formula.
2859 // The divisions must be performed as signed divisions.
2861 APInt TwoA( A << 1 );
2862 if (TwoA.isMinValue()) {
2863 SCEV *CNC = SE.getCouldNotCompute();
2864 return std::make_pair(CNC, CNC);
2867 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2868 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2870 return std::make_pair(SE.getConstant(Solution1),
2871 SE.getConstant(Solution2));
2872 } // end APIntOps namespace
2875 /// HowFarToZero - Return the number of times a backedge comparing the specified
2876 /// value to zero will execute. If not computable, return UnknownValue
2877 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2878 // If the value is a constant
2879 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2880 // If the value is already zero, the branch will execute zero times.
2881 if (C->getValue()->isZero()) return C;
2882 return UnknownValue; // Otherwise it will loop infinitely.
2885 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2886 if (!AddRec || AddRec->getLoop() != L)
2887 return UnknownValue;
2889 if (AddRec->isAffine()) {
2890 // If this is an affine expression, the execution count of this branch is
2891 // the minimum unsigned root of the following equation:
2893 // Start + Step*N = 0 (mod 2^BW)
2897 // Step*N = -Start (mod 2^BW)
2899 // where BW is the common bit width of Start and Step.
2901 // Get the initial value for the loop.
2902 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2903 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2905 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2907 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2908 // For now we handle only constant steps.
2910 // First, handle unitary steps.
2911 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2912 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned)
2913 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2914 return Start; // N = Start (as unsigned)
2916 // Then, try to solve the above equation provided that Start is constant.
2917 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2918 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2919 -StartC->getValue()->getValue(),SE);
2921 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2922 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2923 // the quadratic equation to solve it.
2924 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
2925 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2926 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2929 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
2930 << " sol#2: " << *R2 << "\n";
2932 // Pick the smallest positive root value.
2933 if (ConstantInt *CB =
2934 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2935 R1->getValue(), R2->getValue()))) {
2936 if (CB->getZExtValue() == false)
2937 std::swap(R1, R2); // R1 is the minimum root now.
2939 // We can only use this value if the chrec ends up with an exact zero
2940 // value at this index. When solving for "X*X != 5", for example, we
2941 // should not accept a root of 2.
2942 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
2944 return R1; // We found a quadratic root!
2949 return UnknownValue;
2952 /// HowFarToNonZero - Return the number of times a backedge checking the
2953 /// specified value for nonzero will execute. If not computable, return
2955 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2956 // Loops that look like: while (X == 0) are very strange indeed. We don't
2957 // handle them yet except for the trivial case. This could be expanded in the
2958 // future as needed.
2960 // If the value is a constant, check to see if it is known to be non-zero
2961 // already. If so, the backedge will execute zero times.
2962 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2963 if (!C->getValue()->isNullValue())
2964 return SE.getIntegerSCEV(0, C->getType());
2965 return UnknownValue; // Otherwise it will loop infinitely.
2968 // We could implement others, but I really doubt anyone writes loops like
2969 // this, and if they did, they would already be constant folded.
2970 return UnknownValue;
2973 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2974 /// (which may not be an immediate predecessor) which has exactly one
2975 /// successor from which BB is reachable, or null if no such block is
2979 ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2980 // If the block has a unique predecessor, the predecessor must have
2981 // no other successors from which BB is reachable.
2982 if (BasicBlock *Pred = BB->getSinglePredecessor())
2985 // A loop's header is defined to be a block that dominates the loop.
2986 // If the loop has a preheader, it must be a block that has exactly
2987 // one successor that can reach BB. This is slightly more strict
2988 // than necessary, but works if critical edges are split.
2989 if (Loop *L = LI.getLoopFor(BB))
2990 return L->getLoopPreheader();
2995 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
2996 /// a conditional between LHS and RHS.
2997 bool ScalarEvolutionsImpl::isLoopGuardedByCond(const Loop *L,
2998 ICmpInst::Predicate Pred,
2999 SCEV *LHS, SCEV *RHS) {
3000 BasicBlock *Preheader = L->getLoopPreheader();
3001 BasicBlock *PreheaderDest = L->getHeader();
3003 // Starting at the preheader, climb up the predecessor chain, as long as
3004 // there are predecessors that can be found that have unique successors
3005 // leading to the original header.
3007 PreheaderDest = Preheader,
3008 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
3010 BranchInst *LoopEntryPredicate =
3011 dyn_cast<BranchInst>(Preheader->getTerminator());
3012 if (!LoopEntryPredicate ||
3013 LoopEntryPredicate->isUnconditional())
3016 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3019 // Now that we found a conditional branch that dominates the loop, check to
3020 // see if it is the comparison we are looking for.
3021 Value *PreCondLHS = ICI->getOperand(0);
3022 Value *PreCondRHS = ICI->getOperand(1);
3023 ICmpInst::Predicate Cond;
3024 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
3025 Cond = ICI->getPredicate();
3027 Cond = ICI->getInversePredicate();
3030 ; // An exact match.
3031 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3032 ; // The actual condition is beyond sufficient.
3034 // Check a few special cases.
3036 case ICmpInst::ICMP_UGT:
3037 if (Pred == ICmpInst::ICMP_ULT) {
3038 std::swap(PreCondLHS, PreCondRHS);
3039 Cond = ICmpInst::ICMP_ULT;
3043 case ICmpInst::ICMP_SGT:
3044 if (Pred == ICmpInst::ICMP_SLT) {
3045 std::swap(PreCondLHS, PreCondRHS);
3046 Cond = ICmpInst::ICMP_SLT;
3050 case ICmpInst::ICMP_NE:
3051 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3052 // so check for this case by checking if the NE is comparing against
3053 // a minimum or maximum constant.
3054 if (!ICmpInst::isTrueWhenEqual(Pred))
3055 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3056 const APInt &A = CI->getValue();
3058 case ICmpInst::ICMP_SLT:
3059 if (A.isMaxSignedValue()) break;
3061 case ICmpInst::ICMP_SGT:
3062 if (A.isMinSignedValue()) break;
3064 case ICmpInst::ICMP_ULT:
3065 if (A.isMaxValue()) break;
3067 case ICmpInst::ICMP_UGT:
3068 if (A.isMinValue()) break;
3073 Cond = ICmpInst::ICMP_NE;
3074 // NE is symmetric but the original comparison may not be. Swap
3075 // the operands if necessary so that they match below.
3076 if (isa<SCEVConstant>(LHS))
3077 std::swap(PreCondLHS, PreCondRHS);
3082 // We weren't able to reconcile the condition.
3086 if (!PreCondLHS->getType()->isInteger()) continue;
3088 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3089 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3090 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3091 (LHS == SE.getNotSCEV(PreCondRHSSCEV) &&
3092 RHS == SE.getNotSCEV(PreCondLHSSCEV)))
3099 /// HowManyLessThans - Return the number of times a backedge containing the
3100 /// specified less-than comparison will execute. If not computable, return
3102 SCEVHandle ScalarEvolutionsImpl::
3103 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
3104 // Only handle: "ADDREC < LoopInvariant".
3105 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3107 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3108 if (!AddRec || AddRec->getLoop() != L)
3109 return UnknownValue;
3111 if (AddRec->isAffine()) {
3112 // FORNOW: We only support unit strides.
3113 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
3114 if (AddRec->getOperand(1) != One)
3115 return UnknownValue;
3117 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
3118 // m. So, we count the number of iterations in which {n,+,1} < m is true.
3119 // Note that we cannot simply return max(m-n,0) because it's not safe to
3120 // treat m-n as signed nor unsigned due to overflow possibility.
3122 // First, we get the value of the LHS in the first iteration: n
3123 SCEVHandle Start = AddRec->getOperand(0);
3125 if (isLoopGuardedByCond(L,
3126 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3127 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) {
3128 // Since we know that the condition is true in order to enter the loop,
3129 // we know that it will run exactly m-n times.
3130 return SE.getMinusSCEV(RHS, Start);
3132 // Then, we get the value of the LHS in the first iteration in which the
3133 // above condition doesn't hold. This equals to max(m,n).
3134 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
3135 : SE.getUMaxExpr(RHS, Start);
3137 // Finally, we subtract these two values to get the number of times the
3138 // backedge is executed: max(m,n)-n.
3139 return SE.getMinusSCEV(End, Start);
3143 return UnknownValue;
3146 /// getNumIterationsInRange - Return the number of iterations of this loop that
3147 /// produce values in the specified constant range. Another way of looking at
3148 /// this is that it returns the first iteration number where the value is not in
3149 /// the condition, thus computing the exit count. If the iteration count can't
3150 /// be computed, an instance of SCEVCouldNotCompute is returned.
3151 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3152 ScalarEvolution &SE) const {
3153 if (Range.isFullSet()) // Infinite loop.
3154 return SE.getCouldNotCompute();
3156 // If the start is a non-zero constant, shift the range to simplify things.
3157 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3158 if (!SC->getValue()->isZero()) {
3159 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3160 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3161 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3162 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
3163 return ShiftedAddRec->getNumIterationsInRange(
3164 Range.subtract(SC->getValue()->getValue()), SE);
3165 // This is strange and shouldn't happen.
3166 return SE.getCouldNotCompute();
3169 // The only time we can solve this is when we have all constant indices.
3170 // Otherwise, we cannot determine the overflow conditions.
3171 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3172 if (!isa<SCEVConstant>(getOperand(i)))
3173 return SE.getCouldNotCompute();
3176 // Okay at this point we know that all elements of the chrec are constants and
3177 // that the start element is zero.
3179 // First check to see if the range contains zero. If not, the first
3181 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3182 if (!Range.contains(APInt(BitWidth, 0)))
3183 return SE.getConstant(ConstantInt::get(getType(),0));
3186 // If this is an affine expression then we have this situation:
3187 // Solve {0,+,A} in Range === Ax in Range
3189 // We know that zero is in the range. If A is positive then we know that
3190 // the upper value of the range must be the first possible exit value.
3191 // If A is negative then the lower of the range is the last possible loop
3192 // value. Also note that we already checked for a full range.
3193 APInt One(BitWidth,1);
3194 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3195 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3197 // The exit value should be (End+A)/A.
3198 APInt ExitVal = (End + A).udiv(A);
3199 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3201 // Evaluate at the exit value. If we really did fall out of the valid
3202 // range, then we computed our trip count, otherwise wrap around or other
3203 // things must have happened.
3204 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3205 if (Range.contains(Val->getValue()))
3206 return SE.getCouldNotCompute(); // Something strange happened
3208 // Ensure that the previous value is in the range. This is a sanity check.
3209 assert(Range.contains(
3210 EvaluateConstantChrecAtConstant(this,
3211 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3212 "Linear scev computation is off in a bad way!");
3213 return SE.getConstant(ExitValue);
3214 } else if (isQuadratic()) {
3215 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3216 // quadratic equation to solve it. To do this, we must frame our problem in
3217 // terms of figuring out when zero is crossed, instead of when
3218 // Range.getUpper() is crossed.
3219 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3220 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3221 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3223 // Next, solve the constructed addrec
3224 std::pair<SCEVHandle,SCEVHandle> Roots =
3225 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3226 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3227 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3229 // Pick the smallest positive root value.
3230 if (ConstantInt *CB =
3231 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3232 R1->getValue(), R2->getValue()))) {
3233 if (CB->getZExtValue() == false)
3234 std::swap(R1, R2); // R1 is the minimum root now.
3236 // Make sure the root is not off by one. The returned iteration should
3237 // not be in the range, but the previous one should be. When solving
3238 // for "X*X < 5", for example, we should not return a root of 2.
3239 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3242 if (Range.contains(R1Val->getValue())) {
3243 // The next iteration must be out of the range...
3244 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3246 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3247 if (!Range.contains(R1Val->getValue()))
3248 return SE.getConstant(NextVal);
3249 return SE.getCouldNotCompute(); // Something strange happened
3252 // If R1 was not in the range, then it is a good return value. Make
3253 // sure that R1-1 WAS in the range though, just in case.
3254 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3255 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3256 if (Range.contains(R1Val->getValue()))
3258 return SE.getCouldNotCompute(); // Something strange happened
3263 return SE.getCouldNotCompute();
3268 //===----------------------------------------------------------------------===//
3269 // ScalarEvolution Class Implementation
3270 //===----------------------------------------------------------------------===//
3272 bool ScalarEvolution::runOnFunction(Function &F) {
3273 Impl = new ScalarEvolutionsImpl(*this, F,
3274 getAnalysis<LoopInfo>(),
3275 getAnalysisIfAvailable<TargetData>());
3279 void ScalarEvolution::releaseMemory() {
3280 delete (ScalarEvolutionsImpl*)Impl;
3284 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3285 AU.setPreservesAll();
3286 AU.addRequiredTransitive<LoopInfo>();
3289 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
3290 return ((ScalarEvolutionsImpl*)Impl)->isSCEVable(Ty);
3293 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
3294 return ((ScalarEvolutionsImpl*)Impl)->getTypeSizeInBits(Ty);
3297 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
3298 return ((ScalarEvolutionsImpl*)Impl)->getEffectiveSCEVType(Ty);
3301 SCEVHandle ScalarEvolution::getCouldNotCompute() {
3302 return ((ScalarEvolutionsImpl*)Impl)->getCouldNotCompute();
3305 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
3306 return ((ScalarEvolutionsImpl*)Impl)->getIntegerSCEV(Val, Ty);
3309 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
3310 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
3313 /// hasSCEV - Return true if the SCEV for this value has already been
3315 bool ScalarEvolution::hasSCEV(Value *V) const {
3316 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
3320 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
3321 /// the specified value.
3322 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
3323 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
3326 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
3328 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
3329 return ((ScalarEvolutionsImpl*)Impl)->getNegativeSCEV(V);
3332 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
3334 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
3335 return ((ScalarEvolutionsImpl*)Impl)->getNotSCEV(V);
3338 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
3340 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
3341 const SCEVHandle &RHS) {
3342 return ((ScalarEvolutionsImpl*)Impl)->getMinusSCEV(LHS, RHS);
3345 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
3346 /// of the input value to the specified type. If the type must be
3347 /// extended, it is zero extended.
3348 SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
3350 return ((ScalarEvolutionsImpl*)Impl)->getTruncateOrZeroExtend(V, Ty);
3353 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
3354 /// of the input value to the specified type. If the type must be
3355 /// extended, it is sign extended.
3356 SCEVHandle ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
3358 return ((ScalarEvolutionsImpl*)Impl)->getTruncateOrSignExtend(V, Ty);
3362 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3363 ICmpInst::Predicate Pred,
3364 SCEV *LHS, SCEV *RHS) {
3365 return ((ScalarEvolutionsImpl*)Impl)->isLoopGuardedByCond(L, Pred,
3369 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) const {
3370 return ((ScalarEvolutionsImpl*)Impl)->getBackedgeTakenCount(L);
3373 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) const {
3374 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3377 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
3378 return ((ScalarEvolutionsImpl*)Impl)->forgetLoopBackedgeTakenCount(L);
3381 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
3382 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
3385 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
3386 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
3389 static void PrintLoopInfo(raw_ostream &OS, const ScalarEvolution *SE,
3391 // Print all inner loops first
3392 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3393 PrintLoopInfo(OS, SE, *I);
3395 OS << "Loop " << L->getHeader()->getName() << ": ";
3397 SmallVector<BasicBlock*, 8> ExitBlocks;
3398 L->getExitBlocks(ExitBlocks);
3399 if (ExitBlocks.size() != 1)
3400 OS << "<multiple exits> ";
3402 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3403 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3405 OS << "Unpredictable backedge-taken count. ";
3411 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3412 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
3413 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
3415 OS << "Classifying expressions for: " << F.getName() << "\n";
3416 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3417 if (I->getType()->isInteger()) {
3420 SCEVHandle SV = getSCEV(&*I);
3424 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
3426 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
3427 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3428 OS << "<<Unknown>>";
3438 OS << "Determining loop execution counts for: " << F.getName() << "\n";
3439 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
3440 PrintLoopInfo(OS, this, *I);
3443 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3444 raw_os_ostream OS(o);