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 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
1423 /// this function as they are computed.
1424 std::map<const Loop*, SCEVHandle> BackedgeTakenCounts;
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 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
1468 /// has an analyzable loop-invariant backedge-taken count.
1469 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
1471 /// forgetLoopBackedgeTakenCount - 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, or if the loop
1475 void forgetLoopBackedgeTakenCount(const Loop *L);
1477 /// getBackedgeTakenCount - If the specified loop has a predictable
1478 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
1479 /// object. The backedge-taken count is the number of times the loop header
1480 /// will be branched to from within the loop. This is one less than the
1481 /// trip count of the loop, since it doesn't count the first iteration,
1482 /// when the header is branched to from outside the loop.
1484 /// Note that it is not valid to call this method on a loop without a
1485 /// loop-invariant backedge-taken count (see
1486 /// hasLoopInvariantBackedgeTakenCount).
1488 SCEVHandle getBackedgeTakenCount(const Loop *L);
1490 /// deleteValueFromRecords - This method should be called by the
1491 /// client before it removes a value from the program, to make sure
1492 /// that no dangling references are left around.
1493 void deleteValueFromRecords(Value *V);
1496 /// createSCEV - We know that there is no SCEV for the specified value.
1497 /// Analyze the expression.
1498 SCEVHandle createSCEV(Value *V);
1500 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1502 SCEVHandle createNodeForPHI(PHINode *PN);
1504 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1505 /// for the specified instruction and replaces any references to the
1506 /// symbolic value SymName with the specified value. This is used during
1508 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1509 const SCEVHandle &SymName,
1510 const SCEVHandle &NewVal);
1512 /// ComputeBackedgeTakenCount - Compute the number of times the specified
1513 /// loop will iterate.
1514 SCEVHandle ComputeBackedgeTakenCount(const Loop *L);
1516 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
1517 /// of 'icmp op load X, cst', try to see if we can compute the trip count.
1519 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
1522 ICmpInst::Predicate p);
1524 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute
1525 /// a constant number of times (the condition evolves only from constants),
1526 /// try to evaluate a few iterations of the loop until we get the exit
1527 /// condition gets a value of ExitWhen (true or false). If we cannot
1528 /// evaluate the trip count of the loop, return UnknownValue.
1529 SCEVHandle ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond,
1532 /// HowFarToZero - Return the number of times a backedge comparing the
1533 /// specified value to zero will execute. If not computable, return
1535 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1537 /// HowFarToNonZero - Return the number of times a backedge checking the
1538 /// specified value for nonzero will execute. If not computable, return
1540 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1542 /// HowManyLessThans - Return the number of times a backedge containing the
1543 /// specified less-than comparison will execute. If not computable, return
1544 /// UnknownValue. isSigned specifies whether the less-than is signed.
1545 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1548 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
1549 /// (which may not be an immediate predecessor) which has exactly one
1550 /// successor from which BB is reachable, or null if no such block is
1552 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
1554 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1555 /// in the header of its containing loop, we know the loop executes a
1556 /// constant number of times, and the PHI node is just a recurrence
1557 /// involving constants, fold it.
1558 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
1563 //===----------------------------------------------------------------------===//
1564 // Basic SCEV Analysis and PHI Idiom Recognition Code
1567 /// deleteValueFromRecords - This method should be called by the
1568 /// client before it removes an instruction from the program, to make sure
1569 /// that no dangling references are left around.
1570 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1571 SmallVector<Value *, 16> Worklist;
1573 if (Scalars.erase(V)) {
1574 if (PHINode *PN = dyn_cast<PHINode>(V))
1575 ConstantEvolutionLoopExitValue.erase(PN);
1576 Worklist.push_back(V);
1579 while (!Worklist.empty()) {
1580 Value *VV = Worklist.back();
1581 Worklist.pop_back();
1583 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1585 Instruction *Inst = cast<Instruction>(*UI);
1586 if (Scalars.erase(Inst)) {
1587 if (PHINode *PN = dyn_cast<PHINode>(VV))
1588 ConstantEvolutionLoopExitValue.erase(PN);
1589 Worklist.push_back(Inst);
1596 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1597 /// expression and create a new one.
1598 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1599 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1601 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1602 if (I != Scalars.end()) return I->second;
1603 SCEVHandle S = createSCEV(V);
1604 Scalars.insert(std::make_pair(V, S));
1608 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1609 /// the specified instruction and replaces any references to the symbolic value
1610 /// SymName with the specified value. This is used during PHI resolution.
1611 void ScalarEvolutionsImpl::
1612 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1613 const SCEVHandle &NewVal) {
1614 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1615 if (SI == Scalars.end()) return;
1618 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
1619 if (NV == SI->second) return; // No change.
1621 SI->second = NV; // Update the scalars map!
1623 // Any instruction values that use this instruction might also need to be
1625 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1627 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1630 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1631 /// a loop header, making it a potential recurrence, or it doesn't.
1633 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1634 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1635 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1636 if (L->getHeader() == PN->getParent()) {
1637 // If it lives in the loop header, it has two incoming values, one
1638 // from outside the loop, and one from inside.
1639 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1640 unsigned BackEdge = IncomingEdge^1;
1642 // While we are analyzing this PHI node, handle its value symbolically.
1643 SCEVHandle SymbolicName = SE.getUnknown(PN);
1644 assert(Scalars.find(PN) == Scalars.end() &&
1645 "PHI node already processed?");
1646 Scalars.insert(std::make_pair(PN, SymbolicName));
1648 // Using this symbolic name for the PHI, analyze the value coming around
1650 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1652 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1653 // has a special value for the first iteration of the loop.
1655 // If the value coming around the backedge is an add with the symbolic
1656 // value we just inserted, then we found a simple induction variable!
1657 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1658 // If there is a single occurrence of the symbolic value, replace it
1659 // with a recurrence.
1660 unsigned FoundIndex = Add->getNumOperands();
1661 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1662 if (Add->getOperand(i) == SymbolicName)
1663 if (FoundIndex == e) {
1668 if (FoundIndex != Add->getNumOperands()) {
1669 // Create an add with everything but the specified operand.
1670 std::vector<SCEVHandle> Ops;
1671 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1672 if (i != FoundIndex)
1673 Ops.push_back(Add->getOperand(i));
1674 SCEVHandle Accum = SE.getAddExpr(Ops);
1676 // This is not a valid addrec if the step amount is varying each
1677 // loop iteration, but is not itself an addrec in this loop.
1678 if (Accum->isLoopInvariant(L) ||
1679 (isa<SCEVAddRecExpr>(Accum) &&
1680 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1681 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1682 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L);
1684 // Okay, for the entire analysis of this edge we assumed the PHI
1685 // to be symbolic. We now need to go back and update all of the
1686 // entries for the scalars that use the PHI (except for the PHI
1687 // itself) to use the new analyzed value instead of the "symbolic"
1689 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1693 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1694 // Otherwise, this could be a loop like this:
1695 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1696 // In this case, j = {1,+,1} and BEValue is j.
1697 // Because the other in-value of i (0) fits the evolution of BEValue
1698 // i really is an addrec evolution.
1699 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1700 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1702 // If StartVal = j.start - j.stride, we can use StartVal as the
1703 // initial step of the addrec evolution.
1704 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
1705 AddRec->getOperand(1))) {
1706 SCEVHandle PHISCEV =
1707 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1709 // Okay, for the entire analysis of this edge we assumed the PHI
1710 // to be symbolic. We now need to go back and update all of the
1711 // entries for the scalars that use the PHI (except for the PHI
1712 // itself) to use the new analyzed value instead of the "symbolic"
1714 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1720 return SymbolicName;
1723 // If it's not a loop phi, we can't handle it yet.
1724 return SE.getUnknown(PN);
1727 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1728 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1729 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1730 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1731 static uint32_t GetMinTrailingZeros(SCEVHandle S) {
1732 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1733 return C->getValue()->getValue().countTrailingZeros();
1735 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1736 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
1738 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1739 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1740 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1743 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1744 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1745 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1748 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1749 // The result is the min of all operands results.
1750 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1751 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1752 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1756 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1757 // The result is the sum of all operands results.
1758 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
1759 uint32_t BitWidth = M->getBitWidth();
1760 for (unsigned i = 1, e = M->getNumOperands();
1761 SumOpRes != BitWidth && i != e; ++i)
1762 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
1767 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1768 // The result is the min of all operands results.
1769 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1770 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1771 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1775 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1776 // The result is the min of all operands results.
1777 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1778 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1779 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1783 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1784 // The result is the min of all operands results.
1785 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1786 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1787 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1791 // SCEVUDivExpr, SCEVUnknown
1795 /// createSCEV - We know that there is no SCEV for the specified value.
1796 /// Analyze the expression.
1798 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1799 if (!isa<IntegerType>(V->getType()))
1800 return SE.getUnknown(V);
1802 unsigned Opcode = Instruction::UserOp1;
1803 if (Instruction *I = dyn_cast<Instruction>(V))
1804 Opcode = I->getOpcode();
1805 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1806 Opcode = CE->getOpcode();
1808 return SE.getUnknown(V);
1810 User *U = cast<User>(V);
1812 case Instruction::Add:
1813 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1814 getSCEV(U->getOperand(1)));
1815 case Instruction::Mul:
1816 return SE.getMulExpr(getSCEV(U->getOperand(0)),
1817 getSCEV(U->getOperand(1)));
1818 case Instruction::UDiv:
1819 return SE.getUDivExpr(getSCEV(U->getOperand(0)),
1820 getSCEV(U->getOperand(1)));
1821 case Instruction::Sub:
1822 return SE.getMinusSCEV(getSCEV(U->getOperand(0)),
1823 getSCEV(U->getOperand(1)));
1824 case Instruction::Or:
1825 // If the RHS of the Or is a constant, we may have something like:
1826 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1827 // optimizations will transparently handle this case.
1829 // In order for this transformation to be safe, the LHS must be of the
1830 // form X*(2^n) and the Or constant must be less than 2^n.
1831 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1832 SCEVHandle LHS = getSCEV(U->getOperand(0));
1833 const APInt &CIVal = CI->getValue();
1834 if (GetMinTrailingZeros(LHS) >=
1835 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1836 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1)));
1839 case Instruction::Xor:
1840 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1841 // If the RHS of the xor is a signbit, then this is just an add.
1842 // Instcombine turns add of signbit into xor as a strength reduction step.
1843 if (CI->getValue().isSignBit())
1844 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1845 getSCEV(U->getOperand(1)));
1847 // If the RHS of xor is -1, then this is a not operation.
1848 else if (CI->isAllOnesValue())
1849 return SE.getNotSCEV(getSCEV(U->getOperand(0)));
1853 case Instruction::Shl:
1854 // Turn shift left of a constant amount into a multiply.
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.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1863 case Instruction::LShr:
1864 // Turn logical shift right of a constant into a unsigned divide.
1865 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1866 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1867 Constant *X = ConstantInt::get(
1868 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1869 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1873 case Instruction::Trunc:
1874 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1876 case Instruction::ZExt:
1877 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1879 case Instruction::SExt:
1880 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1882 case Instruction::BitCast:
1883 // BitCasts are no-op casts so we just eliminate the cast.
1884 if (U->getType()->isInteger() &&
1885 U->getOperand(0)->getType()->isInteger())
1886 return getSCEV(U->getOperand(0));
1889 case Instruction::PHI:
1890 return createNodeForPHI(cast<PHINode>(U));
1892 case Instruction::Select:
1893 // This could be a smax or umax that was lowered earlier.
1894 // Try to recover it.
1895 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
1896 Value *LHS = ICI->getOperand(0);
1897 Value *RHS = ICI->getOperand(1);
1898 switch (ICI->getPredicate()) {
1899 case ICmpInst::ICMP_SLT:
1900 case ICmpInst::ICMP_SLE:
1901 std::swap(LHS, RHS);
1903 case ICmpInst::ICMP_SGT:
1904 case ICmpInst::ICMP_SGE:
1905 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1906 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1907 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1908 // ~smax(~x, ~y) == smin(x, y).
1909 return SE.getNotSCEV(SE.getSMaxExpr(
1910 SE.getNotSCEV(getSCEV(LHS)),
1911 SE.getNotSCEV(getSCEV(RHS))));
1913 case ICmpInst::ICMP_ULT:
1914 case ICmpInst::ICMP_ULE:
1915 std::swap(LHS, RHS);
1917 case ICmpInst::ICMP_UGT:
1918 case ICmpInst::ICMP_UGE:
1919 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1920 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
1921 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1922 // ~umax(~x, ~y) == umin(x, y)
1923 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
1924 SE.getNotSCEV(getSCEV(RHS))));
1931 default: // We cannot analyze this expression.
1935 return SE.getUnknown(V);
1940 //===----------------------------------------------------------------------===//
1941 // Iteration Count Computation Code
1944 /// getBackedgeTakenCount - If the specified loop has a predictable
1945 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
1946 /// object. The backedge-taken count is the number of times the loop header
1947 /// will be branched to from within the loop. This is one less than the
1948 /// trip count of the loop, since it doesn't count the first iteration,
1949 /// when the header is branched to from outside the loop.
1951 /// Note that it is not valid to call this method on a loop without a
1952 /// loop-invariant backedge-taken count (see
1953 /// hasLoopInvariantBackedgeTakenCount).
1955 SCEVHandle ScalarEvolutionsImpl::getBackedgeTakenCount(const Loop *L) {
1956 std::map<const Loop*, SCEVHandle>::iterator I = BackedgeTakenCounts.find(L);
1957 if (I == BackedgeTakenCounts.end()) {
1958 SCEVHandle ItCount = ComputeBackedgeTakenCount(L);
1959 I = BackedgeTakenCounts.insert(std::make_pair(L, ItCount)).first;
1960 if (ItCount != UnknownValue) {
1961 assert(ItCount->isLoopInvariant(L) &&
1962 "Computed trip count isn't loop invariant for loop!");
1963 ++NumTripCountsComputed;
1964 } else if (isa<PHINode>(L->getHeader()->begin())) {
1965 // Only count loops that have phi nodes as not being computable.
1966 ++NumTripCountsNotComputed;
1972 /// forgetLoopBackedgeTakenCount - This method should be called by the
1973 /// client when it has changed a loop in a way that may effect
1974 /// ScalarEvolution's ability to compute a trip count, or if the loop
1976 void ScalarEvolutionsImpl::forgetLoopBackedgeTakenCount(const Loop *L) {
1977 BackedgeTakenCounts.erase(L);
1980 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
1981 /// of the specified loop will execute.
1982 SCEVHandle ScalarEvolutionsImpl::ComputeBackedgeTakenCount(const Loop *L) {
1983 // If the loop has a non-one exit block count, we can't analyze it.
1984 SmallVector<BasicBlock*, 8> ExitBlocks;
1985 L->getExitBlocks(ExitBlocks);
1986 if (ExitBlocks.size() != 1) return UnknownValue;
1988 // Okay, there is one exit block. Try to find the condition that causes the
1989 // loop to be exited.
1990 BasicBlock *ExitBlock = ExitBlocks[0];
1992 BasicBlock *ExitingBlock = 0;
1993 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1995 if (L->contains(*PI)) {
1996 if (ExitingBlock == 0)
1999 return UnknownValue; // More than one block exiting!
2001 assert(ExitingBlock && "No exits from loop, something is broken!");
2003 // Okay, we've computed the exiting block. See what condition causes us to
2006 // FIXME: we should be able to handle switch instructions (with a single exit)
2007 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2008 if (ExitBr == 0) return UnknownValue;
2009 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2011 // At this point, we know we have a conditional branch that determines whether
2012 // the loop is exited. However, we don't know if the branch is executed each
2013 // time through the loop. If not, then the execution count of the branch will
2014 // not be equal to the trip count of the loop.
2016 // Currently we check for this by checking to see if the Exit branch goes to
2017 // the loop header. If so, we know it will always execute the same number of
2018 // times as the loop. We also handle the case where the exit block *is* the
2019 // loop header. This is common for un-rotated loops. More extensive analysis
2020 // could be done to handle more cases here.
2021 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2022 ExitBr->getSuccessor(1) != L->getHeader() &&
2023 ExitBr->getParent() != L->getHeader())
2024 return UnknownValue;
2026 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2028 // If it's not an integer comparison then compute it the hard way.
2029 // Note that ICmpInst deals with pointer comparisons too so we must check
2030 // the type of the operand.
2031 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2032 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2033 ExitBr->getSuccessor(0) == ExitBlock);
2035 // If the condition was exit on true, convert the condition to exit on false
2036 ICmpInst::Predicate Cond;
2037 if (ExitBr->getSuccessor(1) == ExitBlock)
2038 Cond = ExitCond->getPredicate();
2040 Cond = ExitCond->getInversePredicate();
2042 // Handle common loops like: for (X = "string"; *X; ++X)
2043 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2044 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2046 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2047 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2050 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2051 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2053 // Try to evaluate any dependencies out of the loop.
2054 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2055 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2056 Tmp = getSCEVAtScope(RHS, L);
2057 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2059 // At this point, we would like to compute how many iterations of the
2060 // loop the predicate will return true for these inputs.
2061 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2062 // If there is a loop-invariant, force it into the RHS.
2063 std::swap(LHS, RHS);
2064 Cond = ICmpInst::getSwappedPredicate(Cond);
2067 // FIXME: think about handling pointer comparisons! i.e.:
2068 // while (P != P+100) ++P;
2070 // If we have a comparison of a chrec against a constant, try to use value
2071 // ranges to answer this query.
2072 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2073 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2074 if (AddRec->getLoop() == L) {
2075 // Form the comparison range using the constant of the correct type so
2076 // that the ConstantRange class knows to do a signed or unsigned
2078 ConstantInt *CompVal = RHSC->getValue();
2079 const Type *RealTy = ExitCond->getOperand(0)->getType();
2080 CompVal = dyn_cast<ConstantInt>(
2081 ConstantExpr::getBitCast(CompVal, RealTy));
2083 // Form the constant range.
2084 ConstantRange CompRange(
2085 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2087 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
2088 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2093 case ICmpInst::ICMP_NE: { // while (X != Y)
2094 // Convert to: while (X-Y != 0)
2095 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
2096 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2099 case ICmpInst::ICMP_EQ: {
2100 // Convert to: while (X-Y == 0) // while (X == Y)
2101 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
2102 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2105 case ICmpInst::ICMP_SLT: {
2106 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
2107 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2110 case ICmpInst::ICMP_SGT: {
2111 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2112 SE.getNotSCEV(RHS), L, true);
2113 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2116 case ICmpInst::ICMP_ULT: {
2117 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
2118 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2121 case ICmpInst::ICMP_UGT: {
2122 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
2123 SE.getNotSCEV(RHS), L, false);
2124 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2129 cerr << "ComputeBackedgeTakenCount ";
2130 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2131 cerr << "[unsigned] ";
2133 << Instruction::getOpcodeName(Instruction::ICmp)
2134 << " " << *RHS << "\n";
2139 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2140 ExitBr->getSuccessor(0) == ExitBlock);
2143 static ConstantInt *
2144 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2145 ScalarEvolution &SE) {
2146 SCEVHandle InVal = SE.getConstant(C);
2147 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2148 assert(isa<SCEVConstant>(Val) &&
2149 "Evaluation of SCEV at constant didn't fold correctly?");
2150 return cast<SCEVConstant>(Val)->getValue();
2153 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2154 /// and a GEP expression (missing the pointer index) indexing into it, return
2155 /// the addressed element of the initializer or null if the index expression is
2158 GetAddressedElementFromGlobal(GlobalVariable *GV,
2159 const std::vector<ConstantInt*> &Indices) {
2160 Constant *Init = GV->getInitializer();
2161 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2162 uint64_t Idx = Indices[i]->getZExtValue();
2163 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2164 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2165 Init = cast<Constant>(CS->getOperand(Idx));
2166 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2167 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2168 Init = cast<Constant>(CA->getOperand(Idx));
2169 } else if (isa<ConstantAggregateZero>(Init)) {
2170 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2171 assert(Idx < STy->getNumElements() && "Bad struct index!");
2172 Init = Constant::getNullValue(STy->getElementType(Idx));
2173 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2174 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2175 Init = Constant::getNullValue(ATy->getElementType());
2177 assert(0 && "Unknown constant aggregate type!");
2181 return 0; // Unknown initializer type
2187 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2188 /// 'icmp op load X, cst', try to see if we can compute the backedge
2189 /// execution count.
2190 SCEVHandle ScalarEvolutionsImpl::
2191 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2193 ICmpInst::Predicate predicate) {
2194 if (LI->isVolatile()) return UnknownValue;
2196 // Check to see if the loaded pointer is a getelementptr of a global.
2197 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2198 if (!GEP) return UnknownValue;
2200 // Make sure that it is really a constant global we are gepping, with an
2201 // initializer, and make sure the first IDX is really 0.
2202 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2203 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2204 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2205 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2206 return UnknownValue;
2208 // Okay, we allow one non-constant index into the GEP instruction.
2210 std::vector<ConstantInt*> Indexes;
2211 unsigned VarIdxNum = 0;
2212 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2213 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2214 Indexes.push_back(CI);
2215 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2216 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2217 VarIdx = GEP->getOperand(i);
2219 Indexes.push_back(0);
2222 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2223 // Check to see if X is a loop variant variable value now.
2224 SCEVHandle Idx = getSCEV(VarIdx);
2225 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2226 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2228 // We can only recognize very limited forms of loop index expressions, in
2229 // particular, only affine AddRec's like {C1,+,C2}.
2230 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2231 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2232 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2233 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2234 return UnknownValue;
2236 unsigned MaxSteps = MaxBruteForceIterations;
2237 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2238 ConstantInt *ItCst =
2239 ConstantInt::get(IdxExpr->getType(), IterationNum);
2240 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
2242 // Form the GEP offset.
2243 Indexes[VarIdxNum] = Val;
2245 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2246 if (Result == 0) break; // Cannot compute!
2248 // Evaluate the condition for this iteration.
2249 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2250 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2251 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2253 cerr << "\n***\n*** Computed loop count " << *ItCst
2254 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2257 ++NumArrayLenItCounts;
2258 return SE.getConstant(ItCst); // Found terminating iteration!
2261 return UnknownValue;
2265 /// CanConstantFold - Return true if we can constant fold an instruction of the
2266 /// specified type, assuming that all operands were constants.
2267 static bool CanConstantFold(const Instruction *I) {
2268 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2269 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2272 if (const CallInst *CI = dyn_cast<CallInst>(I))
2273 if (const Function *F = CI->getCalledFunction())
2274 return canConstantFoldCallTo(F);
2278 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2279 /// in the loop that V is derived from. We allow arbitrary operations along the
2280 /// way, but the operands of an operation must either be constants or a value
2281 /// derived from a constant PHI. If this expression does not fit with these
2282 /// constraints, return null.
2283 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2284 // If this is not an instruction, or if this is an instruction outside of the
2285 // loop, it can't be derived from a loop PHI.
2286 Instruction *I = dyn_cast<Instruction>(V);
2287 if (I == 0 || !L->contains(I->getParent())) return 0;
2289 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2290 if (L->getHeader() == I->getParent())
2293 // We don't currently keep track of the control flow needed to evaluate
2294 // PHIs, so we cannot handle PHIs inside of loops.
2298 // If we won't be able to constant fold this expression even if the operands
2299 // are constants, return early.
2300 if (!CanConstantFold(I)) return 0;
2302 // Otherwise, we can evaluate this instruction if all of its operands are
2303 // constant or derived from a PHI node themselves.
2305 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2306 if (!(isa<Constant>(I->getOperand(Op)) ||
2307 isa<GlobalValue>(I->getOperand(Op)))) {
2308 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2309 if (P == 0) return 0; // Not evolving from PHI
2313 return 0; // Evolving from multiple different PHIs.
2316 // This is a expression evolving from a constant PHI!
2320 /// EvaluateExpression - Given an expression that passes the
2321 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2322 /// in the loop has the value PHIVal. If we can't fold this expression for some
2323 /// reason, return null.
2324 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2325 if (isa<PHINode>(V)) return PHIVal;
2326 if (Constant *C = dyn_cast<Constant>(V)) return C;
2327 Instruction *I = cast<Instruction>(V);
2329 std::vector<Constant*> Operands;
2330 Operands.resize(I->getNumOperands());
2332 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2333 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2334 if (Operands[i] == 0) return 0;
2337 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2338 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2339 &Operands[0], Operands.size());
2341 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2342 &Operands[0], Operands.size());
2345 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2346 /// in the header of its containing loop, we know the loop executes a
2347 /// constant number of times, and the PHI node is just a recurrence
2348 /// involving constants, fold it.
2349 Constant *ScalarEvolutionsImpl::
2350 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2351 std::map<PHINode*, Constant*>::iterator I =
2352 ConstantEvolutionLoopExitValue.find(PN);
2353 if (I != ConstantEvolutionLoopExitValue.end())
2356 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2357 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2359 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2361 // Since the loop is canonicalized, the PHI node must have two entries. One
2362 // entry must be a constant (coming in from outside of the loop), and the
2363 // second must be derived from the same PHI.
2364 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2365 Constant *StartCST =
2366 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2368 return RetVal = 0; // Must be a constant.
2370 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2371 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2373 return RetVal = 0; // Not derived from same PHI.
2375 // Execute the loop symbolically to determine the exit value.
2376 if (BEs.getActiveBits() >= 32)
2377 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2379 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2380 unsigned IterationNum = 0;
2381 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2382 if (IterationNum == NumIterations)
2383 return RetVal = PHIVal; // Got exit value!
2385 // Compute the value of the PHI node for the next iteration.
2386 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2387 if (NextPHI == PHIVal)
2388 return RetVal = NextPHI; // Stopped evolving!
2390 return 0; // Couldn't evaluate!
2395 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2396 /// constant number of times (the condition evolves only from constants),
2397 /// try to evaluate a few iterations of the loop until we get the exit
2398 /// condition gets a value of ExitWhen (true or false). If we cannot
2399 /// evaluate the trip count of the loop, return UnknownValue.
2400 SCEVHandle ScalarEvolutionsImpl::
2401 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2402 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2403 if (PN == 0) return UnknownValue;
2405 // Since the loop is canonicalized, the PHI node must have two entries. One
2406 // entry must be a constant (coming in from outside of the loop), and the
2407 // second must be derived from the same PHI.
2408 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2409 Constant *StartCST =
2410 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2411 if (StartCST == 0) return UnknownValue; // Must be a constant.
2413 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2414 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2415 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2417 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2418 // the loop symbolically to determine when the condition gets a value of
2420 unsigned IterationNum = 0;
2421 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2422 for (Constant *PHIVal = StartCST;
2423 IterationNum != MaxIterations; ++IterationNum) {
2424 ConstantInt *CondVal =
2425 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2427 // Couldn't symbolically evaluate.
2428 if (!CondVal) return UnknownValue;
2430 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2431 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2432 ++NumBruteForceTripCountsComputed;
2433 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2436 // Compute the value of the PHI node for the next iteration.
2437 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2438 if (NextPHI == 0 || NextPHI == PHIVal)
2439 return UnknownValue; // Couldn't evaluate or not making progress...
2443 // Too many iterations were needed to evaluate.
2444 return UnknownValue;
2447 /// getSCEVAtScope - Compute the value of the specified expression within the
2448 /// indicated loop (which may be null to indicate in no loop). If the
2449 /// expression cannot be evaluated, return UnknownValue.
2450 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2451 // FIXME: this should be turned into a virtual method on SCEV!
2453 if (isa<SCEVConstant>(V)) return V;
2455 // If this instruction is evolved from a constant-evolving PHI, compute the
2456 // exit value from the loop without using SCEVs.
2457 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2458 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2459 const Loop *LI = this->LI[I->getParent()];
2460 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2461 if (PHINode *PN = dyn_cast<PHINode>(I))
2462 if (PN->getParent() == LI->getHeader()) {
2463 // Okay, there is no closed form solution for the PHI node. Check
2464 // to see if the loop that contains it has a known backedge-taken
2465 // count. If so, we may be able to force computation of the exit
2467 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2468 if (SCEVConstant *BTCC =
2469 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2470 // Okay, we know how many times the containing loop executes. If
2471 // this is a constant evolving PHI node, get the final value at
2472 // the specified iteration number.
2473 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2474 BTCC->getValue()->getValue(),
2476 if (RV) return SE.getUnknown(RV);
2480 // Okay, this is an expression that we cannot symbolically evaluate
2481 // into a SCEV. Check to see if it's possible to symbolically evaluate
2482 // the arguments into constants, and if so, try to constant propagate the
2483 // result. This is particularly useful for computing loop exit values.
2484 if (CanConstantFold(I)) {
2485 std::vector<Constant*> Operands;
2486 Operands.reserve(I->getNumOperands());
2487 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2488 Value *Op = I->getOperand(i);
2489 if (Constant *C = dyn_cast<Constant>(Op)) {
2490 Operands.push_back(C);
2492 // If any of the operands is non-constant and if they are
2493 // non-integer, don't even try to analyze them with scev techniques.
2494 if (!isa<IntegerType>(Op->getType()))
2497 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2498 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2499 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2502 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2503 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2504 Operands.push_back(ConstantExpr::getIntegerCast(C,
2516 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2517 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2518 &Operands[0], Operands.size());
2520 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2521 &Operands[0], Operands.size());
2522 return SE.getUnknown(C);
2526 // This is some other type of SCEVUnknown, just return it.
2530 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2531 // Avoid performing the look-up in the common case where the specified
2532 // expression has no loop-variant portions.
2533 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2534 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2535 if (OpAtScope != Comm->getOperand(i)) {
2536 if (OpAtScope == UnknownValue) return UnknownValue;
2537 // Okay, at least one of these operands is loop variant but might be
2538 // foldable. Build a new instance of the folded commutative expression.
2539 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2540 NewOps.push_back(OpAtScope);
2542 for (++i; i != e; ++i) {
2543 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2544 if (OpAtScope == UnknownValue) return UnknownValue;
2545 NewOps.push_back(OpAtScope);
2547 if (isa<SCEVAddExpr>(Comm))
2548 return SE.getAddExpr(NewOps);
2549 if (isa<SCEVMulExpr>(Comm))
2550 return SE.getMulExpr(NewOps);
2551 if (isa<SCEVSMaxExpr>(Comm))
2552 return SE.getSMaxExpr(NewOps);
2553 if (isa<SCEVUMaxExpr>(Comm))
2554 return SE.getUMaxExpr(NewOps);
2555 assert(0 && "Unknown commutative SCEV type!");
2558 // If we got here, all operands are loop invariant.
2562 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2563 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2564 if (LHS == UnknownValue) return LHS;
2565 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2566 if (RHS == UnknownValue) return RHS;
2567 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2568 return Div; // must be loop invariant
2569 return SE.getUDivExpr(LHS, RHS);
2572 // If this is a loop recurrence for a loop that does not contain L, then we
2573 // are dealing with the final value computed by the loop.
2574 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2575 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2576 // To evaluate this recurrence, we need to know how many times the AddRec
2577 // loop iterates. Compute this now.
2578 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2579 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2581 // Then, evaluate the AddRec.
2582 return AddRec->evaluateAtIteration(BackedgeTakenCount, SE);
2584 return UnknownValue;
2587 //assert(0 && "Unknown SCEV type!");
2588 return UnknownValue;
2591 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2592 /// following equation:
2594 /// A * X = B (mod N)
2596 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2597 /// A and B isn't important.
2599 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2600 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2601 ScalarEvolution &SE) {
2602 uint32_t BW = A.getBitWidth();
2603 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2604 assert(A != 0 && "A must be non-zero.");
2608 // The gcd of A and N may have only one prime factor: 2. The number of
2609 // trailing zeros in A is its multiplicity
2610 uint32_t Mult2 = A.countTrailingZeros();
2613 // 2. Check if B is divisible by D.
2615 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2616 // is not less than multiplicity of this prime factor for D.
2617 if (B.countTrailingZeros() < Mult2)
2618 return new SCEVCouldNotCompute();
2620 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2623 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2624 // bit width during computations.
2625 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2626 APInt Mod(BW + 1, 0);
2627 Mod.set(BW - Mult2); // Mod = N / D
2628 APInt I = AD.multiplicativeInverse(Mod);
2630 // 4. Compute the minimum unsigned root of the equation:
2631 // I * (B / D) mod (N / D)
2632 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2634 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2636 return SE.getConstant(Result.trunc(BW));
2639 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2640 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2641 /// might be the same) or two SCEVCouldNotCompute objects.
2643 static std::pair<SCEVHandle,SCEVHandle>
2644 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2645 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2646 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2647 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2648 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2650 // We currently can only solve this if the coefficients are constants.
2651 if (!LC || !MC || !NC) {
2652 SCEV *CNC = new SCEVCouldNotCompute();
2653 return std::make_pair(CNC, CNC);
2656 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2657 const APInt &L = LC->getValue()->getValue();
2658 const APInt &M = MC->getValue()->getValue();
2659 const APInt &N = NC->getValue()->getValue();
2660 APInt Two(BitWidth, 2);
2661 APInt Four(BitWidth, 4);
2664 using namespace APIntOps;
2666 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2667 // The B coefficient is M-N/2
2671 // The A coefficient is N/2
2672 APInt A(N.sdiv(Two));
2674 // Compute the B^2-4ac term.
2677 SqrtTerm -= Four * (A * C);
2679 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2680 // integer value or else APInt::sqrt() will assert.
2681 APInt SqrtVal(SqrtTerm.sqrt());
2683 // Compute the two solutions for the quadratic formula.
2684 // The divisions must be performed as signed divisions.
2686 APInt TwoA( A << 1 );
2687 if (TwoA.isMinValue()) {
2688 SCEV *CNC = new SCEVCouldNotCompute();
2689 return std::make_pair(CNC, CNC);
2692 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2693 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2695 return std::make_pair(SE.getConstant(Solution1),
2696 SE.getConstant(Solution2));
2697 } // end APIntOps namespace
2700 /// HowFarToZero - Return the number of times a backedge comparing the specified
2701 /// value to zero will execute. If not computable, return UnknownValue
2702 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2703 // If the value is a constant
2704 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2705 // If the value is already zero, the branch will execute zero times.
2706 if (C->getValue()->isZero()) return C;
2707 return UnknownValue; // Otherwise it will loop infinitely.
2710 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2711 if (!AddRec || AddRec->getLoop() != L)
2712 return UnknownValue;
2714 if (AddRec->isAffine()) {
2715 // If this is an affine expression, the execution count of this branch is
2716 // the minimum unsigned root of the following equation:
2718 // Start + Step*N = 0 (mod 2^BW)
2722 // Step*N = -Start (mod 2^BW)
2724 // where BW is the common bit width of Start and Step.
2726 // Get the initial value for the loop.
2727 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2728 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2730 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2732 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2733 // For now we handle only constant steps.
2735 // First, handle unitary steps.
2736 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2737 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned)
2738 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2739 return Start; // N = Start (as unsigned)
2741 // Then, try to solve the above equation provided that Start is constant.
2742 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2743 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2744 -StartC->getValue()->getValue(),SE);
2746 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2747 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2748 // the quadratic equation to solve it.
2749 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
2750 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2751 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2754 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2755 << " sol#2: " << *R2 << "\n";
2757 // Pick the smallest positive root value.
2758 if (ConstantInt *CB =
2759 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2760 R1->getValue(), R2->getValue()))) {
2761 if (CB->getZExtValue() == false)
2762 std::swap(R1, R2); // R1 is the minimum root now.
2764 // We can only use this value if the chrec ends up with an exact zero
2765 // value at this index. When solving for "X*X != 5", for example, we
2766 // should not accept a root of 2.
2767 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
2769 return R1; // We found a quadratic root!
2774 return UnknownValue;
2777 /// HowFarToNonZero - Return the number of times a backedge checking the
2778 /// specified value for nonzero will execute. If not computable, return
2780 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2781 // Loops that look like: while (X == 0) are very strange indeed. We don't
2782 // handle them yet except for the trivial case. This could be expanded in the
2783 // future as needed.
2785 // If the value is a constant, check to see if it is known to be non-zero
2786 // already. If so, the backedge will execute zero times.
2787 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2788 if (!C->getValue()->isNullValue())
2789 return SE.getIntegerSCEV(0, C->getType());
2790 return UnknownValue; // Otherwise it will loop infinitely.
2793 // We could implement others, but I really doubt anyone writes loops like
2794 // this, and if they did, they would already be constant folded.
2795 return UnknownValue;
2798 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2799 /// (which may not be an immediate predecessor) which has exactly one
2800 /// successor from which BB is reachable, or null if no such block is
2804 ScalarEvolutionsImpl::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2805 // If the block has a unique predecessor, the predecessor must have
2806 // no other successors from which BB is reachable.
2807 if (BasicBlock *Pred = BB->getSinglePredecessor())
2810 // A loop's header is defined to be a block that dominates the loop.
2811 // If the loop has a preheader, it must be a block that has exactly
2812 // one successor that can reach BB. This is slightly more strict
2813 // than necessary, but works if critical edges are split.
2814 if (Loop *L = LI.getLoopFor(BB))
2815 return L->getLoopPreheader();
2820 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
2821 /// a conditional between LHS and RHS.
2822 bool ScalarEvolutionsImpl::isLoopGuardedByCond(const Loop *L,
2823 ICmpInst::Predicate Pred,
2824 SCEV *LHS, SCEV *RHS) {
2825 BasicBlock *Preheader = L->getLoopPreheader();
2826 BasicBlock *PreheaderDest = L->getHeader();
2828 // Starting at the preheader, climb up the predecessor chain, as long as
2829 // there are predecessors that can be found that have unique successors
2830 // leading to the original header.
2832 PreheaderDest = Preheader,
2833 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
2835 BranchInst *LoopEntryPredicate =
2836 dyn_cast<BranchInst>(Preheader->getTerminator());
2837 if (!LoopEntryPredicate ||
2838 LoopEntryPredicate->isUnconditional())
2841 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
2844 // Now that we found a conditional branch that dominates the loop, check to
2845 // see if it is the comparison we are looking for.
2846 Value *PreCondLHS = ICI->getOperand(0);
2847 Value *PreCondRHS = ICI->getOperand(1);
2848 ICmpInst::Predicate Cond;
2849 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2850 Cond = ICI->getPredicate();
2852 Cond = ICI->getInversePredicate();
2855 ; // An exact match.
2856 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
2857 ; // The actual condition is beyond sufficient.
2859 // Check a few special cases.
2861 case ICmpInst::ICMP_UGT:
2862 if (Pred == ICmpInst::ICMP_ULT) {
2863 std::swap(PreCondLHS, PreCondRHS);
2864 Cond = ICmpInst::ICMP_ULT;
2868 case ICmpInst::ICMP_SGT:
2869 if (Pred == ICmpInst::ICMP_SLT) {
2870 std::swap(PreCondLHS, PreCondRHS);
2871 Cond = ICmpInst::ICMP_SLT;
2875 case ICmpInst::ICMP_NE:
2876 // Expressions like (x >u 0) are often canonicalized to (x != 0),
2877 // so check for this case by checking if the NE is comparing against
2878 // a minimum or maximum constant.
2879 if (!ICmpInst::isTrueWhenEqual(Pred))
2880 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
2881 const APInt &A = CI->getValue();
2883 case ICmpInst::ICMP_SLT:
2884 if (A.isMaxSignedValue()) break;
2886 case ICmpInst::ICMP_SGT:
2887 if (A.isMinSignedValue()) break;
2889 case ICmpInst::ICMP_ULT:
2890 if (A.isMaxValue()) break;
2892 case ICmpInst::ICMP_UGT:
2893 if (A.isMinValue()) break;
2898 Cond = ICmpInst::ICMP_NE;
2899 // NE is symmetric but the original comparison may not be. Swap
2900 // the operands if necessary so that they match below.
2901 if (isa<SCEVConstant>(LHS))
2902 std::swap(PreCondLHS, PreCondRHS);
2907 // We weren't able to reconcile the condition.
2911 if (!PreCondLHS->getType()->isInteger()) continue;
2913 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
2914 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
2915 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
2916 (LHS == SE.getNotSCEV(PreCondRHSSCEV) &&
2917 RHS == SE.getNotSCEV(PreCondLHSSCEV)))
2924 /// HowManyLessThans - Return the number of times a backedge containing the
2925 /// specified less-than comparison will execute. If not computable, return
2927 SCEVHandle ScalarEvolutionsImpl::
2928 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
2929 // Only handle: "ADDREC < LoopInvariant".
2930 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2932 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2933 if (!AddRec || AddRec->getLoop() != L)
2934 return UnknownValue;
2936 if (AddRec->isAffine()) {
2937 // FORNOW: We only support unit strides.
2938 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
2939 if (AddRec->getOperand(1) != One)
2940 return UnknownValue;
2942 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
2943 // m. So, we count the number of iterations in which {n,+,1} < m is true.
2944 // Note that we cannot simply return max(m-n,0) because it's not safe to
2945 // treat m-n as signed nor unsigned due to overflow possibility.
2947 // First, we get the value of the LHS in the first iteration: n
2948 SCEVHandle Start = AddRec->getOperand(0);
2950 if (isLoopGuardedByCond(L,
2951 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
2952 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) {
2953 // Since we know that the condition is true in order to enter the loop,
2954 // we know that it will run exactly m-n times.
2955 return SE.getMinusSCEV(RHS, Start);
2957 // Then, we get the value of the LHS in the first iteration in which the
2958 // above condition doesn't hold. This equals to max(m,n).
2959 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
2960 : SE.getUMaxExpr(RHS, Start);
2962 // Finally, we subtract these two values to get the number of times the
2963 // backedge is executed: max(m,n)-n.
2964 return SE.getMinusSCEV(End, Start);
2968 return UnknownValue;
2971 /// getNumIterationsInRange - Return the number of iterations of this loop that
2972 /// produce values in the specified constant range. Another way of looking at
2973 /// this is that it returns the first iteration number where the value is not in
2974 /// the condition, thus computing the exit count. If the iteration count can't
2975 /// be computed, an instance of SCEVCouldNotCompute is returned.
2976 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2977 ScalarEvolution &SE) const {
2978 if (Range.isFullSet()) // Infinite loop.
2979 return new SCEVCouldNotCompute();
2981 // If the start is a non-zero constant, shift the range to simplify things.
2982 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2983 if (!SC->getValue()->isZero()) {
2984 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2985 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
2986 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
2987 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2988 return ShiftedAddRec->getNumIterationsInRange(
2989 Range.subtract(SC->getValue()->getValue()), SE);
2990 // This is strange and shouldn't happen.
2991 return new SCEVCouldNotCompute();
2994 // The only time we can solve this is when we have all constant indices.
2995 // Otherwise, we cannot determine the overflow conditions.
2996 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2997 if (!isa<SCEVConstant>(getOperand(i)))
2998 return new SCEVCouldNotCompute();
3001 // Okay at this point we know that all elements of the chrec are constants and
3002 // that the start element is zero.
3004 // First check to see if the range contains zero. If not, the first
3006 if (!Range.contains(APInt(getBitWidth(),0)))
3007 return SE.getConstant(ConstantInt::get(getType(),0));
3010 // If this is an affine expression then we have this situation:
3011 // Solve {0,+,A} in Range === Ax in Range
3013 // We know that zero is in the range. If A is positive then we know that
3014 // the upper value of the range must be the first possible exit value.
3015 // If A is negative then the lower of the range is the last possible loop
3016 // value. Also note that we already checked for a full range.
3017 APInt One(getBitWidth(),1);
3018 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3019 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3021 // The exit value should be (End+A)/A.
3022 APInt ExitVal = (End + A).udiv(A);
3023 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3025 // Evaluate at the exit value. If we really did fall out of the valid
3026 // range, then we computed our trip count, otherwise wrap around or other
3027 // things must have happened.
3028 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3029 if (Range.contains(Val->getValue()))
3030 return new SCEVCouldNotCompute(); // Something strange happened
3032 // Ensure that the previous value is in the range. This is a sanity check.
3033 assert(Range.contains(
3034 EvaluateConstantChrecAtConstant(this,
3035 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3036 "Linear scev computation is off in a bad way!");
3037 return SE.getConstant(ExitValue);
3038 } else if (isQuadratic()) {
3039 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3040 // quadratic equation to solve it. To do this, we must frame our problem in
3041 // terms of figuring out when zero is crossed, instead of when
3042 // Range.getUpper() is crossed.
3043 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3044 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3045 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3047 // Next, solve the constructed addrec
3048 std::pair<SCEVHandle,SCEVHandle> Roots =
3049 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3050 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3051 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3053 // Pick the smallest positive root value.
3054 if (ConstantInt *CB =
3055 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3056 R1->getValue(), R2->getValue()))) {
3057 if (CB->getZExtValue() == false)
3058 std::swap(R1, R2); // R1 is the minimum root now.
3060 // Make sure the root is not off by one. The returned iteration should
3061 // not be in the range, but the previous one should be. When solving
3062 // for "X*X < 5", for example, we should not return a root of 2.
3063 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3066 if (Range.contains(R1Val->getValue())) {
3067 // The next iteration must be out of the range...
3068 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3070 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3071 if (!Range.contains(R1Val->getValue()))
3072 return SE.getConstant(NextVal);
3073 return new SCEVCouldNotCompute(); // Something strange happened
3076 // If R1 was not in the range, then it is a good return value. Make
3077 // sure that R1-1 WAS in the range though, just in case.
3078 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3079 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3080 if (Range.contains(R1Val->getValue()))
3082 return new SCEVCouldNotCompute(); // Something strange happened
3087 return new SCEVCouldNotCompute();
3092 //===----------------------------------------------------------------------===//
3093 // ScalarEvolution Class Implementation
3094 //===----------------------------------------------------------------------===//
3096 bool ScalarEvolution::runOnFunction(Function &F) {
3097 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
3101 void ScalarEvolution::releaseMemory() {
3102 delete (ScalarEvolutionsImpl*)Impl;
3106 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3107 AU.setPreservesAll();
3108 AU.addRequiredTransitive<LoopInfo>();
3111 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
3112 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
3115 /// hasSCEV - Return true if the SCEV for this value has already been
3117 bool ScalarEvolution::hasSCEV(Value *V) const {
3118 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
3122 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
3123 /// the specified value.
3124 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
3125 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
3129 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3130 ICmpInst::Predicate Pred,
3131 SCEV *LHS, SCEV *RHS) {
3132 return ((ScalarEvolutionsImpl*)Impl)->isLoopGuardedByCond(L, Pred,
3136 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) const {
3137 return ((ScalarEvolutionsImpl*)Impl)->getBackedgeTakenCount(L);
3140 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) const {
3141 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3144 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
3145 return ((ScalarEvolutionsImpl*)Impl)->forgetLoopBackedgeTakenCount(L);
3148 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
3149 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
3152 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
3153 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
3156 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
3158 // Print all inner loops first
3159 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3160 PrintLoopInfo(OS, SE, *I);
3162 OS << "Loop " << L->getHeader()->getName() << ": ";
3164 SmallVector<BasicBlock*, 8> ExitBlocks;
3165 L->getExitBlocks(ExitBlocks);
3166 if (ExitBlocks.size() != 1)
3167 OS << "<multiple exits> ";
3169 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3170 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3172 OS << "Unpredictable backedge-taken count. ";
3178 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
3179 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
3180 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
3182 OS << "Classifying expressions for: " << F.getName() << "\n";
3183 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3184 if (I->getType()->isInteger()) {
3187 SCEVHandle SV = getSCEV(&*I);
3191 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
3193 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
3194 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3195 OS << "<<Unknown>>";
3205 OS << "Determining loop execution counts for: " << F.getName() << "\n";
3206 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
3207 PrintLoopInfo(OS, this, *I);