1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Transforms/Scalar.h"
73 #include "llvm/Support/CFG.h"
74 #include "llvm/Support/CommandLine.h"
75 #include "llvm/Support/Compiler.h"
76 #include "llvm/Support/ConstantRange.h"
77 #include "llvm/Support/InstIterator.h"
78 #include "llvm/Support/ManagedStatic.h"
79 #include "llvm/Support/MathExtras.h"
80 #include "llvm/Support/Streams.h"
81 #include "llvm/ADT/Statistic.h"
87 STATISTIC(NumArrayLenItCounts,
88 "Number of trip counts computed with array length");
89 STATISTIC(NumTripCountsComputed,
90 "Number of loops with predictable loop counts");
91 STATISTIC(NumTripCountsNotComputed,
92 "Number of loops without predictable loop counts");
93 STATISTIC(NumBruteForceTripCountsComputed,
94 "Number of loops with trip counts computed by force");
96 static cl::opt<unsigned>
97 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
98 cl::desc("Maximum number of iterations SCEV will "
99 "symbolically execute a constant derived loop"),
102 static RegisterPass<ScalarEvolution>
103 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
104 char ScalarEvolution::ID = 0;
106 //===----------------------------------------------------------------------===//
107 // SCEV class definitions
108 //===----------------------------------------------------------------------===//
110 //===----------------------------------------------------------------------===//
111 // Implementation of the SCEV class.
114 void SCEV::dump() const {
119 uint32_t SCEV::getBitWidth() const {
120 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
121 return ITy->getBitWidth();
125 bool SCEV::isZero() const {
126 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
127 return SC->getValue()->isZero();
132 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
134 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
135 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
139 const Type *SCEVCouldNotCompute::getType() const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
144 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149 SCEVHandle SCEVCouldNotCompute::
150 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
151 const SCEVHandle &Conc,
152 ScalarEvolution &SE) const {
156 void SCEVCouldNotCompute::print(std::ostream &OS) const {
157 OS << "***COULDNOTCOMPUTE***";
160 bool SCEVCouldNotCompute::classof(const SCEV *S) {
161 return S->getSCEVType() == scCouldNotCompute;
165 // SCEVConstants - Only allow the creation of one SCEVConstant for any
166 // particular value. Don't use a SCEVHandle here, or else the object will
168 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
171 SCEVConstant::~SCEVConstant() {
172 SCEVConstants->erase(V);
175 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
176 SCEVConstant *&R = (*SCEVConstants)[V];
177 if (R == 0) R = new SCEVConstant(V);
181 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
182 return getConstant(ConstantInt::get(Val));
185 const Type *SCEVConstant::getType() const { return V->getType(); }
187 void SCEVConstant::print(std::ostream &OS) const {
188 WriteAsOperand(OS, V, false);
191 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
192 // particular input. Don't use a SCEVHandle here, or else the object will
194 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
195 SCEVTruncateExpr*> > SCEVTruncates;
197 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
198 : SCEV(scTruncate), Op(op), Ty(ty) {
199 assert(Op->getType()->isInteger() && Ty->isInteger() &&
200 "Cannot truncate non-integer value!");
201 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
202 && "This is not a truncating conversion!");
205 SCEVTruncateExpr::~SCEVTruncateExpr() {
206 SCEVTruncates->erase(std::make_pair(Op, Ty));
209 bool SCEVTruncateExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
210 return Op->dominates(BB, DT);
213 void SCEVTruncateExpr::print(std::ostream &OS) const {
214 OS << "(truncate " << *Op << " to " << *Ty << ")";
217 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
218 // particular input. Don't use a SCEVHandle here, or else the object will never
220 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
221 SCEVZeroExtendExpr*> > SCEVZeroExtends;
223 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
224 : SCEV(scZeroExtend), Op(op), Ty(ty) {
225 assert(Op->getType()->isInteger() && Ty->isInteger() &&
226 "Cannot zero extend non-integer value!");
227 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
228 && "This is not an extending conversion!");
231 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
232 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
235 bool SCEVZeroExtendExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
236 return Op->dominates(BB, DT);
239 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
240 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
243 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
244 // particular input. Don't use a SCEVHandle here, or else the object will never
246 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
247 SCEVSignExtendExpr*> > SCEVSignExtends;
249 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
250 : SCEV(scSignExtend), Op(op), Ty(ty) {
251 assert(Op->getType()->isInteger() && Ty->isInteger() &&
252 "Cannot sign extend non-integer value!");
253 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
254 && "This is not an extending conversion!");
257 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
258 SCEVSignExtends->erase(std::make_pair(Op, Ty));
261 bool SCEVSignExtendExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
262 return Op->dominates(BB, DT);
265 void SCEVSignExtendExpr::print(std::ostream &OS) const {
266 OS << "(signextend " << *Op << " to " << *Ty << ")";
269 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
270 // particular input. Don't use a SCEVHandle here, or else the object will never
272 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
273 SCEVCommutativeExpr*> > SCEVCommExprs;
275 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
276 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
277 std::vector<SCEV*>(Operands.begin(),
281 void SCEVCommutativeExpr::print(std::ostream &OS) const {
282 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
283 const char *OpStr = getOperationStr();
284 OS << "(" << *Operands[0];
285 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
286 OS << OpStr << *Operands[i];
290 SCEVHandle SCEVCommutativeExpr::
291 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
292 const SCEVHandle &Conc,
293 ScalarEvolution &SE) const {
294 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
296 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
297 if (H != getOperand(i)) {
298 std::vector<SCEVHandle> NewOps;
299 NewOps.reserve(getNumOperands());
300 for (unsigned j = 0; j != i; ++j)
301 NewOps.push_back(getOperand(j));
303 for (++i; i != e; ++i)
304 NewOps.push_back(getOperand(i)->
305 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
307 if (isa<SCEVAddExpr>(this))
308 return SE.getAddExpr(NewOps);
309 else if (isa<SCEVMulExpr>(this))
310 return SE.getMulExpr(NewOps);
311 else if (isa<SCEVSMaxExpr>(this))
312 return SE.getSMaxExpr(NewOps);
313 else if (isa<SCEVUMaxExpr>(this))
314 return SE.getUMaxExpr(NewOps);
316 assert(0 && "Unknown commutative expr!");
322 bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
323 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
324 if (!getOperand(i)->dominates(BB, DT))
331 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
332 // input. Don't use a SCEVHandle here, or else the object will never be
334 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
335 SCEVUDivExpr*> > SCEVUDivs;
337 SCEVUDivExpr::~SCEVUDivExpr() {
338 SCEVUDivs->erase(std::make_pair(LHS, RHS));
341 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
342 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
345 void SCEVUDivExpr::print(std::ostream &OS) const {
346 OS << "(" << *LHS << " /u " << *RHS << ")";
349 const Type *SCEVUDivExpr::getType() const {
350 return LHS->getType();
353 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
354 // particular input. Don't use a SCEVHandle here, or else the object will never
356 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
357 SCEVAddRecExpr*> > SCEVAddRecExprs;
359 SCEVAddRecExpr::~SCEVAddRecExpr() {
360 SCEVAddRecExprs->erase(std::make_pair(L,
361 std::vector<SCEV*>(Operands.begin(),
365 bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
366 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
367 if (!getOperand(i)->dominates(BB, DT))
374 SCEVHandle SCEVAddRecExpr::
375 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
376 const SCEVHandle &Conc,
377 ScalarEvolution &SE) const {
378 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
380 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
381 if (H != getOperand(i)) {
382 std::vector<SCEVHandle> NewOps;
383 NewOps.reserve(getNumOperands());
384 for (unsigned j = 0; j != i; ++j)
385 NewOps.push_back(getOperand(j));
387 for (++i; i != e; ++i)
388 NewOps.push_back(getOperand(i)->
389 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
391 return SE.getAddRecExpr(NewOps, L);
398 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
399 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
400 // contain L and if the start is invariant.
401 return !QueryLoop->contains(L->getHeader()) &&
402 getOperand(0)->isLoopInvariant(QueryLoop);
406 void SCEVAddRecExpr::print(std::ostream &OS) const {
407 OS << "{" << *Operands[0];
408 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
409 OS << ",+," << *Operands[i];
410 OS << "}<" << L->getHeader()->getName() + ">";
413 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
414 // value. Don't use a SCEVHandle here, or else the object will never be
416 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
418 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
420 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
421 // All non-instruction values are loop invariant. All instructions are loop
422 // invariant if they are not contained in the specified loop.
423 if (Instruction *I = dyn_cast<Instruction>(V))
424 return !L->contains(I->getParent());
428 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
429 if (Instruction *I = dyn_cast<Instruction>(getValue()))
430 return DT->dominates(I->getParent(), BB);
434 const Type *SCEVUnknown::getType() const {
438 void SCEVUnknown::print(std::ostream &OS) const {
439 WriteAsOperand(OS, V, false);
442 //===----------------------------------------------------------------------===//
444 //===----------------------------------------------------------------------===//
447 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
448 /// than the complexity of the RHS. This comparator is used to canonicalize
450 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
451 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
452 return LHS->getSCEVType() < RHS->getSCEVType();
457 /// GroupByComplexity - Given a list of SCEV objects, order them by their
458 /// complexity, and group objects of the same complexity together by value.
459 /// When this routine is finished, we know that any duplicates in the vector are
460 /// consecutive and that complexity is monotonically increasing.
462 /// Note that we go take special precautions to ensure that we get determinstic
463 /// results from this routine. In other words, we don't want the results of
464 /// this to depend on where the addresses of various SCEV objects happened to
467 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
468 if (Ops.size() < 2) return; // Noop
469 if (Ops.size() == 2) {
470 // This is the common case, which also happens to be trivially simple.
472 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
473 std::swap(Ops[0], Ops[1]);
477 // Do the rough sort by complexity.
478 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
480 // Now that we are sorted by complexity, group elements of the same
481 // complexity. Note that this is, at worst, N^2, but the vector is likely to
482 // be extremely short in practice. Note that we take this approach because we
483 // do not want to depend on the addresses of the objects we are grouping.
484 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
486 unsigned Complexity = S->getSCEVType();
488 // If there are any objects of the same complexity and same value as this
490 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
491 if (Ops[j] == S) { // Found a duplicate.
492 // Move it to immediately after i'th element.
493 std::swap(Ops[i+1], Ops[j]);
494 ++i; // no need to rescan it.
495 if (i == e-2) return; // Done!
503 //===----------------------------------------------------------------------===//
504 // Simple SCEV method implementations
505 //===----------------------------------------------------------------------===//
507 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
508 /// specified signed integer value and return a SCEV for the constant.
509 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
512 C = Constant::getNullValue(Ty);
513 else if (Ty->isFloatingPoint())
514 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
515 APFloat::IEEEdouble, Val));
517 C = ConstantInt::get(Ty, Val);
518 return getUnknown(C);
521 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
523 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
524 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
525 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
527 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType())));
530 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
531 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
532 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
533 return getUnknown(ConstantExpr::getNot(VC->getValue()));
535 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType()));
536 return getMinusSCEV(AllOnes, V);
539 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
541 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
542 const SCEVHandle &RHS) {
544 return getAddExpr(LHS, getNegativeSCEV(RHS));
548 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
550 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
552 const IntegerType* ResultTy) {
553 // Handle the simplest case efficiently.
555 return SE.getTruncateOrZeroExtend(It, ResultTy);
557 // We are using the following formula for BC(It, K):
559 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
561 // Suppose, W is the bitwidth of the return value. We must be prepared for
562 // overflow. Hence, we must assure that the result of our computation is
563 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
564 // safe in modular arithmetic.
566 // However, this code doesn't use exactly that formula; the formula it uses
567 // is something like the following, where T is the number of factors of 2 in
568 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
571 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
573 // This formula is trivially equivalent to the previous formula. However,
574 // this formula can be implemented much more efficiently. The trick is that
575 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
576 // arithmetic. To do exact division in modular arithmetic, all we have
577 // to do is multiply by the inverse. Therefore, this step can be done at
580 // The next issue is how to safely do the division by 2^T. The way this
581 // is done is by doing the multiplication step at a width of at least W + T
582 // bits. This way, the bottom W+T bits of the product are accurate. Then,
583 // when we perform the division by 2^T (which is equivalent to a right shift
584 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
585 // truncated out after the division by 2^T.
587 // In comparison to just directly using the first formula, this technique
588 // is much more efficient; using the first formula requires W * K bits,
589 // but this formula less than W + K bits. Also, the first formula requires
590 // a division step, whereas this formula only requires multiplies and shifts.
592 // It doesn't matter whether the subtraction step is done in the calculation
593 // width or the input iteration count's width; if the subtraction overflows,
594 // the result must be zero anyway. We prefer here to do it in the width of
595 // the induction variable because it helps a lot for certain cases; CodeGen
596 // isn't smart enough to ignore the overflow, which leads to much less
597 // efficient code if the width of the subtraction is wider than the native
600 // (It's possible to not widen at all by pulling out factors of 2 before
601 // the multiplication; for example, K=2 can be calculated as
602 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
603 // extra arithmetic, so it's not an obvious win, and it gets
604 // much more complicated for K > 3.)
606 // Protection from insane SCEVs; this bound is conservative,
607 // but it probably doesn't matter.
609 return new SCEVCouldNotCompute();
611 unsigned W = ResultTy->getBitWidth();
613 // Calculate K! / 2^T and T; we divide out the factors of two before
614 // multiplying for calculating K! / 2^T to avoid overflow.
615 // Other overflow doesn't matter because we only care about the bottom
616 // W bits of the result.
617 APInt OddFactorial(W, 1);
619 for (unsigned i = 3; i <= K; ++i) {
621 unsigned TwoFactors = Mult.countTrailingZeros();
623 Mult = Mult.lshr(TwoFactors);
624 OddFactorial *= Mult;
627 // We need at least W + T bits for the multiplication step
628 unsigned CalculationBits = W + T;
630 // Calcuate 2^T, at width T+W.
631 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
633 // Calculate the multiplicative inverse of K! / 2^T;
634 // this multiplication factor will perform the exact division by
636 APInt Mod = APInt::getSignedMinValue(W+1);
637 APInt MultiplyFactor = OddFactorial.zext(W+1);
638 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
639 MultiplyFactor = MultiplyFactor.trunc(W);
641 // Calculate the product, at width T+W
642 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
643 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
644 for (unsigned i = 1; i != K; ++i) {
645 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
646 Dividend = SE.getMulExpr(Dividend,
647 SE.getTruncateOrZeroExtend(S, CalculationTy));
651 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
653 // Truncate the result, and divide by K! / 2^T.
655 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
656 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
659 /// evaluateAtIteration - Return the value of this chain of recurrences at
660 /// the specified iteration number. We can evaluate this recurrence by
661 /// multiplying each element in the chain by the binomial coefficient
662 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
664 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
666 /// where BC(It, k) stands for binomial coefficient.
668 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
669 ScalarEvolution &SE) const {
670 SCEVHandle Result = getStart();
671 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
672 // The computation is correct in the face of overflow provided that the
673 // multiplication is performed _after_ the evaluation of the binomial
675 SCEVHandle Coeff = BinomialCoefficient(It, i, SE,
676 cast<IntegerType>(getType()));
677 if (isa<SCEVCouldNotCompute>(Coeff))
680 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
685 //===----------------------------------------------------------------------===//
686 // SCEV Expression folder implementations
687 //===----------------------------------------------------------------------===//
689 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
690 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
692 ConstantExpr::getTrunc(SC->getValue(), Ty));
694 // If the input value is a chrec scev made out of constants, truncate
695 // all of the constants.
696 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
697 std::vector<SCEVHandle> Operands;
698 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
699 // FIXME: This should allow truncation of other expression types!
700 if (isa<SCEVConstant>(AddRec->getOperand(i)))
701 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
704 if (Operands.size() == AddRec->getNumOperands())
705 return getAddRecExpr(Operands, AddRec->getLoop());
708 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
709 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
713 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) {
714 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
716 ConstantExpr::getZExt(SC->getValue(), Ty));
718 // FIXME: If the input value is a chrec scev, and we can prove that the value
719 // did not overflow the old, smaller, value, we can zero extend all of the
720 // operands (often constants). This would allow analysis of something like
721 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
723 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
724 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
728 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
729 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
731 ConstantExpr::getSExt(SC->getValue(), Ty));
733 // FIXME: If the input value is a chrec scev, and we can prove that the value
734 // did not overflow the old, smaller, value, we can sign extend all of the
735 // operands (often constants). This would allow analysis of something like
736 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
738 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
739 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
743 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
744 /// of the input value to the specified type. If the type must be
745 /// extended, it is zero extended.
746 SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
748 const Type *SrcTy = V->getType();
749 assert(SrcTy->isInteger() && Ty->isInteger() &&
750 "Cannot truncate or zero extend with non-integer arguments!");
751 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
752 return V; // No conversion
753 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
754 return getTruncateExpr(V, Ty);
755 return getZeroExtendExpr(V, Ty);
758 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
759 /// of the input value to the specified type. If the type must be
760 /// extended, it is sign extended.
761 SCEVHandle ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
763 const Type *SrcTy = V->getType();
764 assert(SrcTy->isInteger() && Ty->isInteger() &&
765 "Cannot truncate or sign extend with non-integer arguments!");
766 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
767 return V; // No conversion
768 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
769 return getTruncateExpr(V, Ty);
770 return getSignExtendExpr(V, Ty);
773 // get - Get a canonical add expression, or something simpler if possible.
774 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
775 assert(!Ops.empty() && "Cannot get empty add!");
776 if (Ops.size() == 1) return Ops[0];
778 // Sort by complexity, this groups all similar expression types together.
779 GroupByComplexity(Ops);
781 // If there are any constants, fold them together.
783 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
785 assert(Idx < Ops.size());
786 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
787 // We found two constants, fold them together!
788 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
789 RHSC->getValue()->getValue());
790 Ops[0] = getConstant(Fold);
791 Ops.erase(Ops.begin()+1); // Erase the folded element
792 if (Ops.size() == 1) return Ops[0];
793 LHSC = cast<SCEVConstant>(Ops[0]);
796 // If we are left with a constant zero being added, strip it off.
797 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
798 Ops.erase(Ops.begin());
803 if (Ops.size() == 1) return Ops[0];
805 // Okay, check to see if the same value occurs in the operand list twice. If
806 // so, merge them together into an multiply expression. Since we sorted the
807 // list, these values are required to be adjacent.
808 const Type *Ty = Ops[0]->getType();
809 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
810 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
811 // Found a match, merge the two values into a multiply, and add any
812 // remaining values to the result.
813 SCEVHandle Two = getIntegerSCEV(2, Ty);
814 SCEVHandle Mul = getMulExpr(Ops[i], Two);
817 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
819 return getAddExpr(Ops);
822 // Now we know the first non-constant operand. Skip past any cast SCEVs.
823 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
826 // If there are add operands they would be next.
827 if (Idx < Ops.size()) {
828 bool DeletedAdd = false;
829 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
830 // If we have an add, expand the add operands onto the end of the operands
832 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
833 Ops.erase(Ops.begin()+Idx);
837 // If we deleted at least one add, we added operands to the end of the list,
838 // and they are not necessarily sorted. Recurse to resort and resimplify
839 // any operands we just aquired.
841 return getAddExpr(Ops);
844 // Skip over the add expression until we get to a multiply.
845 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
848 // If we are adding something to a multiply expression, make sure the
849 // something is not already an operand of the multiply. If so, merge it into
851 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
852 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
853 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
854 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
855 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
856 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
857 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
858 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
859 if (Mul->getNumOperands() != 2) {
860 // If the multiply has more than two operands, we must get the
862 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
863 MulOps.erase(MulOps.begin()+MulOp);
864 InnerMul = getMulExpr(MulOps);
866 SCEVHandle One = getIntegerSCEV(1, Ty);
867 SCEVHandle AddOne = getAddExpr(InnerMul, One);
868 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
869 if (Ops.size() == 2) return OuterMul;
871 Ops.erase(Ops.begin()+AddOp);
872 Ops.erase(Ops.begin()+Idx-1);
874 Ops.erase(Ops.begin()+Idx);
875 Ops.erase(Ops.begin()+AddOp-1);
877 Ops.push_back(OuterMul);
878 return getAddExpr(Ops);
881 // Check this multiply against other multiplies being added together.
882 for (unsigned OtherMulIdx = Idx+1;
883 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
885 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
886 // If MulOp occurs in OtherMul, we can fold the two multiplies
888 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
889 OMulOp != e; ++OMulOp)
890 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
891 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
892 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
893 if (Mul->getNumOperands() != 2) {
894 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
895 MulOps.erase(MulOps.begin()+MulOp);
896 InnerMul1 = getMulExpr(MulOps);
898 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
899 if (OtherMul->getNumOperands() != 2) {
900 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
902 MulOps.erase(MulOps.begin()+OMulOp);
903 InnerMul2 = getMulExpr(MulOps);
905 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
906 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
907 if (Ops.size() == 2) return OuterMul;
908 Ops.erase(Ops.begin()+Idx);
909 Ops.erase(Ops.begin()+OtherMulIdx-1);
910 Ops.push_back(OuterMul);
911 return getAddExpr(Ops);
917 // If there are any add recurrences in the operands list, see if any other
918 // added values are loop invariant. If so, we can fold them into the
920 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
923 // Scan over all recurrences, trying to fold loop invariants into them.
924 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
925 // Scan all of the other operands to this add and add them to the vector if
926 // they are loop invariant w.r.t. the recurrence.
927 std::vector<SCEVHandle> LIOps;
928 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
929 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
930 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
931 LIOps.push_back(Ops[i]);
932 Ops.erase(Ops.begin()+i);
936 // If we found some loop invariants, fold them into the recurrence.
937 if (!LIOps.empty()) {
938 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
939 LIOps.push_back(AddRec->getStart());
941 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
942 AddRecOps[0] = getAddExpr(LIOps);
944 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
945 // If all of the other operands were loop invariant, we are done.
946 if (Ops.size() == 1) return NewRec;
948 // Otherwise, add the folded AddRec by the non-liv parts.
949 for (unsigned i = 0;; ++i)
950 if (Ops[i] == AddRec) {
954 return getAddExpr(Ops);
957 // Okay, if there weren't any loop invariants to be folded, check to see if
958 // there are multiple AddRec's with the same loop induction variable being
959 // added together. If so, we can fold them.
960 for (unsigned OtherIdx = Idx+1;
961 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
962 if (OtherIdx != Idx) {
963 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
964 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
965 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
966 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
967 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
968 if (i >= NewOps.size()) {
969 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
970 OtherAddRec->op_end());
973 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
975 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
977 if (Ops.size() == 2) return NewAddRec;
979 Ops.erase(Ops.begin()+Idx);
980 Ops.erase(Ops.begin()+OtherIdx-1);
981 Ops.push_back(NewAddRec);
982 return getAddExpr(Ops);
986 // Otherwise couldn't fold anything into this recurrence. Move onto the
990 // Okay, it looks like we really DO need an add expr. Check to see if we
991 // already have one, otherwise create a new one.
992 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
993 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
995 if (Result == 0) Result = new SCEVAddExpr(Ops);
1000 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1001 assert(!Ops.empty() && "Cannot get empty mul!");
1003 // Sort by complexity, this groups all similar expression types together.
1004 GroupByComplexity(Ops);
1006 // If there are any constants, fold them together.
1008 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1010 // C1*(C2+V) -> C1*C2 + C1*V
1011 if (Ops.size() == 2)
1012 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1013 if (Add->getNumOperands() == 2 &&
1014 isa<SCEVConstant>(Add->getOperand(0)))
1015 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1016 getMulExpr(LHSC, Add->getOperand(1)));
1020 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1021 // We found two constants, fold them together!
1022 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1023 RHSC->getValue()->getValue());
1024 Ops[0] = getConstant(Fold);
1025 Ops.erase(Ops.begin()+1); // Erase the folded element
1026 if (Ops.size() == 1) return Ops[0];
1027 LHSC = cast<SCEVConstant>(Ops[0]);
1030 // If we are left with a constant one being multiplied, strip it off.
1031 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1032 Ops.erase(Ops.begin());
1034 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1035 // If we have a multiply of zero, it will always be zero.
1040 // Skip over the add expression until we get to a multiply.
1041 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1044 if (Ops.size() == 1)
1047 // If there are mul operands inline them all into this expression.
1048 if (Idx < Ops.size()) {
1049 bool DeletedMul = false;
1050 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1051 // If we have an mul, expand the mul operands onto the end of the operands
1053 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1054 Ops.erase(Ops.begin()+Idx);
1058 // If we deleted at least one mul, we added operands to the end of the list,
1059 // and they are not necessarily sorted. Recurse to resort and resimplify
1060 // any operands we just aquired.
1062 return getMulExpr(Ops);
1065 // If there are any add recurrences in the operands list, see if any other
1066 // added values are loop invariant. If so, we can fold them into the
1068 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1071 // Scan over all recurrences, trying to fold loop invariants into them.
1072 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1073 // Scan all of the other operands to this mul and add them to the vector if
1074 // they are loop invariant w.r.t. the recurrence.
1075 std::vector<SCEVHandle> LIOps;
1076 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1077 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1078 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1079 LIOps.push_back(Ops[i]);
1080 Ops.erase(Ops.begin()+i);
1084 // If we found some loop invariants, fold them into the recurrence.
1085 if (!LIOps.empty()) {
1086 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1087 std::vector<SCEVHandle> NewOps;
1088 NewOps.reserve(AddRec->getNumOperands());
1089 if (LIOps.size() == 1) {
1090 SCEV *Scale = LIOps[0];
1091 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1092 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1094 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1095 std::vector<SCEVHandle> MulOps(LIOps);
1096 MulOps.push_back(AddRec->getOperand(i));
1097 NewOps.push_back(getMulExpr(MulOps));
1101 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1103 // If all of the other operands were loop invariant, we are done.
1104 if (Ops.size() == 1) return NewRec;
1106 // Otherwise, multiply the folded AddRec by the non-liv parts.
1107 for (unsigned i = 0;; ++i)
1108 if (Ops[i] == AddRec) {
1112 return getMulExpr(Ops);
1115 // Okay, if there weren't any loop invariants to be folded, check to see if
1116 // there are multiple AddRec's with the same loop induction variable being
1117 // multiplied together. If so, we can fold them.
1118 for (unsigned OtherIdx = Idx+1;
1119 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1120 if (OtherIdx != Idx) {
1121 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1122 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1123 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1124 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1125 SCEVHandle NewStart = getMulExpr(F->getStart(),
1127 SCEVHandle B = F->getStepRecurrence(*this);
1128 SCEVHandle D = G->getStepRecurrence(*this);
1129 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1132 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1134 if (Ops.size() == 2) return NewAddRec;
1136 Ops.erase(Ops.begin()+Idx);
1137 Ops.erase(Ops.begin()+OtherIdx-1);
1138 Ops.push_back(NewAddRec);
1139 return getMulExpr(Ops);
1143 // Otherwise couldn't fold anything into this recurrence. Move onto the
1147 // Okay, it looks like we really DO need an mul expr. Check to see if we
1148 // already have one, otherwise create a new one.
1149 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1150 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1153 Result = new SCEVMulExpr(Ops);
1157 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1158 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1159 if (RHSC->getValue()->equalsInt(1))
1160 return LHS; // X udiv 1 --> x
1162 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1163 Constant *LHSCV = LHSC->getValue();
1164 Constant *RHSCV = RHSC->getValue();
1165 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1169 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1171 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1172 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1177 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1178 /// specified loop. Simplify the expression as much as possible.
1179 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1180 const SCEVHandle &Step, const Loop *L) {
1181 std::vector<SCEVHandle> Operands;
1182 Operands.push_back(Start);
1183 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1184 if (StepChrec->getLoop() == L) {
1185 Operands.insert(Operands.end(), StepChrec->op_begin(),
1186 StepChrec->op_end());
1187 return getAddRecExpr(Operands, L);
1190 Operands.push_back(Step);
1191 return getAddRecExpr(Operands, L);
1194 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1195 /// specified loop. Simplify the expression as much as possible.
1196 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1198 if (Operands.size() == 1) return Operands[0];
1200 if (Operands.back()->isZero()) {
1201 Operands.pop_back();
1202 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1205 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1206 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1207 const Loop* NestedLoop = NestedAR->getLoop();
1208 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1209 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1210 NestedAR->op_end());
1211 SCEVHandle NestedARHandle(NestedAR);
1212 Operands[0] = NestedAR->getStart();
1213 NestedOperands[0] = getAddRecExpr(Operands, L);
1214 return getAddRecExpr(NestedOperands, NestedLoop);
1218 SCEVAddRecExpr *&Result =
1219 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1221 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1225 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1226 const SCEVHandle &RHS) {
1227 std::vector<SCEVHandle> Ops;
1230 return getSMaxExpr(Ops);
1233 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1234 assert(!Ops.empty() && "Cannot get empty smax!");
1235 if (Ops.size() == 1) return Ops[0];
1237 // Sort by complexity, this groups all similar expression types together.
1238 GroupByComplexity(Ops);
1240 // If there are any constants, fold them together.
1242 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1244 assert(Idx < Ops.size());
1245 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1246 // We found two constants, fold them together!
1247 ConstantInt *Fold = ConstantInt::get(
1248 APIntOps::smax(LHSC->getValue()->getValue(),
1249 RHSC->getValue()->getValue()));
1250 Ops[0] = getConstant(Fold);
1251 Ops.erase(Ops.begin()+1); // Erase the folded element
1252 if (Ops.size() == 1) return Ops[0];
1253 LHSC = cast<SCEVConstant>(Ops[0]);
1256 // If we are left with a constant -inf, strip it off.
1257 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1258 Ops.erase(Ops.begin());
1263 if (Ops.size() == 1) return Ops[0];
1265 // Find the first SMax
1266 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1269 // Check to see if one of the operands is an SMax. If so, expand its operands
1270 // onto our operand list, and recurse to simplify.
1271 if (Idx < Ops.size()) {
1272 bool DeletedSMax = false;
1273 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1274 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1275 Ops.erase(Ops.begin()+Idx);
1280 return getSMaxExpr(Ops);
1283 // Okay, check to see if the same value occurs in the operand list twice. If
1284 // so, delete one. Since we sorted the list, these values are required to
1286 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1287 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1288 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1292 if (Ops.size() == 1) return Ops[0];
1294 assert(!Ops.empty() && "Reduced smax down to nothing!");
1296 // Okay, it looks like we really DO need an smax expr. Check to see if we
1297 // already have one, otherwise create a new one.
1298 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1299 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1301 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1305 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1306 const SCEVHandle &RHS) {
1307 std::vector<SCEVHandle> Ops;
1310 return getUMaxExpr(Ops);
1313 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1314 assert(!Ops.empty() && "Cannot get empty umax!");
1315 if (Ops.size() == 1) return Ops[0];
1317 // Sort by complexity, this groups all similar expression types together.
1318 GroupByComplexity(Ops);
1320 // If there are any constants, fold them together.
1322 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1324 assert(Idx < Ops.size());
1325 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1326 // We found two constants, fold them together!
1327 ConstantInt *Fold = ConstantInt::get(
1328 APIntOps::umax(LHSC->getValue()->getValue(),
1329 RHSC->getValue()->getValue()));
1330 Ops[0] = getConstant(Fold);
1331 Ops.erase(Ops.begin()+1); // Erase the folded element
1332 if (Ops.size() == 1) return Ops[0];
1333 LHSC = cast<SCEVConstant>(Ops[0]);
1336 // If we are left with a constant zero, strip it off.
1337 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1338 Ops.erase(Ops.begin());
1343 if (Ops.size() == 1) return Ops[0];
1345 // Find the first UMax
1346 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1349 // Check to see if one of the operands is a UMax. If so, expand its operands
1350 // onto our operand list, and recurse to simplify.
1351 if (Idx < Ops.size()) {
1352 bool DeletedUMax = false;
1353 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1354 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1355 Ops.erase(Ops.begin()+Idx);
1360 return getUMaxExpr(Ops);
1363 // Okay, check to see if the same value occurs in the operand list twice. If
1364 // so, delete one. Since we sorted the list, these values are required to
1366 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1367 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1368 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1372 if (Ops.size() == 1) return Ops[0];
1374 assert(!Ops.empty() && "Reduced umax down to nothing!");
1376 // Okay, it looks like we really DO need a umax expr. Check to see if we
1377 // already have one, otherwise create a new one.
1378 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1379 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1381 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1385 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1386 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1387 return getConstant(CI);
1388 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1389 if (Result == 0) Result = new SCEVUnknown(V);
1394 //===----------------------------------------------------------------------===//
1395 // ScalarEvolutionsImpl Definition and Implementation
1396 //===----------------------------------------------------------------------===//
1398 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1402 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1403 /// SE - A reference to the public ScalarEvolution object.
1404 ScalarEvolution &SE;
1406 /// F - The function we are analyzing.
1410 /// LI - The loop information for the function we are currently analyzing.
1414 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1416 SCEVHandle UnknownValue;
1418 /// Scalars - This is a cache of the scalars we have analyzed so far.
1420 std::map<Value*, SCEVHandle> Scalars;
1422 /// IterationCounts - Cache the iteration count of the loops for this
1423 /// function as they are computed.
1424 std::map<const Loop*, SCEVHandle> IterationCounts;
1426 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1427 /// the PHI instructions that we attempt to compute constant evolutions for.
1428 /// This allows us to avoid potentially expensive recomputation of these
1429 /// properties. An instruction maps to null if we are unable to compute its
1431 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1434 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li)
1435 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1437 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1438 /// expression and create a new one.
1439 SCEVHandle getSCEV(Value *V);
1441 /// hasSCEV - Return true if the SCEV for this value has already been
1443 bool hasSCEV(Value *V) const {
1444 return Scalars.count(V);
1447 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1448 /// the specified value.
1449 void setSCEV(Value *V, const SCEVHandle &H) {
1450 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1451 assert(isNew && "This entry already existed!");
1456 /// getSCEVAtScope - Compute the value of the specified expression within
1457 /// the indicated loop (which may be null to indicate in no loop). If the
1458 /// expression cannot be evaluated, return UnknownValue itself.
1459 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1462 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
1463 /// a conditional between LHS and RHS.
1464 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
1465 SCEV *LHS, SCEV *RHS);
1467 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1468 /// an analyzable loop-invariant iteration count.
1469 bool hasLoopInvariantIterationCount(const Loop *L);
1471 /// forgetLoopIterationCount - This method should be called by the
1472 /// client when it has changed a loop in a way that may effect
1473 /// ScalarEvolution's ability to compute a trip count.
1474 void forgetLoopIterationCount(const Loop *L);
1476 /// getIterationCount - If the specified loop has a predictable iteration
1477 /// count, return it. Note that it is not valid to call this method on a
1478 /// loop without a loop-invariant iteration count.
1479 SCEVHandle getIterationCount(const Loop *L);
1481 /// deleteValueFromRecords - This method should be called by the
1482 /// client before it removes a value from the program, to make sure
1483 /// that no dangling references are left around.
1484 void deleteValueFromRecords(Value *V);
1487 /// createSCEV - We know that there is no SCEV for the specified value.
1488 /// Analyze the expression.
1489 SCEVHandle createSCEV(Value *V);
1491 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1493 SCEVHandle createNodeForPHI(PHINode *PN);
1495 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1496 /// for the specified instruction and replaces any references to the
1497 /// symbolic value SymName with the specified value. This is used during
1499 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1500 const SCEVHandle &SymName,
1501 const SCEVHandle &NewVal);
1503 /// ComputeIterationCount - Compute the number of times the specified loop
1505 SCEVHandle ComputeIterationCount(const Loop *L);
1507 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1508 /// 'icmp op load X, cst', try to see if we can compute the trip count.
1509 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1512 ICmpInst::Predicate p);
1514 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1515 /// constant number of times (the condition evolves only from constants),
1516 /// try to evaluate a few iterations of the loop until we get the exit
1517 /// condition gets a value of ExitWhen (true or false). If we cannot
1518 /// evaluate the trip count of the loop, return UnknownValue.
1519 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1522 /// HowFarToZero - Return the number of times a backedge comparing the
1523 /// specified value to zero will execute. If not computable, return
1525 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1527 /// HowFarToNonZero - Return the number of times a backedge checking the
1528 /// specified value for nonzero will execute. If not computable, return
1530 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1532 /// HowManyLessThans - Return the number of times a backedge containing the
1533 /// specified less-than comparison will execute. If not computable, return
1534 /// UnknownValue. isSigned specifies whether the less-than is signed.
1535 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1538 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
1539 /// (which may not be an immediate predecessor) which has exactly one
1540 /// successor from which BB is reachable, or null if no such block is
1542 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1544 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1545 /// in the header of its containing loop, we know the loop executes a
1546 /// constant number of times, and the PHI node is just a recurrence
1547 /// involving constants, fold it.
1548 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1553 //===----------------------------------------------------------------------===//
1554 // Basic SCEV Analysis and PHI Idiom Recognition Code
1557 /// deleteValueFromRecords - This method should be called by the
1558 /// client before it removes an instruction from the program, to make sure
1559 /// that no dangling references are left around.
1560 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1561 SmallVector<Value *, 16> Worklist;
1563 if (Scalars.erase(V)) {
1564 if (PHINode *PN = dyn_cast<PHINode>(V))
1565 ConstantEvolutionLoopExitValue.erase(PN);
1566 Worklist.push_back(V);
1569 while (!Worklist.empty()) {
1570 Value *VV = Worklist.back();
1571 Worklist.pop_back();
1573 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1575 Instruction *Inst = cast<Instruction>(*UI);
1576 if (Scalars.erase(Inst)) {
1577 if (PHINode *PN = dyn_cast<PHINode>(VV))
1578 ConstantEvolutionLoopExitValue.erase(PN);
1579 Worklist.push_back(Inst);
1586 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1587 /// expression and create a new one.
1588 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1589 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1591 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1592 if (I != Scalars.end()) return I->second;
1593 SCEVHandle S = createSCEV(V);
1594 Scalars.insert(std::make_pair(V, S));
1598 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1599 /// the specified instruction and replaces any references to the symbolic value
1600 /// SymName with the specified value. This is used during PHI resolution.
1601 void ScalarEvolutionsImpl::
1602 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1603 const SCEVHandle &NewVal) {
1604 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1605 if (SI == Scalars.end()) return;
1608 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
1609 if (NV == SI->second) return; // No change.
1611 SI->second = NV; // Update the scalars map!
1613 // Any instruction values that use this instruction might also need to be
1615 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1617 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1620 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1621 /// a loop header, making it a potential recurrence, or it doesn't.
1623 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1624 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1625 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1626 if (L->getHeader() == PN->getParent()) {
1627 // If it lives in the loop header, it has two incoming values, one
1628 // from outside the loop, and one from inside.
1629 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1630 unsigned BackEdge = IncomingEdge^1;
1632 // While we are analyzing this PHI node, handle its value symbolically.
1633 SCEVHandle SymbolicName = SE.getUnknown(PN);
1634 assert(Scalars.find(PN) == Scalars.end() &&
1635 "PHI node already processed?");
1636 Scalars.insert(std::make_pair(PN, SymbolicName));
1638 // Using this symbolic name for the PHI, analyze the value coming around
1640 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1642 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1643 // has a special value for the first iteration of the loop.
1645 // If the value coming around the backedge is an add with the symbolic
1646 // value we just inserted, then we found a simple induction variable!
1647 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1648 // If there is a single occurrence of the symbolic value, replace it
1649 // with a recurrence.
1650 unsigned FoundIndex = Add->getNumOperands();
1651 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1652 if (Add->getOperand(i) == SymbolicName)
1653 if (FoundIndex == e) {
1658 if (FoundIndex != Add->getNumOperands()) {
1659 // Create an add with everything but the specified operand.
1660 std::vector<SCEVHandle> Ops;
1661 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1662 if (i != FoundIndex)
1663 Ops.push_back(Add->getOperand(i));
1664 SCEVHandle Accum = SE.getAddExpr(Ops);
1666 // This is not a valid addrec if the step amount is varying each
1667 // loop iteration, but is not itself an addrec in this loop.
1668 if (Accum->isLoopInvariant(L) ||
1669 (isa<SCEVAddRecExpr>(Accum) &&
1670 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1671 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1672 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L);
1674 // Okay, for the entire analysis of this edge we assumed the PHI
1675 // to be symbolic. We now need to go back and update all of the
1676 // entries for the scalars that use the PHI (except for the PHI
1677 // itself) to use the new analyzed value instead of the "symbolic"
1679 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1683 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1684 // Otherwise, this could be a loop like this:
1685 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1686 // In this case, j = {1,+,1} and BEValue is j.
1687 // Because the other in-value of i (0) fits the evolution of BEValue
1688 // i really is an addrec evolution.
1689 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1690 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1692 // If StartVal = j.start - j.stride, we can use StartVal as the
1693 // initial step of the addrec evolution.
1694 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
1695 AddRec->getOperand(1))) {
1696 SCEVHandle PHISCEV =
1697 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1699 // Okay, for the entire analysis of this edge we assumed the PHI
1700 // to be symbolic. We now need to go back and update all of the
1701 // entries for the scalars that use the PHI (except for the PHI
1702 // itself) to use the new analyzed value instead of the "symbolic"
1704 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1710 return SymbolicName;
1713 // If it's not a loop phi, we can't handle it yet.
1714 return SE.getUnknown(PN);
1717 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1718 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1719 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1720 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1721 static uint32_t GetMinTrailingZeros(SCEVHandle S) {
1722 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1723 return C->getValue()->getValue().countTrailingZeros();
1725 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1726 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
1728 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1729 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1730 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1733 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1734 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1735 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1738 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1739 // The result is the min of all operands results.
1740 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1741 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1742 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1746 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1747 // The result is the sum of all operands results.
1748 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
1749 uint32_t BitWidth = M->getBitWidth();
1750 for (unsigned i = 1, e = M->getNumOperands();
1751 SumOpRes != BitWidth && i != e; ++i)
1752 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
1757 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1758 // The result is the min of all operands results.
1759 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1760 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1761 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1765 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1766 // The result is the min of all operands results.
1767 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1768 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1769 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1773 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1774 // The result is the min of all operands results.
1775 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1776 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1777 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1781 // SCEVUDivExpr, SCEVUnknown
1785 /// createSCEV - We know that there is no SCEV for the specified value.
1786 /// Analyze the expression.
1788 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1789 if (!isa<IntegerType>(V->getType()))
1790 return SE.getUnknown(V);
1792 unsigned Opcode = Instruction::UserOp1;
1793 if (Instruction *I = dyn_cast<Instruction>(V))
1794 Opcode = I->getOpcode();
1795 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1796 Opcode = CE->getOpcode();
1798 return SE.getUnknown(V);
1800 User *U = cast<User>(V);
1802 case Instruction::Add:
1803 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1804 getSCEV(U->getOperand(1)));
1805 case Instruction::Mul:
1806 return SE.getMulExpr(getSCEV(U->getOperand(0)),
1807 getSCEV(U->getOperand(1)));
1808 case Instruction::UDiv:
1809 return SE.getUDivExpr(getSCEV(U->getOperand(0)),
1810 getSCEV(U->getOperand(1)));
1811 case Instruction::Sub:
1812 return SE.getMinusSCEV(getSCEV(U->getOperand(0)),
1813 getSCEV(U->getOperand(1)));
1814 case Instruction::Or:
1815 // If the RHS of the Or is a constant, we may have something like:
1816 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1817 // optimizations will transparently handle this case.
1819 // In order for this transformation to be safe, the LHS must be of the
1820 // form X*(2^n) and the Or constant must be less than 2^n.
1821 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1822 SCEVHandle LHS = getSCEV(U->getOperand(0));
1823 const APInt &CIVal = CI->getValue();
1824 if (GetMinTrailingZeros(LHS) >=
1825 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1826 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1)));
1829 case Instruction::Xor:
1830 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1831 // If the RHS of the xor is a signbit, then this is just an add.
1832 // Instcombine turns add of signbit into xor as a strength reduction step.
1833 if (CI->getValue().isSignBit())
1834 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1835 getSCEV(U->getOperand(1)));
1837 // If the RHS of xor is -1, then this is a not operation.
1838 else if (CI->isAllOnesValue())
1839 return SE.getNotSCEV(getSCEV(U->getOperand(0)));
1843 case Instruction::Shl:
1844 // Turn shift left of a constant amount into a multiply.
1845 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1846 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1847 Constant *X = ConstantInt::get(
1848 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1849 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1853 case Instruction::LShr:
1854 // Turn logical shift right of a constant into a unsigned divide.
1855 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1856 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1857 Constant *X = ConstantInt::get(
1858 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1859 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1863 case Instruction::Trunc:
1864 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1866 case Instruction::ZExt:
1867 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1869 case Instruction::SExt:
1870 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1872 case Instruction::BitCast:
1873 // BitCasts are no-op casts so we just eliminate the cast.
1874 if (U->getType()->isInteger() &&
1875 U->getOperand(0)->getType()->isInteger())
1876 return getSCEV(U->getOperand(0));
1879 case Instruction::PHI:
1880 return createNodeForPHI(cast<PHINode>(U));
1882 case Instruction::Select:
1883 // This could be a smax or umax that was lowered earlier.
1884 // Try to recover it.
1885 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
1886 Value *LHS = ICI->getOperand(0);
1887 Value *RHS = ICI->getOperand(1);
1888 switch (ICI->getPredicate()) {
1889 case ICmpInst::ICMP_SLT:
1890 case ICmpInst::ICMP_SLE:
1891 std::swap(LHS, RHS);
1893 case ICmpInst::ICMP_SGT:
1894 case ICmpInst::ICMP_SGE:
1895 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1896 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1897 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1898 // ~smax(~x, ~y) == smin(x, y).
1899 return SE.getNotSCEV(SE.getSMaxExpr(
1900 SE.getNotSCEV(getSCEV(LHS)),
1901 SE.getNotSCEV(getSCEV(RHS))));
1903 case ICmpInst::ICMP_ULT:
1904 case ICmpInst::ICMP_ULE:
1905 std::swap(LHS, RHS);
1907 case ICmpInst::ICMP_UGT:
1908 case ICmpInst::ICMP_UGE:
1909 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1910 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
1911 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1912 // ~umax(~x, ~y) == umin(x, y)
1913 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
1914 SE.getNotSCEV(getSCEV(RHS))));
1921 default: // We cannot analyze this expression.
1925 return SE.getUnknown(V);
1930 //===----------------------------------------------------------------------===//
1931 // Iteration Count Computation Code
1934 /// getIterationCount - If the specified loop has a predictable iteration
1935 /// count, return it. Note that it is not valid to call this method on a
1936 /// loop without a loop-invariant iteration count.
1937 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1938 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1939 if (I == IterationCounts.end()) {
1940 SCEVHandle ItCount = ComputeIterationCount(L);
1941 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1942 if (ItCount != UnknownValue) {
1943 assert(ItCount->isLoopInvariant(L) &&
1944 "Computed trip count isn't loop invariant for loop!");
1945 ++NumTripCountsComputed;
1946 } else if (isa<PHINode>(L->getHeader()->begin())) {
1947 // Only count loops that have phi nodes as not being computable.
1948 ++NumTripCountsNotComputed;
1954 /// forgetLoopIterationCount - This method should be called by the
1955 /// client when it has changed a loop in a way that may effect
1956 /// ScalarEvolution's ability to compute a trip count.
1957 void ScalarEvolutionsImpl::forgetLoopIterationCount(const Loop *L) {
1958 IterationCounts.erase(L);
1961 /// ComputeIterationCount - Compute the number of times the specified loop
1963 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1964 // If the loop has a non-one exit block count, we can't analyze it.
1965 SmallVector<BasicBlock*, 8> ExitBlocks;
1966 L->getExitBlocks(ExitBlocks);
1967 if (ExitBlocks.size() != 1) return UnknownValue;
1969 // Okay, there is one exit block. Try to find the condition that causes the
1970 // loop to be exited.
1971 BasicBlock *ExitBlock = ExitBlocks[0];
1973 BasicBlock *ExitingBlock = 0;
1974 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1976 if (L->contains(*PI)) {
1977 if (ExitingBlock == 0)
1980 return UnknownValue; // More than one block exiting!
1982 assert(ExitingBlock && "No exits from loop, something is broken!");
1984 // Okay, we've computed the exiting block. See what condition causes us to
1987 // FIXME: we should be able to handle switch instructions (with a single exit)
1988 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1989 if (ExitBr == 0) return UnknownValue;
1990 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1992 // At this point, we know we have a conditional branch that determines whether
1993 // the loop is exited. However, we don't know if the branch is executed each
1994 // time through the loop. If not, then the execution count of the branch will
1995 // not be equal to the trip count of the loop.
1997 // Currently we check for this by checking to see if the Exit branch goes to
1998 // the loop header. If so, we know it will always execute the same number of
1999 // times as the loop. We also handle the case where the exit block *is* the
2000 // loop header. This is common for un-rotated loops. More extensive analysis
2001 // could be done to handle more cases here.
2002 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2003 ExitBr->getSuccessor(1) != L->getHeader() &&
2004 ExitBr->getParent() != L->getHeader())
2005 return UnknownValue;
2007 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2009 // If it's not an integer comparison then compute it the hard way.
2010 // Note that ICmpInst deals with pointer comparisons too so we must check
2011 // the type of the operand.
2012 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2013 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
2014 ExitBr->getSuccessor(0) == ExitBlock);
2016 // If the condition was exit on true, convert the condition to exit on false
2017 ICmpInst::Predicate Cond;
2018 if (ExitBr->getSuccessor(1) == ExitBlock)
2019 Cond = ExitCond->getPredicate();
2021 Cond = ExitCond->getInversePredicate();
2023 // Handle common loops like: for (X = "string"; *X; ++X)
2024 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2025 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2027 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
2028 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2031 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2032 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2034 // Try to evaluate any dependencies out of the loop.
2035 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2036 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2037 Tmp = getSCEVAtScope(RHS, L);
2038 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2040 // At this point, we would like to compute how many iterations of the
2041 // loop the predicate will return true for these inputs.
2042 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2043 // If there is a loop-invariant, force it into the RHS.
2044 std::swap(LHS, RHS);
2045 Cond = ICmpInst::getSwappedPredicate(Cond);
2048 // FIXME: think about handling pointer comparisons! i.e.:
2049 // while (P != P+100) ++P;
2051 // If we have a comparison of a chrec against a constant, try to use value
2052 // ranges to answer this query.
2053 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2054 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2055 if (AddRec->getLoop() == L) {
2056 // Form the comparison range using the constant of the correct type so
2057 // that the ConstantRange class knows to do a signed or unsigned
2059 ConstantInt *CompVal = RHSC->getValue();
2060 const Type *RealTy = ExitCond->getOperand(0)->getType();
2061 CompVal = dyn_cast<ConstantInt>(
2062 ConstantExpr::getBitCast(CompVal, RealTy));
2064 // Form the constant range.
2065 ConstantRange CompRange(
2066 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2068 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
2069 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2074 case ICmpInst::ICMP_NE: { // while (X != Y)
2075 // Convert to: while (X-Y != 0)
2076 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
2077 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2080 case ICmpInst::ICMP_EQ: {
2081 // Convert to: while (X-Y == 0) // while (X == Y)
2082 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
2083 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2086 case ICmpInst::ICMP_SLT: {
2087 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
2088 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2091 case ICmpInst::ICMP_SGT: {
2092 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2093 SE.getNotSCEV(RHS), L, true);
2094 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2097 case ICmpInst::ICMP_ULT: {
2098 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
2099 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2102 case ICmpInst::ICMP_UGT: {
2103 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2104 SE.getNotSCEV(RHS), L, false);
2105 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2110 cerr << "ComputeIterationCount ";
2111 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2112 cerr << "[unsigned] ";
2114 << Instruction::getOpcodeName(Instruction::ICmp)
2115 << " " << *RHS << "\n";
2119 return ComputeIterationCountExhaustively(L, ExitCond,
2120 ExitBr->getSuccessor(0) == ExitBlock);
2123 static ConstantInt *
2124 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2125 ScalarEvolution &SE) {
2126 SCEVHandle InVal = SE.getConstant(C);
2127 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2128 assert(isa<SCEVConstant>(Val) &&
2129 "Evaluation of SCEV at constant didn't fold correctly?");
2130 return cast<SCEVConstant>(Val)->getValue();
2133 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2134 /// and a GEP expression (missing the pointer index) indexing into it, return
2135 /// the addressed element of the initializer or null if the index expression is
2138 GetAddressedElementFromGlobal(GlobalVariable *GV,
2139 const std::vector<ConstantInt*> &Indices) {
2140 Constant *Init = GV->getInitializer();
2141 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2142 uint64_t Idx = Indices[i]->getZExtValue();
2143 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2144 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2145 Init = cast<Constant>(CS->getOperand(Idx));
2146 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2147 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2148 Init = cast<Constant>(CA->getOperand(Idx));
2149 } else if (isa<ConstantAggregateZero>(Init)) {
2150 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2151 assert(Idx < STy->getNumElements() && "Bad struct index!");
2152 Init = Constant::getNullValue(STy->getElementType(Idx));
2153 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2154 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2155 Init = Constant::getNullValue(ATy->getElementType());
2157 assert(0 && "Unknown constant aggregate type!");
2161 return 0; // Unknown initializer type
2167 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
2168 /// 'icmp op load X, cst', try to see if we can compute the trip count.
2169 SCEVHandle ScalarEvolutionsImpl::
2170 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
2172 ICmpInst::Predicate predicate) {
2173 if (LI->isVolatile()) return UnknownValue;
2175 // Check to see if the loaded pointer is a getelementptr of a global.
2176 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2177 if (!GEP) return UnknownValue;
2179 // Make sure that it is really a constant global we are gepping, with an
2180 // initializer, and make sure the first IDX is really 0.
2181 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2182 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2183 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2184 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2185 return UnknownValue;
2187 // Okay, we allow one non-constant index into the GEP instruction.
2189 std::vector<ConstantInt*> Indexes;
2190 unsigned VarIdxNum = 0;
2191 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2192 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2193 Indexes.push_back(CI);
2194 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2195 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2196 VarIdx = GEP->getOperand(i);
2198 Indexes.push_back(0);
2201 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2202 // Check to see if X is a loop variant variable value now.
2203 SCEVHandle Idx = getSCEV(VarIdx);
2204 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2205 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2207 // We can only recognize very limited forms of loop index expressions, in
2208 // particular, only affine AddRec's like {C1,+,C2}.
2209 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2210 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2211 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2212 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2213 return UnknownValue;
2215 unsigned MaxSteps = MaxBruteForceIterations;
2216 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2217 ConstantInt *ItCst =
2218 ConstantInt::get(IdxExpr->getType(), IterationNum);
2219 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
2221 // Form the GEP offset.
2222 Indexes[VarIdxNum] = Val;
2224 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2225 if (Result == 0) break; // Cannot compute!
2227 // Evaluate the condition for this iteration.
2228 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2229 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2230 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2232 cerr << "\n***\n*** Computed loop count " << *ItCst
2233 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2236 ++NumArrayLenItCounts;
2237 return SE.getConstant(ItCst); // Found terminating iteration!
2240 return UnknownValue;
2244 /// CanConstantFold - Return true if we can constant fold an instruction of the
2245 /// specified type, assuming that all operands were constants.
2246 static bool CanConstantFold(const Instruction *I) {
2247 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2248 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2251 if (const CallInst *CI = dyn_cast<CallInst>(I))
2252 if (const Function *F = CI->getCalledFunction())
2253 return canConstantFoldCallTo(F);
2257 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2258 /// in the loop that V is derived from. We allow arbitrary operations along the
2259 /// way, but the operands of an operation must either be constants or a value
2260 /// derived from a constant PHI. If this expression does not fit with these
2261 /// constraints, return null.
2262 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2263 // If this is not an instruction, or if this is an instruction outside of the
2264 // loop, it can't be derived from a loop PHI.
2265 Instruction *I = dyn_cast<Instruction>(V);
2266 if (I == 0 || !L->contains(I->getParent())) return 0;
2268 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2269 if (L->getHeader() == I->getParent())
2272 // We don't currently keep track of the control flow needed to evaluate
2273 // PHIs, so we cannot handle PHIs inside of loops.
2277 // If we won't be able to constant fold this expression even if the operands
2278 // are constants, return early.
2279 if (!CanConstantFold(I)) return 0;
2281 // Otherwise, we can evaluate this instruction if all of its operands are
2282 // constant or derived from a PHI node themselves.
2284 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2285 if (!(isa<Constant>(I->getOperand(Op)) ||
2286 isa<GlobalValue>(I->getOperand(Op)))) {
2287 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2288 if (P == 0) return 0; // Not evolving from PHI
2292 return 0; // Evolving from multiple different PHIs.
2295 // This is a expression evolving from a constant PHI!
2299 /// EvaluateExpression - Given an expression that passes the
2300 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2301 /// in the loop has the value PHIVal. If we can't fold this expression for some
2302 /// reason, return null.
2303 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2304 if (isa<PHINode>(V)) return PHIVal;
2305 if (Constant *C = dyn_cast<Constant>(V)) return C;
2306 Instruction *I = cast<Instruction>(V);
2308 std::vector<Constant*> Operands;
2309 Operands.resize(I->getNumOperands());
2311 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2312 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2313 if (Operands[i] == 0) return 0;
2316 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2317 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2318 &Operands[0], Operands.size());
2320 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2321 &Operands[0], Operands.size());
2324 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2325 /// in the header of its containing loop, we know the loop executes a
2326 /// constant number of times, and the PHI node is just a recurrence
2327 /// involving constants, fold it.
2328 Constant *ScalarEvolutionsImpl::
2329 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
2330 std::map<PHINode*, Constant*>::iterator I =
2331 ConstantEvolutionLoopExitValue.find(PN);
2332 if (I != ConstantEvolutionLoopExitValue.end())
2335 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
2336 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2338 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2340 // Since the loop is canonicalized, the PHI node must have two entries. One
2341 // entry must be a constant (coming in from outside of the loop), and the
2342 // second must be derived from the same PHI.
2343 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2344 Constant *StartCST =
2345 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2347 return RetVal = 0; // Must be a constant.
2349 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2350 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2352 return RetVal = 0; // Not derived from same PHI.
2354 // Execute the loop symbolically to determine the exit value.
2355 if (Its.getActiveBits() >= 32)
2356 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2358 unsigned NumIterations = Its.getZExtValue(); // must be in range
2359 unsigned IterationNum = 0;
2360 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2361 if (IterationNum == NumIterations)
2362 return RetVal = PHIVal; // Got exit value!
2364 // Compute the value of the PHI node for the next iteration.
2365 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2366 if (NextPHI == PHIVal)
2367 return RetVal = NextPHI; // Stopped evolving!
2369 return 0; // Couldn't evaluate!
2374 /// ComputeIterationCountExhaustively - If the trip is known to execute a
2375 /// constant number of times (the condition evolves only from constants),
2376 /// try to evaluate a few iterations of the loop until we get the exit
2377 /// condition gets a value of ExitWhen (true or false). If we cannot
2378 /// evaluate the trip count of the loop, return UnknownValue.
2379 SCEVHandle ScalarEvolutionsImpl::
2380 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2381 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2382 if (PN == 0) return UnknownValue;
2384 // Since the loop is canonicalized, the PHI node must have two entries. One
2385 // entry must be a constant (coming in from outside of the loop), and the
2386 // second must be derived from the same PHI.
2387 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2388 Constant *StartCST =
2389 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2390 if (StartCST == 0) return UnknownValue; // Must be a constant.
2392 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2393 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2394 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2396 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2397 // the loop symbolically to determine when the condition gets a value of
2399 unsigned IterationNum = 0;
2400 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2401 for (Constant *PHIVal = StartCST;
2402 IterationNum != MaxIterations; ++IterationNum) {
2403 ConstantInt *CondVal =
2404 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2406 // Couldn't symbolically evaluate.
2407 if (!CondVal) return UnknownValue;
2409 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2410 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2411 ++NumBruteForceTripCountsComputed;
2412 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2415 // Compute the value of the PHI node for the next iteration.
2416 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2417 if (NextPHI == 0 || NextPHI == PHIVal)
2418 return UnknownValue; // Couldn't evaluate or not making progress...
2422 // Too many iterations were needed to evaluate.
2423 return UnknownValue;
2426 /// getSCEVAtScope - Compute the value of the specified expression within the
2427 /// indicated loop (which may be null to indicate in no loop). If the
2428 /// expression cannot be evaluated, return UnknownValue.
2429 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2430 // FIXME: this should be turned into a virtual method on SCEV!
2432 if (isa<SCEVConstant>(V)) return V;
2434 // If this instruction is evolved from a constant-evolving PHI, compute the
2435 // exit value from the loop without using SCEVs.
2436 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2437 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2438 const Loop *LI = this->LI[I->getParent()];
2439 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2440 if (PHINode *PN = dyn_cast<PHINode>(I))
2441 if (PN->getParent() == LI->getHeader()) {
2442 // Okay, there is no closed form solution for the PHI node. Check
2443 // to see if the loop that contains it has a known iteration count.
2444 // If so, we may be able to force computation of the exit value.
2445 SCEVHandle IterationCount = getIterationCount(LI);
2446 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
2447 // Okay, we know how many times the containing loop executes. If
2448 // this is a constant evolving PHI node, get the final value at
2449 // the specified iteration number.
2450 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2451 ICC->getValue()->getValue(),
2453 if (RV) return SE.getUnknown(RV);
2457 // Okay, this is an expression that we cannot symbolically evaluate
2458 // into a SCEV. Check to see if it's possible to symbolically evaluate
2459 // the arguments into constants, and if so, try to constant propagate the
2460 // result. This is particularly useful for computing loop exit values.
2461 if (CanConstantFold(I)) {
2462 std::vector<Constant*> Operands;
2463 Operands.reserve(I->getNumOperands());
2464 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2465 Value *Op = I->getOperand(i);
2466 if (Constant *C = dyn_cast<Constant>(Op)) {
2467 Operands.push_back(C);
2469 // If any of the operands is non-constant and if they are
2470 // non-integer, don't even try to analyze them with scev techniques.
2471 if (!isa<IntegerType>(Op->getType()))
2474 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2475 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2476 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2479 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2480 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2481 Operands.push_back(ConstantExpr::getIntegerCast(C,
2493 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2494 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2495 &Operands[0], Operands.size());
2497 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2498 &Operands[0], Operands.size());
2499 return SE.getUnknown(C);
2503 // This is some other type of SCEVUnknown, just return it.
2507 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2508 // Avoid performing the look-up in the common case where the specified
2509 // expression has no loop-variant portions.
2510 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2511 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2512 if (OpAtScope != Comm->getOperand(i)) {
2513 if (OpAtScope == UnknownValue) return UnknownValue;
2514 // Okay, at least one of these operands is loop variant but might be
2515 // foldable. Build a new instance of the folded commutative expression.
2516 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2517 NewOps.push_back(OpAtScope);
2519 for (++i; i != e; ++i) {
2520 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2521 if (OpAtScope == UnknownValue) return UnknownValue;
2522 NewOps.push_back(OpAtScope);
2524 if (isa<SCEVAddExpr>(Comm))
2525 return SE.getAddExpr(NewOps);
2526 if (isa<SCEVMulExpr>(Comm))
2527 return SE.getMulExpr(NewOps);
2528 if (isa<SCEVSMaxExpr>(Comm))
2529 return SE.getSMaxExpr(NewOps);
2530 if (isa<SCEVUMaxExpr>(Comm))
2531 return SE.getUMaxExpr(NewOps);
2532 assert(0 && "Unknown commutative SCEV type!");
2535 // If we got here, all operands are loop invariant.
2539 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2540 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2541 if (LHS == UnknownValue) return LHS;
2542 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2543 if (RHS == UnknownValue) return RHS;
2544 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2545 return Div; // must be loop invariant
2546 return SE.getUDivExpr(LHS, RHS);
2549 // If this is a loop recurrence for a loop that does not contain L, then we
2550 // are dealing with the final value computed by the loop.
2551 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2552 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2553 // To evaluate this recurrence, we need to know how many times the AddRec
2554 // loop iterates. Compute this now.
2555 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2556 if (IterationCount == UnknownValue) return UnknownValue;
2558 // Then, evaluate the AddRec.
2559 return AddRec->evaluateAtIteration(IterationCount, SE);
2561 return UnknownValue;
2564 //assert(0 && "Unknown SCEV type!");
2565 return UnknownValue;
2568 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2569 /// following equation:
2571 /// A * X = B (mod N)
2573 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2574 /// A and B isn't important.
2576 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2577 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2578 ScalarEvolution &SE) {
2579 uint32_t BW = A.getBitWidth();
2580 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2581 assert(A != 0 && "A must be non-zero.");
2585 // The gcd of A and N may have only one prime factor: 2. The number of
2586 // trailing zeros in A is its multiplicity
2587 uint32_t Mult2 = A.countTrailingZeros();
2590 // 2. Check if B is divisible by D.
2592 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2593 // is not less than multiplicity of this prime factor for D.
2594 if (B.countTrailingZeros() < Mult2)
2595 return new SCEVCouldNotCompute();
2597 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2600 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2601 // bit width during computations.
2602 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2603 APInt Mod(BW + 1, 0);
2604 Mod.set(BW - Mult2); // Mod = N / D
2605 APInt I = AD.multiplicativeInverse(Mod);
2607 // 4. Compute the minimum unsigned root of the equation:
2608 // I * (B / D) mod (N / D)
2609 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2611 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2613 return SE.getConstant(Result.trunc(BW));
2616 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2617 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2618 /// might be the same) or two SCEVCouldNotCompute objects.
2620 static std::pair<SCEVHandle,SCEVHandle>
2621 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2622 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2623 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2624 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2625 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2627 // We currently can only solve this if the coefficients are constants.
2628 if (!LC || !MC || !NC) {
2629 SCEV *CNC = new SCEVCouldNotCompute();
2630 return std::make_pair(CNC, CNC);
2633 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2634 const APInt &L = LC->getValue()->getValue();
2635 const APInt &M = MC->getValue()->getValue();
2636 const APInt &N = NC->getValue()->getValue();
2637 APInt Two(BitWidth, 2);
2638 APInt Four(BitWidth, 4);
2641 using namespace APIntOps;
2643 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2644 // The B coefficient is M-N/2
2648 // The A coefficient is N/2
2649 APInt A(N.sdiv(Two));
2651 // Compute the B^2-4ac term.
2654 SqrtTerm -= Four * (A * C);
2656 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2657 // integer value or else APInt::sqrt() will assert.
2658 APInt SqrtVal(SqrtTerm.sqrt());
2660 // Compute the two solutions for the quadratic formula.
2661 // The divisions must be performed as signed divisions.
2663 APInt TwoA( A << 1 );
2664 if (TwoA.isMinValue()) {
2665 SCEV *CNC = new SCEVCouldNotCompute();
2666 return std::make_pair(CNC, CNC);
2669 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2670 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2672 return std::make_pair(SE.getConstant(Solution1),
2673 SE.getConstant(Solution2));
2674 } // end APIntOps namespace
2677 /// HowFarToZero - Return the number of times a backedge comparing the specified
2678 /// value to zero will execute. If not computable, return UnknownValue
2679 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2680 // If the value is a constant
2681 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2682 // If the value is already zero, the branch will execute zero times.
2683 if (C->getValue()->isZero()) return C;
2684 return UnknownValue; // Otherwise it will loop infinitely.
2687 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2688 if (!AddRec || AddRec->getLoop() != L)
2689 return UnknownValue;
2691 if (AddRec->isAffine()) {
2692 // If this is an affine expression, the execution count of this branch is
2693 // the minimum unsigned root of the following equation:
2695 // Start + Step*N = 0 (mod 2^BW)
2699 // Step*N = -Start (mod 2^BW)
2701 // where BW is the common bit width of Start and Step.
2703 // Get the initial value for the loop.
2704 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2705 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2707 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2709 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2710 // For now we handle only constant steps.
2712 // First, handle unitary steps.
2713 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2714 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned)
2715 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2716 return Start; // N = Start (as unsigned)
2718 // Then, try to solve the above equation provided that Start is constant.
2719 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2720 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2721 -StartC->getValue()->getValue(),SE);
2723 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2724 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2725 // the quadratic equation to solve it.
2726 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
2727 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2728 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2731 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2732 << " sol#2: " << *R2 << "\n";
2734 // Pick the smallest positive root value.
2735 if (ConstantInt *CB =
2736 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2737 R1->getValue(), R2->getValue()))) {
2738 if (CB->getZExtValue() == false)
2739 std::swap(R1, R2); // R1 is the minimum root now.
2741 // We can only use this value if the chrec ends up with an exact zero
2742 // value at this index. When solving for "X*X != 5", for example, we
2743 // should not accept a root of 2.
2744 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
2746 return R1; // We found a quadratic root!
2751 return UnknownValue;
2754 /// HowFarToNonZero - Return the number of times a backedge checking the
2755 /// specified value for nonzero will execute. If not computable, return
2757 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2758 // Loops that look like: while (X == 0) are very strange indeed. We don't
2759 // handle them yet except for the trivial case. This could be expanded in the
2760 // future as needed.
2762 // If the value is a constant, check to see if it is known to be non-zero
2763 // already. If so, the backedge will execute zero times.
2764 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2765 if (!C->getValue()->isNullValue())
2766 return SE.getIntegerSCEV(0, C->getType());
2767 return UnknownValue; // Otherwise it will loop infinitely.
2770 // We could implement others, but I really doubt anyone writes loops like
2771 // this, and if they did, they would already be constant folded.
2772 return UnknownValue;
2775 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2776 /// (which may not be an immediate predecessor) which has exactly one
2777 /// successor from which BB is reachable, or null if no such block is
2781 ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2782 // If the block has a unique predecessor, the predecessor must have
2783 // no other successors from which BB is reachable.
2784 if (BasicBlock *Pred = BB->getSinglePredecessor())
2787 // A loop's header is defined to be a block that dominates the loop.
2788 // If the loop has a preheader, it must be a block that has exactly
2789 // one successor that can reach BB. This is slightly more strict
2790 // than necessary, but works if critical edges are split.
2791 if (Loop *L = LI.getLoopFor(BB))
2792 return L->getLoopPreheader();
2797 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
2798 /// a conditional between LHS and RHS.
2799 bool ScalarEvolutionsImpl::isLoopGuardedByCond(const Loop *L,
2800 ICmpInst::Predicate Pred,
2801 SCEV *LHS, SCEV *RHS) {
2802 BasicBlock *Preheader = L->getLoopPreheader();
2803 BasicBlock *PreheaderDest = L->getHeader();
2805 // Starting at the preheader, climb up the predecessor chain, as long as
2806 // there are predecessors that can be found that have unique successors
2807 // leading to the original header.
2809 PreheaderDest = Preheader,
2810 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
2812 BranchInst *LoopEntryPredicate =
2813 dyn_cast<BranchInst>(Preheader->getTerminator());
2814 if (!LoopEntryPredicate ||
2815 LoopEntryPredicate->isUnconditional())
2818 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
2821 // Now that we found a conditional branch that dominates the loop, check to
2822 // see if it is the comparison we are looking for.
2823 Value *PreCondLHS = ICI->getOperand(0);
2824 Value *PreCondRHS = ICI->getOperand(1);
2825 ICmpInst::Predicate Cond;
2826 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2827 Cond = ICI->getPredicate();
2829 Cond = ICI->getInversePredicate();
2832 ; // An exact match.
2833 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
2834 ; // The actual condition is beyond sufficient.
2836 // Check a few special cases.
2838 case ICmpInst::ICMP_UGT:
2839 if (Pred == ICmpInst::ICMP_ULT) {
2840 std::swap(PreCondLHS, PreCondRHS);
2841 Cond = ICmpInst::ICMP_ULT;
2845 case ICmpInst::ICMP_SGT:
2846 if (Pred == ICmpInst::ICMP_SLT) {
2847 std::swap(PreCondLHS, PreCondRHS);
2848 Cond = ICmpInst::ICMP_SLT;
2852 case ICmpInst::ICMP_NE:
2853 // Expressions like (x >u 0) are often canonicalized to (x != 0),
2854 // so check for this case by checking if the NE is comparing against
2855 // a minimum or maximum constant.
2856 if (!ICmpInst::isTrueWhenEqual(Pred))
2857 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
2858 const APInt &A = CI->getValue();
2860 case ICmpInst::ICMP_SLT:
2861 if (A.isMaxSignedValue()) break;
2863 case ICmpInst::ICMP_SGT:
2864 if (A.isMinSignedValue()) break;
2866 case ICmpInst::ICMP_ULT:
2867 if (A.isMaxValue()) break;
2869 case ICmpInst::ICMP_UGT:
2870 if (A.isMinValue()) break;
2875 Cond = ICmpInst::ICMP_NE;
2876 // NE is symmetric but the original comparison may not be. Swap
2877 // the operands if necessary so that they match below.
2878 if (isa<SCEVConstant>(LHS))
2879 std::swap(PreCondLHS, PreCondRHS);
2884 // We weren't able to reconcile the condition.
2888 if (!PreCondLHS->getType()->isInteger()) continue;
2890 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
2891 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
2892 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
2893 (LHS == SE.getNotSCEV(PreCondRHSSCEV) &&
2894 RHS == SE.getNotSCEV(PreCondLHSSCEV)))
2901 /// HowManyLessThans - Return the number of times a backedge containing the
2902 /// specified less-than comparison will execute. If not computable, return
2904 SCEVHandle ScalarEvolutionsImpl::
2905 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
2906 // Only handle: "ADDREC < LoopInvariant".
2907 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2909 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2910 if (!AddRec || AddRec->getLoop() != L)
2911 return UnknownValue;
2913 if (AddRec->isAffine()) {
2914 // FORNOW: We only support unit strides.
2915 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
2916 if (AddRec->getOperand(1) != One)
2917 return UnknownValue;
2919 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
2920 // m. So, we count the number of iterations in which {n,+,1} < m is true.
2921 // Note that we cannot simply return max(m-n,0) because it's not safe to
2922 // treat m-n as signed nor unsigned due to overflow possibility.
2924 // First, we get the value of the LHS in the first iteration: n
2925 SCEVHandle Start = AddRec->getOperand(0);
2927 if (isLoopGuardedByCond(L,
2928 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
2929 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) {
2930 // Since we know that the condition is true in order to enter the loop,
2931 // we know that it will run exactly m-n times.
2932 return SE.getMinusSCEV(RHS, Start);
2934 // Then, we get the value of the LHS in the first iteration in which the
2935 // above condition doesn't hold. This equals to max(m,n).
2936 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
2937 : SE.getUMaxExpr(RHS, Start);
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.getMinusSCEV(End, Start);
2945 return UnknownValue;
2948 /// getNumIterationsInRange - Return the number of iterations of this loop that
2949 /// produce values in the specified constant range. Another way of looking at
2950 /// this is that it returns the first iteration number where the value is not in
2951 /// the condition, thus computing the exit count. If the iteration count can't
2952 /// be computed, an instance of SCEVCouldNotCompute is returned.
2953 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2954 ScalarEvolution &SE) const {
2955 if (Range.isFullSet()) // Infinite loop.
2956 return new SCEVCouldNotCompute();
2958 // If the start is a non-zero constant, shift the range to simplify things.
2959 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2960 if (!SC->getValue()->isZero()) {
2961 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2962 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
2963 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
2964 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2965 return ShiftedAddRec->getNumIterationsInRange(
2966 Range.subtract(SC->getValue()->getValue()), SE);
2967 // This is strange and shouldn't happen.
2968 return new SCEVCouldNotCompute();
2971 // The only time we can solve this is when we have all constant indices.
2972 // Otherwise, we cannot determine the overflow conditions.
2973 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2974 if (!isa<SCEVConstant>(getOperand(i)))
2975 return new SCEVCouldNotCompute();
2978 // Okay at this point we know that all elements of the chrec are constants and
2979 // that the start element is zero.
2981 // First check to see if the range contains zero. If not, the first
2983 if (!Range.contains(APInt(getBitWidth(),0)))
2984 return SE.getConstant(ConstantInt::get(getType(),0));
2987 // If this is an affine expression then we have this situation:
2988 // Solve {0,+,A} in Range === Ax in Range
2990 // We know that zero is in the range. If A is positive then we know that
2991 // the upper value of the range must be the first possible exit value.
2992 // If A is negative then the lower of the range is the last possible loop
2993 // value. Also note that we already checked for a full range.
2994 APInt One(getBitWidth(),1);
2995 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2996 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
2998 // The exit value should be (End+A)/A.
2999 APInt ExitVal = (End + A).udiv(A);
3000 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3002 // Evaluate at the exit value. If we really did fall out of the valid
3003 // range, then we computed our trip count, otherwise wrap around or other
3004 // things must have happened.
3005 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3006 if (Range.contains(Val->getValue()))
3007 return new SCEVCouldNotCompute(); // Something strange happened
3009 // Ensure that the previous value is in the range. This is a sanity check.
3010 assert(Range.contains(
3011 EvaluateConstantChrecAtConstant(this,
3012 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3013 "Linear scev computation is off in a bad way!");
3014 return SE.getConstant(ExitValue);
3015 } else if (isQuadratic()) {
3016 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3017 // quadratic equation to solve it. To do this, we must frame our problem in
3018 // terms of figuring out when zero is crossed, instead of when
3019 // Range.getUpper() is crossed.
3020 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3021 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3022 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3024 // Next, solve the constructed addrec
3025 std::pair<SCEVHandle,SCEVHandle> Roots =
3026 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3027 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3028 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3030 // Pick the smallest positive root value.
3031 if (ConstantInt *CB =
3032 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3033 R1->getValue(), R2->getValue()))) {
3034 if (CB->getZExtValue() == false)
3035 std::swap(R1, R2); // R1 is the minimum root now.
3037 // Make sure the root is not off by one. The returned iteration should
3038 // not be in the range, but the previous one should be. When solving
3039 // for "X*X < 5", for example, we should not return a root of 2.
3040 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3043 if (Range.contains(R1Val->getValue())) {
3044 // The next iteration must be out of the range...
3045 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3047 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3048 if (!Range.contains(R1Val->getValue()))
3049 return SE.getConstant(NextVal);
3050 return new SCEVCouldNotCompute(); // Something strange happened
3053 // If R1 was not in the range, then it is a good return value. Make
3054 // sure that R1-1 WAS in the range though, just in case.
3055 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3056 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3057 if (Range.contains(R1Val->getValue()))
3059 return new SCEVCouldNotCompute(); // Something strange happened
3064 return new SCEVCouldNotCompute();
3069 //===----------------------------------------------------------------------===//
3070 // ScalarEvolution Class Implementation
3071 //===----------------------------------------------------------------------===//
3073 bool ScalarEvolution::runOnFunction(Function &F) {
3074 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
3078 void ScalarEvolution::releaseMemory() {
3079 delete (ScalarEvolutionsImpl*)Impl;
3083 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3084 AU.setPreservesAll();
3085 AU.addRequiredTransitive<LoopInfo>();
3088 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
3089 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
3092 /// hasSCEV - Return true if the SCEV for this value has already been
3094 bool ScalarEvolution::hasSCEV(Value *V) const {
3095 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
3099 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
3100 /// the specified value.
3101 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
3102 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
3106 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3107 ICmpInst::Predicate Pred,
3108 SCEV *LHS, SCEV *RHS) {
3109 return ((ScalarEvolutionsImpl*)Impl)->isLoopGuardedByCond(L, Pred,
3113 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
3114 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
3117 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
3118 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
3121 void ScalarEvolution::forgetLoopIterationCount(const Loop *L) {
3122 return ((ScalarEvolutionsImpl*)Impl)->forgetLoopIterationCount(L);
3125 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
3126 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
3129 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
3130 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
3133 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
3135 // Print all inner loops first
3136 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3137 PrintLoopInfo(OS, SE, *I);
3139 OS << "Loop " << L->getHeader()->getName() << ": ";
3141 SmallVector<BasicBlock*, 8> ExitBlocks;
3142 L->getExitBlocks(ExitBlocks);
3143 if (ExitBlocks.size() != 1)
3144 OS << "<multiple exits> ";
3146 if (SE->hasLoopInvariantIterationCount(L)) {
3147 OS << *SE->getIterationCount(L) << " iterations! ";
3149 OS << "Unpredictable iteration count. ";
3155 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
3156 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
3157 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
3159 OS << "Classifying expressions for: " << F.getName() << "\n";
3160 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3161 if (I->getType()->isInteger()) {
3164 SCEVHandle SV = getSCEV(&*I);
3168 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
3170 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
3171 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3172 OS << "<<Unknown>>";
3182 OS << "Determining loop execution counts for: " << F.getName() << "\n";
3183 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
3184 PrintLoopInfo(OS, this, *I);