1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Assembly/Writer.h"
71 #include "llvm/Transforms/Scalar.h"
72 #include "llvm/Support/CFG.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/InstIterator.h"
77 #include "llvm/Support/ManagedStatic.h"
78 #include "llvm/Support/MathExtras.h"
79 #include "llvm/Support/Streams.h"
80 #include "llvm/ADT/Statistic.h"
86 STATISTIC(NumArrayLenItCounts,
87 "Number of trip counts computed with array length");
88 STATISTIC(NumTripCountsComputed,
89 "Number of loops with predictable loop counts");
90 STATISTIC(NumTripCountsNotComputed,
91 "Number of loops without predictable loop counts");
92 STATISTIC(NumBruteForceTripCountsComputed,
93 "Number of loops with trip counts computed by force");
95 static cl::opt<unsigned>
96 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
97 cl::desc("Maximum number of iterations SCEV will "
98 "symbolically execute a constant derived loop"),
101 static RegisterPass<ScalarEvolution>
102 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
103 char ScalarEvolution::ID = 0;
105 //===----------------------------------------------------------------------===//
106 // SCEV class definitions
107 //===----------------------------------------------------------------------===//
109 //===----------------------------------------------------------------------===//
110 // Implementation of the SCEV class.
113 void SCEV::dump() const {
117 uint32_t SCEV::getBitWidth() const {
118 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
119 return ITy->getBitWidth();
123 bool SCEV::isZero() const {
124 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
125 return SC->getValue()->isZero();
130 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
132 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
133 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
137 const Type *SCEVCouldNotCompute::getType() const {
138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
142 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
147 SCEVHandle SCEVCouldNotCompute::
148 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
149 const SCEVHandle &Conc,
150 ScalarEvolution &SE) const {
154 void SCEVCouldNotCompute::print(std::ostream &OS) const {
155 OS << "***COULDNOTCOMPUTE***";
158 bool SCEVCouldNotCompute::classof(const SCEV *S) {
159 return S->getSCEVType() == scCouldNotCompute;
163 // SCEVConstants - Only allow the creation of one SCEVConstant for any
164 // particular value. Don't use a SCEVHandle here, or else the object will
166 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
169 SCEVConstant::~SCEVConstant() {
170 SCEVConstants->erase(V);
173 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
174 SCEVConstant *&R = (*SCEVConstants)[V];
175 if (R == 0) R = new SCEVConstant(V);
179 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
180 return getConstant(ConstantInt::get(Val));
183 const Type *SCEVConstant::getType() const { return V->getType(); }
185 void SCEVConstant::print(std::ostream &OS) const {
186 WriteAsOperand(OS, V, false);
189 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
190 // particular input. Don't use a SCEVHandle here, or else the object will
192 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
193 SCEVTruncateExpr*> > SCEVTruncates;
195 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
196 : SCEV(scTruncate), Op(op), Ty(ty) {
197 assert(Op->getType()->isInteger() && Ty->isInteger() &&
198 "Cannot truncate non-integer value!");
199 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
200 && "This is not a truncating conversion!");
203 SCEVTruncateExpr::~SCEVTruncateExpr() {
204 SCEVTruncates->erase(std::make_pair(Op, Ty));
207 void SCEVTruncateExpr::print(std::ostream &OS) const {
208 OS << "(truncate " << *Op << " to " << *Ty << ")";
211 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
212 // particular input. Don't use a SCEVHandle here, or else the object will never
214 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
215 SCEVZeroExtendExpr*> > SCEVZeroExtends;
217 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
218 : SCEV(scZeroExtend), Op(op), Ty(ty) {
219 assert(Op->getType()->isInteger() && Ty->isInteger() &&
220 "Cannot zero extend non-integer value!");
221 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
222 && "This is not an extending conversion!");
225 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
226 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
229 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
230 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
233 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
234 // particular input. Don't use a SCEVHandle here, or else the object will never
236 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
237 SCEVSignExtendExpr*> > SCEVSignExtends;
239 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
240 : SCEV(scSignExtend), Op(op), Ty(ty) {
241 assert(Op->getType()->isInteger() && Ty->isInteger() &&
242 "Cannot sign extend non-integer value!");
243 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
244 && "This is not an extending conversion!");
247 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
248 SCEVSignExtends->erase(std::make_pair(Op, Ty));
251 void SCEVSignExtendExpr::print(std::ostream &OS) const {
252 OS << "(signextend " << *Op << " to " << *Ty << ")";
255 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
256 // particular input. Don't use a SCEVHandle here, or else the object will never
258 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
259 SCEVCommutativeExpr*> > SCEVCommExprs;
261 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
262 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
263 std::vector<SCEV*>(Operands.begin(),
267 void SCEVCommutativeExpr::print(std::ostream &OS) const {
268 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
269 const char *OpStr = getOperationStr();
270 OS << "(" << *Operands[0];
271 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
272 OS << OpStr << *Operands[i];
276 SCEVHandle SCEVCommutativeExpr::
277 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
278 const SCEVHandle &Conc,
279 ScalarEvolution &SE) const {
280 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
282 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
283 if (H != getOperand(i)) {
284 std::vector<SCEVHandle> NewOps;
285 NewOps.reserve(getNumOperands());
286 for (unsigned j = 0; j != i; ++j)
287 NewOps.push_back(getOperand(j));
289 for (++i; i != e; ++i)
290 NewOps.push_back(getOperand(i)->
291 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
293 if (isa<SCEVAddExpr>(this))
294 return SE.getAddExpr(NewOps);
295 else if (isa<SCEVMulExpr>(this))
296 return SE.getMulExpr(NewOps);
297 else if (isa<SCEVSMaxExpr>(this))
298 return SE.getSMaxExpr(NewOps);
299 else if (isa<SCEVUMaxExpr>(this))
300 return SE.getUMaxExpr(NewOps);
302 assert(0 && "Unknown commutative expr!");
309 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
310 // input. Don't use a SCEVHandle here, or else the object will never be
312 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
313 SCEVUDivExpr*> > SCEVUDivs;
315 SCEVUDivExpr::~SCEVUDivExpr() {
316 SCEVUDivs->erase(std::make_pair(LHS, RHS));
319 void SCEVUDivExpr::print(std::ostream &OS) const {
320 OS << "(" << *LHS << " /u " << *RHS << ")";
323 const Type *SCEVUDivExpr::getType() const {
324 return LHS->getType();
327 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
328 // particular input. Don't use a SCEVHandle here, or else the object will never
330 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
331 SCEVAddRecExpr*> > SCEVAddRecExprs;
333 SCEVAddRecExpr::~SCEVAddRecExpr() {
334 SCEVAddRecExprs->erase(std::make_pair(L,
335 std::vector<SCEV*>(Operands.begin(),
339 SCEVHandle SCEVAddRecExpr::
340 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
341 const SCEVHandle &Conc,
342 ScalarEvolution &SE) const {
343 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
345 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
346 if (H != getOperand(i)) {
347 std::vector<SCEVHandle> NewOps;
348 NewOps.reserve(getNumOperands());
349 for (unsigned j = 0; j != i; ++j)
350 NewOps.push_back(getOperand(j));
352 for (++i; i != e; ++i)
353 NewOps.push_back(getOperand(i)->
354 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
356 return SE.getAddRecExpr(NewOps, L);
363 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
364 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
365 // contain L and if the start is invariant.
366 return !QueryLoop->contains(L->getHeader()) &&
367 getOperand(0)->isLoopInvariant(QueryLoop);
371 void SCEVAddRecExpr::print(std::ostream &OS) const {
372 OS << "{" << *Operands[0];
373 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
374 OS << ",+," << *Operands[i];
375 OS << "}<" << L->getHeader()->getName() + ">";
378 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
379 // value. Don't use a SCEVHandle here, or else the object will never be
381 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
383 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
385 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
386 // All non-instruction values are loop invariant. All instructions are loop
387 // invariant if they are not contained in the specified loop.
388 if (Instruction *I = dyn_cast<Instruction>(V))
389 return !L->contains(I->getParent());
393 const Type *SCEVUnknown::getType() const {
397 void SCEVUnknown::print(std::ostream &OS) const {
398 WriteAsOperand(OS, V, false);
401 //===----------------------------------------------------------------------===//
403 //===----------------------------------------------------------------------===//
406 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
407 /// than the complexity of the RHS. This comparator is used to canonicalize
409 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
410 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
411 return LHS->getSCEVType() < RHS->getSCEVType();
416 /// GroupByComplexity - Given a list of SCEV objects, order them by their
417 /// complexity, and group objects of the same complexity together by value.
418 /// When this routine is finished, we know that any duplicates in the vector are
419 /// consecutive and that complexity is monotonically increasing.
421 /// Note that we go take special precautions to ensure that we get determinstic
422 /// results from this routine. In other words, we don't want the results of
423 /// this to depend on where the addresses of various SCEV objects happened to
426 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
427 if (Ops.size() < 2) return; // Noop
428 if (Ops.size() == 2) {
429 // This is the common case, which also happens to be trivially simple.
431 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
432 std::swap(Ops[0], Ops[1]);
436 // Do the rough sort by complexity.
437 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
439 // Now that we are sorted by complexity, group elements of the same
440 // complexity. Note that this is, at worst, N^2, but the vector is likely to
441 // be extremely short in practice. Note that we take this approach because we
442 // do not want to depend on the addresses of the objects we are grouping.
443 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
445 unsigned Complexity = S->getSCEVType();
447 // If there are any objects of the same complexity and same value as this
449 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
450 if (Ops[j] == S) { // Found a duplicate.
451 // Move it to immediately after i'th element.
452 std::swap(Ops[i+1], Ops[j]);
453 ++i; // no need to rescan it.
454 if (i == e-2) return; // Done!
462 //===----------------------------------------------------------------------===//
463 // Simple SCEV method implementations
464 //===----------------------------------------------------------------------===//
466 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
467 /// specified signed integer value and return a SCEV for the constant.
468 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
471 C = Constant::getNullValue(Ty);
472 else if (Ty->isFloatingPoint())
473 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
474 APFloat::IEEEdouble, Val));
476 C = ConstantInt::get(Ty, Val);
477 return getUnknown(C);
480 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
482 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
483 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
484 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
486 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType())));
489 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
490 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
491 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
492 return getUnknown(ConstantExpr::getNot(VC->getValue()));
494 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType()));
495 return getMinusSCEV(AllOnes, V);
498 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
500 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
501 const SCEVHandle &RHS) {
503 return getAddExpr(LHS, getNegativeSCEV(RHS));
507 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
509 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
511 const IntegerType* ResultTy) {
512 // Handle the simplest case efficiently.
514 return SE.getTruncateOrZeroExtend(It, ResultTy);
516 // We are using the following formula for BC(It, K):
518 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
520 // Suppose, W is the bitwidth of the return value. We must be prepared for
521 // overflow. Hence, we must assure that the result of our computation is
522 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
523 // safe in modular arithmetic.
525 // However, this code doesn't use exactly that formula; the formula it uses
526 // is something like the following, where T is the number of factors of 2 in
527 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
530 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
532 // This formula is trivially equivalent to the previous formula. However,
533 // this formula can be implemented much more efficiently. The trick is that
534 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
535 // arithmetic. To do exact division in modular arithmetic, all we have
536 // to do is multiply by the inverse. Therefore, this step can be done at
539 // The next issue is how to safely do the division by 2^T. The way this
540 // is done is by doing the multiplication step at a width of at least W + T
541 // bits. This way, the bottom W+T bits of the product are accurate. Then,
542 // when we perform the division by 2^T (which is equivalent to a right shift
543 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
544 // truncated out after the division by 2^T.
546 // In comparison to just directly using the first formula, this technique
547 // is much more efficient; using the first formula requires W * K bits,
548 // but this formula less than W + K bits. Also, the first formula requires
549 // a division step, whereas this formula only requires multiplies and shifts.
551 // It doesn't matter whether the subtraction step is done in the calculation
552 // width or the input iteration count's width; if the subtraction overflows,
553 // the result must be zero anyway. We prefer here to do it in the width of
554 // the induction variable because it helps a lot for certain cases; CodeGen
555 // isn't smart enough to ignore the overflow, which leads to much less
556 // efficient code if the width of the subtraction is wider than the native
559 // (It's possible to not widen at all by pulling out factors of 2 before
560 // the multiplication; for example, K=2 can be calculated as
561 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
562 // extra arithmetic, so it's not an obvious win, and it gets
563 // much more complicated for K > 3.)
565 // Protection from insane SCEVs; this bound is conservative,
566 // but it probably doesn't matter.
568 return new SCEVCouldNotCompute();
570 unsigned W = ResultTy->getBitWidth();
572 // Calculate K! / 2^T and T; we divide out the factors of two before
573 // multiplying for calculating K! / 2^T to avoid overflow.
574 // Other overflow doesn't matter because we only care about the bottom
575 // W bits of the result.
576 APInt OddFactorial(W, 1);
578 for (unsigned i = 3; i <= K; ++i) {
580 unsigned TwoFactors = Mult.countTrailingZeros();
582 Mult = Mult.lshr(TwoFactors);
583 OddFactorial *= Mult;
586 // We need at least W + T bits for the multiplication step
587 // FIXME: A temporary hack; we round up the bitwidths
588 // to the nearest power of 2 to be nice to the code generator.
589 unsigned CalculationBits = 1U << Log2_32_Ceil(W + T);
590 // FIXME: Temporary hack to avoid generating integers that are too wide.
591 // Although, it's not completely clear how to determine how much
592 // widening is safe; for example, on X86, we can't really widen
593 // beyond 64 because we need to be able to do multiplication
594 // that's CalculationBits wide, but on X86-64, we can safely widen up to
596 if (CalculationBits > 64)
597 return new SCEVCouldNotCompute();
599 // Calcuate 2^T, at width T+W.
600 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
602 // Calculate the multiplicative inverse of K! / 2^T;
603 // this multiplication factor will perform the exact division by
605 APInt Mod = APInt::getSignedMinValue(W+1);
606 APInt MultiplyFactor = OddFactorial.zext(W+1);
607 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
608 MultiplyFactor = MultiplyFactor.trunc(W);
610 // Calculate the product, at width T+W
611 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
612 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
613 for (unsigned i = 1; i != K; ++i) {
614 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
615 Dividend = SE.getMulExpr(Dividend,
616 SE.getTruncateOrZeroExtend(S, CalculationTy));
620 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
622 // Truncate the result, and divide by K! / 2^T.
624 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
625 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
628 /// evaluateAtIteration - Return the value of this chain of recurrences at
629 /// the specified iteration number. We can evaluate this recurrence by
630 /// multiplying each element in the chain by the binomial coefficient
631 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
633 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
635 /// where BC(It, k) stands for binomial coefficient.
637 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
638 ScalarEvolution &SE) const {
639 SCEVHandle Result = getStart();
640 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
641 // The computation is correct in the face of overflow provided that the
642 // multiplication is performed _after_ the evaluation of the binomial
644 SCEVHandle Coeff = BinomialCoefficient(It, i, SE,
645 cast<IntegerType>(getType()));
646 if (isa<SCEVCouldNotCompute>(Coeff))
649 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
654 //===----------------------------------------------------------------------===//
655 // SCEV Expression folder implementations
656 //===----------------------------------------------------------------------===//
658 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
659 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
661 ConstantExpr::getTrunc(SC->getValue(), Ty));
663 // If the input value is a chrec scev made out of constants, truncate
664 // all of the constants.
665 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
666 std::vector<SCEVHandle> Operands;
667 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
668 // FIXME: This should allow truncation of other expression types!
669 if (isa<SCEVConstant>(AddRec->getOperand(i)))
670 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
673 if (Operands.size() == AddRec->getNumOperands())
674 return getAddRecExpr(Operands, AddRec->getLoop());
677 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
678 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
682 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) {
683 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
685 ConstantExpr::getZExt(SC->getValue(), Ty));
687 // FIXME: If the input value is a chrec scev, and we can prove that the value
688 // did not overflow the old, smaller, value, we can zero extend all of the
689 // operands (often constants). This would allow analysis of something like
690 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
692 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
693 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
697 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
698 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
700 ConstantExpr::getSExt(SC->getValue(), Ty));
702 // FIXME: If the input value is a chrec scev, and we can prove that the value
703 // did not overflow the old, smaller, value, we can sign extend all of the
704 // operands (often constants). This would allow analysis of something like
705 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
707 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
708 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
712 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
713 /// of the input value to the specified type. If the type must be
714 /// extended, it is zero extended.
715 SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
717 const Type *SrcTy = V->getType();
718 assert(SrcTy->isInteger() && Ty->isInteger() &&
719 "Cannot truncate or zero extend with non-integer arguments!");
720 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
721 return V; // No conversion
722 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
723 return getTruncateExpr(V, Ty);
724 return getZeroExtendExpr(V, Ty);
727 // get - Get a canonical add expression, or something simpler if possible.
728 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
729 assert(!Ops.empty() && "Cannot get empty add!");
730 if (Ops.size() == 1) return Ops[0];
732 // Sort by complexity, this groups all similar expression types together.
733 GroupByComplexity(Ops);
735 // If there are any constants, fold them together.
737 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
739 assert(Idx < Ops.size());
740 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
741 // We found two constants, fold them together!
742 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
743 RHSC->getValue()->getValue());
744 Ops[0] = getConstant(Fold);
745 Ops.erase(Ops.begin()+1); // Erase the folded element
746 if (Ops.size() == 1) return Ops[0];
747 LHSC = cast<SCEVConstant>(Ops[0]);
750 // If we are left with a constant zero being added, strip it off.
751 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
752 Ops.erase(Ops.begin());
757 if (Ops.size() == 1) return Ops[0];
759 // Okay, check to see if the same value occurs in the operand list twice. If
760 // so, merge them together into an multiply expression. Since we sorted the
761 // list, these values are required to be adjacent.
762 const Type *Ty = Ops[0]->getType();
763 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
764 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
765 // Found a match, merge the two values into a multiply, and add any
766 // remaining values to the result.
767 SCEVHandle Two = getIntegerSCEV(2, Ty);
768 SCEVHandle Mul = getMulExpr(Ops[i], Two);
771 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
773 return getAddExpr(Ops);
776 // Now we know the first non-constant operand. Skip past any cast SCEVs.
777 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
780 // If there are add operands they would be next.
781 if (Idx < Ops.size()) {
782 bool DeletedAdd = false;
783 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
784 // If we have an add, expand the add operands onto the end of the operands
786 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
787 Ops.erase(Ops.begin()+Idx);
791 // If we deleted at least one add, we added operands to the end of the list,
792 // and they are not necessarily sorted. Recurse to resort and resimplify
793 // any operands we just aquired.
795 return getAddExpr(Ops);
798 // Skip over the add expression until we get to a multiply.
799 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
802 // If we are adding something to a multiply expression, make sure the
803 // something is not already an operand of the multiply. If so, merge it into
805 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
806 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
807 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
808 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
809 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
810 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
811 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
812 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
813 if (Mul->getNumOperands() != 2) {
814 // If the multiply has more than two operands, we must get the
816 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
817 MulOps.erase(MulOps.begin()+MulOp);
818 InnerMul = getMulExpr(MulOps);
820 SCEVHandle One = getIntegerSCEV(1, Ty);
821 SCEVHandle AddOne = getAddExpr(InnerMul, One);
822 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
823 if (Ops.size() == 2) return OuterMul;
825 Ops.erase(Ops.begin()+AddOp);
826 Ops.erase(Ops.begin()+Idx-1);
828 Ops.erase(Ops.begin()+Idx);
829 Ops.erase(Ops.begin()+AddOp-1);
831 Ops.push_back(OuterMul);
832 return getAddExpr(Ops);
835 // Check this multiply against other multiplies being added together.
836 for (unsigned OtherMulIdx = Idx+1;
837 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
839 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
840 // If MulOp occurs in OtherMul, we can fold the two multiplies
842 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
843 OMulOp != e; ++OMulOp)
844 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
845 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
846 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
847 if (Mul->getNumOperands() != 2) {
848 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
849 MulOps.erase(MulOps.begin()+MulOp);
850 InnerMul1 = getMulExpr(MulOps);
852 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
853 if (OtherMul->getNumOperands() != 2) {
854 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
856 MulOps.erase(MulOps.begin()+OMulOp);
857 InnerMul2 = getMulExpr(MulOps);
859 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
860 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
861 if (Ops.size() == 2) return OuterMul;
862 Ops.erase(Ops.begin()+Idx);
863 Ops.erase(Ops.begin()+OtherMulIdx-1);
864 Ops.push_back(OuterMul);
865 return getAddExpr(Ops);
871 // If there are any add recurrences in the operands list, see if any other
872 // added values are loop invariant. If so, we can fold them into the
874 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
877 // Scan over all recurrences, trying to fold loop invariants into them.
878 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
879 // Scan all of the other operands to this add and add them to the vector if
880 // they are loop invariant w.r.t. the recurrence.
881 std::vector<SCEVHandle> LIOps;
882 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
883 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
884 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
885 LIOps.push_back(Ops[i]);
886 Ops.erase(Ops.begin()+i);
890 // If we found some loop invariants, fold them into the recurrence.
891 if (!LIOps.empty()) {
892 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
893 LIOps.push_back(AddRec->getStart());
895 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
896 AddRecOps[0] = getAddExpr(LIOps);
898 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
899 // If all of the other operands were loop invariant, we are done.
900 if (Ops.size() == 1) return NewRec;
902 // Otherwise, add the folded AddRec by the non-liv parts.
903 for (unsigned i = 0;; ++i)
904 if (Ops[i] == AddRec) {
908 return getAddExpr(Ops);
911 // Okay, if there weren't any loop invariants to be folded, check to see if
912 // there are multiple AddRec's with the same loop induction variable being
913 // added together. If so, we can fold them.
914 for (unsigned OtherIdx = Idx+1;
915 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
916 if (OtherIdx != Idx) {
917 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
918 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
919 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
920 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
921 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
922 if (i >= NewOps.size()) {
923 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
924 OtherAddRec->op_end());
927 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
929 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
931 if (Ops.size() == 2) return NewAddRec;
933 Ops.erase(Ops.begin()+Idx);
934 Ops.erase(Ops.begin()+OtherIdx-1);
935 Ops.push_back(NewAddRec);
936 return getAddExpr(Ops);
940 // Otherwise couldn't fold anything into this recurrence. Move onto the
944 // Okay, it looks like we really DO need an add expr. Check to see if we
945 // already have one, otherwise create a new one.
946 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
947 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
949 if (Result == 0) Result = new SCEVAddExpr(Ops);
954 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
955 assert(!Ops.empty() && "Cannot get empty mul!");
957 // Sort by complexity, this groups all similar expression types together.
958 GroupByComplexity(Ops);
960 // If there are any constants, fold them together.
962 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
964 // C1*(C2+V) -> C1*C2 + C1*V
966 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
967 if (Add->getNumOperands() == 2 &&
968 isa<SCEVConstant>(Add->getOperand(0)))
969 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
970 getMulExpr(LHSC, Add->getOperand(1)));
974 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
975 // We found two constants, fold them together!
976 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
977 RHSC->getValue()->getValue());
978 Ops[0] = getConstant(Fold);
979 Ops.erase(Ops.begin()+1); // Erase the folded element
980 if (Ops.size() == 1) return Ops[0];
981 LHSC = cast<SCEVConstant>(Ops[0]);
984 // If we are left with a constant one being multiplied, strip it off.
985 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
986 Ops.erase(Ops.begin());
988 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
989 // If we have a multiply of zero, it will always be zero.
994 // Skip over the add expression until we get to a multiply.
995 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1001 // If there are mul operands inline them all into this expression.
1002 if (Idx < Ops.size()) {
1003 bool DeletedMul = false;
1004 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1005 // If we have an mul, expand the mul operands onto the end of the operands
1007 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1008 Ops.erase(Ops.begin()+Idx);
1012 // If we deleted at least one mul, we added operands to the end of the list,
1013 // and they are not necessarily sorted. Recurse to resort and resimplify
1014 // any operands we just aquired.
1016 return getMulExpr(Ops);
1019 // If there are any add recurrences in the operands list, see if any other
1020 // added values are loop invariant. If so, we can fold them into the
1022 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1025 // Scan over all recurrences, trying to fold loop invariants into them.
1026 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1027 // Scan all of the other operands to this mul and add them to the vector if
1028 // they are loop invariant w.r.t. the recurrence.
1029 std::vector<SCEVHandle> LIOps;
1030 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1031 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1032 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1033 LIOps.push_back(Ops[i]);
1034 Ops.erase(Ops.begin()+i);
1038 // If we found some loop invariants, fold them into the recurrence.
1039 if (!LIOps.empty()) {
1040 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1041 std::vector<SCEVHandle> NewOps;
1042 NewOps.reserve(AddRec->getNumOperands());
1043 if (LIOps.size() == 1) {
1044 SCEV *Scale = LIOps[0];
1045 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1046 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1048 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1049 std::vector<SCEVHandle> MulOps(LIOps);
1050 MulOps.push_back(AddRec->getOperand(i));
1051 NewOps.push_back(getMulExpr(MulOps));
1055 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1057 // If all of the other operands were loop invariant, we are done.
1058 if (Ops.size() == 1) return NewRec;
1060 // Otherwise, multiply the folded AddRec by the non-liv parts.
1061 for (unsigned i = 0;; ++i)
1062 if (Ops[i] == AddRec) {
1066 return getMulExpr(Ops);
1069 // Okay, if there weren't any loop invariants to be folded, check to see if
1070 // there are multiple AddRec's with the same loop induction variable being
1071 // multiplied together. If so, we can fold them.
1072 for (unsigned OtherIdx = Idx+1;
1073 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1074 if (OtherIdx != Idx) {
1075 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1076 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1077 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1078 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1079 SCEVHandle NewStart = getMulExpr(F->getStart(),
1081 SCEVHandle B = F->getStepRecurrence(*this);
1082 SCEVHandle D = G->getStepRecurrence(*this);
1083 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1086 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1088 if (Ops.size() == 2) return NewAddRec;
1090 Ops.erase(Ops.begin()+Idx);
1091 Ops.erase(Ops.begin()+OtherIdx-1);
1092 Ops.push_back(NewAddRec);
1093 return getMulExpr(Ops);
1097 // Otherwise couldn't fold anything into this recurrence. Move onto the
1101 // Okay, it looks like we really DO need an mul expr. Check to see if we
1102 // already have one, otherwise create a new one.
1103 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1104 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1107 Result = new SCEVMulExpr(Ops);
1111 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1112 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1113 if (RHSC->getValue()->equalsInt(1))
1114 return LHS; // X udiv 1 --> x
1116 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1117 Constant *LHSCV = LHSC->getValue();
1118 Constant *RHSCV = RHSC->getValue();
1119 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1123 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1125 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1126 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1131 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1132 /// specified loop. Simplify the expression as much as possible.
1133 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1134 const SCEVHandle &Step, const Loop *L) {
1135 std::vector<SCEVHandle> Operands;
1136 Operands.push_back(Start);
1137 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1138 if (StepChrec->getLoop() == L) {
1139 Operands.insert(Operands.end(), StepChrec->op_begin(),
1140 StepChrec->op_end());
1141 return getAddRecExpr(Operands, L);
1144 Operands.push_back(Step);
1145 return getAddRecExpr(Operands, L);
1148 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1149 /// specified loop. Simplify the expression as much as possible.
1150 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1152 if (Operands.size() == 1) return Operands[0];
1154 if (Operands.back()->isZero()) {
1155 Operands.pop_back();
1156 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1159 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1160 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1161 const Loop* NestedLoop = NestedAR->getLoop();
1162 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1163 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1164 NestedAR->op_end());
1165 SCEVHandle NestedARHandle(NestedAR);
1166 Operands[0] = NestedAR->getStart();
1167 NestedOperands[0] = getAddRecExpr(Operands, L);
1168 return getAddRecExpr(NestedOperands, NestedLoop);
1172 SCEVAddRecExpr *&Result =
1173 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1175 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1179 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1180 const SCEVHandle &RHS) {
1181 std::vector<SCEVHandle> Ops;
1184 return getSMaxExpr(Ops);
1187 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1188 assert(!Ops.empty() && "Cannot get empty smax!");
1189 if (Ops.size() == 1) return Ops[0];
1191 // Sort by complexity, this groups all similar expression types together.
1192 GroupByComplexity(Ops);
1194 // If there are any constants, fold them together.
1196 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1198 assert(Idx < Ops.size());
1199 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1200 // We found two constants, fold them together!
1201 ConstantInt *Fold = ConstantInt::get(
1202 APIntOps::smax(LHSC->getValue()->getValue(),
1203 RHSC->getValue()->getValue()));
1204 Ops[0] = getConstant(Fold);
1205 Ops.erase(Ops.begin()+1); // Erase the folded element
1206 if (Ops.size() == 1) return Ops[0];
1207 LHSC = cast<SCEVConstant>(Ops[0]);
1210 // If we are left with a constant -inf, strip it off.
1211 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1212 Ops.erase(Ops.begin());
1217 if (Ops.size() == 1) return Ops[0];
1219 // Find the first SMax
1220 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1223 // Check to see if one of the operands is an SMax. If so, expand its operands
1224 // onto our operand list, and recurse to simplify.
1225 if (Idx < Ops.size()) {
1226 bool DeletedSMax = false;
1227 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1228 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1229 Ops.erase(Ops.begin()+Idx);
1234 return getSMaxExpr(Ops);
1237 // Okay, check to see if the same value occurs in the operand list twice. If
1238 // so, delete one. Since we sorted the list, these values are required to
1240 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1241 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1242 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1246 if (Ops.size() == 1) return Ops[0];
1248 assert(!Ops.empty() && "Reduced smax down to nothing!");
1250 // Okay, it looks like we really DO need an smax expr. Check to see if we
1251 // already have one, otherwise create a new one.
1252 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1253 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1255 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1259 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1260 const SCEVHandle &RHS) {
1261 std::vector<SCEVHandle> Ops;
1264 return getUMaxExpr(Ops);
1267 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1268 assert(!Ops.empty() && "Cannot get empty umax!");
1269 if (Ops.size() == 1) return Ops[0];
1271 // Sort by complexity, this groups all similar expression types together.
1272 GroupByComplexity(Ops);
1274 // If there are any constants, fold them together.
1276 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1278 assert(Idx < Ops.size());
1279 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1280 // We found two constants, fold them together!
1281 ConstantInt *Fold = ConstantInt::get(
1282 APIntOps::umax(LHSC->getValue()->getValue(),
1283 RHSC->getValue()->getValue()));
1284 Ops[0] = getConstant(Fold);
1285 Ops.erase(Ops.begin()+1); // Erase the folded element
1286 if (Ops.size() == 1) return Ops[0];
1287 LHSC = cast<SCEVConstant>(Ops[0]);
1290 // If we are left with a constant zero, strip it off.
1291 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1292 Ops.erase(Ops.begin());
1297 if (Ops.size() == 1) return Ops[0];
1299 // Find the first UMax
1300 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1303 // Check to see if one of the operands is a UMax. If so, expand its operands
1304 // onto our operand list, and recurse to simplify.
1305 if (Idx < Ops.size()) {
1306 bool DeletedUMax = false;
1307 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1308 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1309 Ops.erase(Ops.begin()+Idx);
1314 return getUMaxExpr(Ops);
1317 // Okay, check to see if the same value occurs in the operand list twice. If
1318 // so, delete one. Since we sorted the list, these values are required to
1320 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1321 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1322 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1326 if (Ops.size() == 1) return Ops[0];
1328 assert(!Ops.empty() && "Reduced umax down to nothing!");
1330 // Okay, it looks like we really DO need a umax expr. Check to see if we
1331 // already have one, otherwise create a new one.
1332 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1333 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1335 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1339 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1340 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1341 return getConstant(CI);
1342 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1343 if (Result == 0) Result = new SCEVUnknown(V);
1348 //===----------------------------------------------------------------------===//
1349 // ScalarEvolutionsImpl Definition and Implementation
1350 //===----------------------------------------------------------------------===//
1352 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1356 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1357 /// SE - A reference to the public ScalarEvolution object.
1358 ScalarEvolution &SE;
1360 /// F - The function we are analyzing.
1364 /// LI - The loop information for the function we are currently analyzing.
1368 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1370 SCEVHandle UnknownValue;
1372 /// Scalars - This is a cache of the scalars we have analyzed so far.
1374 std::map<Value*, SCEVHandle> Scalars;
1376 /// IterationCounts - Cache the iteration count of the loops for this
1377 /// function as they are computed.
1378 std::map<const Loop*, SCEVHandle> IterationCounts;
1380 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1381 /// the PHI instructions that we attempt to compute constant evolutions for.
1382 /// This allows us to avoid potentially expensive recomputation of these
1383 /// properties. An instruction maps to null if we are unable to compute its
1385 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1388 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li)
1389 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1391 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1392 /// expression and create a new one.
1393 SCEVHandle getSCEV(Value *V);
1395 /// hasSCEV - Return true if the SCEV for this value has already been
1397 bool hasSCEV(Value *V) const {
1398 return Scalars.count(V);
1401 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1402 /// the specified value.
1403 void setSCEV(Value *V, const SCEVHandle &H) {
1404 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1405 assert(isNew && "This entry already existed!");
1410 /// getSCEVAtScope - Compute the value of the specified expression within
1411 /// the indicated loop (which may be null to indicate in no loop). If the
1412 /// expression cannot be evaluated, return UnknownValue itself.
1413 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1416 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1417 /// an analyzable loop-invariant iteration count.
1418 bool hasLoopInvariantIterationCount(const Loop *L);
1420 /// getIterationCount - If the specified loop has a predictable iteration
1421 /// count, return it. Note that it is not valid to call this method on a
1422 /// loop without a loop-invariant iteration count.
1423 SCEVHandle getIterationCount(const Loop *L);
1425 /// deleteValueFromRecords - This method should be called by the
1426 /// client before it removes a value from the program, to make sure
1427 /// that no dangling references are left around.
1428 void deleteValueFromRecords(Value *V);
1431 /// createSCEV - We know that there is no SCEV for the specified value.
1432 /// Analyze the expression.
1433 SCEVHandle createSCEV(Value *V);
1435 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1437 SCEVHandle createNodeForPHI(PHINode *PN);
1439 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1440 /// for the specified instruction and replaces any references to the
1441 /// symbolic value SymName with the specified value. This is used during
1443 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1444 const SCEVHandle &SymName,
1445 const SCEVHandle &NewVal);
1447 /// ComputeIterationCount - Compute the number of times the specified loop
1449 SCEVHandle ComputeIterationCount(const Loop *L);
1451 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1452 /// 'icmp op load X, cst', try to see if we can compute the trip count.
1453 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1456 ICmpInst::Predicate p);
1458 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1459 /// constant number of times (the condition evolves only from constants),
1460 /// try to evaluate a few iterations of the loop until we get the exit
1461 /// condition gets a value of ExitWhen (true or false). If we cannot
1462 /// evaluate the trip count of the loop, return UnknownValue.
1463 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1466 /// HowFarToZero - Return the number of times a backedge comparing the
1467 /// specified value to zero will execute. If not computable, return
1469 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1471 /// HowFarToNonZero - Return the number of times a backedge checking the
1472 /// specified value for nonzero will execute. If not computable, return
1474 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1476 /// HowManyLessThans - Return the number of times a backedge containing the
1477 /// specified less-than comparison will execute. If not computable, return
1478 /// UnknownValue. isSigned specifies whether the less-than is signed.
1479 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1480 bool isSigned, bool trueWhenEqual);
1482 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
1483 /// (which may not be an immediate predecessor) which has exactly one
1484 /// successor from which BB is reachable, or null if no such block is
1486 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1488 /// executesAtLeastOnce - Test whether entry to the loop is protected by
1489 /// a conditional between LHS and RHS.
1490 bool executesAtLeastOnce(const Loop *L, bool isSigned, bool trueWhenEqual,
1491 SCEV *LHS, SCEV *RHS);
1493 /// potentialInfiniteLoop - Test whether the loop might jump over the exit value
1494 /// due to wrapping.
1495 bool potentialInfiniteLoop(SCEV *Stride, SCEV *RHS, bool isSigned,
1496 bool trueWhenEqual);
1498 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1499 /// in the header of its containing loop, we know the loop executes a
1500 /// constant number of times, and the PHI node is just a recurrence
1501 /// involving constants, fold it.
1502 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1507 //===----------------------------------------------------------------------===//
1508 // Basic SCEV Analysis and PHI Idiom Recognition Code
1511 /// deleteValueFromRecords - This method should be called by the
1512 /// client before it removes an instruction from the program, to make sure
1513 /// that no dangling references are left around.
1514 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1515 SmallVector<Value *, 16> Worklist;
1517 if (Scalars.erase(V)) {
1518 if (PHINode *PN = dyn_cast<PHINode>(V))
1519 ConstantEvolutionLoopExitValue.erase(PN);
1520 Worklist.push_back(V);
1523 while (!Worklist.empty()) {
1524 Value *VV = Worklist.back();
1525 Worklist.pop_back();
1527 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1529 Instruction *Inst = cast<Instruction>(*UI);
1530 if (Scalars.erase(Inst)) {
1531 if (PHINode *PN = dyn_cast<PHINode>(VV))
1532 ConstantEvolutionLoopExitValue.erase(PN);
1533 Worklist.push_back(Inst);
1540 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1541 /// expression and create a new one.
1542 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1543 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1545 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1546 if (I != Scalars.end()) return I->second;
1547 SCEVHandle S = createSCEV(V);
1548 Scalars.insert(std::make_pair(V, S));
1552 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1553 /// the specified instruction and replaces any references to the symbolic value
1554 /// SymName with the specified value. This is used during PHI resolution.
1555 void ScalarEvolutionsImpl::
1556 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1557 const SCEVHandle &NewVal) {
1558 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1559 if (SI == Scalars.end()) return;
1562 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
1563 if (NV == SI->second) return; // No change.
1565 SI->second = NV; // Update the scalars map!
1567 // Any instruction values that use this instruction might also need to be
1569 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1571 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1574 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1575 /// a loop header, making it a potential recurrence, or it doesn't.
1577 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1578 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1579 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1580 if (L->getHeader() == PN->getParent()) {
1581 // If it lives in the loop header, it has two incoming values, one
1582 // from outside the loop, and one from inside.
1583 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1584 unsigned BackEdge = IncomingEdge^1;
1586 // While we are analyzing this PHI node, handle its value symbolically.
1587 SCEVHandle SymbolicName = SE.getUnknown(PN);
1588 assert(Scalars.find(PN) == Scalars.end() &&
1589 "PHI node already processed?");
1590 Scalars.insert(std::make_pair(PN, SymbolicName));
1592 // Using this symbolic name for the PHI, analyze the value coming around
1594 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1596 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1597 // has a special value for the first iteration of the loop.
1599 // If the value coming around the backedge is an add with the symbolic
1600 // value we just inserted, then we found a simple induction variable!
1601 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1602 // If there is a single occurrence of the symbolic value, replace it
1603 // with a recurrence.
1604 unsigned FoundIndex = Add->getNumOperands();
1605 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1606 if (Add->getOperand(i) == SymbolicName)
1607 if (FoundIndex == e) {
1612 if (FoundIndex != Add->getNumOperands()) {
1613 // Create an add with everything but the specified operand.
1614 std::vector<SCEVHandle> Ops;
1615 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1616 if (i != FoundIndex)
1617 Ops.push_back(Add->getOperand(i));
1618 SCEVHandle Accum = SE.getAddExpr(Ops);
1620 // This is not a valid addrec if the step amount is varying each
1621 // loop iteration, but is not itself an addrec in this loop.
1622 if (Accum->isLoopInvariant(L) ||
1623 (isa<SCEVAddRecExpr>(Accum) &&
1624 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1625 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1626 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L);
1628 // Okay, for the entire analysis of this edge we assumed the PHI
1629 // to be symbolic. We now need to go back and update all of the
1630 // entries for the scalars that use the PHI (except for the PHI
1631 // itself) to use the new analyzed value instead of the "symbolic"
1633 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1637 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1638 // Otherwise, this could be a loop like this:
1639 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1640 // In this case, j = {1,+,1} and BEValue is j.
1641 // Because the other in-value of i (0) fits the evolution of BEValue
1642 // i really is an addrec evolution.
1643 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1644 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1646 // If StartVal = j.start - j.stride, we can use StartVal as the
1647 // initial step of the addrec evolution.
1648 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
1649 AddRec->getOperand(1))) {
1650 SCEVHandle PHISCEV =
1651 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1653 // Okay, for the entire analysis of this edge we assumed the PHI
1654 // to be symbolic. We now need to go back and update all of the
1655 // entries for the scalars that use the PHI (except for the PHI
1656 // itself) to use the new analyzed value instead of the "symbolic"
1658 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1664 return SymbolicName;
1667 // If it's not a loop phi, we can't handle it yet.
1668 return SE.getUnknown(PN);
1671 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1672 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1673 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1674 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1675 static uint32_t GetMinTrailingZeros(SCEVHandle S) {
1676 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1677 return C->getValue()->getValue().countTrailingZeros();
1679 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1680 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
1682 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1683 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1684 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1687 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1688 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1689 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1692 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1693 // The result is the min of all operands results.
1694 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1695 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1696 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1700 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1701 // The result is the sum of all operands results.
1702 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
1703 uint32_t BitWidth = M->getBitWidth();
1704 for (unsigned i = 1, e = M->getNumOperands();
1705 SumOpRes != BitWidth && i != e; ++i)
1706 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
1711 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1712 // The result is the min of all operands results.
1713 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1714 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1715 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1719 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1720 // The result is the min of all operands results.
1721 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1722 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1723 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1727 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1728 // The result is the min of all operands results.
1729 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1730 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1731 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1735 // SCEVUDivExpr, SCEVUnknown
1739 /// createSCEV - We know that there is no SCEV for the specified value.
1740 /// Analyze the expression.
1742 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1743 if (!isa<IntegerType>(V->getType()))
1744 return SE.getUnknown(V);
1746 unsigned Opcode = Instruction::UserOp1;
1747 if (Instruction *I = dyn_cast<Instruction>(V))
1748 Opcode = I->getOpcode();
1749 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1750 Opcode = CE->getOpcode();
1752 return SE.getUnknown(V);
1754 User *U = cast<User>(V);
1756 case Instruction::Add:
1757 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1758 getSCEV(U->getOperand(1)));
1759 case Instruction::Mul:
1760 return SE.getMulExpr(getSCEV(U->getOperand(0)),
1761 getSCEV(U->getOperand(1)));
1762 case Instruction::UDiv:
1763 return SE.getUDivExpr(getSCEV(U->getOperand(0)),
1764 getSCEV(U->getOperand(1)));
1765 case Instruction::Sub:
1766 return SE.getMinusSCEV(getSCEV(U->getOperand(0)),
1767 getSCEV(U->getOperand(1)));
1768 case Instruction::Or:
1769 // If the RHS of the Or is a constant, we may have something like:
1770 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1771 // optimizations will transparently handle this case.
1773 // In order for this transformation to be safe, the LHS must be of the
1774 // form X*(2^n) and the Or constant must be less than 2^n.
1775 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1776 SCEVHandle LHS = getSCEV(U->getOperand(0));
1777 const APInt &CIVal = CI->getValue();
1778 if (GetMinTrailingZeros(LHS) >=
1779 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1780 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1)));
1783 case Instruction::Xor:
1784 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1785 // If the RHS of the xor is a signbit, then this is just an add.
1786 // Instcombine turns add of signbit into xor as a strength reduction step.
1787 if (CI->getValue().isSignBit())
1788 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1789 getSCEV(U->getOperand(1)));
1791 // If the RHS of xor is -1, then this is a not operation.
1792 else if (CI->isAllOnesValue())
1793 return SE.getNotSCEV(getSCEV(U->getOperand(0)));
1797 case Instruction::Shl:
1798 // Turn shift left of a constant amount into a multiply.
1799 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1800 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1801 Constant *X = ConstantInt::get(
1802 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1803 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1807 case Instruction::LShr:
1808 // Turn logical shift right of a constant into a unsigned divide.
1809 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1810 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1811 Constant *X = ConstantInt::get(
1812 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1813 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1817 case Instruction::Trunc:
1818 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1820 case Instruction::ZExt:
1821 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1823 case Instruction::SExt:
1824 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1826 case Instruction::BitCast:
1827 // BitCasts are no-op casts so we just eliminate the cast.
1828 if (U->getType()->isInteger() &&
1829 U->getOperand(0)->getType()->isInteger())
1830 return getSCEV(U->getOperand(0));
1833 case Instruction::PHI:
1834 return createNodeForPHI(cast<PHINode>(U));
1836 case Instruction::Select:
1837 // This could be a smax or umax that was lowered earlier.
1838 // Try to recover it.
1839 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
1840 Value *LHS = ICI->getOperand(0);
1841 Value *RHS = ICI->getOperand(1);
1842 switch (ICI->getPredicate()) {
1843 case ICmpInst::ICMP_SLT:
1844 case ICmpInst::ICMP_SLE:
1845 std::swap(LHS, RHS);
1847 case ICmpInst::ICMP_SGT:
1848 case ICmpInst::ICMP_SGE:
1849 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1850 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1851 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1852 // ~smax(~x, ~y) == smin(x, y).
1853 return SE.getNotSCEV(SE.getSMaxExpr(
1854 SE.getNotSCEV(getSCEV(LHS)),
1855 SE.getNotSCEV(getSCEV(RHS))));
1857 case ICmpInst::ICMP_ULT:
1858 case ICmpInst::ICMP_ULE:
1859 std::swap(LHS, RHS);
1861 case ICmpInst::ICMP_UGT:
1862 case ICmpInst::ICMP_UGE:
1863 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1864 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
1865 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1866 // ~umax(~x, ~y) == umin(x, y)
1867 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
1868 SE.getNotSCEV(getSCEV(RHS))));
1875 default: // We cannot analyze this expression.
1879 return SE.getUnknown(V);
1884 //===----------------------------------------------------------------------===//
1885 // Iteration Count Computation Code
1888 /// getIterationCount - If the specified loop has a predictable iteration
1889 /// count, return it. Note that it is not valid to call this method on a
1890 /// loop without a loop-invariant iteration count.
1891 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1892 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1893 if (I == IterationCounts.end()) {
1894 SCEVHandle ItCount = ComputeIterationCount(L);
1895 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1896 if (ItCount != UnknownValue) {
1897 assert(ItCount->isLoopInvariant(L) &&
1898 "Computed trip count isn't loop invariant for loop!");
1899 ++NumTripCountsComputed;
1900 } else if (isa<PHINode>(L->getHeader()->begin())) {
1901 // Only count loops that have phi nodes as not being computable.
1902 ++NumTripCountsNotComputed;
1908 /// ComputeIterationCount - Compute the number of times the specified loop
1910 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1911 // If the loop has a non-one exit block count, we can't analyze it.
1912 SmallVector<BasicBlock*, 8> ExitBlocks;
1913 L->getExitBlocks(ExitBlocks);
1914 if (ExitBlocks.size() != 1) return UnknownValue;
1916 // Okay, there is one exit block. Try to find the condition that causes the
1917 // loop to be exited.
1918 BasicBlock *ExitBlock = ExitBlocks[0];
1920 BasicBlock *ExitingBlock = 0;
1921 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1923 if (L->contains(*PI)) {
1924 if (ExitingBlock == 0)
1927 return UnknownValue; // More than one block exiting!
1929 assert(ExitingBlock && "No exits from loop, something is broken!");
1931 // Okay, we've computed the exiting block. See what condition causes us to
1934 // FIXME: we should be able to handle switch instructions (with a single exit)
1935 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1936 if (ExitBr == 0) return UnknownValue;
1937 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1939 // At this point, we know we have a conditional branch that determines whether
1940 // the loop is exited. However, we don't know if the branch is executed each
1941 // time through the loop. If not, then the execution count of the branch will
1942 // not be equal to the trip count of the loop.
1944 // Currently we check for this by checking to see if the Exit branch goes to
1945 // the loop header. If so, we know it will always execute the same number of
1946 // times as the loop. We also handle the case where the exit block *is* the
1947 // loop header. This is common for un-rotated loops. More extensive analysis
1948 // could be done to handle more cases here.
1949 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1950 ExitBr->getSuccessor(1) != L->getHeader() &&
1951 ExitBr->getParent() != L->getHeader())
1952 return UnknownValue;
1954 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1956 // If it's not an integer comparison then compute it the hard way.
1957 // Note that ICmpInst deals with pointer comparisons too so we must check
1958 // the type of the operand.
1959 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1960 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1961 ExitBr->getSuccessor(0) == ExitBlock);
1963 // If the condition was exit on true, convert the condition to exit on false
1964 ICmpInst::Predicate Cond;
1965 if (ExitBr->getSuccessor(1) == ExitBlock)
1966 Cond = ExitCond->getPredicate();
1968 Cond = ExitCond->getInversePredicate();
1970 // Handle common loops like: for (X = "string"; *X; ++X)
1971 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1972 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1974 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1975 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1978 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1979 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1981 // Try to evaluate any dependencies out of the loop.
1982 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1983 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1984 Tmp = getSCEVAtScope(RHS, L);
1985 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1987 // At this point, we would like to compute how many iterations of the
1988 // loop the predicate will return true for these inputs.
1989 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
1990 // If there is a loop-invariant, force it into the RHS.
1991 std::swap(LHS, RHS);
1992 Cond = ICmpInst::getSwappedPredicate(Cond);
1995 // FIXME: think about handling pointer comparisons! i.e.:
1996 // while (P != P+100) ++P;
1998 // If we have a comparison of a chrec against a constant, try to use value
1999 // ranges to answer this query.
2000 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2001 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2002 if (AddRec->getLoop() == L) {
2003 // Form the comparison range using the constant of the correct type so
2004 // that the ConstantRange class knows to do a signed or unsigned
2006 ConstantInt *CompVal = RHSC->getValue();
2007 const Type *RealTy = ExitCond->getOperand(0)->getType();
2008 CompVal = dyn_cast<ConstantInt>(
2009 ConstantExpr::getBitCast(CompVal, RealTy));
2011 // Form the constant range.
2012 ConstantRange CompRange(
2013 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2015 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
2016 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2021 case ICmpInst::ICMP_NE: { // while (X != Y)
2022 // Convert to: while (X-Y != 0)
2023 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
2024 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2027 case ICmpInst::ICMP_EQ: {
2028 // Convert to: while (X-Y == 0) // while (X == Y)
2029 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
2030 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2033 case ICmpInst::ICMP_SLT: {
2034 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true, false);
2035 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2038 case ICmpInst::ICMP_SGT: {
2039 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2040 SE.getNotSCEV(RHS), L, true, false);
2041 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2044 case ICmpInst::ICMP_ULT: {
2045 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false, false);
2046 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2049 case ICmpInst::ICMP_UGT: {
2050 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2051 SE.getNotSCEV(RHS), L, false, false);
2052 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2055 case ICmpInst::ICMP_SLE: {
2056 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true, true);
2057 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2060 case ICmpInst::ICMP_SGE: {
2061 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2062 SE.getNotSCEV(RHS), L, true, true);
2063 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2066 case ICmpInst::ICMP_ULE: {
2067 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false, true);
2068 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2071 case ICmpInst::ICMP_UGE: {
2072 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2073 SE.getNotSCEV(RHS), L, false, true);
2074 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2079 cerr << "ComputeIterationCount ";
2080 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2081 cerr << "[unsigned] ";
2083 << Instruction::getOpcodeName(Instruction::ICmp)
2084 << " " << *RHS << "\n";
2088 return ComputeIterationCountExhaustively(L, ExitCond,
2089 ExitBr->getSuccessor(0) == ExitBlock);
2092 static ConstantInt *
2093 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2094 ScalarEvolution &SE) {
2095 SCEVHandle InVal = SE.getConstant(C);
2096 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2097 assert(isa<SCEVConstant>(Val) &&
2098 "Evaluation of SCEV at constant didn't fold correctly?");
2099 return cast<SCEVConstant>(Val)->getValue();
2102 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2103 /// and a GEP expression (missing the pointer index) indexing into it, return
2104 /// the addressed element of the initializer or null if the index expression is
2107 GetAddressedElementFromGlobal(GlobalVariable *GV,
2108 const std::vector<ConstantInt*> &Indices) {
2109 Constant *Init = GV->getInitializer();
2110 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2111 uint64_t Idx = Indices[i]->getZExtValue();
2112 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2113 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2114 Init = cast<Constant>(CS->getOperand(Idx));
2115 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2116 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2117 Init = cast<Constant>(CA->getOperand(Idx));
2118 } else if (isa<ConstantAggregateZero>(Init)) {
2119 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2120 assert(Idx < STy->getNumElements() && "Bad struct index!");
2121 Init = Constant::getNullValue(STy->getElementType(Idx));
2122 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2123 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2124 Init = Constant::getNullValue(ATy->getElementType());
2126 assert(0 && "Unknown constant aggregate type!");
2130 return 0; // Unknown initializer type
2136 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
2137 /// 'icmp op load X, cst', try to see if we can compute the trip count.
2138 SCEVHandle ScalarEvolutionsImpl::
2139 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
2141 ICmpInst::Predicate predicate) {
2142 if (LI->isVolatile()) return UnknownValue;
2144 // Check to see if the loaded pointer is a getelementptr of a global.
2145 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2146 if (!GEP) return UnknownValue;
2148 // Make sure that it is really a constant global we are gepping, with an
2149 // initializer, and make sure the first IDX is really 0.
2150 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2151 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2152 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2153 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2154 return UnknownValue;
2156 // Okay, we allow one non-constant index into the GEP instruction.
2158 std::vector<ConstantInt*> Indexes;
2159 unsigned VarIdxNum = 0;
2160 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2161 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2162 Indexes.push_back(CI);
2163 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2164 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2165 VarIdx = GEP->getOperand(i);
2167 Indexes.push_back(0);
2170 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2171 // Check to see if X is a loop variant variable value now.
2172 SCEVHandle Idx = getSCEV(VarIdx);
2173 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2174 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2176 // We can only recognize very limited forms of loop index expressions, in
2177 // particular, only affine AddRec's like {C1,+,C2}.
2178 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2179 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2180 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2181 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2182 return UnknownValue;
2184 unsigned MaxSteps = MaxBruteForceIterations;
2185 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2186 ConstantInt *ItCst =
2187 ConstantInt::get(IdxExpr->getType(), IterationNum);
2188 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
2190 // Form the GEP offset.
2191 Indexes[VarIdxNum] = Val;
2193 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2194 if (Result == 0) break; // Cannot compute!
2196 // Evaluate the condition for this iteration.
2197 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2198 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2199 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2201 cerr << "\n***\n*** Computed loop count " << *ItCst
2202 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2205 ++NumArrayLenItCounts;
2206 return SE.getConstant(ItCst); // Found terminating iteration!
2209 return UnknownValue;
2213 /// CanConstantFold - Return true if we can constant fold an instruction of the
2214 /// specified type, assuming that all operands were constants.
2215 static bool CanConstantFold(const Instruction *I) {
2216 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2217 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2220 if (const CallInst *CI = dyn_cast<CallInst>(I))
2221 if (const Function *F = CI->getCalledFunction())
2222 return canConstantFoldCallTo(F);
2226 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2227 /// in the loop that V is derived from. We allow arbitrary operations along the
2228 /// way, but the operands of an operation must either be constants or a value
2229 /// derived from a constant PHI. If this expression does not fit with these
2230 /// constraints, return null.
2231 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2232 // If this is not an instruction, or if this is an instruction outside of the
2233 // loop, it can't be derived from a loop PHI.
2234 Instruction *I = dyn_cast<Instruction>(V);
2235 if (I == 0 || !L->contains(I->getParent())) return 0;
2237 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2238 if (L->getHeader() == I->getParent())
2241 // We don't currently keep track of the control flow needed to evaluate
2242 // PHIs, so we cannot handle PHIs inside of loops.
2246 // If we won't be able to constant fold this expression even if the operands
2247 // are constants, return early.
2248 if (!CanConstantFold(I)) return 0;
2250 // Otherwise, we can evaluate this instruction if all of its operands are
2251 // constant or derived from a PHI node themselves.
2253 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2254 if (!(isa<Constant>(I->getOperand(Op)) ||
2255 isa<GlobalValue>(I->getOperand(Op)))) {
2256 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2257 if (P == 0) return 0; // Not evolving from PHI
2261 return 0; // Evolving from multiple different PHIs.
2264 // This is a expression evolving from a constant PHI!
2268 /// EvaluateExpression - Given an expression that passes the
2269 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2270 /// in the loop has the value PHIVal. If we can't fold this expression for some
2271 /// reason, return null.
2272 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2273 if (isa<PHINode>(V)) return PHIVal;
2274 if (Constant *C = dyn_cast<Constant>(V)) return C;
2275 Instruction *I = cast<Instruction>(V);
2277 std::vector<Constant*> Operands;
2278 Operands.resize(I->getNumOperands());
2280 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2281 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2282 if (Operands[i] == 0) return 0;
2285 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2286 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2287 &Operands[0], Operands.size());
2289 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2290 &Operands[0], Operands.size());
2293 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2294 /// in the header of its containing loop, we know the loop executes a
2295 /// constant number of times, and the PHI node is just a recurrence
2296 /// involving constants, fold it.
2297 Constant *ScalarEvolutionsImpl::
2298 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
2299 std::map<PHINode*, Constant*>::iterator I =
2300 ConstantEvolutionLoopExitValue.find(PN);
2301 if (I != ConstantEvolutionLoopExitValue.end())
2304 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
2305 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2307 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2309 // Since the loop is canonicalized, the PHI node must have two entries. One
2310 // entry must be a constant (coming in from outside of the loop), and the
2311 // second must be derived from the same PHI.
2312 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2313 Constant *StartCST =
2314 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2316 return RetVal = 0; // Must be a constant.
2318 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2319 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2321 return RetVal = 0; // Not derived from same PHI.
2323 // Execute the loop symbolically to determine the exit value.
2324 if (Its.getActiveBits() >= 32)
2325 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2327 unsigned NumIterations = Its.getZExtValue(); // must be in range
2328 unsigned IterationNum = 0;
2329 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2330 if (IterationNum == NumIterations)
2331 return RetVal = PHIVal; // Got exit value!
2333 // Compute the value of the PHI node for the next iteration.
2334 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2335 if (NextPHI == PHIVal)
2336 return RetVal = NextPHI; // Stopped evolving!
2338 return 0; // Couldn't evaluate!
2343 /// ComputeIterationCountExhaustively - If the trip is known to execute a
2344 /// constant number of times (the condition evolves only from constants),
2345 /// try to evaluate a few iterations of the loop until we get the exit
2346 /// condition gets a value of ExitWhen (true or false). If we cannot
2347 /// evaluate the trip count of the loop, return UnknownValue.
2348 SCEVHandle ScalarEvolutionsImpl::
2349 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2350 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2351 if (PN == 0) return UnknownValue;
2353 // Since the loop is canonicalized, the PHI node must have two entries. One
2354 // entry must be a constant (coming in from outside of the loop), and the
2355 // second must be derived from the same PHI.
2356 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2357 Constant *StartCST =
2358 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2359 if (StartCST == 0) return UnknownValue; // Must be a constant.
2361 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2362 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2363 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2365 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2366 // the loop symbolically to determine when the condition gets a value of
2368 unsigned IterationNum = 0;
2369 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2370 for (Constant *PHIVal = StartCST;
2371 IterationNum != MaxIterations; ++IterationNum) {
2372 ConstantInt *CondVal =
2373 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2375 // Couldn't symbolically evaluate.
2376 if (!CondVal) return UnknownValue;
2378 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2379 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2380 ++NumBruteForceTripCountsComputed;
2381 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2384 // Compute the value of the PHI node for the next iteration.
2385 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2386 if (NextPHI == 0 || NextPHI == PHIVal)
2387 return UnknownValue; // Couldn't evaluate or not making progress...
2391 // Too many iterations were needed to evaluate.
2392 return UnknownValue;
2395 /// getSCEVAtScope - Compute the value of the specified expression within the
2396 /// indicated loop (which may be null to indicate in no loop). If the
2397 /// expression cannot be evaluated, return UnknownValue.
2398 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2399 // FIXME: this should be turned into a virtual method on SCEV!
2401 if (isa<SCEVConstant>(V)) return V;
2403 // If this instruction is evolved from a constant-evolving PHI, compute the
2404 // exit value from the loop without using SCEVs.
2405 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2406 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2407 const Loop *LI = this->LI[I->getParent()];
2408 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2409 if (PHINode *PN = dyn_cast<PHINode>(I))
2410 if (PN->getParent() == LI->getHeader()) {
2411 // Okay, there is no closed form solution for the PHI node. Check
2412 // to see if the loop that contains it has a known iteration count.
2413 // If so, we may be able to force computation of the exit value.
2414 SCEVHandle IterationCount = getIterationCount(LI);
2415 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
2416 // Okay, we know how many times the containing loop executes. If
2417 // this is a constant evolving PHI node, get the final value at
2418 // the specified iteration number.
2419 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2420 ICC->getValue()->getValue(),
2422 if (RV) return SE.getUnknown(RV);
2426 // Okay, this is an expression that we cannot symbolically evaluate
2427 // into a SCEV. Check to see if it's possible to symbolically evaluate
2428 // the arguments into constants, and if so, try to constant propagate the
2429 // result. This is particularly useful for computing loop exit values.
2430 if (CanConstantFold(I)) {
2431 std::vector<Constant*> Operands;
2432 Operands.reserve(I->getNumOperands());
2433 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2434 Value *Op = I->getOperand(i);
2435 if (Constant *C = dyn_cast<Constant>(Op)) {
2436 Operands.push_back(C);
2438 // If any of the operands is non-constant and if they are
2439 // non-integer, don't even try to analyze them with scev techniques.
2440 if (!isa<IntegerType>(Op->getType()))
2443 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2444 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2445 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2448 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2449 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2450 Operands.push_back(ConstantExpr::getIntegerCast(C,
2462 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2463 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2464 &Operands[0], Operands.size());
2466 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2467 &Operands[0], Operands.size());
2468 return SE.getUnknown(C);
2472 // This is some other type of SCEVUnknown, just return it.
2476 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2477 // Avoid performing the look-up in the common case where the specified
2478 // expression has no loop-variant portions.
2479 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2480 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2481 if (OpAtScope != Comm->getOperand(i)) {
2482 if (OpAtScope == UnknownValue) return UnknownValue;
2483 // Okay, at least one of these operands is loop variant but might be
2484 // foldable. Build a new instance of the folded commutative expression.
2485 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2486 NewOps.push_back(OpAtScope);
2488 for (++i; i != e; ++i) {
2489 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2490 if (OpAtScope == UnknownValue) return UnknownValue;
2491 NewOps.push_back(OpAtScope);
2493 if (isa<SCEVAddExpr>(Comm))
2494 return SE.getAddExpr(NewOps);
2495 if (isa<SCEVMulExpr>(Comm))
2496 return SE.getMulExpr(NewOps);
2497 if (isa<SCEVSMaxExpr>(Comm))
2498 return SE.getSMaxExpr(NewOps);
2499 if (isa<SCEVUMaxExpr>(Comm))
2500 return SE.getUMaxExpr(NewOps);
2501 assert(0 && "Unknown commutative SCEV type!");
2504 // If we got here, all operands are loop invariant.
2508 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2509 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2510 if (LHS == UnknownValue) return LHS;
2511 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2512 if (RHS == UnknownValue) return RHS;
2513 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2514 return Div; // must be loop invariant
2515 return SE.getUDivExpr(LHS, RHS);
2518 // If this is a loop recurrence for a loop that does not contain L, then we
2519 // are dealing with the final value computed by the loop.
2520 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2521 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2522 // To evaluate this recurrence, we need to know how many times the AddRec
2523 // loop iterates. Compute this now.
2524 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2525 if (IterationCount == UnknownValue) return UnknownValue;
2527 // Then, evaluate the AddRec.
2528 return AddRec->evaluateAtIteration(IterationCount, SE);
2530 return UnknownValue;
2533 //assert(0 && "Unknown SCEV type!");
2534 return UnknownValue;
2537 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2538 /// following equation:
2540 /// A * X = B (mod N)
2542 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2543 /// A and B isn't important.
2545 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2546 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2547 ScalarEvolution &SE) {
2548 uint32_t BW = A.getBitWidth();
2549 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2550 assert(A != 0 && "A must be non-zero.");
2554 // The gcd of A and N may have only one prime factor: 2. The number of
2555 // trailing zeros in A is its multiplicity
2556 uint32_t Mult2 = A.countTrailingZeros();
2559 // 2. Check if B is divisible by D.
2561 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2562 // is not less than multiplicity of this prime factor for D.
2563 if (B.countTrailingZeros() < Mult2)
2564 return new SCEVCouldNotCompute();
2566 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2569 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2570 // bit width during computations.
2571 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2572 APInt Mod(BW + 1, 0);
2573 Mod.set(BW - Mult2); // Mod = N / D
2574 APInt I = AD.multiplicativeInverse(Mod);
2576 // 4. Compute the minimum unsigned root of the equation:
2577 // I * (B / D) mod (N / D)
2578 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2580 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2582 return SE.getConstant(Result.trunc(BW));
2585 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2586 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2587 /// might be the same) or two SCEVCouldNotCompute objects.
2589 static std::pair<SCEVHandle,SCEVHandle>
2590 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2591 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2592 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2593 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2594 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2596 // We currently can only solve this if the coefficients are constants.
2597 if (!LC || !MC || !NC) {
2598 SCEV *CNC = new SCEVCouldNotCompute();
2599 return std::make_pair(CNC, CNC);
2602 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2603 const APInt &L = LC->getValue()->getValue();
2604 const APInt &M = MC->getValue()->getValue();
2605 const APInt &N = NC->getValue()->getValue();
2606 APInt Two(BitWidth, 2);
2607 APInt Four(BitWidth, 4);
2610 using namespace APIntOps;
2612 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2613 // The B coefficient is M-N/2
2617 // The A coefficient is N/2
2618 APInt A(N.sdiv(Two));
2620 // Compute the B^2-4ac term.
2623 SqrtTerm -= Four * (A * C);
2625 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2626 // integer value or else APInt::sqrt() will assert.
2627 APInt SqrtVal(SqrtTerm.sqrt());
2629 // Compute the two solutions for the quadratic formula.
2630 // The divisions must be performed as signed divisions.
2632 APInt TwoA( A << 1 );
2633 if (TwoA.isMinValue()) {
2634 SCEV *CNC = new SCEVCouldNotCompute();
2635 return std::make_pair(CNC, CNC);
2638 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2639 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2641 return std::make_pair(SE.getConstant(Solution1),
2642 SE.getConstant(Solution2));
2643 } // end APIntOps namespace
2646 /// HowFarToZero - Return the number of times a backedge comparing the specified
2647 /// value to zero will execute. If not computable, return UnknownValue
2648 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2649 // If the value is a constant
2650 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2651 // If the value is already zero, the branch will execute zero times.
2652 if (C->getValue()->isZero()) return C;
2653 return UnknownValue; // Otherwise it will loop infinitely.
2656 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2657 if (!AddRec || AddRec->getLoop() != L)
2658 return UnknownValue;
2660 if (AddRec->isAffine()) {
2661 // If this is an affine expression, the execution count of this branch is
2662 // the minimum unsigned root of the following equation:
2664 // Start + Step*N = 0 (mod 2^BW)
2668 // Step*N = -Start (mod 2^BW)
2670 // where BW is the common bit width of Start and Step.
2672 // Get the initial value for the loop.
2673 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2674 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2676 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2678 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2679 // For now we handle only constant steps.
2681 // First, handle unitary steps.
2682 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2683 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned)
2684 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2685 return Start; // N = Start (as unsigned)
2687 // Then, try to solve the above equation provided that Start is constant.
2688 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2689 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2690 -StartC->getValue()->getValue(),SE);
2692 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2693 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2694 // the quadratic equation to solve it.
2695 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
2696 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2697 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2700 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2701 << " sol#2: " << *R2 << "\n";
2703 // Pick the smallest positive root value.
2704 if (ConstantInt *CB =
2705 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2706 R1->getValue(), R2->getValue()))) {
2707 if (CB->getZExtValue() == false)
2708 std::swap(R1, R2); // R1 is the minimum root now.
2710 // We can only use this value if the chrec ends up with an exact zero
2711 // value at this index. When solving for "X*X != 5", for example, we
2712 // should not accept a root of 2.
2713 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
2715 return R1; // We found a quadratic root!
2720 return UnknownValue;
2723 /// HowFarToNonZero - Return the number of times a backedge checking the
2724 /// specified value for nonzero will execute. If not computable, return
2726 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2727 // Loops that look like: while (X == 0) are very strange indeed. We don't
2728 // handle them yet except for the trivial case. This could be expanded in the
2729 // future as needed.
2731 // If the value is a constant, check to see if it is known to be non-zero
2732 // already. If so, the backedge will execute zero times.
2733 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2734 if (!C->getValue()->isNullValue())
2735 return SE.getIntegerSCEV(0, C->getType());
2736 return UnknownValue; // Otherwise it will loop infinitely.
2739 // We could implement others, but I really doubt anyone writes loops like
2740 // this, and if they did, they would already be constant folded.
2741 return UnknownValue;
2744 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2745 /// (which may not be an immediate predecessor) which has exactly one
2746 /// successor from which BB is reachable, or null if no such block is
2750 ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2751 // If the block has a unique predecessor, the predecessor must have
2752 // no other successors from which BB is reachable.
2753 if (BasicBlock *Pred = BB->getSinglePredecessor())
2756 // A loop's header is defined to be a block that dominates the loop.
2757 // If the loop has a preheader, it must be a block that has exactly
2758 // one successor that can reach BB. This is slightly more strict
2759 // than necessary, but works if critical edges are split.
2760 if (Loop *L = LI.getLoopFor(BB))
2761 return L->getLoopPreheader();
2766 /// executesAtLeastOnce - Test whether entry to the loop is protected by
2767 /// a conditional between LHS and RHS.
2768 bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned,
2770 SCEV *LHS, SCEV *RHS) {
2771 BasicBlock *Preheader = L->getLoopPreheader();
2772 BasicBlock *PreheaderDest = L->getHeader();
2774 // Starting at the preheader, climb up the predecessor chain, as long as
2775 // there are predecessors that can be found that have unique successors
2776 // leading to the original header.
2778 PreheaderDest = Preheader,
2779 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
2781 BranchInst *LoopEntryPredicate =
2782 dyn_cast<BranchInst>(Preheader->getTerminator());
2783 if (!LoopEntryPredicate ||
2784 LoopEntryPredicate->isUnconditional())
2787 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
2790 // Now that we found a conditional branch that dominates the loop, check to
2791 // see if it is the comparison we are looking for.
2792 Value *PreCondLHS = ICI->getOperand(0);
2793 Value *PreCondRHS = ICI->getOperand(1);
2794 ICmpInst::Predicate Cond;
2795 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2796 Cond = ICI->getPredicate();
2798 Cond = ICI->getInversePredicate();
2801 case ICmpInst::ICMP_UGT:
2802 if (isSigned || trueWhenEqual) continue;
2803 std::swap(PreCondLHS, PreCondRHS);
2804 Cond = ICmpInst::ICMP_ULT;
2806 case ICmpInst::ICMP_SGT:
2807 if (!isSigned || trueWhenEqual) continue;
2808 std::swap(PreCondLHS, PreCondRHS);
2809 Cond = ICmpInst::ICMP_SLT;
2811 case ICmpInst::ICMP_ULT:
2812 if (isSigned || trueWhenEqual) continue;
2814 case ICmpInst::ICMP_SLT:
2815 if (!isSigned || trueWhenEqual) continue;
2817 case ICmpInst::ICMP_UGE:
2818 if (isSigned || !trueWhenEqual) continue;
2819 std::swap(PreCondLHS, PreCondRHS);
2820 Cond = ICmpInst::ICMP_ULE;
2822 case ICmpInst::ICMP_SGE:
2823 if (!isSigned || !trueWhenEqual) continue;
2824 std::swap(PreCondLHS, PreCondRHS);
2825 Cond = ICmpInst::ICMP_SLE;
2827 case ICmpInst::ICMP_ULE:
2828 if (isSigned || !trueWhenEqual) continue;
2830 case ICmpInst::ICMP_SLE:
2831 if (!isSigned || !trueWhenEqual) continue;
2837 if (!PreCondLHS->getType()->isInteger()) continue;
2839 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
2840 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
2841 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
2842 (LHS == SE.getNotSCEV(PreCondRHSSCEV) &&
2843 RHS == SE.getNotSCEV(PreCondLHSSCEV)))
2850 /// potentialInfiniteLoop - Test whether the loop might jump over the exit value
2851 /// due to wrapping around 2^n.
2852 bool ScalarEvolutionsImpl::potentialInfiniteLoop(SCEV *Stride, SCEV *RHS,
2853 bool isSigned, bool trueWhenEqual) {
2854 // Return true when the distance from RHS to maxint > Stride.
2856 if (!isa<SCEVConstant>(Stride))
2858 SCEVConstant *SC = cast<SCEVConstant>(Stride);
2860 if (SC->getValue()->isZero())
2862 if (!trueWhenEqual && SC->getValue()->isOne())
2865 if (!isa<SCEVConstant>(RHS))
2867 SCEVConstant *R = cast<SCEVConstant>(RHS);
2870 return true; // XXX: because we don't have an sdiv scev.
2872 // If negative, it wraps around every iteration, but we don't care about that.
2873 APInt S = SC->getValue()->getValue().abs();
2875 APInt Dist = APInt::getMaxValue(R->getValue()->getBitWidth()) -
2876 R->getValue()->getValue();
2879 return !S.ult(Dist);
2881 return !S.ule(Dist);
2884 /// HowManyLessThans - Return the number of times a backedge containing the
2885 /// specified less-than comparison will execute. If not computable, return
2887 SCEVHandle ScalarEvolutionsImpl::
2888 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
2889 bool isSigned, bool trueWhenEqual) {
2890 // Only handle: "ADDREC < LoopInvariant".
2891 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2893 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2894 if (!AddRec || AddRec->getLoop() != L)
2895 return UnknownValue;
2897 if (AddRec->isAffine()) {
2898 SCEVHandle Stride = AddRec->getOperand(1);
2899 if (potentialInfiniteLoop(Stride, RHS, isSigned, trueWhenEqual))
2900 return UnknownValue;
2902 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
2903 // m. So, we count the number of iterations in which {n,+,s} < m is true.
2904 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
2905 // treat m-n as signed nor unsigned due to overflow possibility.
2907 // First, we get the value of the LHS in the first iteration: n
2908 SCEVHandle Start = AddRec->getOperand(0);
2910 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
2912 // Assuming that the loop will run at least once, we know that it will
2913 // run (m-n)/s times.
2914 SCEVHandle End = RHS;
2916 if (!executesAtLeastOnce(L, isSigned, trueWhenEqual,
2917 SE.getMinusSCEV(Start, One), RHS)) {
2918 // If not, we get the value of the LHS in the first iteration in which
2919 // the above condition doesn't hold. This equals to max(m,n).
2920 End = isSigned ? SE.getSMaxExpr(RHS, Start)
2921 : SE.getUMaxExpr(RHS, Start);
2924 // If the expression is less-than-or-equal to, we need to extend the
2925 // loop by one iteration.
2927 // The loop won't actually run (m-n)/s times because the loop iterations
2928 // won't divide evenly. For example, if you have {2,+,5} u< 10 the
2929 // division would equal one, but the loop runs twice putting the
2930 // induction variable at 12.
2933 // (Stride - 1) is correct only because we know it's unsigned.
2934 // What we really want is to decrease the magnitude of Stride by one.
2935 Start = SE.getMinusSCEV(Start, SE.getMinusSCEV(Stride, One));
2937 Start = SE.getMinusSCEV(Start, Stride);
2939 // Finally, we subtract these two values to get the number of times the
2940 // backedge is executed: max(m,n)-n.
2941 return SE.getUDivExpr(SE.getMinusSCEV(End, Start), Stride);
2944 return UnknownValue;
2947 /// getNumIterationsInRange - Return the number of iterations of this loop that
2948 /// produce values in the specified constant range. Another way of looking at
2949 /// this is that it returns the first iteration number where the value is not in
2950 /// the condition, thus computing the exit count. If the iteration count can't
2951 /// be computed, an instance of SCEVCouldNotCompute is returned.
2952 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2953 ScalarEvolution &SE) const {
2954 if (Range.isFullSet()) // Infinite loop.
2955 return new SCEVCouldNotCompute();
2957 // If the start is a non-zero constant, shift the range to simplify things.
2958 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2959 if (!SC->getValue()->isZero()) {
2960 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2961 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
2962 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
2963 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2964 return ShiftedAddRec->getNumIterationsInRange(
2965 Range.subtract(SC->getValue()->getValue()), SE);
2966 // This is strange and shouldn't happen.
2967 return new SCEVCouldNotCompute();
2970 // The only time we can solve this is when we have all constant indices.
2971 // Otherwise, we cannot determine the overflow conditions.
2972 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2973 if (!isa<SCEVConstant>(getOperand(i)))
2974 return new SCEVCouldNotCompute();
2977 // Okay at this point we know that all elements of the chrec are constants and
2978 // that the start element is zero.
2980 // First check to see if the range contains zero. If not, the first
2982 if (!Range.contains(APInt(getBitWidth(),0)))
2983 return SE.getConstant(ConstantInt::get(getType(),0));
2986 // If this is an affine expression then we have this situation:
2987 // Solve {0,+,A} in Range === Ax in Range
2989 // We know that zero is in the range. If A is positive then we know that
2990 // the upper value of the range must be the first possible exit value.
2991 // If A is negative then the lower of the range is the last possible loop
2992 // value. Also note that we already checked for a full range.
2993 APInt One(getBitWidth(),1);
2994 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2995 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
2997 // The exit value should be (End+A)/A.
2998 APInt ExitVal = (End + A).udiv(A);
2999 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3001 // Evaluate at the exit value. If we really did fall out of the valid
3002 // range, then we computed our trip count, otherwise wrap around or other
3003 // things must have happened.
3004 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3005 if (Range.contains(Val->getValue()))
3006 return new SCEVCouldNotCompute(); // Something strange happened
3008 // Ensure that the previous value is in the range. This is a sanity check.
3009 assert(Range.contains(
3010 EvaluateConstantChrecAtConstant(this,
3011 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3012 "Linear scev computation is off in a bad way!");
3013 return SE.getConstant(ExitValue);
3014 } else if (isQuadratic()) {
3015 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3016 // quadratic equation to solve it. To do this, we must frame our problem in
3017 // terms of figuring out when zero is crossed, instead of when
3018 // Range.getUpper() is crossed.
3019 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3020 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3021 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3023 // Next, solve the constructed addrec
3024 std::pair<SCEVHandle,SCEVHandle> Roots =
3025 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3026 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3027 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3029 // Pick the smallest positive root value.
3030 if (ConstantInt *CB =
3031 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3032 R1->getValue(), R2->getValue()))) {
3033 if (CB->getZExtValue() == false)
3034 std::swap(R1, R2); // R1 is the minimum root now.
3036 // Make sure the root is not off by one. The returned iteration should
3037 // not be in the range, but the previous one should be. When solving
3038 // for "X*X < 5", for example, we should not return a root of 2.
3039 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3042 if (Range.contains(R1Val->getValue())) {
3043 // The next iteration must be out of the range...
3044 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3046 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3047 if (!Range.contains(R1Val->getValue()))
3048 return SE.getConstant(NextVal);
3049 return new SCEVCouldNotCompute(); // Something strange happened
3052 // If R1 was not in the range, then it is a good return value. Make
3053 // sure that R1-1 WAS in the range though, just in case.
3054 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3055 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3056 if (Range.contains(R1Val->getValue()))
3058 return new SCEVCouldNotCompute(); // Something strange happened
3063 return new SCEVCouldNotCompute();
3068 //===----------------------------------------------------------------------===//
3069 // ScalarEvolution Class Implementation
3070 //===----------------------------------------------------------------------===//
3072 bool ScalarEvolution::runOnFunction(Function &F) {
3073 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
3077 void ScalarEvolution::releaseMemory() {
3078 delete (ScalarEvolutionsImpl*)Impl;
3082 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3083 AU.setPreservesAll();
3084 AU.addRequiredTransitive<LoopInfo>();
3087 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
3088 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
3091 /// hasSCEV - Return true if the SCEV for this value has already been
3093 bool ScalarEvolution::hasSCEV(Value *V) const {
3094 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
3098 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
3099 /// the specified value.
3100 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
3101 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
3105 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
3106 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
3109 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
3110 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
3113 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
3114 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
3117 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
3118 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
3121 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
3123 // Print all inner loops first
3124 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3125 PrintLoopInfo(OS, SE, *I);
3127 OS << "Loop " << L->getHeader()->getName() << ": ";
3129 SmallVector<BasicBlock*, 8> ExitBlocks;
3130 L->getExitBlocks(ExitBlocks);
3131 if (ExitBlocks.size() != 1)
3132 OS << "<multiple exits> ";
3134 if (SE->hasLoopInvariantIterationCount(L)) {
3135 OS << *SE->getIterationCount(L) << " iterations! ";
3137 OS << "Unpredictable iteration count. ";
3143 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
3144 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
3145 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
3147 OS << "Classifying expressions for: " << F.getName() << "\n";
3148 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3149 if (I->getType()->isInteger()) {
3152 SCEVHandle SV = getSCEV(&*I);
3156 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
3158 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
3159 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3160 OS << "<<Unknown>>";
3170 OS << "Determining loop execution counts for: " << F.getName() << "\n";
3171 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
3172 PrintLoopInfo(OS, this, *I);