1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Assembly/Writer.h"
71 #include "llvm/Transforms/Scalar.h"
72 #include "llvm/Support/CFG.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/InstIterator.h"
77 #include "llvm/Support/ManagedStatic.h"
78 #include "llvm/Support/MathExtras.h"
79 #include "llvm/Support/Streams.h"
80 #include "llvm/ADT/Statistic.h"
86 STATISTIC(NumBruteForceEvaluations,
87 "Number of brute force evaluations needed to "
88 "calculate high-order polynomial exit values");
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
98 static cl::opt<unsigned>
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant derived loop"),
104 static RegisterPass<ScalarEvolution>
105 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
106 char ScalarEvolution::ID = 0;
108 //===----------------------------------------------------------------------===//
109 // SCEV class definitions
110 //===----------------------------------------------------------------------===//
112 //===----------------------------------------------------------------------===//
113 // Implementation of the SCEV class.
116 void SCEV::dump() const {
120 uint32_t SCEV::getBitWidth() const {
121 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
122 return ITy->getBitWidth();
126 bool SCEV::isZero() const {
127 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
128 return SC->getValue()->isZero();
133 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
135 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
136 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
140 const Type *SCEVCouldNotCompute::getType() const {
141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 SCEVHandle SCEVCouldNotCompute::
151 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
152 const SCEVHandle &Conc,
153 ScalarEvolution &SE) const {
157 void SCEVCouldNotCompute::print(std::ostream &OS) const {
158 OS << "***COULDNOTCOMPUTE***";
161 bool SCEVCouldNotCompute::classof(const SCEV *S) {
162 return S->getSCEVType() == scCouldNotCompute;
166 // SCEVConstants - Only allow the creation of one SCEVConstant for any
167 // particular value. Don't use a SCEVHandle here, or else the object will
169 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
172 SCEVConstant::~SCEVConstant() {
173 SCEVConstants->erase(V);
176 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
177 SCEVConstant *&R = (*SCEVConstants)[V];
178 if (R == 0) R = new SCEVConstant(V);
182 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
183 return getConstant(ConstantInt::get(Val));
186 const Type *SCEVConstant::getType() const { return V->getType(); }
188 void SCEVConstant::print(std::ostream &OS) const {
189 WriteAsOperand(OS, V, false);
192 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
193 // particular input. Don't use a SCEVHandle here, or else the object will
195 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
196 SCEVTruncateExpr*> > SCEVTruncates;
198 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
199 : SCEV(scTruncate), Op(op), Ty(ty) {
200 assert(Op->getType()->isInteger() && Ty->isInteger() &&
201 "Cannot truncate non-integer value!");
202 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
203 && "This is not a truncating conversion!");
206 SCEVTruncateExpr::~SCEVTruncateExpr() {
207 SCEVTruncates->erase(std::make_pair(Op, Ty));
210 void SCEVTruncateExpr::print(std::ostream &OS) const {
211 OS << "(truncate " << *Op << " to " << *Ty << ")";
214 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
215 // particular input. Don't use a SCEVHandle here, or else the object will never
217 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
218 SCEVZeroExtendExpr*> > SCEVZeroExtends;
220 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
221 : SCEV(scZeroExtend), Op(op), Ty(ty) {
222 assert(Op->getType()->isInteger() && Ty->isInteger() &&
223 "Cannot zero extend non-integer value!");
224 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
225 && "This is not an extending conversion!");
228 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
229 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
232 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
233 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
236 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
237 // particular input. Don't use a SCEVHandle here, or else the object will never
239 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
240 SCEVSignExtendExpr*> > SCEVSignExtends;
242 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
243 : SCEV(scSignExtend), Op(op), Ty(ty) {
244 assert(Op->getType()->isInteger() && Ty->isInteger() &&
245 "Cannot sign extend non-integer value!");
246 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
247 && "This is not an extending conversion!");
250 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
251 SCEVSignExtends->erase(std::make_pair(Op, Ty));
254 void SCEVSignExtendExpr::print(std::ostream &OS) const {
255 OS << "(signextend " << *Op << " to " << *Ty << ")";
258 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
259 // particular input. Don't use a SCEVHandle here, or else the object will never
261 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
262 SCEVCommutativeExpr*> > SCEVCommExprs;
264 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
265 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
266 std::vector<SCEV*>(Operands.begin(),
270 void SCEVCommutativeExpr::print(std::ostream &OS) const {
271 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
272 const char *OpStr = getOperationStr();
273 OS << "(" << *Operands[0];
274 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
275 OS << OpStr << *Operands[i];
279 SCEVHandle SCEVCommutativeExpr::
280 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
281 const SCEVHandle &Conc,
282 ScalarEvolution &SE) const {
283 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
285 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
286 if (H != getOperand(i)) {
287 std::vector<SCEVHandle> NewOps;
288 NewOps.reserve(getNumOperands());
289 for (unsigned j = 0; j != i; ++j)
290 NewOps.push_back(getOperand(j));
292 for (++i; i != e; ++i)
293 NewOps.push_back(getOperand(i)->
294 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
296 if (isa<SCEVAddExpr>(this))
297 return SE.getAddExpr(NewOps);
298 else if (isa<SCEVMulExpr>(this))
299 return SE.getMulExpr(NewOps);
300 else if (isa<SCEVSMaxExpr>(this))
301 return SE.getSMaxExpr(NewOps);
302 else if (isa<SCEVUMaxExpr>(this))
303 return SE.getUMaxExpr(NewOps);
305 assert(0 && "Unknown commutative expr!");
312 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
313 // input. Don't use a SCEVHandle here, or else the object will never be
315 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
316 SCEVUDivExpr*> > SCEVUDivs;
318 SCEVUDivExpr::~SCEVUDivExpr() {
319 SCEVUDivs->erase(std::make_pair(LHS, RHS));
322 void SCEVUDivExpr::print(std::ostream &OS) const {
323 OS << "(" << *LHS << " /u " << *RHS << ")";
326 const Type *SCEVUDivExpr::getType() const {
327 return LHS->getType();
330 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
331 // particular input. Don't use a SCEVHandle here, or else the object will never
333 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
334 SCEVAddRecExpr*> > SCEVAddRecExprs;
336 SCEVAddRecExpr::~SCEVAddRecExpr() {
337 SCEVAddRecExprs->erase(std::make_pair(L,
338 std::vector<SCEV*>(Operands.begin(),
342 SCEVHandle SCEVAddRecExpr::
343 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
344 const SCEVHandle &Conc,
345 ScalarEvolution &SE) const {
346 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
348 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
349 if (H != getOperand(i)) {
350 std::vector<SCEVHandle> NewOps;
351 NewOps.reserve(getNumOperands());
352 for (unsigned j = 0; j != i; ++j)
353 NewOps.push_back(getOperand(j));
355 for (++i; i != e; ++i)
356 NewOps.push_back(getOperand(i)->
357 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
359 return SE.getAddRecExpr(NewOps, L);
366 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
367 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
368 // contain L and if the start is invariant.
369 return !QueryLoop->contains(L->getHeader()) &&
370 getOperand(0)->isLoopInvariant(QueryLoop);
374 void SCEVAddRecExpr::print(std::ostream &OS) const {
375 OS << "{" << *Operands[0];
376 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
377 OS << ",+," << *Operands[i];
378 OS << "}<" << L->getHeader()->getName() + ">";
381 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
382 // value. Don't use a SCEVHandle here, or else the object will never be
384 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
386 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
388 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
389 // All non-instruction values are loop invariant. All instructions are loop
390 // invariant if they are not contained in the specified loop.
391 if (Instruction *I = dyn_cast<Instruction>(V))
392 return !L->contains(I->getParent());
396 const Type *SCEVUnknown::getType() const {
400 void SCEVUnknown::print(std::ostream &OS) const {
401 WriteAsOperand(OS, V, false);
404 //===----------------------------------------------------------------------===//
406 //===----------------------------------------------------------------------===//
409 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
410 /// than the complexity of the RHS. This comparator is used to canonicalize
412 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
413 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
414 return LHS->getSCEVType() < RHS->getSCEVType();
419 /// GroupByComplexity - Given a list of SCEV objects, order them by their
420 /// complexity, and group objects of the same complexity together by value.
421 /// When this routine is finished, we know that any duplicates in the vector are
422 /// consecutive and that complexity is monotonically increasing.
424 /// Note that we go take special precautions to ensure that we get determinstic
425 /// results from this routine. In other words, we don't want the results of
426 /// this to depend on where the addresses of various SCEV objects happened to
429 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
430 if (Ops.size() < 2) return; // Noop
431 if (Ops.size() == 2) {
432 // This is the common case, which also happens to be trivially simple.
434 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
435 std::swap(Ops[0], Ops[1]);
439 // Do the rough sort by complexity.
440 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
442 // Now that we are sorted by complexity, group elements of the same
443 // complexity. Note that this is, at worst, N^2, but the vector is likely to
444 // be extremely short in practice. Note that we take this approach because we
445 // do not want to depend on the addresses of the objects we are grouping.
446 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
448 unsigned Complexity = S->getSCEVType();
450 // If there are any objects of the same complexity and same value as this
452 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
453 if (Ops[j] == S) { // Found a duplicate.
454 // Move it to immediately after i'th element.
455 std::swap(Ops[i+1], Ops[j]);
456 ++i; // no need to rescan it.
457 if (i == e-2) return; // Done!
465 //===----------------------------------------------------------------------===//
466 // Simple SCEV method implementations
467 //===----------------------------------------------------------------------===//
469 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
470 /// specified signed integer value and return a SCEV for the constant.
471 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
474 C = Constant::getNullValue(Ty);
475 else if (Ty->isFloatingPoint())
476 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
477 APFloat::IEEEdouble, Val));
479 C = ConstantInt::get(Ty, Val);
480 return getUnknown(C);
483 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
485 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
486 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
487 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
489 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(V->getType())));
492 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
493 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
494 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
495 return getUnknown(ConstantExpr::getNot(VC->getValue()));
497 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(V->getType()));
498 return getMinusSCEV(AllOnes, V);
501 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
503 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
504 const SCEVHandle &RHS) {
506 return getAddExpr(LHS, getNegativeSCEV(RHS));
510 /// BinomialCoefficient - Compute BC(It, K). The result is of the same type as
511 /// It. Assume, K > 0.
512 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
513 ScalarEvolution &SE) {
514 // We are using the following formula for BC(It, K):
516 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
518 // Suppose, W is the bitwidth of It (and of the return value as well). We
519 // must be prepared for overflow. Hence, we must assure that the result of
520 // our computation is equal to the accurate one modulo 2^W. Unfortunately,
521 // division isn't safe in modular arithmetic. This means we must perform the
522 // whole computation accurately and then truncate the result to W bits.
524 // The dividend of the formula is a multiplication of K integers of bitwidth
525 // W. K*W bits suffice to compute it accurately.
527 // FIXME: We assume the divisor can be accurately computed using 16-bit
528 // unsigned integer type. It is true up to K = 8 (AddRecs of length 9). In
529 // future we may use APInt to use the minimum number of bits necessary to
530 // compute it accurately.
532 // It is safe to use unsigned division here: the dividend is nonnegative and
533 // the divisor is positive.
535 // Handle the simplest case efficiently.
539 assert(K < 9 && "We cannot handle such long AddRecs yet.");
541 // FIXME: A temporary hack to remove in future. Arbitrary precision integers
542 // aren't supported by the code generator yet. For the dividend, the bitwidth
543 // we use is the smallest power of 2 greater or equal to K*W and less or equal
544 // to 64. Note that setting the upper bound for bitwidth may still lead to
545 // miscompilation in some cases.
546 unsigned DividendBits = 1U << Log2_32_Ceil(K * It->getBitWidth());
547 if (DividendBits > 64)
549 #if 0 // Waiting for the APInt support in the code generator...
550 unsigned DividendBits = K * It->getBitWidth();
553 const IntegerType *DividendTy = IntegerType::get(DividendBits);
554 const SCEVHandle ExIt = SE.getTruncateOrZeroExtend(It, DividendTy);
556 // The final number of bits we need to perform the division is the maximum of
557 // dividend and divisor bitwidths.
558 const IntegerType *DivisionTy =
559 IntegerType::get(std::max(DividendBits, 16U));
561 // Compute K! We know K >= 2 here.
563 for (unsigned i = 3; i <= K; ++i)
565 APInt Divisor(DivisionTy->getBitWidth(), F);
567 // Handle this case efficiently, it is common to have constant iteration
568 // counts while computing loop exit values.
569 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(ExIt)) {
570 const APInt& N = SC->getValue()->getValue();
571 APInt Dividend(N.getBitWidth(), 1);
574 if (DividendTy != DivisionTy)
575 Dividend = Dividend.zext(DivisionTy->getBitWidth());
577 APInt Result = Dividend.udiv(Divisor);
578 if (Result.getBitWidth() != It->getBitWidth())
579 Result = Result.trunc(It->getBitWidth());
581 return SE.getConstant(Result);
584 SCEVHandle Dividend = ExIt;
585 for (unsigned i = 1; i != K; ++i)
587 SE.getMulExpr(Dividend,
588 SE.getMinusSCEV(ExIt, SE.getIntegerSCEV(i, DividendTy)));
590 return SE.getTruncateOrZeroExtend(
592 SE.getTruncateOrZeroExtend(Dividend, DivisionTy),
593 SE.getConstant(Divisor)
597 /// evaluateAtIteration - Return the value of this chain of recurrences at
598 /// the specified iteration number. We can evaluate this recurrence by
599 /// multiplying each element in the chain by the binomial coefficient
600 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
602 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
604 /// where BC(It, k) stands for binomial coefficient.
606 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
607 ScalarEvolution &SE) const {
608 SCEVHandle Result = getStart();
609 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
610 // The computation is correct in the face of overflow provided that the
611 // multiplication is performed _after_ the evaluation of the binomial
613 SCEVHandle Val = SE.getMulExpr(getOperand(i),
614 BinomialCoefficient(It, i, SE));
615 Result = SE.getAddExpr(Result, Val);
620 //===----------------------------------------------------------------------===//
621 // SCEV Expression folder implementations
622 //===----------------------------------------------------------------------===//
624 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
625 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
627 ConstantExpr::getTrunc(SC->getValue(), Ty));
629 // If the input value is a chrec scev made out of constants, truncate
630 // all of the constants.
631 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
632 std::vector<SCEVHandle> Operands;
633 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
634 // FIXME: This should allow truncation of other expression types!
635 if (isa<SCEVConstant>(AddRec->getOperand(i)))
636 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
639 if (Operands.size() == AddRec->getNumOperands())
640 return getAddRecExpr(Operands, AddRec->getLoop());
643 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
644 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
648 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty) {
649 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
651 ConstantExpr::getZExt(SC->getValue(), Ty));
653 // FIXME: If the input value is a chrec scev, and we can prove that the value
654 // did not overflow the old, smaller, value, we can zero extend all of the
655 // operands (often constants). This would allow analysis of something like
656 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
658 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
659 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
663 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op, const Type *Ty) {
664 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
666 ConstantExpr::getSExt(SC->getValue(), Ty));
668 // FIXME: If the input value is a chrec scev, and we can prove that the value
669 // did not overflow the old, smaller, value, we can sign extend all of the
670 // operands (often constants). This would allow analysis of something like
671 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
673 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
674 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
678 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
679 /// of the input value to the specified type. If the type must be
680 /// extended, it is zero extended.
681 SCEVHandle ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
683 const Type *SrcTy = V->getType();
684 assert(SrcTy->isInteger() && Ty->isInteger() &&
685 "Cannot truncate or zero extend with non-integer arguments!");
686 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
687 return V; // No conversion
688 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
689 return getTruncateExpr(V, Ty);
690 return getZeroExtendExpr(V, Ty);
693 // get - Get a canonical add expression, or something simpler if possible.
694 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
695 assert(!Ops.empty() && "Cannot get empty add!");
696 if (Ops.size() == 1) return Ops[0];
698 // Sort by complexity, this groups all similar expression types together.
699 GroupByComplexity(Ops);
701 // If there are any constants, fold them together.
703 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
705 assert(Idx < Ops.size());
706 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
707 // We found two constants, fold them together!
708 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
709 RHSC->getValue()->getValue());
710 Ops[0] = getConstant(Fold);
711 Ops.erase(Ops.begin()+1); // Erase the folded element
712 if (Ops.size() == 1) return Ops[0];
713 LHSC = cast<SCEVConstant>(Ops[0]);
716 // If we are left with a constant zero being added, strip it off.
717 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
718 Ops.erase(Ops.begin());
723 if (Ops.size() == 1) return Ops[0];
725 // Okay, check to see if the same value occurs in the operand list twice. If
726 // so, merge them together into an multiply expression. Since we sorted the
727 // list, these values are required to be adjacent.
728 const Type *Ty = Ops[0]->getType();
729 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
730 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
731 // Found a match, merge the two values into a multiply, and add any
732 // remaining values to the result.
733 SCEVHandle Two = getIntegerSCEV(2, Ty);
734 SCEVHandle Mul = getMulExpr(Ops[i], Two);
737 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
739 return getAddExpr(Ops);
742 // Now we know the first non-constant operand. Skip past any cast SCEVs.
743 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
746 // If there are add operands they would be next.
747 if (Idx < Ops.size()) {
748 bool DeletedAdd = false;
749 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
750 // If we have an add, expand the add operands onto the end of the operands
752 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
753 Ops.erase(Ops.begin()+Idx);
757 // If we deleted at least one add, we added operands to the end of the list,
758 // and they are not necessarily sorted. Recurse to resort and resimplify
759 // any operands we just aquired.
761 return getAddExpr(Ops);
764 // Skip over the add expression until we get to a multiply.
765 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
768 // If we are adding something to a multiply expression, make sure the
769 // something is not already an operand of the multiply. If so, merge it into
771 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
772 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
773 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
774 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
775 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
776 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
777 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
778 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
779 if (Mul->getNumOperands() != 2) {
780 // If the multiply has more than two operands, we must get the
782 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
783 MulOps.erase(MulOps.begin()+MulOp);
784 InnerMul = getMulExpr(MulOps);
786 SCEVHandle One = getIntegerSCEV(1, Ty);
787 SCEVHandle AddOne = getAddExpr(InnerMul, One);
788 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
789 if (Ops.size() == 2) return OuterMul;
791 Ops.erase(Ops.begin()+AddOp);
792 Ops.erase(Ops.begin()+Idx-1);
794 Ops.erase(Ops.begin()+Idx);
795 Ops.erase(Ops.begin()+AddOp-1);
797 Ops.push_back(OuterMul);
798 return getAddExpr(Ops);
801 // Check this multiply against other multiplies being added together.
802 for (unsigned OtherMulIdx = Idx+1;
803 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
805 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
806 // If MulOp occurs in OtherMul, we can fold the two multiplies
808 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
809 OMulOp != e; ++OMulOp)
810 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
811 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
812 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
813 if (Mul->getNumOperands() != 2) {
814 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
815 MulOps.erase(MulOps.begin()+MulOp);
816 InnerMul1 = getMulExpr(MulOps);
818 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
819 if (OtherMul->getNumOperands() != 2) {
820 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
822 MulOps.erase(MulOps.begin()+OMulOp);
823 InnerMul2 = getMulExpr(MulOps);
825 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
826 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
827 if (Ops.size() == 2) return OuterMul;
828 Ops.erase(Ops.begin()+Idx);
829 Ops.erase(Ops.begin()+OtherMulIdx-1);
830 Ops.push_back(OuterMul);
831 return getAddExpr(Ops);
837 // If there are any add recurrences in the operands list, see if any other
838 // added values are loop invariant. If so, we can fold them into the
840 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
843 // Scan over all recurrences, trying to fold loop invariants into them.
844 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
845 // Scan all of the other operands to this add and add them to the vector if
846 // they are loop invariant w.r.t. the recurrence.
847 std::vector<SCEVHandle> LIOps;
848 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
849 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
850 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
851 LIOps.push_back(Ops[i]);
852 Ops.erase(Ops.begin()+i);
856 // If we found some loop invariants, fold them into the recurrence.
857 if (!LIOps.empty()) {
858 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
859 LIOps.push_back(AddRec->getStart());
861 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
862 AddRecOps[0] = getAddExpr(LIOps);
864 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
865 // If all of the other operands were loop invariant, we are done.
866 if (Ops.size() == 1) return NewRec;
868 // Otherwise, add the folded AddRec by the non-liv parts.
869 for (unsigned i = 0;; ++i)
870 if (Ops[i] == AddRec) {
874 return getAddExpr(Ops);
877 // Okay, if there weren't any loop invariants to be folded, check to see if
878 // there are multiple AddRec's with the same loop induction variable being
879 // added together. If so, we can fold them.
880 for (unsigned OtherIdx = Idx+1;
881 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
882 if (OtherIdx != Idx) {
883 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
884 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
885 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
886 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
887 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
888 if (i >= NewOps.size()) {
889 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
890 OtherAddRec->op_end());
893 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
895 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
897 if (Ops.size() == 2) return NewAddRec;
899 Ops.erase(Ops.begin()+Idx);
900 Ops.erase(Ops.begin()+OtherIdx-1);
901 Ops.push_back(NewAddRec);
902 return getAddExpr(Ops);
906 // Otherwise couldn't fold anything into this recurrence. Move onto the
910 // Okay, it looks like we really DO need an add expr. Check to see if we
911 // already have one, otherwise create a new one.
912 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
913 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
915 if (Result == 0) Result = new SCEVAddExpr(Ops);
920 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
921 assert(!Ops.empty() && "Cannot get empty mul!");
923 // Sort by complexity, this groups all similar expression types together.
924 GroupByComplexity(Ops);
926 // If there are any constants, fold them together.
928 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
930 // C1*(C2+V) -> C1*C2 + C1*V
932 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
933 if (Add->getNumOperands() == 2 &&
934 isa<SCEVConstant>(Add->getOperand(0)))
935 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
936 getMulExpr(LHSC, Add->getOperand(1)));
940 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
941 // We found two constants, fold them together!
942 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
943 RHSC->getValue()->getValue());
944 Ops[0] = getConstant(Fold);
945 Ops.erase(Ops.begin()+1); // Erase the folded element
946 if (Ops.size() == 1) return Ops[0];
947 LHSC = cast<SCEVConstant>(Ops[0]);
950 // If we are left with a constant one being multiplied, strip it off.
951 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
952 Ops.erase(Ops.begin());
954 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
955 // If we have a multiply of zero, it will always be zero.
960 // Skip over the add expression until we get to a multiply.
961 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
967 // If there are mul operands inline them all into this expression.
968 if (Idx < Ops.size()) {
969 bool DeletedMul = false;
970 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
971 // If we have an mul, expand the mul operands onto the end of the operands
973 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
974 Ops.erase(Ops.begin()+Idx);
978 // If we deleted at least one mul, we added operands to the end of the list,
979 // and they are not necessarily sorted. Recurse to resort and resimplify
980 // any operands we just aquired.
982 return getMulExpr(Ops);
985 // If there are any add recurrences in the operands list, see if any other
986 // added values are loop invariant. If so, we can fold them into the
988 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
991 // Scan over all recurrences, trying to fold loop invariants into them.
992 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
993 // Scan all of the other operands to this mul and add them to the vector if
994 // they are loop invariant w.r.t. the recurrence.
995 std::vector<SCEVHandle> LIOps;
996 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
997 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
998 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
999 LIOps.push_back(Ops[i]);
1000 Ops.erase(Ops.begin()+i);
1004 // If we found some loop invariants, fold them into the recurrence.
1005 if (!LIOps.empty()) {
1006 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
1007 std::vector<SCEVHandle> NewOps;
1008 NewOps.reserve(AddRec->getNumOperands());
1009 if (LIOps.size() == 1) {
1010 SCEV *Scale = LIOps[0];
1011 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1012 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1014 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1015 std::vector<SCEVHandle> MulOps(LIOps);
1016 MulOps.push_back(AddRec->getOperand(i));
1017 NewOps.push_back(getMulExpr(MulOps));
1021 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1023 // If all of the other operands were loop invariant, we are done.
1024 if (Ops.size() == 1) return NewRec;
1026 // Otherwise, multiply the folded AddRec by the non-liv parts.
1027 for (unsigned i = 0;; ++i)
1028 if (Ops[i] == AddRec) {
1032 return getMulExpr(Ops);
1035 // Okay, if there weren't any loop invariants to be folded, check to see if
1036 // there are multiple AddRec's with the same loop induction variable being
1037 // multiplied together. If so, we can fold them.
1038 for (unsigned OtherIdx = Idx+1;
1039 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1040 if (OtherIdx != Idx) {
1041 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1042 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1043 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1044 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1045 SCEVHandle NewStart = getMulExpr(F->getStart(),
1047 SCEVHandle B = F->getStepRecurrence(*this);
1048 SCEVHandle D = G->getStepRecurrence(*this);
1049 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1052 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1054 if (Ops.size() == 2) return NewAddRec;
1056 Ops.erase(Ops.begin()+Idx);
1057 Ops.erase(Ops.begin()+OtherIdx-1);
1058 Ops.push_back(NewAddRec);
1059 return getMulExpr(Ops);
1063 // Otherwise couldn't fold anything into this recurrence. Move onto the
1067 // Okay, it looks like we really DO need an mul expr. Check to see if we
1068 // already have one, otherwise create a new one.
1069 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1070 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1073 Result = new SCEVMulExpr(Ops);
1077 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1078 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1079 if (RHSC->getValue()->equalsInt(1))
1080 return LHS; // X udiv 1 --> x
1082 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1083 Constant *LHSCV = LHSC->getValue();
1084 Constant *RHSCV = RHSC->getValue();
1085 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1089 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1091 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1092 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1097 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1098 /// specified loop. Simplify the expression as much as possible.
1099 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1100 const SCEVHandle &Step, const Loop *L) {
1101 std::vector<SCEVHandle> Operands;
1102 Operands.push_back(Start);
1103 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1104 if (StepChrec->getLoop() == L) {
1105 Operands.insert(Operands.end(), StepChrec->op_begin(),
1106 StepChrec->op_end());
1107 return getAddRecExpr(Operands, L);
1110 Operands.push_back(Step);
1111 return getAddRecExpr(Operands, L);
1114 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1115 /// specified loop. Simplify the expression as much as possible.
1116 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1118 if (Operands.size() == 1) return Operands[0];
1120 if (Operands.back()->isZero()) {
1121 Operands.pop_back();
1122 return getAddRecExpr(Operands, L); // { X,+,0 } --> X
1125 SCEVAddRecExpr *&Result =
1126 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1128 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1132 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1133 const SCEVHandle &RHS) {
1134 std::vector<SCEVHandle> Ops;
1137 return getSMaxExpr(Ops);
1140 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1141 assert(!Ops.empty() && "Cannot get empty smax!");
1142 if (Ops.size() == 1) return Ops[0];
1144 // Sort by complexity, this groups all similar expression types together.
1145 GroupByComplexity(Ops);
1147 // If there are any constants, fold them together.
1149 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1151 assert(Idx < Ops.size());
1152 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1153 // We found two constants, fold them together!
1154 ConstantInt *Fold = ConstantInt::get(
1155 APIntOps::smax(LHSC->getValue()->getValue(),
1156 RHSC->getValue()->getValue()));
1157 Ops[0] = getConstant(Fold);
1158 Ops.erase(Ops.begin()+1); // Erase the folded element
1159 if (Ops.size() == 1) return Ops[0];
1160 LHSC = cast<SCEVConstant>(Ops[0]);
1163 // If we are left with a constant -inf, strip it off.
1164 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1165 Ops.erase(Ops.begin());
1170 if (Ops.size() == 1) return Ops[0];
1172 // Find the first SMax
1173 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1176 // Check to see if one of the operands is an SMax. If so, expand its operands
1177 // onto our operand list, and recurse to simplify.
1178 if (Idx < Ops.size()) {
1179 bool DeletedSMax = false;
1180 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1181 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1182 Ops.erase(Ops.begin()+Idx);
1187 return getSMaxExpr(Ops);
1190 // Okay, check to see if the same value occurs in the operand list twice. If
1191 // so, delete one. Since we sorted the list, these values are required to
1193 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1194 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1195 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1199 if (Ops.size() == 1) return Ops[0];
1201 assert(!Ops.empty() && "Reduced smax down to nothing!");
1203 // Okay, it looks like we really DO need an smax expr. Check to see if we
1204 // already have one, otherwise create a new one.
1205 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1206 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1208 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1212 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1213 const SCEVHandle &RHS) {
1214 std::vector<SCEVHandle> Ops;
1217 return getUMaxExpr(Ops);
1220 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1221 assert(!Ops.empty() && "Cannot get empty umax!");
1222 if (Ops.size() == 1) return Ops[0];
1224 // Sort by complexity, this groups all similar expression types together.
1225 GroupByComplexity(Ops);
1227 // If there are any constants, fold them together.
1229 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1231 assert(Idx < Ops.size());
1232 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1233 // We found two constants, fold them together!
1234 ConstantInt *Fold = ConstantInt::get(
1235 APIntOps::umax(LHSC->getValue()->getValue(),
1236 RHSC->getValue()->getValue()));
1237 Ops[0] = getConstant(Fold);
1238 Ops.erase(Ops.begin()+1); // Erase the folded element
1239 if (Ops.size() == 1) return Ops[0];
1240 LHSC = cast<SCEVConstant>(Ops[0]);
1243 // If we are left with a constant zero, strip it off.
1244 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1245 Ops.erase(Ops.begin());
1250 if (Ops.size() == 1) return Ops[0];
1252 // Find the first UMax
1253 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1256 // Check to see if one of the operands is a UMax. If so, expand its operands
1257 // onto our operand list, and recurse to simplify.
1258 if (Idx < Ops.size()) {
1259 bool DeletedUMax = false;
1260 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1261 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1262 Ops.erase(Ops.begin()+Idx);
1267 return getUMaxExpr(Ops);
1270 // Okay, check to see if the same value occurs in the operand list twice. If
1271 // so, delete one. Since we sorted the list, these values are required to
1273 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1274 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1275 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1279 if (Ops.size() == 1) return Ops[0];
1281 assert(!Ops.empty() && "Reduced umax down to nothing!");
1283 // Okay, it looks like we really DO need a umax expr. Check to see if we
1284 // already have one, otherwise create a new one.
1285 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1286 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1288 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1292 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1293 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1294 return getConstant(CI);
1295 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1296 if (Result == 0) Result = new SCEVUnknown(V);
1301 //===----------------------------------------------------------------------===//
1302 // ScalarEvolutionsImpl Definition and Implementation
1303 //===----------------------------------------------------------------------===//
1305 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1309 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1310 /// SE - A reference to the public ScalarEvolution object.
1311 ScalarEvolution &SE;
1313 /// F - The function we are analyzing.
1317 /// LI - The loop information for the function we are currently analyzing.
1321 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1323 SCEVHandle UnknownValue;
1325 /// Scalars - This is a cache of the scalars we have analyzed so far.
1327 std::map<Value*, SCEVHandle> Scalars;
1329 /// IterationCounts - Cache the iteration count of the loops for this
1330 /// function as they are computed.
1331 std::map<const Loop*, SCEVHandle> IterationCounts;
1333 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1334 /// the PHI instructions that we attempt to compute constant evolutions for.
1335 /// This allows us to avoid potentially expensive recomputation of these
1336 /// properties. An instruction maps to null if we are unable to compute its
1338 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1341 ScalarEvolutionsImpl(ScalarEvolution &se, Function &f, LoopInfo &li)
1342 : SE(se), F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1344 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1345 /// expression and create a new one.
1346 SCEVHandle getSCEV(Value *V);
1348 /// hasSCEV - Return true if the SCEV for this value has already been
1350 bool hasSCEV(Value *V) const {
1351 return Scalars.count(V);
1354 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1355 /// the specified value.
1356 void setSCEV(Value *V, const SCEVHandle &H) {
1357 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1358 assert(isNew && "This entry already existed!");
1362 /// getSCEVAtScope - Compute the value of the specified expression within
1363 /// the indicated loop (which may be null to indicate in no loop). If the
1364 /// expression cannot be evaluated, return UnknownValue itself.
1365 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1368 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1369 /// an analyzable loop-invariant iteration count.
1370 bool hasLoopInvariantIterationCount(const Loop *L);
1372 /// getIterationCount - If the specified loop has a predictable iteration
1373 /// count, return it. Note that it is not valid to call this method on a
1374 /// loop without a loop-invariant iteration count.
1375 SCEVHandle getIterationCount(const Loop *L);
1377 /// deleteValueFromRecords - This method should be called by the
1378 /// client before it removes a value from the program, to make sure
1379 /// that no dangling references are left around.
1380 void deleteValueFromRecords(Value *V);
1383 /// createSCEV - We know that there is no SCEV for the specified value.
1384 /// Analyze the expression.
1385 SCEVHandle createSCEV(Value *V);
1387 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1389 SCEVHandle createNodeForPHI(PHINode *PN);
1391 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1392 /// for the specified instruction and replaces any references to the
1393 /// symbolic value SymName with the specified value. This is used during
1395 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1396 const SCEVHandle &SymName,
1397 const SCEVHandle &NewVal);
1399 /// ComputeIterationCount - Compute the number of times the specified loop
1401 SCEVHandle ComputeIterationCount(const Loop *L);
1403 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1404 /// 'icmp op load X, cst', try to see if we can compute the trip count.
1405 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1408 ICmpInst::Predicate p);
1410 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1411 /// constant number of times (the condition evolves only from constants),
1412 /// try to evaluate a few iterations of the loop until we get the exit
1413 /// condition gets a value of ExitWhen (true or false). If we cannot
1414 /// evaluate the trip count of the loop, return UnknownValue.
1415 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1418 /// HowFarToZero - Return the number of times a backedge comparing the
1419 /// specified value to zero will execute. If not computable, return
1421 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1423 /// HowFarToNonZero - Return the number of times a backedge checking the
1424 /// specified value for nonzero will execute. If not computable, return
1426 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1428 /// HowManyLessThans - Return the number of times a backedge containing the
1429 /// specified less-than comparison will execute. If not computable, return
1430 /// UnknownValue. isSigned specifies whether the less-than is signed.
1431 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1434 /// executesAtLeastOnce - Test whether entry to the loop is protected by
1435 /// a conditional between LHS and RHS.
1436 bool executesAtLeastOnce(const Loop *L, bool isSigned, SCEV *LHS, SCEV *RHS);
1438 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1439 /// in the header of its containing loop, we know the loop executes a
1440 /// constant number of times, and the PHI node is just a recurrence
1441 /// involving constants, fold it.
1442 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1447 //===----------------------------------------------------------------------===//
1448 // Basic SCEV Analysis and PHI Idiom Recognition Code
1451 /// deleteValueFromRecords - This method should be called by the
1452 /// client before it removes an instruction from the program, to make sure
1453 /// that no dangling references are left around.
1454 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1455 SmallVector<Value *, 16> Worklist;
1457 if (Scalars.erase(V)) {
1458 if (PHINode *PN = dyn_cast<PHINode>(V))
1459 ConstantEvolutionLoopExitValue.erase(PN);
1460 Worklist.push_back(V);
1463 while (!Worklist.empty()) {
1464 Value *VV = Worklist.back();
1465 Worklist.pop_back();
1467 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1469 Instruction *Inst = cast<Instruction>(*UI);
1470 if (Scalars.erase(Inst)) {
1471 if (PHINode *PN = dyn_cast<PHINode>(VV))
1472 ConstantEvolutionLoopExitValue.erase(PN);
1473 Worklist.push_back(Inst);
1480 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1481 /// expression and create a new one.
1482 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1483 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1485 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1486 if (I != Scalars.end()) return I->second;
1487 SCEVHandle S = createSCEV(V);
1488 Scalars.insert(std::make_pair(V, S));
1492 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1493 /// the specified instruction and replaces any references to the symbolic value
1494 /// SymName with the specified value. This is used during PHI resolution.
1495 void ScalarEvolutionsImpl::
1496 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1497 const SCEVHandle &NewVal) {
1498 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1499 if (SI == Scalars.end()) return;
1502 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, SE);
1503 if (NV == SI->second) return; // No change.
1505 SI->second = NV; // Update the scalars map!
1507 // Any instruction values that use this instruction might also need to be
1509 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1511 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1514 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1515 /// a loop header, making it a potential recurrence, or it doesn't.
1517 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1518 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1519 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1520 if (L->getHeader() == PN->getParent()) {
1521 // If it lives in the loop header, it has two incoming values, one
1522 // from outside the loop, and one from inside.
1523 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1524 unsigned BackEdge = IncomingEdge^1;
1526 // While we are analyzing this PHI node, handle its value symbolically.
1527 SCEVHandle SymbolicName = SE.getUnknown(PN);
1528 assert(Scalars.find(PN) == Scalars.end() &&
1529 "PHI node already processed?");
1530 Scalars.insert(std::make_pair(PN, SymbolicName));
1532 // Using this symbolic name for the PHI, analyze the value coming around
1534 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1536 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1537 // has a special value for the first iteration of the loop.
1539 // If the value coming around the backedge is an add with the symbolic
1540 // value we just inserted, then we found a simple induction variable!
1541 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1542 // If there is a single occurrence of the symbolic value, replace it
1543 // with a recurrence.
1544 unsigned FoundIndex = Add->getNumOperands();
1545 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1546 if (Add->getOperand(i) == SymbolicName)
1547 if (FoundIndex == e) {
1552 if (FoundIndex != Add->getNumOperands()) {
1553 // Create an add with everything but the specified operand.
1554 std::vector<SCEVHandle> Ops;
1555 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1556 if (i != FoundIndex)
1557 Ops.push_back(Add->getOperand(i));
1558 SCEVHandle Accum = SE.getAddExpr(Ops);
1560 // This is not a valid addrec if the step amount is varying each
1561 // loop iteration, but is not itself an addrec in this loop.
1562 if (Accum->isLoopInvariant(L) ||
1563 (isa<SCEVAddRecExpr>(Accum) &&
1564 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1565 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1566 SCEVHandle PHISCEV = SE.getAddRecExpr(StartVal, Accum, L);
1568 // Okay, for the entire analysis of this edge we assumed the PHI
1569 // to be symbolic. We now need to go back and update all of the
1570 // entries for the scalars that use the PHI (except for the PHI
1571 // itself) to use the new analyzed value instead of the "symbolic"
1573 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1577 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1578 // Otherwise, this could be a loop like this:
1579 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1580 // In this case, j = {1,+,1} and BEValue is j.
1581 // Because the other in-value of i (0) fits the evolution of BEValue
1582 // i really is an addrec evolution.
1583 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1584 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1586 // If StartVal = j.start - j.stride, we can use StartVal as the
1587 // initial step of the addrec evolution.
1588 if (StartVal == SE.getMinusSCEV(AddRec->getOperand(0),
1589 AddRec->getOperand(1))) {
1590 SCEVHandle PHISCEV =
1591 SE.getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1593 // Okay, for the entire analysis of this edge we assumed the PHI
1594 // to be symbolic. We now need to go back and update all of the
1595 // entries for the scalars that use the PHI (except for the PHI
1596 // itself) to use the new analyzed value instead of the "symbolic"
1598 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1604 return SymbolicName;
1607 // If it's not a loop phi, we can't handle it yet.
1608 return SE.getUnknown(PN);
1611 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1612 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1613 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1614 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1615 static uint32_t GetMinTrailingZeros(SCEVHandle S) {
1616 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1617 return C->getValue()->getValue().countTrailingZeros();
1619 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1620 return std::min(GetMinTrailingZeros(T->getOperand()), T->getBitWidth());
1622 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1623 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1624 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1627 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1628 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
1629 return OpRes == E->getOperand()->getBitWidth() ? E->getBitWidth() : OpRes;
1632 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1633 // The result is the min of all operands results.
1634 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1635 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1636 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1640 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1641 // The result is the sum of all operands results.
1642 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
1643 uint32_t BitWidth = M->getBitWidth();
1644 for (unsigned i = 1, e = M->getNumOperands();
1645 SumOpRes != BitWidth && i != e; ++i)
1646 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
1651 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1652 // The result is the min of all operands results.
1653 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
1654 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1655 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
1659 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1660 // The result is the min of all operands results.
1661 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1662 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1663 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1667 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1668 // The result is the min of all operands results.
1669 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
1670 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1671 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
1675 // SCEVUDivExpr, SCEVUnknown
1679 /// createSCEV - We know that there is no SCEV for the specified value.
1680 /// Analyze the expression.
1682 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1683 if (!isa<IntegerType>(V->getType()))
1684 return SE.getUnknown(V);
1686 unsigned Opcode = Instruction::UserOp1;
1687 if (Instruction *I = dyn_cast<Instruction>(V))
1688 Opcode = I->getOpcode();
1689 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1690 Opcode = CE->getOpcode();
1692 return SE.getUnknown(V);
1694 User *U = cast<User>(V);
1696 case Instruction::Add:
1697 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1698 getSCEV(U->getOperand(1)));
1699 case Instruction::Mul:
1700 return SE.getMulExpr(getSCEV(U->getOperand(0)),
1701 getSCEV(U->getOperand(1)));
1702 case Instruction::UDiv:
1703 return SE.getUDivExpr(getSCEV(U->getOperand(0)),
1704 getSCEV(U->getOperand(1)));
1705 case Instruction::Sub:
1706 return SE.getMinusSCEV(getSCEV(U->getOperand(0)),
1707 getSCEV(U->getOperand(1)));
1708 case Instruction::Or:
1709 // If the RHS of the Or is a constant, we may have something like:
1710 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1711 // optimizations will transparently handle this case.
1713 // In order for this transformation to be safe, the LHS must be of the
1714 // form X*(2^n) and the Or constant must be less than 2^n.
1715 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1716 SCEVHandle LHS = getSCEV(U->getOperand(0));
1717 const APInt &CIVal = CI->getValue();
1718 if (GetMinTrailingZeros(LHS) >=
1719 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1720 return SE.getAddExpr(LHS, getSCEV(U->getOperand(1)));
1723 case Instruction::Xor:
1724 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1725 // If the RHS of the xor is a signbit, then this is just an add.
1726 // Instcombine turns add of signbit into xor as a strength reduction step.
1727 if (CI->getValue().isSignBit())
1728 return SE.getAddExpr(getSCEV(U->getOperand(0)),
1729 getSCEV(U->getOperand(1)));
1731 // If the RHS of xor is -1, then this is a not operation.
1732 else if (CI->isAllOnesValue())
1733 return SE.getNotSCEV(getSCEV(U->getOperand(0)));
1737 case Instruction::Shl:
1738 // Turn shift left of a constant amount into a multiply.
1739 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1740 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1741 Constant *X = ConstantInt::get(
1742 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1743 return SE.getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1747 case Instruction::LShr:
1748 // Turn logical shift right of a constant into a unsigned divide.
1749 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1750 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1751 Constant *X = ConstantInt::get(
1752 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1753 return SE.getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1757 case Instruction::Trunc:
1758 return SE.getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1760 case Instruction::ZExt:
1761 return SE.getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1763 case Instruction::SExt:
1764 return SE.getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1766 case Instruction::BitCast:
1767 // BitCasts are no-op casts so we just eliminate the cast.
1768 if (U->getType()->isInteger() &&
1769 U->getOperand(0)->getType()->isInteger())
1770 return getSCEV(U->getOperand(0));
1773 case Instruction::PHI:
1774 return createNodeForPHI(cast<PHINode>(U));
1776 case Instruction::Select:
1777 // This could be a smax or umax that was lowered earlier.
1778 // Try to recover it.
1779 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
1780 Value *LHS = ICI->getOperand(0);
1781 Value *RHS = ICI->getOperand(1);
1782 switch (ICI->getPredicate()) {
1783 case ICmpInst::ICMP_SLT:
1784 case ICmpInst::ICMP_SLE:
1785 std::swap(LHS, RHS);
1787 case ICmpInst::ICMP_SGT:
1788 case ICmpInst::ICMP_SGE:
1789 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1790 return SE.getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
1791 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1792 // ~smax(~x, ~y) == smin(x, y).
1793 return SE.getNotSCEV(SE.getSMaxExpr(
1794 SE.getNotSCEV(getSCEV(LHS)),
1795 SE.getNotSCEV(getSCEV(RHS))));
1797 case ICmpInst::ICMP_ULT:
1798 case ICmpInst::ICMP_ULE:
1799 std::swap(LHS, RHS);
1801 case ICmpInst::ICMP_UGT:
1802 case ICmpInst::ICMP_UGE:
1803 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
1804 return SE.getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
1805 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
1806 // ~umax(~x, ~y) == umin(x, y)
1807 return SE.getNotSCEV(SE.getUMaxExpr(SE.getNotSCEV(getSCEV(LHS)),
1808 SE.getNotSCEV(getSCEV(RHS))));
1815 default: // We cannot analyze this expression.
1819 return SE.getUnknown(V);
1824 //===----------------------------------------------------------------------===//
1825 // Iteration Count Computation Code
1828 /// getIterationCount - If the specified loop has a predictable iteration
1829 /// count, return it. Note that it is not valid to call this method on a
1830 /// loop without a loop-invariant iteration count.
1831 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1832 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1833 if (I == IterationCounts.end()) {
1834 SCEVHandle ItCount = ComputeIterationCount(L);
1835 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1836 if (ItCount != UnknownValue) {
1837 assert(ItCount->isLoopInvariant(L) &&
1838 "Computed trip count isn't loop invariant for loop!");
1839 ++NumTripCountsComputed;
1840 } else if (isa<PHINode>(L->getHeader()->begin())) {
1841 // Only count loops that have phi nodes as not being computable.
1842 ++NumTripCountsNotComputed;
1848 /// ComputeIterationCount - Compute the number of times the specified loop
1850 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1851 // If the loop has a non-one exit block count, we can't analyze it.
1852 SmallVector<BasicBlock*, 8> ExitBlocks;
1853 L->getExitBlocks(ExitBlocks);
1854 if (ExitBlocks.size() != 1) return UnknownValue;
1856 // Okay, there is one exit block. Try to find the condition that causes the
1857 // loop to be exited.
1858 BasicBlock *ExitBlock = ExitBlocks[0];
1860 BasicBlock *ExitingBlock = 0;
1861 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1863 if (L->contains(*PI)) {
1864 if (ExitingBlock == 0)
1867 return UnknownValue; // More than one block exiting!
1869 assert(ExitingBlock && "No exits from loop, something is broken!");
1871 // Okay, we've computed the exiting block. See what condition causes us to
1874 // FIXME: we should be able to handle switch instructions (with a single exit)
1875 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1876 if (ExitBr == 0) return UnknownValue;
1877 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1879 // At this point, we know we have a conditional branch that determines whether
1880 // the loop is exited. However, we don't know if the branch is executed each
1881 // time through the loop. If not, then the execution count of the branch will
1882 // not be equal to the trip count of the loop.
1884 // Currently we check for this by checking to see if the Exit branch goes to
1885 // the loop header. If so, we know it will always execute the same number of
1886 // times as the loop. We also handle the case where the exit block *is* the
1887 // loop header. This is common for un-rotated loops. More extensive analysis
1888 // could be done to handle more cases here.
1889 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1890 ExitBr->getSuccessor(1) != L->getHeader() &&
1891 ExitBr->getParent() != L->getHeader())
1892 return UnknownValue;
1894 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1896 // If it's not an integer comparison then compute it the hard way.
1897 // Note that ICmpInst deals with pointer comparisons too so we must check
1898 // the type of the operand.
1899 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1900 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1901 ExitBr->getSuccessor(0) == ExitBlock);
1903 // If the condition was exit on true, convert the condition to exit on false
1904 ICmpInst::Predicate Cond;
1905 if (ExitBr->getSuccessor(1) == ExitBlock)
1906 Cond = ExitCond->getPredicate();
1908 Cond = ExitCond->getInversePredicate();
1910 // Handle common loops like: for (X = "string"; *X; ++X)
1911 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1912 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1914 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1915 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1918 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1919 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1921 // Try to evaluate any dependencies out of the loop.
1922 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1923 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1924 Tmp = getSCEVAtScope(RHS, L);
1925 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1927 // At this point, we would like to compute how many iterations of the
1928 // loop the predicate will return true for these inputs.
1929 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1930 // If there is a constant, force it into the RHS.
1931 std::swap(LHS, RHS);
1932 Cond = ICmpInst::getSwappedPredicate(Cond);
1935 // FIXME: think about handling pointer comparisons! i.e.:
1936 // while (P != P+100) ++P;
1938 // If we have a comparison of a chrec against a constant, try to use value
1939 // ranges to answer this query.
1940 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1941 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1942 if (AddRec->getLoop() == L) {
1943 // Form the comparison range using the constant of the correct type so
1944 // that the ConstantRange class knows to do a signed or unsigned
1946 ConstantInt *CompVal = RHSC->getValue();
1947 const Type *RealTy = ExitCond->getOperand(0)->getType();
1948 CompVal = dyn_cast<ConstantInt>(
1949 ConstantExpr::getBitCast(CompVal, RealTy));
1951 // Form the constant range.
1952 ConstantRange CompRange(
1953 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
1955 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, SE);
1956 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1961 case ICmpInst::ICMP_NE: { // while (X != Y)
1962 // Convert to: while (X-Y != 0)
1963 SCEVHandle TC = HowFarToZero(SE.getMinusSCEV(LHS, RHS), L);
1964 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1967 case ICmpInst::ICMP_EQ: {
1968 // Convert to: while (X-Y == 0) // while (X == Y)
1969 SCEVHandle TC = HowFarToNonZero(SE.getMinusSCEV(LHS, RHS), L);
1970 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1973 case ICmpInst::ICMP_SLT: {
1974 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
1975 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1978 case ICmpInst::ICMP_SGT: {
1979 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
1980 SE.getNotSCEV(RHS), L, true);
1981 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1984 case ICmpInst::ICMP_ULT: {
1985 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
1986 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1989 case ICmpInst::ICMP_UGT: {
1990 SCEVHandle TC = HowManyLessThans(SE.getNotSCEV(LHS),
1991 SE.getNotSCEV(RHS), L, false);
1992 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1997 cerr << "ComputeIterationCount ";
1998 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1999 cerr << "[unsigned] ";
2001 << Instruction::getOpcodeName(Instruction::ICmp)
2002 << " " << *RHS << "\n";
2006 return ComputeIterationCountExhaustively(L, ExitCond,
2007 ExitBr->getSuccessor(0) == ExitBlock);
2010 static ConstantInt *
2011 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2012 ScalarEvolution &SE) {
2013 SCEVHandle InVal = SE.getConstant(C);
2014 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2015 assert(isa<SCEVConstant>(Val) &&
2016 "Evaluation of SCEV at constant didn't fold correctly?");
2017 return cast<SCEVConstant>(Val)->getValue();
2020 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2021 /// and a GEP expression (missing the pointer index) indexing into it, return
2022 /// the addressed element of the initializer or null if the index expression is
2025 GetAddressedElementFromGlobal(GlobalVariable *GV,
2026 const std::vector<ConstantInt*> &Indices) {
2027 Constant *Init = GV->getInitializer();
2028 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2029 uint64_t Idx = Indices[i]->getZExtValue();
2030 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2031 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2032 Init = cast<Constant>(CS->getOperand(Idx));
2033 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2034 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2035 Init = cast<Constant>(CA->getOperand(Idx));
2036 } else if (isa<ConstantAggregateZero>(Init)) {
2037 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2038 assert(Idx < STy->getNumElements() && "Bad struct index!");
2039 Init = Constant::getNullValue(STy->getElementType(Idx));
2040 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2041 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2042 Init = Constant::getNullValue(ATy->getElementType());
2044 assert(0 && "Unknown constant aggregate type!");
2048 return 0; // Unknown initializer type
2054 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
2055 /// 'icmp op load X, cst', try to see if we can compute the trip count.
2056 SCEVHandle ScalarEvolutionsImpl::
2057 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
2059 ICmpInst::Predicate predicate) {
2060 if (LI->isVolatile()) return UnknownValue;
2062 // Check to see if the loaded pointer is a getelementptr of a global.
2063 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2064 if (!GEP) return UnknownValue;
2066 // Make sure that it is really a constant global we are gepping, with an
2067 // initializer, and make sure the first IDX is really 0.
2068 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2069 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2070 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2071 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2072 return UnknownValue;
2074 // Okay, we allow one non-constant index into the GEP instruction.
2076 std::vector<ConstantInt*> Indexes;
2077 unsigned VarIdxNum = 0;
2078 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2079 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2080 Indexes.push_back(CI);
2081 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2082 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2083 VarIdx = GEP->getOperand(i);
2085 Indexes.push_back(0);
2088 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2089 // Check to see if X is a loop variant variable value now.
2090 SCEVHandle Idx = getSCEV(VarIdx);
2091 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2092 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2094 // We can only recognize very limited forms of loop index expressions, in
2095 // particular, only affine AddRec's like {C1,+,C2}.
2096 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2097 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2098 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2099 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2100 return UnknownValue;
2102 unsigned MaxSteps = MaxBruteForceIterations;
2103 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2104 ConstantInt *ItCst =
2105 ConstantInt::get(IdxExpr->getType(), IterationNum);
2106 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, SE);
2108 // Form the GEP offset.
2109 Indexes[VarIdxNum] = Val;
2111 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2112 if (Result == 0) break; // Cannot compute!
2114 // Evaluate the condition for this iteration.
2115 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2116 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2117 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2119 cerr << "\n***\n*** Computed loop count " << *ItCst
2120 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2123 ++NumArrayLenItCounts;
2124 return SE.getConstant(ItCst); // Found terminating iteration!
2127 return UnknownValue;
2131 /// CanConstantFold - Return true if we can constant fold an instruction of the
2132 /// specified type, assuming that all operands were constants.
2133 static bool CanConstantFold(const Instruction *I) {
2134 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2135 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2138 if (const CallInst *CI = dyn_cast<CallInst>(I))
2139 if (const Function *F = CI->getCalledFunction())
2140 return canConstantFoldCallTo(F);
2144 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2145 /// in the loop that V is derived from. We allow arbitrary operations along the
2146 /// way, but the operands of an operation must either be constants or a value
2147 /// derived from a constant PHI. If this expression does not fit with these
2148 /// constraints, return null.
2149 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2150 // If this is not an instruction, or if this is an instruction outside of the
2151 // loop, it can't be derived from a loop PHI.
2152 Instruction *I = dyn_cast<Instruction>(V);
2153 if (I == 0 || !L->contains(I->getParent())) return 0;
2155 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2156 if (L->getHeader() == I->getParent())
2159 // We don't currently keep track of the control flow needed to evaluate
2160 // PHIs, so we cannot handle PHIs inside of loops.
2164 // If we won't be able to constant fold this expression even if the operands
2165 // are constants, return early.
2166 if (!CanConstantFold(I)) return 0;
2168 // Otherwise, we can evaluate this instruction if all of its operands are
2169 // constant or derived from a PHI node themselves.
2171 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2172 if (!(isa<Constant>(I->getOperand(Op)) ||
2173 isa<GlobalValue>(I->getOperand(Op)))) {
2174 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2175 if (P == 0) return 0; // Not evolving from PHI
2179 return 0; // Evolving from multiple different PHIs.
2182 // This is a expression evolving from a constant PHI!
2186 /// EvaluateExpression - Given an expression that passes the
2187 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2188 /// in the loop has the value PHIVal. If we can't fold this expression for some
2189 /// reason, return null.
2190 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2191 if (isa<PHINode>(V)) return PHIVal;
2192 if (Constant *C = dyn_cast<Constant>(V)) return C;
2193 Instruction *I = cast<Instruction>(V);
2195 std::vector<Constant*> Operands;
2196 Operands.resize(I->getNumOperands());
2198 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2199 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2200 if (Operands[i] == 0) return 0;
2203 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2204 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2205 &Operands[0], Operands.size());
2207 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2208 &Operands[0], Operands.size());
2211 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2212 /// in the header of its containing loop, we know the loop executes a
2213 /// constant number of times, and the PHI node is just a recurrence
2214 /// involving constants, fold it.
2215 Constant *ScalarEvolutionsImpl::
2216 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
2217 std::map<PHINode*, Constant*>::iterator I =
2218 ConstantEvolutionLoopExitValue.find(PN);
2219 if (I != ConstantEvolutionLoopExitValue.end())
2222 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
2223 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2225 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2227 // Since the loop is canonicalized, the PHI node must have two entries. One
2228 // entry must be a constant (coming in from outside of the loop), and the
2229 // second must be derived from the same PHI.
2230 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2231 Constant *StartCST =
2232 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2234 return RetVal = 0; // Must be a constant.
2236 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2237 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2239 return RetVal = 0; // Not derived from same PHI.
2241 // Execute the loop symbolically to determine the exit value.
2242 if (Its.getActiveBits() >= 32)
2243 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2245 unsigned NumIterations = Its.getZExtValue(); // must be in range
2246 unsigned IterationNum = 0;
2247 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2248 if (IterationNum == NumIterations)
2249 return RetVal = PHIVal; // Got exit value!
2251 // Compute the value of the PHI node for the next iteration.
2252 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2253 if (NextPHI == PHIVal)
2254 return RetVal = NextPHI; // Stopped evolving!
2256 return 0; // Couldn't evaluate!
2261 /// ComputeIterationCountExhaustively - If the trip is known to execute a
2262 /// constant number of times (the condition evolves only from constants),
2263 /// try to evaluate a few iterations of the loop until we get the exit
2264 /// condition gets a value of ExitWhen (true or false). If we cannot
2265 /// evaluate the trip count of the loop, return UnknownValue.
2266 SCEVHandle ScalarEvolutionsImpl::
2267 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2268 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2269 if (PN == 0) return UnknownValue;
2271 // Since the loop is canonicalized, the PHI node must have two entries. One
2272 // entry must be a constant (coming in from outside of the loop), and the
2273 // second must be derived from the same PHI.
2274 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2275 Constant *StartCST =
2276 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2277 if (StartCST == 0) return UnknownValue; // Must be a constant.
2279 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2280 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2281 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2283 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2284 // the loop symbolically to determine when the condition gets a value of
2286 unsigned IterationNum = 0;
2287 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2288 for (Constant *PHIVal = StartCST;
2289 IterationNum != MaxIterations; ++IterationNum) {
2290 ConstantInt *CondVal =
2291 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2293 // Couldn't symbolically evaluate.
2294 if (!CondVal) return UnknownValue;
2296 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2297 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2298 ++NumBruteForceTripCountsComputed;
2299 return SE.getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2302 // Compute the value of the PHI node for the next iteration.
2303 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2304 if (NextPHI == 0 || NextPHI == PHIVal)
2305 return UnknownValue; // Couldn't evaluate or not making progress...
2309 // Too many iterations were needed to evaluate.
2310 return UnknownValue;
2313 /// getSCEVAtScope - Compute the value of the specified expression within the
2314 /// indicated loop (which may be null to indicate in no loop). If the
2315 /// expression cannot be evaluated, return UnknownValue.
2316 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2317 // FIXME: this should be turned into a virtual method on SCEV!
2319 if (isa<SCEVConstant>(V)) return V;
2321 // If this instruction is evolved from a constant-evolving PHI, compute the
2322 // exit value from the loop without using SCEVs.
2323 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2324 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2325 const Loop *LI = this->LI[I->getParent()];
2326 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2327 if (PHINode *PN = dyn_cast<PHINode>(I))
2328 if (PN->getParent() == LI->getHeader()) {
2329 // Okay, there is no closed form solution for the PHI node. Check
2330 // to see if the loop that contains it has a known iteration count.
2331 // If so, we may be able to force computation of the exit value.
2332 SCEVHandle IterationCount = getIterationCount(LI);
2333 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
2334 // Okay, we know how many times the containing loop executes. If
2335 // this is a constant evolving PHI node, get the final value at
2336 // the specified iteration number.
2337 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2338 ICC->getValue()->getValue(),
2340 if (RV) return SE.getUnknown(RV);
2344 // Okay, this is an expression that we cannot symbolically evaluate
2345 // into a SCEV. Check to see if it's possible to symbolically evaluate
2346 // the arguments into constants, and if so, try to constant propagate the
2347 // result. This is particularly useful for computing loop exit values.
2348 if (CanConstantFold(I)) {
2349 std::vector<Constant*> Operands;
2350 Operands.reserve(I->getNumOperands());
2351 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2352 Value *Op = I->getOperand(i);
2353 if (Constant *C = dyn_cast<Constant>(Op)) {
2354 Operands.push_back(C);
2356 // If any of the operands is non-constant and if they are
2357 // non-integer, don't even try to analyze them with scev techniques.
2358 if (!isa<IntegerType>(Op->getType()))
2361 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2362 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2363 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2366 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2367 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2368 Operands.push_back(ConstantExpr::getIntegerCast(C,
2380 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2381 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2382 &Operands[0], Operands.size());
2384 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2385 &Operands[0], Operands.size());
2386 return SE.getUnknown(C);
2390 // This is some other type of SCEVUnknown, just return it.
2394 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2395 // Avoid performing the look-up in the common case where the specified
2396 // expression has no loop-variant portions.
2397 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2398 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2399 if (OpAtScope != Comm->getOperand(i)) {
2400 if (OpAtScope == UnknownValue) return UnknownValue;
2401 // Okay, at least one of these operands is loop variant but might be
2402 // foldable. Build a new instance of the folded commutative expression.
2403 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2404 NewOps.push_back(OpAtScope);
2406 for (++i; i != e; ++i) {
2407 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2408 if (OpAtScope == UnknownValue) return UnknownValue;
2409 NewOps.push_back(OpAtScope);
2411 if (isa<SCEVAddExpr>(Comm))
2412 return SE.getAddExpr(NewOps);
2413 if (isa<SCEVMulExpr>(Comm))
2414 return SE.getMulExpr(NewOps);
2415 if (isa<SCEVSMaxExpr>(Comm))
2416 return SE.getSMaxExpr(NewOps);
2417 if (isa<SCEVUMaxExpr>(Comm))
2418 return SE.getUMaxExpr(NewOps);
2419 assert(0 && "Unknown commutative SCEV type!");
2422 // If we got here, all operands are loop invariant.
2426 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2427 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2428 if (LHS == UnknownValue) return LHS;
2429 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2430 if (RHS == UnknownValue) return RHS;
2431 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2432 return Div; // must be loop invariant
2433 return SE.getUDivExpr(LHS, RHS);
2436 // If this is a loop recurrence for a loop that does not contain L, then we
2437 // are dealing with the final value computed by the loop.
2438 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2439 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2440 // To evaluate this recurrence, we need to know how many times the AddRec
2441 // loop iterates. Compute this now.
2442 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2443 if (IterationCount == UnknownValue) return UnknownValue;
2444 IterationCount = SE.getTruncateOrZeroExtend(IterationCount,
2447 // If the value is affine, simplify the expression evaluation to just
2448 // Start + Step*IterationCount.
2449 if (AddRec->isAffine())
2450 return SE.getAddExpr(AddRec->getStart(),
2451 SE.getMulExpr(IterationCount,
2452 AddRec->getOperand(1)));
2454 // Otherwise, evaluate it the hard way.
2455 return AddRec->evaluateAtIteration(IterationCount, SE);
2457 return UnknownValue;
2460 //assert(0 && "Unknown SCEV type!");
2461 return UnknownValue;
2464 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2465 /// following equation:
2467 /// A * X = B (mod N)
2469 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2470 /// A and B isn't important.
2472 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2473 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2474 ScalarEvolution &SE) {
2475 uint32_t BW = A.getBitWidth();
2476 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2477 assert(A != 0 && "A must be non-zero.");
2481 // The gcd of A and N may have only one prime factor: 2. The number of
2482 // trailing zeros in A is its multiplicity
2483 uint32_t Mult2 = A.countTrailingZeros();
2486 // 2. Check if B is divisible by D.
2488 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2489 // is not less than multiplicity of this prime factor for D.
2490 if (B.countTrailingZeros() < Mult2)
2491 return new SCEVCouldNotCompute();
2493 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2496 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2497 // bit width during computations.
2498 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2499 APInt Mod(BW + 1, 0);
2500 Mod.set(BW - Mult2); // Mod = N / D
2501 APInt I = AD.multiplicativeInverse(Mod);
2503 // 4. Compute the minimum unsigned root of the equation:
2504 // I * (B / D) mod (N / D)
2505 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2507 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2509 return SE.getConstant(Result.trunc(BW));
2512 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2513 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2514 /// might be the same) or two SCEVCouldNotCompute objects.
2516 static std::pair<SCEVHandle,SCEVHandle>
2517 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2518 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2519 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2520 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2521 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2523 // We currently can only solve this if the coefficients are constants.
2524 if (!LC || !MC || !NC) {
2525 SCEV *CNC = new SCEVCouldNotCompute();
2526 return std::make_pair(CNC, CNC);
2529 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2530 const APInt &L = LC->getValue()->getValue();
2531 const APInt &M = MC->getValue()->getValue();
2532 const APInt &N = NC->getValue()->getValue();
2533 APInt Two(BitWidth, 2);
2534 APInt Four(BitWidth, 4);
2537 using namespace APIntOps;
2539 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2540 // The B coefficient is M-N/2
2544 // The A coefficient is N/2
2545 APInt A(N.sdiv(Two));
2547 // Compute the B^2-4ac term.
2550 SqrtTerm -= Four * (A * C);
2552 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2553 // integer value or else APInt::sqrt() will assert.
2554 APInt SqrtVal(SqrtTerm.sqrt());
2556 // Compute the two solutions for the quadratic formula.
2557 // The divisions must be performed as signed divisions.
2559 APInt TwoA( A << 1 );
2560 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2561 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2563 return std::make_pair(SE.getConstant(Solution1),
2564 SE.getConstant(Solution2));
2565 } // end APIntOps namespace
2568 /// HowFarToZero - Return the number of times a backedge comparing the specified
2569 /// value to zero will execute. If not computable, return UnknownValue
2570 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2571 // If the value is a constant
2572 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2573 // If the value is already zero, the branch will execute zero times.
2574 if (C->getValue()->isZero()) return C;
2575 return UnknownValue; // Otherwise it will loop infinitely.
2578 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2579 if (!AddRec || AddRec->getLoop() != L)
2580 return UnknownValue;
2582 if (AddRec->isAffine()) {
2583 // If this is an affine expression, the execution count of this branch is
2584 // the minimum unsigned root of the following equation:
2586 // Start + Step*N = 0 (mod 2^BW)
2590 // Step*N = -Start (mod 2^BW)
2592 // where BW is the common bit width of Start and Step.
2594 // Get the initial value for the loop.
2595 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2596 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2598 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2600 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2601 // For now we handle only constant steps.
2603 // First, handle unitary steps.
2604 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2605 return SE.getNegativeSCEV(Start); // N = -Start (as unsigned)
2606 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2607 return Start; // N = Start (as unsigned)
2609 // Then, try to solve the above equation provided that Start is constant.
2610 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2611 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2612 -StartC->getValue()->getValue(),SE);
2614 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2615 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2616 // the quadratic equation to solve it.
2617 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec, SE);
2618 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2619 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2622 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2623 << " sol#2: " << *R2 << "\n";
2625 // Pick the smallest positive root value.
2626 if (ConstantInt *CB =
2627 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2628 R1->getValue(), R2->getValue()))) {
2629 if (CB->getZExtValue() == false)
2630 std::swap(R1, R2); // R1 is the minimum root now.
2632 // We can only use this value if the chrec ends up with an exact zero
2633 // value at this index. When solving for "X*X != 5", for example, we
2634 // should not accept a root of 2.
2635 SCEVHandle Val = AddRec->evaluateAtIteration(R1, SE);
2637 return R1; // We found a quadratic root!
2642 return UnknownValue;
2645 /// HowFarToNonZero - Return the number of times a backedge checking the
2646 /// specified value for nonzero will execute. If not computable, return
2648 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2649 // Loops that look like: while (X == 0) are very strange indeed. We don't
2650 // handle them yet except for the trivial case. This could be expanded in the
2651 // future as needed.
2653 // If the value is a constant, check to see if it is known to be non-zero
2654 // already. If so, the backedge will execute zero times.
2655 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2656 if (!C->getValue()->isNullValue())
2657 return SE.getIntegerSCEV(0, C->getType());
2658 return UnknownValue; // Otherwise it will loop infinitely.
2661 // We could implement others, but I really doubt anyone writes loops like
2662 // this, and if they did, they would already be constant folded.
2663 return UnknownValue;
2666 /// executesAtLeastOnce - Test whether entry to the loop is protected by
2667 /// a conditional between LHS and RHS.
2668 bool ScalarEvolutionsImpl::executesAtLeastOnce(const Loop *L, bool isSigned,
2669 SCEV *LHS, SCEV *RHS) {
2670 BasicBlock *Preheader = L->getLoopPreheader();
2671 BasicBlock *PreheaderDest = L->getHeader();
2672 if (Preheader == 0) return false;
2674 BranchInst *LoopEntryPredicate =
2675 dyn_cast<BranchInst>(Preheader->getTerminator());
2676 if (!LoopEntryPredicate) return false;
2678 // This might be a critical edge broken out. If the loop preheader ends in
2679 // an unconditional branch to the loop, check to see if the preheader has a
2680 // single predecessor, and if so, look for its terminator.
2681 while (LoopEntryPredicate->isUnconditional()) {
2682 PreheaderDest = Preheader;
2683 Preheader = Preheader->getSinglePredecessor();
2684 if (!Preheader) return false; // Multiple preds.
2686 LoopEntryPredicate =
2687 dyn_cast<BranchInst>(Preheader->getTerminator());
2688 if (!LoopEntryPredicate) return false;
2691 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
2692 if (!ICI) return false;
2694 // Now that we found a conditional branch that dominates the loop, check to
2695 // see if it is the comparison we are looking for.
2696 Value *PreCondLHS = ICI->getOperand(0);
2697 Value *PreCondRHS = ICI->getOperand(1);
2698 ICmpInst::Predicate Cond;
2699 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2700 Cond = ICI->getPredicate();
2702 Cond = ICI->getInversePredicate();
2705 case ICmpInst::ICMP_UGT:
2706 if (isSigned) return false;
2707 std::swap(PreCondLHS, PreCondRHS);
2708 Cond = ICmpInst::ICMP_ULT;
2710 case ICmpInst::ICMP_SGT:
2711 if (!isSigned) return false;
2712 std::swap(PreCondLHS, PreCondRHS);
2713 Cond = ICmpInst::ICMP_SLT;
2715 case ICmpInst::ICMP_ULT:
2716 if (isSigned) return false;
2718 case ICmpInst::ICMP_SLT:
2719 if (!isSigned) return false;
2725 if (!PreCondLHS->getType()->isInteger()) return false;
2727 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
2728 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
2729 return (LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
2730 (LHS == SE.getNotSCEV(PreCondRHSSCEV) &&
2731 RHS == SE.getNotSCEV(PreCondLHSSCEV));
2734 /// HowManyLessThans - Return the number of times a backedge containing the
2735 /// specified less-than comparison will execute. If not computable, return
2737 SCEVHandle ScalarEvolutionsImpl::
2738 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
2739 // Only handle: "ADDREC < LoopInvariant".
2740 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2742 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2743 if (!AddRec || AddRec->getLoop() != L)
2744 return UnknownValue;
2746 if (AddRec->isAffine()) {
2747 // FORNOW: We only support unit strides.
2748 SCEVHandle One = SE.getIntegerSCEV(1, RHS->getType());
2749 if (AddRec->getOperand(1) != One)
2750 return UnknownValue;
2752 // We know the LHS is of the form {n,+,1} and the RHS is some loop-invariant
2753 // m. So, we count the number of iterations in which {n,+,1} < m is true.
2754 // Note that we cannot simply return max(m-n,0) because it's not safe to
2755 // treat m-n as signed nor unsigned due to overflow possibility.
2757 // First, we get the value of the LHS in the first iteration: n
2758 SCEVHandle Start = AddRec->getOperand(0);
2760 if (executesAtLeastOnce(L, isSigned,
2761 SE.getMinusSCEV(AddRec->getOperand(0), One), RHS)) {
2762 // Since we know that the condition is true in order to enter the loop,
2763 // we know that it will run exactly m-n times.
2764 return SE.getMinusSCEV(RHS, Start);
2766 // Then, we get the value of the LHS in the first iteration in which the
2767 // above condition doesn't hold. This equals to max(m,n).
2768 SCEVHandle End = isSigned ? SE.getSMaxExpr(RHS, Start)
2769 : SE.getUMaxExpr(RHS, Start);
2771 // Finally, we subtract these two values to get the number of times the
2772 // backedge is executed: max(m,n)-n.
2773 return SE.getMinusSCEV(End, Start);
2777 return UnknownValue;
2780 /// getNumIterationsInRange - Return the number of iterations of this loop that
2781 /// produce values in the specified constant range. Another way of looking at
2782 /// this is that it returns the first iteration number where the value is not in
2783 /// the condition, thus computing the exit count. If the iteration count can't
2784 /// be computed, an instance of SCEVCouldNotCompute is returned.
2785 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2786 ScalarEvolution &SE) const {
2787 if (Range.isFullSet()) // Infinite loop.
2788 return new SCEVCouldNotCompute();
2790 // If the start is a non-zero constant, shift the range to simplify things.
2791 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2792 if (!SC->getValue()->isZero()) {
2793 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2794 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
2795 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
2796 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2797 return ShiftedAddRec->getNumIterationsInRange(
2798 Range.subtract(SC->getValue()->getValue()), SE);
2799 // This is strange and shouldn't happen.
2800 return new SCEVCouldNotCompute();
2803 // The only time we can solve this is when we have all constant indices.
2804 // Otherwise, we cannot determine the overflow conditions.
2805 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2806 if (!isa<SCEVConstant>(getOperand(i)))
2807 return new SCEVCouldNotCompute();
2810 // Okay at this point we know that all elements of the chrec are constants and
2811 // that the start element is zero.
2813 // First check to see if the range contains zero. If not, the first
2815 if (!Range.contains(APInt(getBitWidth(),0)))
2816 return SE.getConstant(ConstantInt::get(getType(),0));
2819 // If this is an affine expression then we have this situation:
2820 // Solve {0,+,A} in Range === Ax in Range
2822 // We know that zero is in the range. If A is positive then we know that
2823 // the upper value of the range must be the first possible exit value.
2824 // If A is negative then the lower of the range is the last possible loop
2825 // value. Also note that we already checked for a full range.
2826 APInt One(getBitWidth(),1);
2827 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2828 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
2830 // The exit value should be (End+A)/A.
2831 APInt ExitVal = (End + A).udiv(A);
2832 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
2834 // Evaluate at the exit value. If we really did fall out of the valid
2835 // range, then we computed our trip count, otherwise wrap around or other
2836 // things must have happened.
2837 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
2838 if (Range.contains(Val->getValue()))
2839 return new SCEVCouldNotCompute(); // Something strange happened
2841 // Ensure that the previous value is in the range. This is a sanity check.
2842 assert(Range.contains(
2843 EvaluateConstantChrecAtConstant(this,
2844 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
2845 "Linear scev computation is off in a bad way!");
2846 return SE.getConstant(ExitValue);
2847 } else if (isQuadratic()) {
2848 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2849 // quadratic equation to solve it. To do this, we must frame our problem in
2850 // terms of figuring out when zero is crossed, instead of when
2851 // Range.getUpper() is crossed.
2852 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2853 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
2854 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
2856 // Next, solve the constructed addrec
2857 std::pair<SCEVHandle,SCEVHandle> Roots =
2858 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
2859 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2860 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2862 // Pick the smallest positive root value.
2863 if (ConstantInt *CB =
2864 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2865 R1->getValue(), R2->getValue()))) {
2866 if (CB->getZExtValue() == false)
2867 std::swap(R1, R2); // R1 is the minimum root now.
2869 // Make sure the root is not off by one. The returned iteration should
2870 // not be in the range, but the previous one should be. When solving
2871 // for "X*X < 5", for example, we should not return a root of 2.
2872 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2875 if (Range.contains(R1Val->getValue())) {
2876 // The next iteration must be out of the range...
2877 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
2879 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
2880 if (!Range.contains(R1Val->getValue()))
2881 return SE.getConstant(NextVal);
2882 return new SCEVCouldNotCompute(); // Something strange happened
2885 // If R1 was not in the range, then it is a good return value. Make
2886 // sure that R1-1 WAS in the range though, just in case.
2887 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
2888 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
2889 if (Range.contains(R1Val->getValue()))
2891 return new SCEVCouldNotCompute(); // Something strange happened
2896 // Fallback, if this is a general polynomial, figure out the progression
2897 // through brute force: evaluate until we find an iteration that fails the
2898 // test. This is likely to be slow, but getting an accurate trip count is
2899 // incredibly important, we will be able to simplify the exit test a lot, and
2900 // we are almost guaranteed to get a trip count in this case.
2901 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2902 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2904 ++NumBruteForceEvaluations;
2905 SCEVHandle Val = evaluateAtIteration(SE.getConstant(TestVal), SE);
2906 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2907 return new SCEVCouldNotCompute();
2909 // Check to see if we found the value!
2910 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
2911 return SE.getConstant(TestVal);
2913 // Increment to test the next index.
2914 TestVal = ConstantInt::get(TestVal->getValue()+1);
2915 } while (TestVal != EndVal);
2917 return new SCEVCouldNotCompute();
2922 //===----------------------------------------------------------------------===//
2923 // ScalarEvolution Class Implementation
2924 //===----------------------------------------------------------------------===//
2926 bool ScalarEvolution::runOnFunction(Function &F) {
2927 Impl = new ScalarEvolutionsImpl(*this, F, getAnalysis<LoopInfo>());
2931 void ScalarEvolution::releaseMemory() {
2932 delete (ScalarEvolutionsImpl*)Impl;
2936 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2937 AU.setPreservesAll();
2938 AU.addRequiredTransitive<LoopInfo>();
2941 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2942 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2945 /// hasSCEV - Return true if the SCEV for this value has already been
2947 bool ScalarEvolution::hasSCEV(Value *V) const {
2948 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2952 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2953 /// the specified value.
2954 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2955 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2959 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2960 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2963 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2964 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2967 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2968 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2971 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
2972 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
2975 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2977 // Print all inner loops first
2978 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2979 PrintLoopInfo(OS, SE, *I);
2981 OS << "Loop " << L->getHeader()->getName() << ": ";
2983 SmallVector<BasicBlock*, 8> ExitBlocks;
2984 L->getExitBlocks(ExitBlocks);
2985 if (ExitBlocks.size() != 1)
2986 OS << "<multiple exits> ";
2988 if (SE->hasLoopInvariantIterationCount(L)) {
2989 OS << *SE->getIterationCount(L) << " iterations! ";
2991 OS << "Unpredictable iteration count. ";
2997 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2998 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2999 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
3001 OS << "Classifying expressions for: " << F.getName() << "\n";
3002 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3003 if (I->getType()->isInteger()) {
3006 SCEVHandle SV = getSCEV(&*I);
3010 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
3012 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
3013 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3014 OS << "<<Unknown>>";
3024 OS << "Determining loop execution counts for: " << F.getName() << "\n";
3025 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
3026 PrintLoopInfo(OS, this, *I);