1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Transforms/Scalar.h"
74 #include "llvm/Support/CFG.h"
75 #include "llvm/Support/CommandLine.h"
76 #include "llvm/Support/Compiler.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/GetElementPtrTypeIterator.h"
79 #include "llvm/Support/InstIterator.h"
80 #include "llvm/Support/ManagedStatic.h"
81 #include "llvm/Support/MathExtras.h"
82 #include "llvm/Support/raw_ostream.h"
83 #include "llvm/ADT/Statistic.h"
84 #include "llvm/ADT/STLExtras.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant derived loop"),
105 static RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
107 char ScalarEvolution::ID = 0;
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
117 void SCEV::dump() const {
122 void SCEV::print(std::ostream &o) const {
123 raw_os_ostream OS(o);
127 bool SCEV::isZero() const {
128 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
129 return SC->getValue()->isZero();
134 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
135 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
137 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
142 const Type *SCEVCouldNotCompute::getType() const {
143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
147 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
148 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
152 SCEVHandle SCEVCouldNotCompute::
153 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
154 const SCEVHandle &Conc,
155 ScalarEvolution &SE) const {
159 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
160 OS << "***COULDNOTCOMPUTE***";
163 bool SCEVCouldNotCompute::classof(const SCEV *S) {
164 return S->getSCEVType() == scCouldNotCompute;
168 // SCEVConstants - Only allow the creation of one SCEVConstant for any
169 // particular value. Don't use a SCEVHandle here, or else the object will
171 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
174 SCEVConstant::~SCEVConstant() {
175 SCEVConstants->erase(V);
178 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
179 SCEVConstant *&R = (*SCEVConstants)[V];
180 if (R == 0) R = new SCEVConstant(V);
184 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
185 return getConstant(ConstantInt::get(Val));
188 const Type *SCEVConstant::getType() const { return V->getType(); }
190 void SCEVConstant::print(raw_ostream &OS) const {
191 WriteAsOperand(OS, V, false);
194 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
195 const SCEVHandle &op, const Type *ty)
196 : SCEV(SCEVTy), Op(op), Ty(ty) {}
198 SCEVCastExpr::~SCEVCastExpr() {}
200 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
201 return Op->dominates(BB, DT);
204 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
205 // particular input. Don't use a SCEVHandle here, or else the object will
207 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
208 SCEVTruncateExpr*> > SCEVTruncates;
210 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
211 : SCEVCastExpr(scTruncate, op, ty) {
212 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
213 (Ty->isInteger() || isa<PointerType>(Ty)) &&
214 "Cannot truncate non-integer value!");
217 SCEVTruncateExpr::~SCEVTruncateExpr() {
218 SCEVTruncates->erase(std::make_pair(Op, Ty));
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
226 // particular input. Don't use a SCEVHandle here, or else the object will never
228 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
229 SCEVZeroExtendExpr*> > SCEVZeroExtends;
231 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
232 : SCEVCastExpr(scZeroExtend, op, ty) {
233 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
234 (Ty->isInteger() || isa<PointerType>(Ty)) &&
235 "Cannot zero extend non-integer value!");
238 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
239 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
242 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
243 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
246 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
247 // particular input. Don't use a SCEVHandle here, or else the object will never
249 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
250 SCEVSignExtendExpr*> > SCEVSignExtends;
252 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
253 : SCEVCastExpr(scSignExtend, op, ty) {
254 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
255 (Ty->isInteger() || isa<PointerType>(Ty)) &&
256 "Cannot sign extend non-integer value!");
259 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
260 SCEVSignExtends->erase(std::make_pair(Op, Ty));
263 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
264 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
267 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
268 // particular input. Don't use a SCEVHandle here, or else the object will never
270 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
271 SCEVCommutativeExpr*> > SCEVCommExprs;
273 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
274 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
275 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
278 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
279 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
280 const char *OpStr = getOperationStr();
281 OS << "(" << *Operands[0];
282 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
283 OS << OpStr << *Operands[i];
287 SCEVHandle SCEVCommutativeExpr::
288 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
289 const SCEVHandle &Conc,
290 ScalarEvolution &SE) const {
291 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
293 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
294 if (H != getOperand(i)) {
295 std::vector<SCEVHandle> NewOps;
296 NewOps.reserve(getNumOperands());
297 for (unsigned j = 0; j != i; ++j)
298 NewOps.push_back(getOperand(j));
300 for (++i; i != e; ++i)
301 NewOps.push_back(getOperand(i)->
302 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
304 if (isa<SCEVAddExpr>(this))
305 return SE.getAddExpr(NewOps);
306 else if (isa<SCEVMulExpr>(this))
307 return SE.getMulExpr(NewOps);
308 else if (isa<SCEVSMaxExpr>(this))
309 return SE.getSMaxExpr(NewOps);
310 else if (isa<SCEVUMaxExpr>(this))
311 return SE.getUMaxExpr(NewOps);
313 assert(0 && "Unknown commutative expr!");
319 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
320 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
321 if (!getOperand(i)->dominates(BB, DT))
328 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
329 // input. Don't use a SCEVHandle here, or else the object will never be
331 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
332 SCEVUDivExpr*> > SCEVUDivs;
334 SCEVUDivExpr::~SCEVUDivExpr() {
335 SCEVUDivs->erase(std::make_pair(LHS, RHS));
338 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
339 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
342 void SCEVUDivExpr::print(raw_ostream &OS) const {
343 OS << "(" << *LHS << " /u " << *RHS << ")";
346 const Type *SCEVUDivExpr::getType() const {
347 return LHS->getType();
350 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
351 // particular input. Don't use a SCEVHandle here, or else the object will never
353 static ManagedStatic<std::map<std::pair<const Loop *,
354 std::vector<const SCEV*> >,
355 SCEVAddRecExpr*> > SCEVAddRecExprs;
357 SCEVAddRecExpr::~SCEVAddRecExpr() {
358 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
359 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
362 SCEVHandle SCEVAddRecExpr::
363 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
364 const SCEVHandle &Conc,
365 ScalarEvolution &SE) const {
366 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
368 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
369 if (H != getOperand(i)) {
370 std::vector<SCEVHandle> NewOps;
371 NewOps.reserve(getNumOperands());
372 for (unsigned j = 0; j != i; ++j)
373 NewOps.push_back(getOperand(j));
375 for (++i; i != e; ++i)
376 NewOps.push_back(getOperand(i)->
377 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
379 return SE.getAddRecExpr(NewOps, L);
386 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
387 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
388 // contain L and if the start is invariant.
389 return !QueryLoop->contains(L->getHeader()) &&
390 getOperand(0)->isLoopInvariant(QueryLoop);
394 void SCEVAddRecExpr::print(raw_ostream &OS) const {
395 OS << "{" << *Operands[0];
396 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
397 OS << ",+," << *Operands[i];
398 OS << "}<" << L->getHeader()->getName() + ">";
401 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
402 // value. Don't use a SCEVHandle here, or else the object will never be
404 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
406 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
408 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
409 // All non-instruction values are loop invariant. All instructions are loop
410 // invariant if they are not contained in the specified loop.
411 if (Instruction *I = dyn_cast<Instruction>(V))
412 return !L->contains(I->getParent());
416 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
417 if (Instruction *I = dyn_cast<Instruction>(getValue()))
418 return DT->dominates(I->getParent(), BB);
422 const Type *SCEVUnknown::getType() const {
426 void SCEVUnknown::print(raw_ostream &OS) const {
427 WriteAsOperand(OS, V, false);
430 //===----------------------------------------------------------------------===//
432 //===----------------------------------------------------------------------===//
435 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
436 /// than the complexity of the RHS. This comparator is used to canonicalize
438 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
439 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
440 return LHS->getSCEVType() < RHS->getSCEVType();
445 /// GroupByComplexity - Given a list of SCEV objects, order them by their
446 /// complexity, and group objects of the same complexity together by value.
447 /// When this routine is finished, we know that any duplicates in the vector are
448 /// consecutive and that complexity is monotonically increasing.
450 /// Note that we go take special precautions to ensure that we get determinstic
451 /// results from this routine. In other words, we don't want the results of
452 /// this to depend on where the addresses of various SCEV objects happened to
455 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
456 if (Ops.size() < 2) return; // Noop
457 if (Ops.size() == 2) {
458 // This is the common case, which also happens to be trivially simple.
460 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
461 std::swap(Ops[0], Ops[1]);
465 // Do the rough sort by complexity.
466 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
468 // Now that we are sorted by complexity, group elements of the same
469 // complexity. Note that this is, at worst, N^2, but the vector is likely to
470 // be extremely short in practice. Note that we take this approach because we
471 // do not want to depend on the addresses of the objects we are grouping.
472 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
473 const SCEV *S = Ops[i];
474 unsigned Complexity = S->getSCEVType();
476 // If there are any objects of the same complexity and same value as this
478 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
479 if (Ops[j] == S) { // Found a duplicate.
480 // Move it to immediately after i'th element.
481 std::swap(Ops[i+1], Ops[j]);
482 ++i; // no need to rescan it.
483 if (i == e-2) return; // Done!
491 //===----------------------------------------------------------------------===//
492 // Simple SCEV method implementations
493 //===----------------------------------------------------------------------===//
495 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
497 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
499 const Type* ResultTy) {
500 // Handle the simplest case efficiently.
502 return SE.getTruncateOrZeroExtend(It, ResultTy);
504 // We are using the following formula for BC(It, K):
506 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
508 // Suppose, W is the bitwidth of the return value. We must be prepared for
509 // overflow. Hence, we must assure that the result of our computation is
510 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
511 // safe in modular arithmetic.
513 // However, this code doesn't use exactly that formula; the formula it uses
514 // is something like the following, where T is the number of factors of 2 in
515 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
518 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
520 // This formula is trivially equivalent to the previous formula. However,
521 // this formula can be implemented much more efficiently. The trick is that
522 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
523 // arithmetic. To do exact division in modular arithmetic, all we have
524 // to do is multiply by the inverse. Therefore, this step can be done at
527 // The next issue is how to safely do the division by 2^T. The way this
528 // is done is by doing the multiplication step at a width of at least W + T
529 // bits. This way, the bottom W+T bits of the product are accurate. Then,
530 // when we perform the division by 2^T (which is equivalent to a right shift
531 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
532 // truncated out after the division by 2^T.
534 // In comparison to just directly using the first formula, this technique
535 // is much more efficient; using the first formula requires W * K bits,
536 // but this formula less than W + K bits. Also, the first formula requires
537 // a division step, whereas this formula only requires multiplies and shifts.
539 // It doesn't matter whether the subtraction step is done in the calculation
540 // width or the input iteration count's width; if the subtraction overflows,
541 // the result must be zero anyway. We prefer here to do it in the width of
542 // the induction variable because it helps a lot for certain cases; CodeGen
543 // isn't smart enough to ignore the overflow, which leads to much less
544 // efficient code if the width of the subtraction is wider than the native
547 // (It's possible to not widen at all by pulling out factors of 2 before
548 // the multiplication; for example, K=2 can be calculated as
549 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
550 // extra arithmetic, so it's not an obvious win, and it gets
551 // much more complicated for K > 3.)
553 // Protection from insane SCEVs; this bound is conservative,
554 // but it probably doesn't matter.
556 return SE.getCouldNotCompute();
558 unsigned W = SE.getTypeSizeInBits(ResultTy);
560 // Calculate K! / 2^T and T; we divide out the factors of two before
561 // multiplying for calculating K! / 2^T to avoid overflow.
562 // Other overflow doesn't matter because we only care about the bottom
563 // W bits of the result.
564 APInt OddFactorial(W, 1);
566 for (unsigned i = 3; i <= K; ++i) {
568 unsigned TwoFactors = Mult.countTrailingZeros();
570 Mult = Mult.lshr(TwoFactors);
571 OddFactorial *= Mult;
574 // We need at least W + T bits for the multiplication step
575 unsigned CalculationBits = W + T;
577 // Calcuate 2^T, at width T+W.
578 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
580 // Calculate the multiplicative inverse of K! / 2^T;
581 // this multiplication factor will perform the exact division by
583 APInt Mod = APInt::getSignedMinValue(W+1);
584 APInt MultiplyFactor = OddFactorial.zext(W+1);
585 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
586 MultiplyFactor = MultiplyFactor.trunc(W);
588 // Calculate the product, at width T+W
589 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
590 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
591 for (unsigned i = 1; i != K; ++i) {
592 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
593 Dividend = SE.getMulExpr(Dividend,
594 SE.getTruncateOrZeroExtend(S, CalculationTy));
598 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
600 // Truncate the result, and divide by K! / 2^T.
602 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
603 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
606 /// evaluateAtIteration - Return the value of this chain of recurrences at
607 /// the specified iteration number. We can evaluate this recurrence by
608 /// multiplying each element in the chain by the binomial coefficient
609 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
611 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
613 /// where BC(It, k) stands for binomial coefficient.
615 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
616 ScalarEvolution &SE) const {
617 SCEVHandle Result = getStart();
618 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
619 // The computation is correct in the face of overflow provided that the
620 // multiplication is performed _after_ the evaluation of the binomial
622 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
623 if (isa<SCEVCouldNotCompute>(Coeff))
626 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
631 //===----------------------------------------------------------------------===//
632 // SCEV Expression folder implementations
633 //===----------------------------------------------------------------------===//
635 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
637 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
638 "This is not a truncating conversion!");
639 assert(isSCEVable(Ty) &&
640 "This is not a conversion to a SCEVable type!");
641 Ty = getEffectiveSCEVType(Ty);
643 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
645 ConstantExpr::getTrunc(SC->getValue(), Ty));
647 // trunc(trunc(x)) --> trunc(x)
648 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
649 return getTruncateExpr(ST->getOperand(), Ty);
651 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
652 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
653 return getTruncateOrSignExtend(SS->getOperand(), Ty);
655 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
656 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
657 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
659 // If the input value is a chrec scev made out of constants, truncate
660 // all of the constants.
661 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
662 std::vector<SCEVHandle> Operands;
663 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
664 // FIXME: This should allow truncation of other expression types!
665 if (isa<SCEVConstant>(AddRec->getOperand(i)))
666 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
669 if (Operands.size() == AddRec->getNumOperands())
670 return getAddRecExpr(Operands, AddRec->getLoop());
673 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
674 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
678 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
680 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
681 "This is not an extending conversion!");
682 assert(isSCEVable(Ty) &&
683 "This is not a conversion to a SCEVable type!");
684 Ty = getEffectiveSCEVType(Ty);
686 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
687 const Type *IntTy = getEffectiveSCEVType(Ty);
688 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
689 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
690 return getUnknown(C);
693 // zext(zext(x)) --> zext(x)
694 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
695 return getZeroExtendExpr(SZ->getOperand(), Ty);
697 // If the input value is a chrec scev, and we can prove that the value
698 // did not overflow the old, smaller, value, we can zero extend all of the
699 // operands (often constants). This allows analysis of something like
700 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
701 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
702 if (AR->isAffine()) {
703 // Check whether the backedge-taken count is SCEVCouldNotCompute.
704 // Note that this serves two purposes: It filters out loops that are
705 // simply not analyzable, and it covers the case where this code is
706 // being called from within backedge-taken count analysis, such that
707 // attempting to ask for the backedge-taken count would likely result
708 // in infinite recursion. In the later case, the analysis code will
709 // cope with a conservative value, and it will take care to purge
710 // that value once it has finished.
711 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
712 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
713 // Manually compute the final value for AR, checking for
715 SCEVHandle Start = AR->getStart();
716 SCEVHandle Step = AR->getStepRecurrence(*this);
718 // Check whether the backedge-taken count can be losslessly casted to
719 // the addrec's type. The count is always unsigned.
720 SCEVHandle CastedMaxBECount =
721 getTruncateOrZeroExtend(MaxBECount, Start->getType());
723 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
725 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
726 // Check whether Start+Step*MaxBECount has no unsigned overflow.
728 getMulExpr(CastedMaxBECount,
729 getTruncateOrZeroExtend(Step, Start->getType()));
730 SCEVHandle Add = getAddExpr(Start, ZMul);
731 if (getZeroExtendExpr(Add, WideTy) ==
732 getAddExpr(getZeroExtendExpr(Start, WideTy),
733 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
734 getZeroExtendExpr(Step, WideTy))))
735 // Return the expression with the addrec on the outside.
736 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
737 getZeroExtendExpr(Step, Ty),
740 // Similar to above, only this time treat the step value as signed.
741 // This covers loops that count down.
743 getMulExpr(CastedMaxBECount,
744 getTruncateOrSignExtend(Step, Start->getType()));
745 Add = getAddExpr(Start, SMul);
746 if (getZeroExtendExpr(Add, WideTy) ==
747 getAddExpr(getZeroExtendExpr(Start, WideTy),
748 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
749 getSignExtendExpr(Step, WideTy))))
750 // Return the expression with the addrec on the outside.
751 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
752 getSignExtendExpr(Step, Ty),
758 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
759 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
763 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
765 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
766 "This is not an extending conversion!");
767 assert(isSCEVable(Ty) &&
768 "This is not a conversion to a SCEVable type!");
769 Ty = getEffectiveSCEVType(Ty);
771 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
772 const Type *IntTy = getEffectiveSCEVType(Ty);
773 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
774 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
775 return getUnknown(C);
778 // sext(sext(x)) --> sext(x)
779 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
780 return getSignExtendExpr(SS->getOperand(), Ty);
782 // If the input value is a chrec scev, and we can prove that the value
783 // did not overflow the old, smaller, value, we can sign extend all of the
784 // operands (often constants). This allows analysis of something like
785 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
786 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
787 if (AR->isAffine()) {
788 // Check whether the backedge-taken count is SCEVCouldNotCompute.
789 // Note that this serves two purposes: It filters out loops that are
790 // simply not analyzable, and it covers the case where this code is
791 // being called from within backedge-taken count analysis, such that
792 // attempting to ask for the backedge-taken count would likely result
793 // in infinite recursion. In the later case, the analysis code will
794 // cope with a conservative value, and it will take care to purge
795 // that value once it has finished.
796 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
797 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
798 // Manually compute the final value for AR, checking for
800 SCEVHandle Start = AR->getStart();
801 SCEVHandle Step = AR->getStepRecurrence(*this);
803 // Check whether the backedge-taken count can be losslessly casted to
804 // the addrec's type. The count is always unsigned.
805 SCEVHandle CastedMaxBECount =
806 getTruncateOrZeroExtend(MaxBECount, Start->getType());
808 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
810 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
811 // Check whether Start+Step*MaxBECount has no signed overflow.
813 getMulExpr(CastedMaxBECount,
814 getTruncateOrSignExtend(Step, Start->getType()));
815 SCEVHandle Add = getAddExpr(Start, SMul);
816 if (getSignExtendExpr(Add, WideTy) ==
817 getAddExpr(getSignExtendExpr(Start, WideTy),
818 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
819 getSignExtendExpr(Step, WideTy))))
820 // Return the expression with the addrec on the outside.
821 return getAddRecExpr(getSignExtendExpr(Start, Ty),
822 getSignExtendExpr(Step, Ty),
828 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
829 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
833 // get - Get a canonical add expression, or something simpler if possible.
834 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
835 assert(!Ops.empty() && "Cannot get empty add!");
836 if (Ops.size() == 1) return Ops[0];
838 // Sort by complexity, this groups all similar expression types together.
839 GroupByComplexity(Ops);
841 // If there are any constants, fold them together.
843 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
845 assert(Idx < Ops.size());
846 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
847 // We found two constants, fold them together!
848 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
849 RHSC->getValue()->getValue());
850 Ops[0] = getConstant(Fold);
851 Ops.erase(Ops.begin()+1); // Erase the folded element
852 if (Ops.size() == 1) return Ops[0];
853 LHSC = cast<SCEVConstant>(Ops[0]);
856 // If we are left with a constant zero being added, strip it off.
857 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
858 Ops.erase(Ops.begin());
863 if (Ops.size() == 1) return Ops[0];
865 // Okay, check to see if the same value occurs in the operand list twice. If
866 // so, merge them together into an multiply expression. Since we sorted the
867 // list, these values are required to be adjacent.
868 const Type *Ty = Ops[0]->getType();
869 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
870 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
871 // Found a match, merge the two values into a multiply, and add any
872 // remaining values to the result.
873 SCEVHandle Two = getIntegerSCEV(2, Ty);
874 SCEVHandle Mul = getMulExpr(Ops[i], Two);
877 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
879 return getAddExpr(Ops);
882 // Now we know the first non-constant operand. Skip past any cast SCEVs.
883 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
886 // If there are add operands they would be next.
887 if (Idx < Ops.size()) {
888 bool DeletedAdd = false;
889 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
890 // If we have an add, expand the add operands onto the end of the operands
892 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
893 Ops.erase(Ops.begin()+Idx);
897 // If we deleted at least one add, we added operands to the end of the list,
898 // and they are not necessarily sorted. Recurse to resort and resimplify
899 // any operands we just aquired.
901 return getAddExpr(Ops);
904 // Skip over the add expression until we get to a multiply.
905 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
908 // If we are adding something to a multiply expression, make sure the
909 // something is not already an operand of the multiply. If so, merge it into
911 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
912 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
913 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
914 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
915 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
916 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
917 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
918 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
919 if (Mul->getNumOperands() != 2) {
920 // If the multiply has more than two operands, we must get the
922 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
923 MulOps.erase(MulOps.begin()+MulOp);
924 InnerMul = getMulExpr(MulOps);
926 SCEVHandle One = getIntegerSCEV(1, Ty);
927 SCEVHandle AddOne = getAddExpr(InnerMul, One);
928 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
929 if (Ops.size() == 2) return OuterMul;
931 Ops.erase(Ops.begin()+AddOp);
932 Ops.erase(Ops.begin()+Idx-1);
934 Ops.erase(Ops.begin()+Idx);
935 Ops.erase(Ops.begin()+AddOp-1);
937 Ops.push_back(OuterMul);
938 return getAddExpr(Ops);
941 // Check this multiply against other multiplies being added together.
942 for (unsigned OtherMulIdx = Idx+1;
943 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
945 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
946 // If MulOp occurs in OtherMul, we can fold the two multiplies
948 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
949 OMulOp != e; ++OMulOp)
950 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
951 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
952 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
953 if (Mul->getNumOperands() != 2) {
954 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
955 MulOps.erase(MulOps.begin()+MulOp);
956 InnerMul1 = getMulExpr(MulOps);
958 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
959 if (OtherMul->getNumOperands() != 2) {
960 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
962 MulOps.erase(MulOps.begin()+OMulOp);
963 InnerMul2 = getMulExpr(MulOps);
965 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
966 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
967 if (Ops.size() == 2) return OuterMul;
968 Ops.erase(Ops.begin()+Idx);
969 Ops.erase(Ops.begin()+OtherMulIdx-1);
970 Ops.push_back(OuterMul);
971 return getAddExpr(Ops);
977 // If there are any add recurrences in the operands list, see if any other
978 // added values are loop invariant. If so, we can fold them into the
980 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
983 // Scan over all recurrences, trying to fold loop invariants into them.
984 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
985 // Scan all of the other operands to this add and add them to the vector if
986 // they are loop invariant w.r.t. the recurrence.
987 std::vector<SCEVHandle> LIOps;
988 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
989 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
990 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
991 LIOps.push_back(Ops[i]);
992 Ops.erase(Ops.begin()+i);
996 // If we found some loop invariants, fold them into the recurrence.
997 if (!LIOps.empty()) {
998 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
999 LIOps.push_back(AddRec->getStart());
1001 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1002 AddRecOps[0] = getAddExpr(LIOps);
1004 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1005 // If all of the other operands were loop invariant, we are done.
1006 if (Ops.size() == 1) return NewRec;
1008 // Otherwise, add the folded AddRec by the non-liv parts.
1009 for (unsigned i = 0;; ++i)
1010 if (Ops[i] == AddRec) {
1014 return getAddExpr(Ops);
1017 // Okay, if there weren't any loop invariants to be folded, check to see if
1018 // there are multiple AddRec's with the same loop induction variable being
1019 // added together. If so, we can fold them.
1020 for (unsigned OtherIdx = Idx+1;
1021 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1022 if (OtherIdx != Idx) {
1023 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1024 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1025 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1026 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1027 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1028 if (i >= NewOps.size()) {
1029 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1030 OtherAddRec->op_end());
1033 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1035 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1037 if (Ops.size() == 2) return NewAddRec;
1039 Ops.erase(Ops.begin()+Idx);
1040 Ops.erase(Ops.begin()+OtherIdx-1);
1041 Ops.push_back(NewAddRec);
1042 return getAddExpr(Ops);
1046 // Otherwise couldn't fold anything into this recurrence. Move onto the
1050 // Okay, it looks like we really DO need an add expr. Check to see if we
1051 // already have one, otherwise create a new one.
1052 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1053 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1055 if (Result == 0) Result = new SCEVAddExpr(Ops);
1060 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1061 assert(!Ops.empty() && "Cannot get empty mul!");
1063 // Sort by complexity, this groups all similar expression types together.
1064 GroupByComplexity(Ops);
1066 // If there are any constants, fold them together.
1068 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1070 // C1*(C2+V) -> C1*C2 + C1*V
1071 if (Ops.size() == 2)
1072 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1073 if (Add->getNumOperands() == 2 &&
1074 isa<SCEVConstant>(Add->getOperand(0)))
1075 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1076 getMulExpr(LHSC, Add->getOperand(1)));
1080 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1081 // We found two constants, fold them together!
1082 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1083 RHSC->getValue()->getValue());
1084 Ops[0] = getConstant(Fold);
1085 Ops.erase(Ops.begin()+1); // Erase the folded element
1086 if (Ops.size() == 1) return Ops[0];
1087 LHSC = cast<SCEVConstant>(Ops[0]);
1090 // If we are left with a constant one being multiplied, strip it off.
1091 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1092 Ops.erase(Ops.begin());
1094 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1095 // If we have a multiply of zero, it will always be zero.
1100 // Skip over the add expression until we get to a multiply.
1101 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1104 if (Ops.size() == 1)
1107 // If there are mul operands inline them all into this expression.
1108 if (Idx < Ops.size()) {
1109 bool DeletedMul = false;
1110 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1111 // If we have an mul, expand the mul operands onto the end of the operands
1113 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1114 Ops.erase(Ops.begin()+Idx);
1118 // If we deleted at least one mul, we added operands to the end of the list,
1119 // and they are not necessarily sorted. Recurse to resort and resimplify
1120 // any operands we just aquired.
1122 return getMulExpr(Ops);
1125 // If there are any add recurrences in the operands list, see if any other
1126 // added values are loop invariant. If so, we can fold them into the
1128 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1131 // Scan over all recurrences, trying to fold loop invariants into them.
1132 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1133 // Scan all of the other operands to this mul and add them to the vector if
1134 // they are loop invariant w.r.t. the recurrence.
1135 std::vector<SCEVHandle> LIOps;
1136 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1137 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1138 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1139 LIOps.push_back(Ops[i]);
1140 Ops.erase(Ops.begin()+i);
1144 // If we found some loop invariants, fold them into the recurrence.
1145 if (!LIOps.empty()) {
1146 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1147 std::vector<SCEVHandle> NewOps;
1148 NewOps.reserve(AddRec->getNumOperands());
1149 if (LIOps.size() == 1) {
1150 const SCEV *Scale = LIOps[0];
1151 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1152 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1154 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1155 std::vector<SCEVHandle> MulOps(LIOps);
1156 MulOps.push_back(AddRec->getOperand(i));
1157 NewOps.push_back(getMulExpr(MulOps));
1161 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1163 // If all of the other operands were loop invariant, we are done.
1164 if (Ops.size() == 1) return NewRec;
1166 // Otherwise, multiply the folded AddRec by the non-liv parts.
1167 for (unsigned i = 0;; ++i)
1168 if (Ops[i] == AddRec) {
1172 return getMulExpr(Ops);
1175 // Okay, if there weren't any loop invariants to be folded, check to see if
1176 // there are multiple AddRec's with the same loop induction variable being
1177 // multiplied together. If so, we can fold them.
1178 for (unsigned OtherIdx = Idx+1;
1179 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1180 if (OtherIdx != Idx) {
1181 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1182 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1183 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1184 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1185 SCEVHandle NewStart = getMulExpr(F->getStart(),
1187 SCEVHandle B = F->getStepRecurrence(*this);
1188 SCEVHandle D = G->getStepRecurrence(*this);
1189 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1192 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1194 if (Ops.size() == 2) return NewAddRec;
1196 Ops.erase(Ops.begin()+Idx);
1197 Ops.erase(Ops.begin()+OtherIdx-1);
1198 Ops.push_back(NewAddRec);
1199 return getMulExpr(Ops);
1203 // Otherwise couldn't fold anything into this recurrence. Move onto the
1207 // Okay, it looks like we really DO need an mul expr. Check to see if we
1208 // already have one, otherwise create a new one.
1209 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1210 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1213 Result = new SCEVMulExpr(Ops);
1217 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1218 const SCEVHandle &RHS) {
1219 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1220 if (RHSC->getValue()->equalsInt(1))
1221 return LHS; // X udiv 1 --> x
1223 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1224 Constant *LHSCV = LHSC->getValue();
1225 Constant *RHSCV = RHSC->getValue();
1226 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1230 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1232 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1233 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1238 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1239 /// specified loop. Simplify the expression as much as possible.
1240 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1241 const SCEVHandle &Step, const Loop *L) {
1242 std::vector<SCEVHandle> Operands;
1243 Operands.push_back(Start);
1244 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1245 if (StepChrec->getLoop() == L) {
1246 Operands.insert(Operands.end(), StepChrec->op_begin(),
1247 StepChrec->op_end());
1248 return getAddRecExpr(Operands, L);
1251 Operands.push_back(Step);
1252 return getAddRecExpr(Operands, L);
1255 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1256 /// specified loop. Simplify the expression as much as possible.
1257 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1259 if (Operands.size() == 1) return Operands[0];
1261 if (Operands.back()->isZero()) {
1262 Operands.pop_back();
1263 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1266 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1267 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1268 const Loop* NestedLoop = NestedAR->getLoop();
1269 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1270 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1271 NestedAR->op_end());
1272 SCEVHandle NestedARHandle(NestedAR);
1273 Operands[0] = NestedAR->getStart();
1274 NestedOperands[0] = getAddRecExpr(Operands, L);
1275 return getAddRecExpr(NestedOperands, NestedLoop);
1279 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1280 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1281 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1285 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1286 const SCEVHandle &RHS) {
1287 std::vector<SCEVHandle> Ops;
1290 return getSMaxExpr(Ops);
1293 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1294 assert(!Ops.empty() && "Cannot get empty smax!");
1295 if (Ops.size() == 1) return Ops[0];
1297 // Sort by complexity, this groups all similar expression types together.
1298 GroupByComplexity(Ops);
1300 // If there are any constants, fold them together.
1302 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1304 assert(Idx < Ops.size());
1305 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1306 // We found two constants, fold them together!
1307 ConstantInt *Fold = ConstantInt::get(
1308 APIntOps::smax(LHSC->getValue()->getValue(),
1309 RHSC->getValue()->getValue()));
1310 Ops[0] = getConstant(Fold);
1311 Ops.erase(Ops.begin()+1); // Erase the folded element
1312 if (Ops.size() == 1) return Ops[0];
1313 LHSC = cast<SCEVConstant>(Ops[0]);
1316 // If we are left with a constant -inf, strip it off.
1317 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1318 Ops.erase(Ops.begin());
1323 if (Ops.size() == 1) return Ops[0];
1325 // Find the first SMax
1326 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1329 // Check to see if one of the operands is an SMax. If so, expand its operands
1330 // onto our operand list, and recurse to simplify.
1331 if (Idx < Ops.size()) {
1332 bool DeletedSMax = false;
1333 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1334 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1335 Ops.erase(Ops.begin()+Idx);
1340 return getSMaxExpr(Ops);
1343 // Okay, check to see if the same value occurs in the operand list twice. If
1344 // so, delete one. Since we sorted the list, these values are required to
1346 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1347 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1348 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1352 if (Ops.size() == 1) return Ops[0];
1354 assert(!Ops.empty() && "Reduced smax down to nothing!");
1356 // Okay, it looks like we really DO need an smax expr. Check to see if we
1357 // already have one, otherwise create a new one.
1358 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1359 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1361 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1365 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1366 const SCEVHandle &RHS) {
1367 std::vector<SCEVHandle> Ops;
1370 return getUMaxExpr(Ops);
1373 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1374 assert(!Ops.empty() && "Cannot get empty umax!");
1375 if (Ops.size() == 1) return Ops[0];
1377 // Sort by complexity, this groups all similar expression types together.
1378 GroupByComplexity(Ops);
1380 // If there are any constants, fold them together.
1382 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1384 assert(Idx < Ops.size());
1385 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1386 // We found two constants, fold them together!
1387 ConstantInt *Fold = ConstantInt::get(
1388 APIntOps::umax(LHSC->getValue()->getValue(),
1389 RHSC->getValue()->getValue()));
1390 Ops[0] = getConstant(Fold);
1391 Ops.erase(Ops.begin()+1); // Erase the folded element
1392 if (Ops.size() == 1) return Ops[0];
1393 LHSC = cast<SCEVConstant>(Ops[0]);
1396 // If we are left with a constant zero, strip it off.
1397 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1398 Ops.erase(Ops.begin());
1403 if (Ops.size() == 1) return Ops[0];
1405 // Find the first UMax
1406 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1409 // Check to see if one of the operands is a UMax. If so, expand its operands
1410 // onto our operand list, and recurse to simplify.
1411 if (Idx < Ops.size()) {
1412 bool DeletedUMax = false;
1413 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1414 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1415 Ops.erase(Ops.begin()+Idx);
1420 return getUMaxExpr(Ops);
1423 // Okay, check to see if the same value occurs in the operand list twice. If
1424 // so, delete one. Since we sorted the list, these values are required to
1426 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1427 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1428 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1432 if (Ops.size() == 1) return Ops[0];
1434 assert(!Ops.empty() && "Reduced umax down to nothing!");
1436 // Okay, it looks like we really DO need a umax expr. Check to see if we
1437 // already have one, otherwise create a new one.
1438 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1439 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1441 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1445 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1446 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1447 return getConstant(CI);
1448 if (isa<ConstantPointerNull>(V))
1449 return getIntegerSCEV(0, V->getType());
1450 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1451 if (Result == 0) Result = new SCEVUnknown(V);
1455 //===----------------------------------------------------------------------===//
1456 // Basic SCEV Analysis and PHI Idiom Recognition Code
1459 /// isSCEVable - Test if values of the given type are analyzable within
1460 /// the SCEV framework. This primarily includes integer types, and it
1461 /// can optionally include pointer types if the ScalarEvolution class
1462 /// has access to target-specific information.
1463 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1464 // Integers are always SCEVable.
1465 if (Ty->isInteger())
1468 // Pointers are SCEVable if TargetData information is available
1469 // to provide pointer size information.
1470 if (isa<PointerType>(Ty))
1473 // Otherwise it's not SCEVable.
1477 /// getTypeSizeInBits - Return the size in bits of the specified type,
1478 /// for which isSCEVable must return true.
1479 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1480 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1482 // If we have a TargetData, use it!
1484 return TD->getTypeSizeInBits(Ty);
1486 // Otherwise, we support only integer types.
1487 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1488 return Ty->getPrimitiveSizeInBits();
1491 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1492 /// the given type and which represents how SCEV will treat the given
1493 /// type, for which isSCEVable must return true. For pointer types,
1494 /// this is the pointer-sized integer type.
1495 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1496 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1498 if (Ty->isInteger())
1501 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1502 return TD->getIntPtrType();
1505 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1506 return UnknownValue;
1509 /// hasSCEV - Return true if the SCEV for this value has already been
1511 bool ScalarEvolution::hasSCEV(Value *V) const {
1512 return Scalars.count(V);
1515 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1516 /// expression and create a new one.
1517 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1518 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1520 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1521 if (I != Scalars.end()) return I->second;
1522 SCEVHandle S = createSCEV(V);
1523 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1527 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1528 /// specified signed integer value and return a SCEV for the constant.
1529 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1530 Ty = getEffectiveSCEVType(Ty);
1533 C = Constant::getNullValue(Ty);
1534 else if (Ty->isFloatingPoint())
1535 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1536 APFloat::IEEEdouble, Val));
1538 C = ConstantInt::get(Ty, Val);
1539 return getUnknown(C);
1542 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1544 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1545 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1546 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1548 const Type *Ty = V->getType();
1549 Ty = getEffectiveSCEVType(Ty);
1550 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1553 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1554 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1555 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1556 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1558 const Type *Ty = V->getType();
1559 Ty = getEffectiveSCEVType(Ty);
1560 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1561 return getMinusSCEV(AllOnes, V);
1564 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1566 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1567 const SCEVHandle &RHS) {
1569 return getAddExpr(LHS, getNegativeSCEV(RHS));
1572 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1573 /// input value to the specified type. If the type must be extended, it is zero
1576 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1578 const Type *SrcTy = V->getType();
1579 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1580 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1581 "Cannot truncate or zero extend with non-integer arguments!");
1582 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1583 return V; // No conversion
1584 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1585 return getTruncateExpr(V, Ty);
1586 return getZeroExtendExpr(V, Ty);
1589 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1590 /// input value to the specified type. If the type must be extended, it is sign
1593 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1595 const Type *SrcTy = V->getType();
1596 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1597 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1598 "Cannot truncate or zero extend with non-integer arguments!");
1599 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1600 return V; // No conversion
1601 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1602 return getTruncateExpr(V, Ty);
1603 return getSignExtendExpr(V, Ty);
1606 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1607 /// the specified instruction and replaces any references to the symbolic value
1608 /// SymName with the specified value. This is used during PHI resolution.
1609 void ScalarEvolution::
1610 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1611 const SCEVHandle &NewVal) {
1612 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1613 Scalars.find(SCEVCallbackVH(I, this));
1614 if (SI == Scalars.end()) return;
1617 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1618 if (NV == SI->second) return; // No change.
1620 SI->second = NV; // Update the scalars map!
1622 // Any instruction values that use this instruction might also need to be
1624 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1626 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1629 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1630 /// a loop header, making it a potential recurrence, or it doesn't.
1632 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1633 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1634 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1635 if (L->getHeader() == PN->getParent()) {
1636 // If it lives in the loop header, it has two incoming values, one
1637 // from outside the loop, and one from inside.
1638 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1639 unsigned BackEdge = IncomingEdge^1;
1641 // While we are analyzing this PHI node, handle its value symbolically.
1642 SCEVHandle SymbolicName = getUnknown(PN);
1643 assert(Scalars.find(PN) == Scalars.end() &&
1644 "PHI node already processed?");
1645 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1647 // Using this symbolic name for the PHI, analyze the value coming around
1649 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1651 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1652 // has a special value for the first iteration of the loop.
1654 // If the value coming around the backedge is an add with the symbolic
1655 // value we just inserted, then we found a simple induction variable!
1656 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1657 // If there is a single occurrence of the symbolic value, replace it
1658 // with a recurrence.
1659 unsigned FoundIndex = Add->getNumOperands();
1660 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1661 if (Add->getOperand(i) == SymbolicName)
1662 if (FoundIndex == e) {
1667 if (FoundIndex != Add->getNumOperands()) {
1668 // Create an add with everything but the specified operand.
1669 std::vector<SCEVHandle> Ops;
1670 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1671 if (i != FoundIndex)
1672 Ops.push_back(Add->getOperand(i));
1673 SCEVHandle Accum = getAddExpr(Ops);
1675 // This is not a valid addrec if the step amount is varying each
1676 // loop iteration, but is not itself an addrec in this loop.
1677 if (Accum->isLoopInvariant(L) ||
1678 (isa<SCEVAddRecExpr>(Accum) &&
1679 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1680 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1681 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1683 // Okay, for the entire analysis of this edge we assumed the PHI
1684 // to be symbolic. We now need to go back and update all of the
1685 // entries for the scalars that use the PHI (except for the PHI
1686 // itself) to use the new analyzed value instead of the "symbolic"
1688 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1692 } else if (const SCEVAddRecExpr *AddRec =
1693 dyn_cast<SCEVAddRecExpr>(BEValue)) {
1694 // Otherwise, this could be a loop like this:
1695 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1696 // In this case, j = {1,+,1} and BEValue is j.
1697 // Because the other in-value of i (0) fits the evolution of BEValue
1698 // i really is an addrec evolution.
1699 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1700 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1702 // If StartVal = j.start - j.stride, we can use StartVal as the
1703 // initial step of the addrec evolution.
1704 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
1705 AddRec->getOperand(1))) {
1706 SCEVHandle PHISCEV =
1707 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1709 // Okay, for the entire analysis of this edge we assumed the PHI
1710 // to be symbolic. We now need to go back and update all of the
1711 // entries for the scalars that use the PHI (except for the PHI
1712 // itself) to use the new analyzed value instead of the "symbolic"
1714 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1720 return SymbolicName;
1723 // If it's not a loop phi, we can't handle it yet.
1724 return getUnknown(PN);
1727 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1728 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1729 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1730 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1731 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
1732 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1733 return C->getValue()->getValue().countTrailingZeros();
1735 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1736 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
1737 (uint32_t)SE.getTypeSizeInBits(T->getType()));
1739 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1740 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1741 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1742 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1745 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1746 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1747 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1748 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1751 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1752 // The result is the min of all operands results.
1753 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1754 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1755 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1759 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1760 // The result is the sum of all operands results.
1761 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1762 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
1763 for (unsigned i = 1, e = M->getNumOperands();
1764 SumOpRes != BitWidth && i != e; ++i)
1765 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
1770 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1771 // The result is the min of all operands results.
1772 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1773 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1774 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1778 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1779 // The result is the min of all operands results.
1780 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1781 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1782 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1786 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1787 // The result is the min of all operands results.
1788 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1789 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1790 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1794 // SCEVUDivExpr, SCEVUnknown
1798 /// createSCEV - We know that there is no SCEV for the specified value.
1799 /// Analyze the expression.
1801 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
1802 if (!isSCEVable(V->getType()))
1803 return getUnknown(V);
1805 unsigned Opcode = Instruction::UserOp1;
1806 if (Instruction *I = dyn_cast<Instruction>(V))
1807 Opcode = I->getOpcode();
1808 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1809 Opcode = CE->getOpcode();
1811 return getUnknown(V);
1813 User *U = cast<User>(V);
1815 case Instruction::Add:
1816 return getAddExpr(getSCEV(U->getOperand(0)),
1817 getSCEV(U->getOperand(1)));
1818 case Instruction::Mul:
1819 return getMulExpr(getSCEV(U->getOperand(0)),
1820 getSCEV(U->getOperand(1)));
1821 case Instruction::UDiv:
1822 return getUDivExpr(getSCEV(U->getOperand(0)),
1823 getSCEV(U->getOperand(1)));
1824 case Instruction::Sub:
1825 return getMinusSCEV(getSCEV(U->getOperand(0)),
1826 getSCEV(U->getOperand(1)));
1827 case Instruction::And:
1828 // For an expression like x&255 that merely masks off the high bits,
1829 // use zext(trunc(x)) as the SCEV expression.
1830 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1831 if (CI->isNullValue())
1832 return getSCEV(U->getOperand(1));
1833 if (CI->isAllOnesValue())
1834 return getSCEV(U->getOperand(0));
1835 const APInt &A = CI->getValue();
1836 unsigned Ones = A.countTrailingOnes();
1837 if (APIntOps::isMask(Ones, A))
1839 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
1840 IntegerType::get(Ones)),
1844 case Instruction::Or:
1845 // If the RHS of the Or is a constant, we may have something like:
1846 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1847 // optimizations will transparently handle this case.
1849 // In order for this transformation to be safe, the LHS must be of the
1850 // form X*(2^n) and the Or constant must be less than 2^n.
1851 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1852 SCEVHandle LHS = getSCEV(U->getOperand(0));
1853 const APInt &CIVal = CI->getValue();
1854 if (GetMinTrailingZeros(LHS, *this) >=
1855 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1856 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
1859 case Instruction::Xor:
1860 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1861 // If the RHS of the xor is a signbit, then this is just an add.
1862 // Instcombine turns add of signbit into xor as a strength reduction step.
1863 if (CI->getValue().isSignBit())
1864 return getAddExpr(getSCEV(U->getOperand(0)),
1865 getSCEV(U->getOperand(1)));
1867 // If the RHS of xor is -1, then this is a not operation.
1868 else if (CI->isAllOnesValue())
1869 return getNotSCEV(getSCEV(U->getOperand(0)));
1873 case Instruction::Shl:
1874 // Turn shift left of a constant amount into a multiply.
1875 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1876 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1877 Constant *X = ConstantInt::get(
1878 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1879 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1883 case Instruction::LShr:
1884 // Turn logical shift right of a constant into a unsigned divide.
1885 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1886 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1887 Constant *X = ConstantInt::get(
1888 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1889 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1893 case Instruction::AShr:
1894 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
1895 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
1896 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
1897 if (L->getOpcode() == Instruction::Shl &&
1898 L->getOperand(1) == U->getOperand(1)) {
1899 unsigned BitWidth = getTypeSizeInBits(U->getType());
1900 uint64_t Amt = BitWidth - CI->getZExtValue();
1901 if (Amt == BitWidth)
1902 return getSCEV(L->getOperand(0)); // shift by zero --> noop
1904 return getIntegerSCEV(0, U->getType()); // value is undefined
1906 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
1907 IntegerType::get(Amt)),
1912 case Instruction::Trunc:
1913 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1915 case Instruction::ZExt:
1916 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1918 case Instruction::SExt:
1919 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1921 case Instruction::BitCast:
1922 // BitCasts are no-op casts so we just eliminate the cast.
1923 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
1924 return getSCEV(U->getOperand(0));
1927 case Instruction::IntToPtr:
1928 if (!TD) break; // Without TD we can't analyze pointers.
1929 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1930 TD->getIntPtrType());
1932 case Instruction::PtrToInt:
1933 if (!TD) break; // Without TD we can't analyze pointers.
1934 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1937 case Instruction::GetElementPtr: {
1938 if (!TD) break; // Without TD we can't analyze pointers.
1939 const Type *IntPtrTy = TD->getIntPtrType();
1940 Value *Base = U->getOperand(0);
1941 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
1942 gep_type_iterator GTI = gep_type_begin(U);
1943 for (GetElementPtrInst::op_iterator I = next(U->op_begin()),
1947 // Compute the (potentially symbolic) offset in bytes for this index.
1948 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
1949 // For a struct, add the member offset.
1950 const StructLayout &SL = *TD->getStructLayout(STy);
1951 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
1952 uint64_t Offset = SL.getElementOffset(FieldNo);
1953 TotalOffset = getAddExpr(TotalOffset,
1954 getIntegerSCEV(Offset, IntPtrTy));
1956 // For an array, add the element offset, explicitly scaled.
1957 SCEVHandle LocalOffset = getSCEV(Index);
1958 if (!isa<PointerType>(LocalOffset->getType()))
1959 // Getelementptr indicies are signed.
1960 LocalOffset = getTruncateOrSignExtend(LocalOffset,
1963 getMulExpr(LocalOffset,
1964 getIntegerSCEV(TD->getTypePaddedSize(*GTI),
1966 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
1969 return getAddExpr(getSCEV(Base), TotalOffset);
1972 case Instruction::PHI:
1973 return createNodeForPHI(cast<PHINode>(U));
1975 case Instruction::Select:
1976 // This could be a smax or umax that was lowered earlier.
1977 // Try to recover it.
1978 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
1979 Value *LHS = ICI->getOperand(0);
1980 Value *RHS = ICI->getOperand(1);
1981 switch (ICI->getPredicate()) {
1982 case ICmpInst::ICMP_SLT:
1983 case ICmpInst::ICMP_SLE:
1984 std::swap(LHS, RHS);
1986 case ICmpInst::ICMP_SGT:
1987 case ICmpInst::ICMP_SGE:
1988 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1989 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1990 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1991 // ~smax(~x, ~y) == smin(x, y).
1992 return getNotSCEV(getSMaxExpr(
1993 getNotSCEV(getSCEV(LHS)),
1994 getNotSCEV(getSCEV(RHS))));
1996 case ICmpInst::ICMP_ULT:
1997 case ICmpInst::ICMP_ULE:
1998 std::swap(LHS, RHS);
2000 case ICmpInst::ICMP_UGT:
2001 case ICmpInst::ICMP_UGE:
2002 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2003 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2004 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2005 // ~umax(~x, ~y) == umin(x, y)
2006 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2007 getNotSCEV(getSCEV(RHS))));
2014 default: // We cannot analyze this expression.
2018 return getUnknown(V);
2023 //===----------------------------------------------------------------------===//
2024 // Iteration Count Computation Code
2027 /// getBackedgeTakenCount - If the specified loop has a predictable
2028 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2029 /// object. The backedge-taken count is the number of times the loop header
2030 /// will be branched to from within the loop. This is one less than the
2031 /// trip count of the loop, since it doesn't count the first iteration,
2032 /// when the header is branched to from outside the loop.
2034 /// Note that it is not valid to call this method on a loop without a
2035 /// loop-invariant backedge-taken count (see
2036 /// hasLoopInvariantBackedgeTakenCount).
2038 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2039 return getBackedgeTakenInfo(L).Exact;
2042 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2043 /// return the least SCEV value that is known never to be less than the
2044 /// actual backedge taken count.
2045 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2046 return getBackedgeTakenInfo(L).Max;
2049 const ScalarEvolution::BackedgeTakenInfo &
2050 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2051 // Initially insert a CouldNotCompute for this loop. If the insertion
2052 // succeeds, procede to actually compute a backedge-taken count and
2053 // update the value. The temporary CouldNotCompute value tells SCEV
2054 // code elsewhere that it shouldn't attempt to request a new
2055 // backedge-taken count, which could result in infinite recursion.
2056 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2057 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2059 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2060 if (ItCount.Exact != UnknownValue) {
2061 assert(ItCount.Exact->isLoopInvariant(L) &&
2062 ItCount.Max->isLoopInvariant(L) &&
2063 "Computed trip count isn't loop invariant for loop!");
2064 ++NumTripCountsComputed;
2066 // Update the value in the map.
2067 Pair.first->second = ItCount;
2068 } else if (isa<PHINode>(L->getHeader()->begin())) {
2069 // Only count loops that have phi nodes as not being computable.
2070 ++NumTripCountsNotComputed;
2073 // Now that we know more about the trip count for this loop, forget any
2074 // existing SCEV values for PHI nodes in this loop since they are only
2075 // conservative estimates made without the benefit
2076 // of trip count information.
2077 if (ItCount.hasAnyInfo())
2080 return Pair.first->second;
2083 /// forgetLoopBackedgeTakenCount - This method should be called by the
2084 /// client when it has changed a loop in a way that may effect
2085 /// ScalarEvolution's ability to compute a trip count, or if the loop
2087 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2088 BackedgeTakenCounts.erase(L);
2092 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2093 /// PHI nodes in the given loop. This is used when the trip count of
2094 /// the loop may have changed.
2095 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2096 BasicBlock *Header = L->getHeader();
2098 SmallVector<Instruction *, 16> Worklist;
2099 for (BasicBlock::iterator I = Header->begin();
2100 PHINode *PN = dyn_cast<PHINode>(I); ++I)
2101 Worklist.push_back(PN);
2103 while (!Worklist.empty()) {
2104 Instruction *I = Worklist.pop_back_val();
2105 if (Scalars.erase(I))
2106 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2108 Worklist.push_back(cast<Instruction>(UI));
2112 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2113 /// of the specified loop will execute.
2114 ScalarEvolution::BackedgeTakenInfo
2115 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2116 // If the loop has a non-one exit block count, we can't analyze it.
2117 SmallVector<BasicBlock*, 8> ExitBlocks;
2118 L->getExitBlocks(ExitBlocks);
2119 if (ExitBlocks.size() != 1) return UnknownValue;
2121 // Okay, there is one exit block. Try to find the condition that causes the
2122 // loop to be exited.
2123 BasicBlock *ExitBlock = ExitBlocks[0];
2125 BasicBlock *ExitingBlock = 0;
2126 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2128 if (L->contains(*PI)) {
2129 if (ExitingBlock == 0)
2132 return UnknownValue; // More than one block exiting!
2134 assert(ExitingBlock && "No exits from loop, something is broken!");
2136 // Okay, we've computed the exiting block. See what condition causes us to
2139 // FIXME: we should be able to handle switch instructions (with a single exit)
2140 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2141 if (ExitBr == 0) return UnknownValue;
2142 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2144 // At this point, we know we have a conditional branch that determines whether
2145 // the loop is exited. However, we don't know if the branch is executed each
2146 // time through the loop. If not, then the execution count of the branch will
2147 // not be equal to the trip count of the loop.
2149 // Currently we check for this by checking to see if the Exit branch goes to
2150 // the loop header. If so, we know it will always execute the same number of
2151 // times as the loop. We also handle the case where the exit block *is* the
2152 // loop header. This is common for un-rotated loops. More extensive analysis
2153 // could be done to handle more cases here.
2154 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2155 ExitBr->getSuccessor(1) != L->getHeader() &&
2156 ExitBr->getParent() != L->getHeader())
2157 return UnknownValue;
2159 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2161 // If it's not an integer comparison then compute it the hard way.
2162 // Note that ICmpInst deals with pointer comparisons too so we must check
2163 // the type of the operand.
2164 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2165 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2166 ExitBr->getSuccessor(0) == ExitBlock);
2168 // If the condition was exit on true, convert the condition to exit on false
2169 ICmpInst::Predicate Cond;
2170 if (ExitBr->getSuccessor(1) == ExitBlock)
2171 Cond = ExitCond->getPredicate();
2173 Cond = ExitCond->getInversePredicate();
2175 // Handle common loops like: for (X = "string"; *X; ++X)
2176 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2177 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2179 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2180 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2183 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2184 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2186 // Try to evaluate any dependencies out of the loop.
2187 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2188 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2189 Tmp = getSCEVAtScope(RHS, L);
2190 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2192 // At this point, we would like to compute how many iterations of the
2193 // loop the predicate will return true for these inputs.
2194 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2195 // If there is a loop-invariant, force it into the RHS.
2196 std::swap(LHS, RHS);
2197 Cond = ICmpInst::getSwappedPredicate(Cond);
2200 // If we have a comparison of a chrec against a constant, try to use value
2201 // ranges to answer this query.
2202 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2203 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2204 if (AddRec->getLoop() == L) {
2205 // Form the comparison range using the constant of the correct type so
2206 // that the ConstantRange class knows to do a signed or unsigned
2208 ConstantInt *CompVal = RHSC->getValue();
2209 const Type *RealTy = ExitCond->getOperand(0)->getType();
2210 CompVal = dyn_cast<ConstantInt>(
2211 ConstantExpr::getBitCast(CompVal, RealTy));
2213 // Form the constant range.
2214 ConstantRange CompRange(
2215 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2217 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2218 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2223 case ICmpInst::ICMP_NE: { // while (X != Y)
2224 // Convert to: while (X-Y != 0)
2225 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2226 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2229 case ICmpInst::ICMP_EQ: {
2230 // Convert to: while (X-Y == 0) // while (X == Y)
2231 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2232 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2235 case ICmpInst::ICMP_SLT: {
2236 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2237 if (BTI.hasAnyInfo()) return BTI;
2240 case ICmpInst::ICMP_SGT: {
2241 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2242 getNotSCEV(RHS), L, true);
2243 if (BTI.hasAnyInfo()) return BTI;
2246 case ICmpInst::ICMP_ULT: {
2247 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2248 if (BTI.hasAnyInfo()) return BTI;
2251 case ICmpInst::ICMP_UGT: {
2252 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2253 getNotSCEV(RHS), L, false);
2254 if (BTI.hasAnyInfo()) return BTI;
2259 errs() << "ComputeBackedgeTakenCount ";
2260 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2261 errs() << "[unsigned] ";
2262 errs() << *LHS << " "
2263 << Instruction::getOpcodeName(Instruction::ICmp)
2264 << " " << *RHS << "\n";
2269 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2270 ExitBr->getSuccessor(0) == ExitBlock);
2273 static ConstantInt *
2274 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2275 ScalarEvolution &SE) {
2276 SCEVHandle InVal = SE.getConstant(C);
2277 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2278 assert(isa<SCEVConstant>(Val) &&
2279 "Evaluation of SCEV at constant didn't fold correctly?");
2280 return cast<SCEVConstant>(Val)->getValue();
2283 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2284 /// and a GEP expression (missing the pointer index) indexing into it, return
2285 /// the addressed element of the initializer or null if the index expression is
2288 GetAddressedElementFromGlobal(GlobalVariable *GV,
2289 const std::vector<ConstantInt*> &Indices) {
2290 Constant *Init = GV->getInitializer();
2291 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2292 uint64_t Idx = Indices[i]->getZExtValue();
2293 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2294 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2295 Init = cast<Constant>(CS->getOperand(Idx));
2296 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2297 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2298 Init = cast<Constant>(CA->getOperand(Idx));
2299 } else if (isa<ConstantAggregateZero>(Init)) {
2300 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2301 assert(Idx < STy->getNumElements() && "Bad struct index!");
2302 Init = Constant::getNullValue(STy->getElementType(Idx));
2303 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2304 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2305 Init = Constant::getNullValue(ATy->getElementType());
2307 assert(0 && "Unknown constant aggregate type!");
2311 return 0; // Unknown initializer type
2317 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2318 /// 'icmp op load X, cst', try to see if we can compute the backedge
2319 /// execution count.
2320 SCEVHandle ScalarEvolution::
2321 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2323 ICmpInst::Predicate predicate) {
2324 if (LI->isVolatile()) return UnknownValue;
2326 // Check to see if the loaded pointer is a getelementptr of a global.
2327 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2328 if (!GEP) return UnknownValue;
2330 // Make sure that it is really a constant global we are gepping, with an
2331 // initializer, and make sure the first IDX is really 0.
2332 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2333 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2334 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2335 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2336 return UnknownValue;
2338 // Okay, we allow one non-constant index into the GEP instruction.
2340 std::vector<ConstantInt*> Indexes;
2341 unsigned VarIdxNum = 0;
2342 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2343 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2344 Indexes.push_back(CI);
2345 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2346 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2347 VarIdx = GEP->getOperand(i);
2349 Indexes.push_back(0);
2352 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2353 // Check to see if X is a loop variant variable value now.
2354 SCEVHandle Idx = getSCEV(VarIdx);
2355 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2356 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2358 // We can only recognize very limited forms of loop index expressions, in
2359 // particular, only affine AddRec's like {C1,+,C2}.
2360 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2361 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2362 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2363 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2364 return UnknownValue;
2366 unsigned MaxSteps = MaxBruteForceIterations;
2367 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2368 ConstantInt *ItCst =
2369 ConstantInt::get(IdxExpr->getType(), IterationNum);
2370 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2372 // Form the GEP offset.
2373 Indexes[VarIdxNum] = Val;
2375 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2376 if (Result == 0) break; // Cannot compute!
2378 // Evaluate the condition for this iteration.
2379 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2380 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2381 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2383 errs() << "\n***\n*** Computed loop count " << *ItCst
2384 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2387 ++NumArrayLenItCounts;
2388 return getConstant(ItCst); // Found terminating iteration!
2391 return UnknownValue;
2395 /// CanConstantFold - Return true if we can constant fold an instruction of the
2396 /// specified type, assuming that all operands were constants.
2397 static bool CanConstantFold(const Instruction *I) {
2398 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2399 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2402 if (const CallInst *CI = dyn_cast<CallInst>(I))
2403 if (const Function *F = CI->getCalledFunction())
2404 return canConstantFoldCallTo(F);
2408 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2409 /// in the loop that V is derived from. We allow arbitrary operations along the
2410 /// way, but the operands of an operation must either be constants or a value
2411 /// derived from a constant PHI. If this expression does not fit with these
2412 /// constraints, return null.
2413 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2414 // If this is not an instruction, or if this is an instruction outside of the
2415 // loop, it can't be derived from a loop PHI.
2416 Instruction *I = dyn_cast<Instruction>(V);
2417 if (I == 0 || !L->contains(I->getParent())) return 0;
2419 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2420 if (L->getHeader() == I->getParent())
2423 // We don't currently keep track of the control flow needed to evaluate
2424 // PHIs, so we cannot handle PHIs inside of loops.
2428 // If we won't be able to constant fold this expression even if the operands
2429 // are constants, return early.
2430 if (!CanConstantFold(I)) return 0;
2432 // Otherwise, we can evaluate this instruction if all of its operands are
2433 // constant or derived from a PHI node themselves.
2435 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2436 if (!(isa<Constant>(I->getOperand(Op)) ||
2437 isa<GlobalValue>(I->getOperand(Op)))) {
2438 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2439 if (P == 0) return 0; // Not evolving from PHI
2443 return 0; // Evolving from multiple different PHIs.
2446 // This is a expression evolving from a constant PHI!
2450 /// EvaluateExpression - Given an expression that passes the
2451 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2452 /// in the loop has the value PHIVal. If we can't fold this expression for some
2453 /// reason, return null.
2454 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2455 if (isa<PHINode>(V)) return PHIVal;
2456 if (Constant *C = dyn_cast<Constant>(V)) return C;
2457 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2458 Instruction *I = cast<Instruction>(V);
2460 std::vector<Constant*> Operands;
2461 Operands.resize(I->getNumOperands());
2463 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2464 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2465 if (Operands[i] == 0) return 0;
2468 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2469 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2470 &Operands[0], Operands.size());
2472 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2473 &Operands[0], Operands.size());
2476 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2477 /// in the header of its containing loop, we know the loop executes a
2478 /// constant number of times, and the PHI node is just a recurrence
2479 /// involving constants, fold it.
2480 Constant *ScalarEvolution::
2481 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2482 std::map<PHINode*, Constant*>::iterator I =
2483 ConstantEvolutionLoopExitValue.find(PN);
2484 if (I != ConstantEvolutionLoopExitValue.end())
2487 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2488 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2490 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2492 // Since the loop is canonicalized, the PHI node must have two entries. One
2493 // entry must be a constant (coming in from outside of the loop), and the
2494 // second must be derived from the same PHI.
2495 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2496 Constant *StartCST =
2497 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2499 return RetVal = 0; // Must be a constant.
2501 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2502 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2504 return RetVal = 0; // Not derived from same PHI.
2506 // Execute the loop symbolically to determine the exit value.
2507 if (BEs.getActiveBits() >= 32)
2508 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2510 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2511 unsigned IterationNum = 0;
2512 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2513 if (IterationNum == NumIterations)
2514 return RetVal = PHIVal; // Got exit value!
2516 // Compute the value of the PHI node for the next iteration.
2517 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2518 if (NextPHI == PHIVal)
2519 return RetVal = NextPHI; // Stopped evolving!
2521 return 0; // Couldn't evaluate!
2526 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2527 /// constant number of times (the condition evolves only from constants),
2528 /// try to evaluate a few iterations of the loop until we get the exit
2529 /// condition gets a value of ExitWhen (true or false). If we cannot
2530 /// evaluate the trip count of the loop, return UnknownValue.
2531 SCEVHandle ScalarEvolution::
2532 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2533 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2534 if (PN == 0) return UnknownValue;
2536 // Since the loop is canonicalized, the PHI node must have two entries. One
2537 // entry must be a constant (coming in from outside of the loop), and the
2538 // second must be derived from the same PHI.
2539 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2540 Constant *StartCST =
2541 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2542 if (StartCST == 0) return UnknownValue; // Must be a constant.
2544 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2545 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2546 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2548 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2549 // the loop symbolically to determine when the condition gets a value of
2551 unsigned IterationNum = 0;
2552 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2553 for (Constant *PHIVal = StartCST;
2554 IterationNum != MaxIterations; ++IterationNum) {
2555 ConstantInt *CondVal =
2556 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2558 // Couldn't symbolically evaluate.
2559 if (!CondVal) return UnknownValue;
2561 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2562 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2563 ++NumBruteForceTripCountsComputed;
2564 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2567 // Compute the value of the PHI node for the next iteration.
2568 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2569 if (NextPHI == 0 || NextPHI == PHIVal)
2570 return UnknownValue; // Couldn't evaluate or not making progress...
2574 // Too many iterations were needed to evaluate.
2575 return UnknownValue;
2578 /// getSCEVAtScope - Compute the value of the specified expression within the
2579 /// indicated loop (which may be null to indicate in no loop). If the
2580 /// expression cannot be evaluated, return UnknownValue.
2581 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2582 // FIXME: this should be turned into a virtual method on SCEV!
2584 if (isa<SCEVConstant>(V)) return V;
2586 // If this instruction is evolved from a constant-evolving PHI, compute the
2587 // exit value from the loop without using SCEVs.
2588 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2589 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2590 const Loop *LI = (*this->LI)[I->getParent()];
2591 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2592 if (PHINode *PN = dyn_cast<PHINode>(I))
2593 if (PN->getParent() == LI->getHeader()) {
2594 // Okay, there is no closed form solution for the PHI node. Check
2595 // to see if the loop that contains it has a known backedge-taken
2596 // count. If so, we may be able to force computation of the exit
2598 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2599 if (const SCEVConstant *BTCC =
2600 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2601 // Okay, we know how many times the containing loop executes. If
2602 // this is a constant evolving PHI node, get the final value at
2603 // the specified iteration number.
2604 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2605 BTCC->getValue()->getValue(),
2607 if (RV) return getUnknown(RV);
2611 // Okay, this is an expression that we cannot symbolically evaluate
2612 // into a SCEV. Check to see if it's possible to symbolically evaluate
2613 // the arguments into constants, and if so, try to constant propagate the
2614 // result. This is particularly useful for computing loop exit values.
2615 if (CanConstantFold(I)) {
2616 std::vector<Constant*> Operands;
2617 Operands.reserve(I->getNumOperands());
2618 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2619 Value *Op = I->getOperand(i);
2620 if (Constant *C = dyn_cast<Constant>(Op)) {
2621 Operands.push_back(C);
2623 // If any of the operands is non-constant and if they are
2624 // non-integer and non-pointer, don't even try to analyze them
2625 // with scev techniques.
2626 if (!isSCEVable(Op->getType()))
2629 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2630 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2631 Constant *C = SC->getValue();
2632 if (C->getType() != Op->getType())
2633 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2637 Operands.push_back(C);
2638 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2639 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2640 if (C->getType() != Op->getType())
2642 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2646 Operands.push_back(C);
2656 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2657 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2658 &Operands[0], Operands.size());
2660 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2661 &Operands[0], Operands.size());
2662 return getUnknown(C);
2666 // This is some other type of SCEVUnknown, just return it.
2670 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2671 // Avoid performing the look-up in the common case where the specified
2672 // expression has no loop-variant portions.
2673 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2674 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2675 if (OpAtScope != Comm->getOperand(i)) {
2676 if (OpAtScope == UnknownValue) return UnknownValue;
2677 // Okay, at least one of these operands is loop variant but might be
2678 // foldable. Build a new instance of the folded commutative expression.
2679 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2680 NewOps.push_back(OpAtScope);
2682 for (++i; i != e; ++i) {
2683 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2684 if (OpAtScope == UnknownValue) return UnknownValue;
2685 NewOps.push_back(OpAtScope);
2687 if (isa<SCEVAddExpr>(Comm))
2688 return getAddExpr(NewOps);
2689 if (isa<SCEVMulExpr>(Comm))
2690 return getMulExpr(NewOps);
2691 if (isa<SCEVSMaxExpr>(Comm))
2692 return getSMaxExpr(NewOps);
2693 if (isa<SCEVUMaxExpr>(Comm))
2694 return getUMaxExpr(NewOps);
2695 assert(0 && "Unknown commutative SCEV type!");
2698 // If we got here, all operands are loop invariant.
2702 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2703 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2704 if (LHS == UnknownValue) return LHS;
2705 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2706 if (RHS == UnknownValue) return RHS;
2707 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2708 return Div; // must be loop invariant
2709 return getUDivExpr(LHS, RHS);
2712 // If this is a loop recurrence for a loop that does not contain L, then we
2713 // are dealing with the final value computed by the loop.
2714 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2715 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2716 // To evaluate this recurrence, we need to know how many times the AddRec
2717 // loop iterates. Compute this now.
2718 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2719 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2721 // Then, evaluate the AddRec.
2722 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
2724 return UnknownValue;
2727 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
2728 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2729 if (Op == UnknownValue) return Op;
2730 if (Op == Cast->getOperand())
2731 return Cast; // must be loop invariant
2732 return getZeroExtendExpr(Op, Cast->getType());
2735 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
2736 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2737 if (Op == UnknownValue) return Op;
2738 if (Op == Cast->getOperand())
2739 return Cast; // must be loop invariant
2740 return getSignExtendExpr(Op, Cast->getType());
2743 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
2744 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2745 if (Op == UnknownValue) return Op;
2746 if (Op == Cast->getOperand())
2747 return Cast; // must be loop invariant
2748 return getTruncateExpr(Op, Cast->getType());
2751 assert(0 && "Unknown SCEV type!");
2754 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2755 /// at the specified scope in the program. The L value specifies a loop
2756 /// nest to evaluate the expression at, where null is the top-level or a
2757 /// specified loop is immediately inside of the loop.
2759 /// This method can be used to compute the exit value for a variable defined
2760 /// in a loop by querying what the value will hold in the parent loop.
2762 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2763 /// object is returned.
2764 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
2765 return getSCEVAtScope(getSCEV(V), L);
2768 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2769 /// following equation:
2771 /// A * X = B (mod N)
2773 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2774 /// A and B isn't important.
2776 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2777 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2778 ScalarEvolution &SE) {
2779 uint32_t BW = A.getBitWidth();
2780 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2781 assert(A != 0 && "A must be non-zero.");
2785 // The gcd of A and N may have only one prime factor: 2. The number of
2786 // trailing zeros in A is its multiplicity
2787 uint32_t Mult2 = A.countTrailingZeros();
2790 // 2. Check if B is divisible by D.
2792 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2793 // is not less than multiplicity of this prime factor for D.
2794 if (B.countTrailingZeros() < Mult2)
2795 return SE.getCouldNotCompute();
2797 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2800 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2801 // bit width during computations.
2802 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2803 APInt Mod(BW + 1, 0);
2804 Mod.set(BW - Mult2); // Mod = N / D
2805 APInt I = AD.multiplicativeInverse(Mod);
2807 // 4. Compute the minimum unsigned root of the equation:
2808 // I * (B / D) mod (N / D)
2809 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2811 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2813 return SE.getConstant(Result.trunc(BW));
2816 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2817 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2818 /// might be the same) or two SCEVCouldNotCompute objects.
2820 static std::pair<SCEVHandle,SCEVHandle>
2821 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2822 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2823 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2824 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2825 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2827 // We currently can only solve this if the coefficients are constants.
2828 if (!LC || !MC || !NC) {
2829 const SCEV *CNC = SE.getCouldNotCompute();
2830 return std::make_pair(CNC, CNC);
2833 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2834 const APInt &L = LC->getValue()->getValue();
2835 const APInt &M = MC->getValue()->getValue();
2836 const APInt &N = NC->getValue()->getValue();
2837 APInt Two(BitWidth, 2);
2838 APInt Four(BitWidth, 4);
2841 using namespace APIntOps;
2843 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2844 // The B coefficient is M-N/2
2848 // The A coefficient is N/2
2849 APInt A(N.sdiv(Two));
2851 // Compute the B^2-4ac term.
2854 SqrtTerm -= Four * (A * C);
2856 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2857 // integer value or else APInt::sqrt() will assert.
2858 APInt SqrtVal(SqrtTerm.sqrt());
2860 // Compute the two solutions for the quadratic formula.
2861 // The divisions must be performed as signed divisions.
2863 APInt TwoA( A << 1 );
2864 if (TwoA.isMinValue()) {
2865 const SCEV *CNC = SE.getCouldNotCompute();
2866 return std::make_pair(CNC, CNC);
2869 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2870 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2872 return std::make_pair(SE.getConstant(Solution1),
2873 SE.getConstant(Solution2));
2874 } // end APIntOps namespace
2877 /// HowFarToZero - Return the number of times a backedge comparing the specified
2878 /// value to zero will execute. If not computable, return UnknownValue
2879 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
2880 // If the value is a constant
2881 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2882 // If the value is already zero, the branch will execute zero times.
2883 if (C->getValue()->isZero()) return C;
2884 return UnknownValue; // Otherwise it will loop infinitely.
2887 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2888 if (!AddRec || AddRec->getLoop() != L)
2889 return UnknownValue;
2891 if (AddRec->isAffine()) {
2892 // If this is an affine expression, the execution count of this branch is
2893 // the minimum unsigned root of the following equation:
2895 // Start + Step*N = 0 (mod 2^BW)
2899 // Step*N = -Start (mod 2^BW)
2901 // where BW is the common bit width of Start and Step.
2903 // Get the initial value for the loop.
2904 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2905 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2907 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2909 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2910 // For now we handle only constant steps.
2912 // First, handle unitary steps.
2913 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2914 return getNegativeSCEV(Start); // N = -Start (as unsigned)
2915 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2916 return Start; // N = Start (as unsigned)
2918 // Then, try to solve the above equation provided that Start is constant.
2919 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2920 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2921 -StartC->getValue()->getValue(),
2924 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2925 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2926 // the quadratic equation to solve it.
2927 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
2929 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2930 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2933 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
2934 << " sol#2: " << *R2 << "\n";
2936 // Pick the smallest positive root value.
2937 if (ConstantInt *CB =
2938 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2939 R1->getValue(), R2->getValue()))) {
2940 if (CB->getZExtValue() == false)
2941 std::swap(R1, R2); // R1 is the minimum root now.
2943 // We can only use this value if the chrec ends up with an exact zero
2944 // value at this index. When solving for "X*X != 5", for example, we
2945 // should not accept a root of 2.
2946 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
2948 return R1; // We found a quadratic root!
2953 return UnknownValue;
2956 /// HowFarToNonZero - Return the number of times a backedge checking the
2957 /// specified value for nonzero will execute. If not computable, return
2959 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
2960 // Loops that look like: while (X == 0) are very strange indeed. We don't
2961 // handle them yet except for the trivial case. This could be expanded in the
2962 // future as needed.
2964 // If the value is a constant, check to see if it is known to be non-zero
2965 // already. If so, the backedge will execute zero times.
2966 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2967 if (!C->getValue()->isNullValue())
2968 return getIntegerSCEV(0, C->getType());
2969 return UnknownValue; // Otherwise it will loop infinitely.
2972 // We could implement others, but I really doubt anyone writes loops like
2973 // this, and if they did, they would already be constant folded.
2974 return UnknownValue;
2977 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2978 /// (which may not be an immediate predecessor) which has exactly one
2979 /// successor from which BB is reachable, or null if no such block is
2983 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2984 // If the block has a unique predecessor, then there is no path from the
2985 // predecessor to the block that does not go through the direct edge
2986 // from the predecessor to the block.
2987 if (BasicBlock *Pred = BB->getSinglePredecessor())
2990 // A loop's header is defined to be a block that dominates the loop.
2991 // If the loop has a preheader, it must be a block that has exactly
2992 // one successor that can reach BB. This is slightly more strict
2993 // than necessary, but works if critical edges are split.
2994 if (Loop *L = LI->getLoopFor(BB))
2995 return L->getLoopPreheader();
3000 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3001 /// a conditional between LHS and RHS. This is used to help avoid max
3002 /// expressions in loop trip counts.
3003 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3004 ICmpInst::Predicate Pred,
3005 const SCEV *LHS, const SCEV *RHS) {
3006 BasicBlock *Preheader = L->getLoopPreheader();
3007 BasicBlock *PreheaderDest = L->getHeader();
3009 // Starting at the preheader, climb up the predecessor chain, as long as
3010 // there are predecessors that can be found that have unique successors
3011 // leading to the original header.
3013 PreheaderDest = Preheader,
3014 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
3016 BranchInst *LoopEntryPredicate =
3017 dyn_cast<BranchInst>(Preheader->getTerminator());
3018 if (!LoopEntryPredicate ||
3019 LoopEntryPredicate->isUnconditional())
3022 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3025 // Now that we found a conditional branch that dominates the loop, check to
3026 // see if it is the comparison we are looking for.
3027 Value *PreCondLHS = ICI->getOperand(0);
3028 Value *PreCondRHS = ICI->getOperand(1);
3029 ICmpInst::Predicate Cond;
3030 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
3031 Cond = ICI->getPredicate();
3033 Cond = ICI->getInversePredicate();
3036 ; // An exact match.
3037 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3038 ; // The actual condition is beyond sufficient.
3040 // Check a few special cases.
3042 case ICmpInst::ICMP_UGT:
3043 if (Pred == ICmpInst::ICMP_ULT) {
3044 std::swap(PreCondLHS, PreCondRHS);
3045 Cond = ICmpInst::ICMP_ULT;
3049 case ICmpInst::ICMP_SGT:
3050 if (Pred == ICmpInst::ICMP_SLT) {
3051 std::swap(PreCondLHS, PreCondRHS);
3052 Cond = ICmpInst::ICMP_SLT;
3056 case ICmpInst::ICMP_NE:
3057 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3058 // so check for this case by checking if the NE is comparing against
3059 // a minimum or maximum constant.
3060 if (!ICmpInst::isTrueWhenEqual(Pred))
3061 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3062 const APInt &A = CI->getValue();
3064 case ICmpInst::ICMP_SLT:
3065 if (A.isMaxSignedValue()) break;
3067 case ICmpInst::ICMP_SGT:
3068 if (A.isMinSignedValue()) break;
3070 case ICmpInst::ICMP_ULT:
3071 if (A.isMaxValue()) break;
3073 case ICmpInst::ICMP_UGT:
3074 if (A.isMinValue()) break;
3079 Cond = ICmpInst::ICMP_NE;
3080 // NE is symmetric but the original comparison may not be. Swap
3081 // the operands if necessary so that they match below.
3082 if (isa<SCEVConstant>(LHS))
3083 std::swap(PreCondLHS, PreCondRHS);
3088 // We weren't able to reconcile the condition.
3092 if (!PreCondLHS->getType()->isInteger()) continue;
3094 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3095 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3096 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3097 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3098 RHS == getNotSCEV(PreCondLHSSCEV)))
3105 /// HowManyLessThans - Return the number of times a backedge containing the
3106 /// specified less-than comparison will execute. If not computable, return
3108 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3109 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3110 const Loop *L, bool isSigned) {
3111 // Only handle: "ADDREC < LoopInvariant".
3112 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3114 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3115 if (!AddRec || AddRec->getLoop() != L)
3116 return UnknownValue;
3118 if (AddRec->isAffine()) {
3119 // FORNOW: We only support unit strides.
3120 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3121 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3122 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3124 // TODO: handle non-constant strides.
3125 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3126 if (!CStep || CStep->isZero())
3127 return UnknownValue;
3128 if (CStep->getValue()->getValue() == 1) {
3129 // With unit stride, the iteration never steps past the limit value.
3130 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3131 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3132 // Test whether a positive iteration iteration can step past the limit
3133 // value and past the maximum value for its type in a single step.
3135 APInt Max = APInt::getSignedMaxValue(BitWidth);
3136 if ((Max - CStep->getValue()->getValue())
3137 .slt(CLimit->getValue()->getValue()))
3138 return UnknownValue;
3140 APInt Max = APInt::getMaxValue(BitWidth);
3141 if ((Max - CStep->getValue()->getValue())
3142 .ult(CLimit->getValue()->getValue()))
3143 return UnknownValue;
3146 // TODO: handle non-constant limit values below.
3147 return UnknownValue;
3149 // TODO: handle negative strides below.
3150 return UnknownValue;
3152 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3153 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3154 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3155 // treat m-n as signed nor unsigned due to overflow possibility.
3157 // First, we get the value of the LHS in the first iteration: n
3158 SCEVHandle Start = AddRec->getOperand(0);
3160 // Determine the minimum constant start value.
3161 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3162 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3163 APInt::getMinValue(BitWidth));
3165 // If we know that the condition is true in order to enter the loop,
3166 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3167 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3168 // division must round up.
3169 SCEVHandle End = RHS;
3170 if (!isLoopGuardedByCond(L,
3171 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3172 getMinusSCEV(Start, Step), RHS))
3173 End = isSigned ? getSMaxExpr(RHS, Start)
3174 : getUMaxExpr(RHS, Start);
3176 // Determine the maximum constant end value.
3177 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3178 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3179 APInt::getMaxValue(BitWidth));
3181 // Finally, we subtract these two values and divide, rounding up, to get
3182 // the number of times the backedge is executed.
3183 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3184 getAddExpr(Step, NegOne)),
3187 // The maximum backedge count is similar, except using the minimum start
3188 // value and the maximum end value.
3189 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3191 getAddExpr(Step, NegOne)),
3194 return BackedgeTakenInfo(BECount, MaxBECount);
3197 return UnknownValue;
3200 /// getNumIterationsInRange - Return the number of iterations of this loop that
3201 /// produce values in the specified constant range. Another way of looking at
3202 /// this is that it returns the first iteration number where the value is not in
3203 /// the condition, thus computing the exit count. If the iteration count can't
3204 /// be computed, an instance of SCEVCouldNotCompute is returned.
3205 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3206 ScalarEvolution &SE) const {
3207 if (Range.isFullSet()) // Infinite loop.
3208 return SE.getCouldNotCompute();
3210 // If the start is a non-zero constant, shift the range to simplify things.
3211 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3212 if (!SC->getValue()->isZero()) {
3213 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3214 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3215 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3216 if (const SCEVAddRecExpr *ShiftedAddRec =
3217 dyn_cast<SCEVAddRecExpr>(Shifted))
3218 return ShiftedAddRec->getNumIterationsInRange(
3219 Range.subtract(SC->getValue()->getValue()), SE);
3220 // This is strange and shouldn't happen.
3221 return SE.getCouldNotCompute();
3224 // The only time we can solve this is when we have all constant indices.
3225 // Otherwise, we cannot determine the overflow conditions.
3226 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3227 if (!isa<SCEVConstant>(getOperand(i)))
3228 return SE.getCouldNotCompute();
3231 // Okay at this point we know that all elements of the chrec are constants and
3232 // that the start element is zero.
3234 // First check to see if the range contains zero. If not, the first
3236 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3237 if (!Range.contains(APInt(BitWidth, 0)))
3238 return SE.getConstant(ConstantInt::get(getType(),0));
3241 // If this is an affine expression then we have this situation:
3242 // Solve {0,+,A} in Range === Ax in Range
3244 // We know that zero is in the range. If A is positive then we know that
3245 // the upper value of the range must be the first possible exit value.
3246 // If A is negative then the lower of the range is the last possible loop
3247 // value. Also note that we already checked for a full range.
3248 APInt One(BitWidth,1);
3249 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3250 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3252 // The exit value should be (End+A)/A.
3253 APInt ExitVal = (End + A).udiv(A);
3254 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3256 // Evaluate at the exit value. If we really did fall out of the valid
3257 // range, then we computed our trip count, otherwise wrap around or other
3258 // things must have happened.
3259 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3260 if (Range.contains(Val->getValue()))
3261 return SE.getCouldNotCompute(); // Something strange happened
3263 // Ensure that the previous value is in the range. This is a sanity check.
3264 assert(Range.contains(
3265 EvaluateConstantChrecAtConstant(this,
3266 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3267 "Linear scev computation is off in a bad way!");
3268 return SE.getConstant(ExitValue);
3269 } else if (isQuadratic()) {
3270 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3271 // quadratic equation to solve it. To do this, we must frame our problem in
3272 // terms of figuring out when zero is crossed, instead of when
3273 // Range.getUpper() is crossed.
3274 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3275 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3276 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3278 // Next, solve the constructed addrec
3279 std::pair<SCEVHandle,SCEVHandle> Roots =
3280 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3281 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3282 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3284 // Pick the smallest positive root value.
3285 if (ConstantInt *CB =
3286 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3287 R1->getValue(), R2->getValue()))) {
3288 if (CB->getZExtValue() == false)
3289 std::swap(R1, R2); // R1 is the minimum root now.
3291 // Make sure the root is not off by one. The returned iteration should
3292 // not be in the range, but the previous one should be. When solving
3293 // for "X*X < 5", for example, we should not return a root of 2.
3294 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3297 if (Range.contains(R1Val->getValue())) {
3298 // The next iteration must be out of the range...
3299 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3301 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3302 if (!Range.contains(R1Val->getValue()))
3303 return SE.getConstant(NextVal);
3304 return SE.getCouldNotCompute(); // Something strange happened
3307 // If R1 was not in the range, then it is a good return value. Make
3308 // sure that R1-1 WAS in the range though, just in case.
3309 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3310 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3311 if (Range.contains(R1Val->getValue()))
3313 return SE.getCouldNotCompute(); // Something strange happened
3318 return SE.getCouldNotCompute();
3323 //===----------------------------------------------------------------------===//
3324 // SCEVCallbackVH Class Implementation
3325 //===----------------------------------------------------------------------===//
3327 void SCEVCallbackVH::deleted() {
3328 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3329 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3330 SE->ConstantEvolutionLoopExitValue.erase(PN);
3331 SE->Scalars.erase(getValPtr());
3332 // this now dangles!
3335 void SCEVCallbackVH::allUsesReplacedWith(Value *) {
3336 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3338 // Forget all the expressions associated with users of the old value,
3339 // so that future queries will recompute the expressions using the new
3341 SmallVector<User *, 16> Worklist;
3342 Value *Old = getValPtr();
3343 bool DeleteOld = false;
3344 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3346 Worklist.push_back(*UI);
3347 while (!Worklist.empty()) {
3348 User *U = Worklist.pop_back_val();
3349 // Deleting the Old value will cause this to dangle. Postpone
3350 // that until everything else is done.
3355 if (PHINode *PN = dyn_cast<PHINode>(U))
3356 SE->ConstantEvolutionLoopExitValue.erase(PN);
3357 if (SE->Scalars.erase(U))
3358 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3360 Worklist.push_back(*UI);
3363 if (PHINode *PN = dyn_cast<PHINode>(Old))
3364 SE->ConstantEvolutionLoopExitValue.erase(PN);
3365 SE->Scalars.erase(Old);
3366 // this now dangles!
3371 SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3372 : CallbackVH(V), SE(se) {}
3374 //===----------------------------------------------------------------------===//
3375 // ScalarEvolution Class Implementation
3376 //===----------------------------------------------------------------------===//
3378 ScalarEvolution::ScalarEvolution()
3379 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3382 bool ScalarEvolution::runOnFunction(Function &F) {
3384 LI = &getAnalysis<LoopInfo>();
3385 TD = getAnalysisIfAvailable<TargetData>();
3389 void ScalarEvolution::releaseMemory() {
3391 BackedgeTakenCounts.clear();
3392 ConstantEvolutionLoopExitValue.clear();
3395 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3396 AU.setPreservesAll();
3397 AU.addRequiredTransitive<LoopInfo>();
3400 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3401 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3404 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3406 // Print all inner loops first
3407 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3408 PrintLoopInfo(OS, SE, *I);
3410 OS << "Loop " << L->getHeader()->getName() << ": ";
3412 SmallVector<BasicBlock*, 8> ExitBlocks;
3413 L->getExitBlocks(ExitBlocks);
3414 if (ExitBlocks.size() != 1)
3415 OS << "<multiple exits> ";
3417 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3418 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3420 OS << "Unpredictable backedge-taken count. ";
3426 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3427 // ScalarEvolution's implementaiton of the print method is to print
3428 // out SCEV values of all instructions that are interesting. Doing
3429 // this potentially causes it to create new SCEV objects though,
3430 // which technically conflicts with the const qualifier. This isn't
3431 // observable from outside the class though (the hasSCEV function
3432 // notwithstanding), so casting away the const isn't dangerous.
3433 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3435 OS << "Classifying expressions for: " << F->getName() << "\n";
3436 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3437 if (isSCEVable(I->getType())) {
3440 SCEVHandle SV = SE.getSCEV(&*I);
3444 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3446 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3447 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3448 OS << "<<Unknown>>";
3458 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3459 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3460 PrintLoopInfo(OS, &SE, *I);
3463 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3464 raw_os_ostream OS(o);