1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by the LLVM research group and is distributed under
6 // the University of Illinois Open Source 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");
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant derived loop"),
105 RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis");
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
118 void SCEV::dump() const {
122 /// getValueRange - Return the tightest constant bounds that this value is
123 /// known to have. This method is only valid on integer SCEV objects.
124 ConstantRange SCEV::getValueRange() const {
125 const Type *Ty = getType();
126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
127 // Default to a full range if no better information is available.
128 return ConstantRange(getBitWidth());
131 uint32_t SCEV::getBitWidth() const {
132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
133 return ITy->getBitWidth();
138 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
140 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 const Type *SCEVCouldNotCompute::getType() const {
146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
155 SCEVHandle SCEVCouldNotCompute::
156 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
157 const SCEVHandle &Conc) const {
161 void SCEVCouldNotCompute::print(std::ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
165 bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
170 // SCEVConstants - Only allow the creation of one SCEVConstant for any
171 // particular value. Don't use a SCEVHandle here, or else the object will
173 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
176 SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
180 SCEVHandle SCEVConstant::get(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
186 SCEVHandle SCEVConstant::get(const APInt& Val) {
187 return get(ConstantInt::get(Val));
190 ConstantRange SCEVConstant::getValueRange() const {
191 return ConstantRange(V->getValue());
194 const Type *SCEVConstant::getType() const { return V->getType(); }
196 void SCEVConstant::print(std::ostream &OS) const {
197 WriteAsOperand(OS, V, false);
200 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
201 // particular input. Don't use a SCEVHandle here, or else the object will
203 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
204 SCEVTruncateExpr*> > SCEVTruncates;
206 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
207 : SCEV(scTruncate), Op(op), Ty(ty) {
208 assert(Op->getType()->isInteger() && Ty->isInteger() &&
209 "Cannot truncate non-integer value!");
210 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
211 && "This is not a truncating conversion!");
214 SCEVTruncateExpr::~SCEVTruncateExpr() {
215 SCEVTruncates->erase(std::make_pair(Op, Ty));
218 ConstantRange SCEVTruncateExpr::getValueRange() const {
219 return getOperand()->getValueRange().truncate(getBitWidth());
222 void SCEVTruncateExpr::print(std::ostream &OS) const {
223 OS << "(truncate " << *Op << " to " << *Ty << ")";
226 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
227 // particular input. Don't use a SCEVHandle here, or else the object will never
229 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
230 SCEVZeroExtendExpr*> > SCEVZeroExtends;
232 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
233 : SCEV(scZeroExtend), Op(op), Ty(ty) {
234 assert(Op->getType()->isInteger() && Ty->isInteger() &&
235 "Cannot zero extend non-integer value!");
236 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
237 && "This is not an extending conversion!");
240 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
241 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
244 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
245 return getOperand()->getValueRange().zeroExtend(getBitWidth());
248 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
249 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
252 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
253 // particular input. Don't use a SCEVHandle here, or else the object will never
255 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
256 SCEVSignExtendExpr*> > SCEVSignExtends;
258 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
259 : SCEV(scSignExtend), Op(op), Ty(ty) {
260 assert(Op->getType()->isInteger() && Ty->isInteger() &&
261 "Cannot sign extend non-integer value!");
262 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
263 && "This is not an extending conversion!");
266 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
267 SCEVSignExtends->erase(std::make_pair(Op, Ty));
270 ConstantRange SCEVSignExtendExpr::getValueRange() const {
271 return getOperand()->getValueRange().signExtend(getBitWidth());
274 void SCEVSignExtendExpr::print(std::ostream &OS) const {
275 OS << "(signextend " << *Op << " to " << *Ty << ")";
278 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
279 // particular input. Don't use a SCEVHandle here, or else the object will never
281 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
282 SCEVCommutativeExpr*> > SCEVCommExprs;
284 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
285 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
286 std::vector<SCEV*>(Operands.begin(),
290 void SCEVCommutativeExpr::print(std::ostream &OS) const {
291 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
292 const char *OpStr = getOperationStr();
293 OS << "(" << *Operands[0];
294 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
295 OS << OpStr << *Operands[i];
299 SCEVHandle SCEVCommutativeExpr::
300 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
301 const SCEVHandle &Conc) const {
302 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
303 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
304 if (H != getOperand(i)) {
305 std::vector<SCEVHandle> NewOps;
306 NewOps.reserve(getNumOperands());
307 for (unsigned j = 0; j != i; ++j)
308 NewOps.push_back(getOperand(j));
310 for (++i; i != e; ++i)
311 NewOps.push_back(getOperand(i)->
312 replaceSymbolicValuesWithConcrete(Sym, Conc));
314 if (isa<SCEVAddExpr>(this))
315 return SCEVAddExpr::get(NewOps);
316 else if (isa<SCEVMulExpr>(this))
317 return SCEVMulExpr::get(NewOps);
319 assert(0 && "Unknown commutative expr!");
326 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
327 // input. Don't use a SCEVHandle here, or else the object will never be
329 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
330 SCEVSDivExpr*> > SCEVSDivs;
332 SCEVSDivExpr::~SCEVSDivExpr() {
333 SCEVSDivs->erase(std::make_pair(LHS, RHS));
336 void SCEVSDivExpr::print(std::ostream &OS) const {
337 OS << "(" << *LHS << " /s " << *RHS << ")";
340 const Type *SCEVSDivExpr::getType() const {
341 return LHS->getType();
344 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
345 // particular input. Don't use a SCEVHandle here, or else the object will never
347 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
348 SCEVAddRecExpr*> > SCEVAddRecExprs;
350 SCEVAddRecExpr::~SCEVAddRecExpr() {
351 SCEVAddRecExprs->erase(std::make_pair(L,
352 std::vector<SCEV*>(Operands.begin(),
356 SCEVHandle SCEVAddRecExpr::
357 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
358 const SCEVHandle &Conc) const {
359 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
360 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
361 if (H != getOperand(i)) {
362 std::vector<SCEVHandle> NewOps;
363 NewOps.reserve(getNumOperands());
364 for (unsigned j = 0; j != i; ++j)
365 NewOps.push_back(getOperand(j));
367 for (++i; i != e; ++i)
368 NewOps.push_back(getOperand(i)->
369 replaceSymbolicValuesWithConcrete(Sym, Conc));
371 return get(NewOps, L);
378 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
379 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
380 // contain L and if the start is invariant.
381 return !QueryLoop->contains(L->getHeader()) &&
382 getOperand(0)->isLoopInvariant(QueryLoop);
386 void SCEVAddRecExpr::print(std::ostream &OS) const {
387 OS << "{" << *Operands[0];
388 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
389 OS << ",+," << *Operands[i];
390 OS << "}<" << L->getHeader()->getName() + ">";
393 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
394 // value. Don't use a SCEVHandle here, or else the object will never be
396 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
398 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
400 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
401 // All non-instruction values are loop invariant. All instructions are loop
402 // invariant if they are not contained in the specified loop.
403 if (Instruction *I = dyn_cast<Instruction>(V))
404 return !L->contains(I->getParent());
408 const Type *SCEVUnknown::getType() const {
412 void SCEVUnknown::print(std::ostream &OS) const {
413 WriteAsOperand(OS, V, false);
416 //===----------------------------------------------------------------------===//
418 //===----------------------------------------------------------------------===//
421 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
422 /// than the complexity of the RHS. This comparator is used to canonicalize
424 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
425 bool operator()(SCEV *LHS, SCEV *RHS) {
426 return LHS->getSCEVType() < RHS->getSCEVType();
431 /// GroupByComplexity - Given a list of SCEV objects, order them by their
432 /// complexity, and group objects of the same complexity together by value.
433 /// When this routine is finished, we know that any duplicates in the vector are
434 /// consecutive and that complexity is monotonically increasing.
436 /// Note that we go take special precautions to ensure that we get determinstic
437 /// results from this routine. In other words, we don't want the results of
438 /// this to depend on where the addresses of various SCEV objects happened to
441 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
442 if (Ops.size() < 2) return; // Noop
443 if (Ops.size() == 2) {
444 // This is the common case, which also happens to be trivially simple.
446 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
447 std::swap(Ops[0], Ops[1]);
451 // Do the rough sort by complexity.
452 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
454 // Now that we are sorted by complexity, group elements of the same
455 // complexity. Note that this is, at worst, N^2, but the vector is likely to
456 // be extremely short in practice. Note that we take this approach because we
457 // do not want to depend on the addresses of the objects we are grouping.
458 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
460 unsigned Complexity = S->getSCEVType();
462 // If there are any objects of the same complexity and same value as this
464 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
465 if (Ops[j] == S) { // Found a duplicate.
466 // Move it to immediately after i'th element.
467 std::swap(Ops[i+1], Ops[j]);
468 ++i; // no need to rescan it.
469 if (i == e-2) return; // Done!
477 //===----------------------------------------------------------------------===//
478 // Simple SCEV method implementations
479 //===----------------------------------------------------------------------===//
481 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
482 /// specified signed integer value and return a SCEV for the constant.
483 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
486 C = Constant::getNullValue(Ty);
487 else if (Ty->isFloatingPoint())
488 C = ConstantFP::get(Ty, APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
489 APFloat::IEEEdouble, Val));
491 C = ConstantInt::get(Ty, Val);
492 return SCEVUnknown::get(C);
495 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
496 /// input value to the specified type. If the type must be extended, it is zero
498 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
499 const Type *SrcTy = V->getType();
500 assert(SrcTy->isInteger() && Ty->isInteger() &&
501 "Cannot truncate or zero extend with non-integer arguments!");
502 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
503 return V; // No conversion
504 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
505 return SCEVTruncateExpr::get(V, Ty);
506 return SCEVZeroExtendExpr::get(V, Ty);
509 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
511 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
512 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
513 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
515 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
518 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
520 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
522 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
526 /// PartialFact - Compute V!/(V-NumSteps)!
527 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
528 // Handle this case efficiently, it is common to have constant iteration
529 // counts while computing loop exit values.
530 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
531 const APInt& Val = SC->getValue()->getValue();
532 APInt Result(Val.getBitWidth(), 1);
533 for (; NumSteps; --NumSteps)
534 Result *= Val-(NumSteps-1);
535 return SCEVConstant::get(Result);
538 const Type *Ty = V->getType();
540 return SCEVUnknown::getIntegerSCEV(1, Ty);
542 SCEVHandle Result = V;
543 for (unsigned i = 1; i != NumSteps; ++i)
544 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
545 SCEVUnknown::getIntegerSCEV(i, Ty)));
550 /// evaluateAtIteration - Return the value of this chain of recurrences at
551 /// the specified iteration number. We can evaluate this recurrence by
552 /// multiplying each element in the chain by the binomial coefficient
553 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
555 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
557 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
558 /// Is the binomial equation safe using modular arithmetic??
560 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
561 SCEVHandle Result = getStart();
563 const Type *Ty = It->getType();
564 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
565 SCEVHandle BC = PartialFact(It, i);
567 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
568 SCEVUnknown::getIntegerSCEV(Divisor,Ty));
569 Result = SCEVAddExpr::get(Result, Val);
575 //===----------------------------------------------------------------------===//
576 // SCEV Expression folder implementations
577 //===----------------------------------------------------------------------===//
579 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
580 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
581 return SCEVUnknown::get(
582 ConstantExpr::getTrunc(SC->getValue(), Ty));
584 // If the input value is a chrec scev made out of constants, truncate
585 // all of the constants.
586 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
587 std::vector<SCEVHandle> Operands;
588 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
589 // FIXME: This should allow truncation of other expression types!
590 if (isa<SCEVConstant>(AddRec->getOperand(i)))
591 Operands.push_back(get(AddRec->getOperand(i), Ty));
594 if (Operands.size() == AddRec->getNumOperands())
595 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
598 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
599 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
603 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
604 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
605 return SCEVUnknown::get(
606 ConstantExpr::getZExt(SC->getValue(), Ty));
608 // FIXME: If the input value is a chrec scev, and we can prove that the value
609 // did not overflow the old, smaller, value, we can zero extend all of the
610 // operands (often constants). This would allow analysis of something like
611 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
613 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
614 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
618 SCEVHandle SCEVSignExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
619 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
620 return SCEVUnknown::get(
621 ConstantExpr::getSExt(SC->getValue(), Ty));
623 // FIXME: If the input value is a chrec scev, and we can prove that the value
624 // did not overflow the old, smaller, value, we can sign extend all of the
625 // operands (often constants). This would allow analysis of something like
626 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
628 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
629 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
633 // get - Get a canonical add expression, or something simpler if possible.
634 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
635 assert(!Ops.empty() && "Cannot get empty add!");
636 if (Ops.size() == 1) return Ops[0];
638 // Sort by complexity, this groups all similar expression types together.
639 GroupByComplexity(Ops);
641 // If there are any constants, fold them together.
643 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
645 assert(Idx < Ops.size());
646 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
647 // We found two constants, fold them together!
648 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
649 RHSC->getValue()->getValue());
650 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
651 Ops[0] = SCEVConstant::get(CI);
652 Ops.erase(Ops.begin()+1); // Erase the folded element
653 if (Ops.size() == 1) return Ops[0];
654 LHSC = cast<SCEVConstant>(Ops[0]);
656 // If we couldn't fold the expression, move to the next constant. Note
657 // that this is impossible to happen in practice because we always
658 // constant fold constant ints to constant ints.
663 // If we are left with a constant zero being added, strip it off.
664 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
665 Ops.erase(Ops.begin());
670 if (Ops.size() == 1) return Ops[0];
672 // Okay, check to see if the same value occurs in the operand list twice. If
673 // so, merge them together into an multiply expression. Since we sorted the
674 // list, these values are required to be adjacent.
675 const Type *Ty = Ops[0]->getType();
676 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
677 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
678 // Found a match, merge the two values into a multiply, and add any
679 // remaining values to the result.
680 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
681 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
684 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
686 return SCEVAddExpr::get(Ops);
689 // Now we know the first non-constant operand. Skip past any cast SCEVs.
690 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
693 // If there are add operands they would be next.
694 if (Idx < Ops.size()) {
695 bool DeletedAdd = false;
696 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
697 // If we have an add, expand the add operands onto the end of the operands
699 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
700 Ops.erase(Ops.begin()+Idx);
704 // If we deleted at least one add, we added operands to the end of the list,
705 // and they are not necessarily sorted. Recurse to resort and resimplify
706 // any operands we just aquired.
711 // Skip over the add expression until we get to a multiply.
712 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
715 // If we are adding something to a multiply expression, make sure the
716 // something is not already an operand of the multiply. If so, merge it into
718 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
719 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
720 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
721 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
722 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
723 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
724 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
725 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
726 if (Mul->getNumOperands() != 2) {
727 // If the multiply has more than two operands, we must get the
729 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
730 MulOps.erase(MulOps.begin()+MulOp);
731 InnerMul = SCEVMulExpr::get(MulOps);
733 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
734 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
735 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
736 if (Ops.size() == 2) return OuterMul;
738 Ops.erase(Ops.begin()+AddOp);
739 Ops.erase(Ops.begin()+Idx-1);
741 Ops.erase(Ops.begin()+Idx);
742 Ops.erase(Ops.begin()+AddOp-1);
744 Ops.push_back(OuterMul);
745 return SCEVAddExpr::get(Ops);
748 // Check this multiply against other multiplies being added together.
749 for (unsigned OtherMulIdx = Idx+1;
750 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
752 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
753 // If MulOp occurs in OtherMul, we can fold the two multiplies
755 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
756 OMulOp != e; ++OMulOp)
757 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
758 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
759 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
760 if (Mul->getNumOperands() != 2) {
761 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
762 MulOps.erase(MulOps.begin()+MulOp);
763 InnerMul1 = SCEVMulExpr::get(MulOps);
765 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
766 if (OtherMul->getNumOperands() != 2) {
767 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
769 MulOps.erase(MulOps.begin()+OMulOp);
770 InnerMul2 = SCEVMulExpr::get(MulOps);
772 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
773 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
774 if (Ops.size() == 2) return OuterMul;
775 Ops.erase(Ops.begin()+Idx);
776 Ops.erase(Ops.begin()+OtherMulIdx-1);
777 Ops.push_back(OuterMul);
778 return SCEVAddExpr::get(Ops);
784 // If there are any add recurrences in the operands list, see if any other
785 // added values are loop invariant. If so, we can fold them into the
787 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
790 // Scan over all recurrences, trying to fold loop invariants into them.
791 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
792 // Scan all of the other operands to this add and add them to the vector if
793 // they are loop invariant w.r.t. the recurrence.
794 std::vector<SCEVHandle> LIOps;
795 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
796 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
797 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
798 LIOps.push_back(Ops[i]);
799 Ops.erase(Ops.begin()+i);
803 // If we found some loop invariants, fold them into the recurrence.
804 if (!LIOps.empty()) {
805 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
806 LIOps.push_back(AddRec->getStart());
808 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
809 AddRecOps[0] = SCEVAddExpr::get(LIOps);
811 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
812 // If all of the other operands were loop invariant, we are done.
813 if (Ops.size() == 1) return NewRec;
815 // Otherwise, add the folded AddRec by the non-liv parts.
816 for (unsigned i = 0;; ++i)
817 if (Ops[i] == AddRec) {
821 return SCEVAddExpr::get(Ops);
824 // Okay, if there weren't any loop invariants to be folded, check to see if
825 // there are multiple AddRec's with the same loop induction variable being
826 // added together. If so, we can fold them.
827 for (unsigned OtherIdx = Idx+1;
828 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
829 if (OtherIdx != Idx) {
830 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
831 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
832 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
833 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
834 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
835 if (i >= NewOps.size()) {
836 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
837 OtherAddRec->op_end());
840 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
842 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
844 if (Ops.size() == 2) return NewAddRec;
846 Ops.erase(Ops.begin()+Idx);
847 Ops.erase(Ops.begin()+OtherIdx-1);
848 Ops.push_back(NewAddRec);
849 return SCEVAddExpr::get(Ops);
853 // Otherwise couldn't fold anything into this recurrence. Move onto the
857 // Okay, it looks like we really DO need an add expr. Check to see if we
858 // already have one, otherwise create a new one.
859 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
860 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
862 if (Result == 0) Result = new SCEVAddExpr(Ops);
867 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
868 assert(!Ops.empty() && "Cannot get empty mul!");
870 // Sort by complexity, this groups all similar expression types together.
871 GroupByComplexity(Ops);
873 // If there are any constants, fold them together.
875 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
877 // C1*(C2+V) -> C1*C2 + C1*V
879 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
880 if (Add->getNumOperands() == 2 &&
881 isa<SCEVConstant>(Add->getOperand(0)))
882 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
883 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
887 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
888 // We found two constants, fold them together!
889 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
890 RHSC->getValue()->getValue());
891 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
892 Ops[0] = SCEVConstant::get(CI);
893 Ops.erase(Ops.begin()+1); // Erase the folded element
894 if (Ops.size() == 1) return Ops[0];
895 LHSC = cast<SCEVConstant>(Ops[0]);
897 // If we couldn't fold the expression, move to the next constant. Note
898 // that this is impossible to happen in practice because we always
899 // constant fold constant ints to constant ints.
904 // If we are left with a constant one being multiplied, strip it off.
905 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
906 Ops.erase(Ops.begin());
908 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
909 // If we have a multiply of zero, it will always be zero.
914 // Skip over the add expression until we get to a multiply.
915 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
921 // If there are mul operands inline them all into this expression.
922 if (Idx < Ops.size()) {
923 bool DeletedMul = false;
924 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
925 // If we have an mul, expand the mul operands onto the end of the operands
927 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
928 Ops.erase(Ops.begin()+Idx);
932 // If we deleted at least one mul, we added operands to the end of the list,
933 // and they are not necessarily sorted. Recurse to resort and resimplify
934 // any operands we just aquired.
939 // If there are any add recurrences in the operands list, see if any other
940 // added values are loop invariant. If so, we can fold them into the
942 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
945 // Scan over all recurrences, trying to fold loop invariants into them.
946 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
947 // Scan all of the other operands to this mul and add them to the vector if
948 // they are loop invariant w.r.t. the recurrence.
949 std::vector<SCEVHandle> LIOps;
950 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
951 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
952 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
953 LIOps.push_back(Ops[i]);
954 Ops.erase(Ops.begin()+i);
958 // If we found some loop invariants, fold them into the recurrence.
959 if (!LIOps.empty()) {
960 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
961 std::vector<SCEVHandle> NewOps;
962 NewOps.reserve(AddRec->getNumOperands());
963 if (LIOps.size() == 1) {
964 SCEV *Scale = LIOps[0];
965 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
966 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
968 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
969 std::vector<SCEVHandle> MulOps(LIOps);
970 MulOps.push_back(AddRec->getOperand(i));
971 NewOps.push_back(SCEVMulExpr::get(MulOps));
975 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
977 // If all of the other operands were loop invariant, we are done.
978 if (Ops.size() == 1) return NewRec;
980 // Otherwise, multiply the folded AddRec by the non-liv parts.
981 for (unsigned i = 0;; ++i)
982 if (Ops[i] == AddRec) {
986 return SCEVMulExpr::get(Ops);
989 // Okay, if there weren't any loop invariants to be folded, check to see if
990 // there are multiple AddRec's with the same loop induction variable being
991 // multiplied together. If so, we can fold them.
992 for (unsigned OtherIdx = Idx+1;
993 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
994 if (OtherIdx != Idx) {
995 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
996 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
997 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
998 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
999 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
1001 SCEVHandle B = F->getStepRecurrence();
1002 SCEVHandle D = G->getStepRecurrence();
1003 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
1004 SCEVMulExpr::get(G, B),
1005 SCEVMulExpr::get(B, D));
1006 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
1008 if (Ops.size() == 2) return NewAddRec;
1010 Ops.erase(Ops.begin()+Idx);
1011 Ops.erase(Ops.begin()+OtherIdx-1);
1012 Ops.push_back(NewAddRec);
1013 return SCEVMulExpr::get(Ops);
1017 // Otherwise couldn't fold anything into this recurrence. Move onto the
1021 // Okay, it looks like we really DO need an mul expr. Check to see if we
1022 // already have one, otherwise create a new one.
1023 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1024 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1027 Result = new SCEVMulExpr(Ops);
1031 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1032 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1033 if (RHSC->getValue()->equalsInt(1))
1034 return LHS; // X sdiv 1 --> x
1035 if (RHSC->getValue()->isAllOnesValue())
1036 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
1038 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1039 Constant *LHSCV = LHSC->getValue();
1040 Constant *RHSCV = RHSC->getValue();
1041 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
1045 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1047 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
1048 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
1053 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1054 /// specified loop. Simplify the expression as much as possible.
1055 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
1056 const SCEVHandle &Step, const Loop *L) {
1057 std::vector<SCEVHandle> Operands;
1058 Operands.push_back(Start);
1059 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1060 if (StepChrec->getLoop() == L) {
1061 Operands.insert(Operands.end(), StepChrec->op_begin(),
1062 StepChrec->op_end());
1063 return get(Operands, L);
1066 Operands.push_back(Step);
1067 return get(Operands, L);
1070 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1071 /// specified loop. Simplify the expression as much as possible.
1072 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1074 if (Operands.size() == 1) return Operands[0];
1076 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1077 if (StepC->getValue()->isZero()) {
1078 Operands.pop_back();
1079 return get(Operands, L); // { X,+,0 } --> X
1082 SCEVAddRecExpr *&Result =
1083 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1085 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1089 SCEVHandle SCEVUnknown::get(Value *V) {
1090 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1091 return SCEVConstant::get(CI);
1092 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1093 if (Result == 0) Result = new SCEVUnknown(V);
1098 //===----------------------------------------------------------------------===//
1099 // ScalarEvolutionsImpl Definition and Implementation
1100 //===----------------------------------------------------------------------===//
1102 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1106 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1107 /// F - The function we are analyzing.
1111 /// LI - The loop information for the function we are currently analyzing.
1115 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1117 SCEVHandle UnknownValue;
1119 /// Scalars - This is a cache of the scalars we have analyzed so far.
1121 std::map<Value*, SCEVHandle> Scalars;
1123 /// IterationCounts - Cache the iteration count of the loops for this
1124 /// function as they are computed.
1125 std::map<const Loop*, SCEVHandle> IterationCounts;
1127 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1128 /// the PHI instructions that we attempt to compute constant evolutions for.
1129 /// This allows us to avoid potentially expensive recomputation of these
1130 /// properties. An instruction maps to null if we are unable to compute its
1132 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1135 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1136 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1138 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1139 /// expression and create a new one.
1140 SCEVHandle getSCEV(Value *V);
1142 /// hasSCEV - Return true if the SCEV for this value has already been
1144 bool hasSCEV(Value *V) const {
1145 return Scalars.count(V);
1148 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1149 /// the specified value.
1150 void setSCEV(Value *V, const SCEVHandle &H) {
1151 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1152 assert(isNew && "This entry already existed!");
1156 /// getSCEVAtScope - Compute the value of the specified expression within
1157 /// the indicated loop (which may be null to indicate in no loop). If the
1158 /// expression cannot be evaluated, return UnknownValue itself.
1159 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1162 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1163 /// an analyzable loop-invariant iteration count.
1164 bool hasLoopInvariantIterationCount(const Loop *L);
1166 /// getIterationCount - If the specified loop has a predictable iteration
1167 /// count, return it. Note that it is not valid to call this method on a
1168 /// loop without a loop-invariant iteration count.
1169 SCEVHandle getIterationCount(const Loop *L);
1171 /// deleteValueFromRecords - This method should be called by the
1172 /// client before it removes a value from the program, to make sure
1173 /// that no dangling references are left around.
1174 void deleteValueFromRecords(Value *V);
1177 /// createSCEV - We know that there is no SCEV for the specified value.
1178 /// Analyze the expression.
1179 SCEVHandle createSCEV(Value *V);
1181 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1183 SCEVHandle createNodeForPHI(PHINode *PN);
1185 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1186 /// for the specified instruction and replaces any references to the
1187 /// symbolic value SymName with the specified value. This is used during
1189 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1190 const SCEVHandle &SymName,
1191 const SCEVHandle &NewVal);
1193 /// ComputeIterationCount - Compute the number of times the specified loop
1195 SCEVHandle ComputeIterationCount(const Loop *L);
1197 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1198 /// 'setcc load X, cst', try to see if we can compute the trip count.
1199 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1202 ICmpInst::Predicate p);
1204 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1205 /// constant number of times (the condition evolves only from constants),
1206 /// try to evaluate a few iterations of the loop until we get the exit
1207 /// condition gets a value of ExitWhen (true or false). If we cannot
1208 /// evaluate the trip count of the loop, return UnknownValue.
1209 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1212 /// HowFarToZero - Return the number of times a backedge comparing the
1213 /// specified value to zero will execute. If not computable, return
1215 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1217 /// HowFarToNonZero - Return the number of times a backedge checking the
1218 /// specified value for nonzero will execute. If not computable, return
1220 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1222 /// HowManyLessThans - Return the number of times a backedge containing the
1223 /// specified less-than comparison will execute. If not computable, return
1224 /// UnknownValue. isSigned specifies whether the less-than is signed.
1225 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L,
1228 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1229 /// in the header of its containing loop, we know the loop executes a
1230 /// constant number of times, and the PHI node is just a recurrence
1231 /// involving constants, fold it.
1232 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1237 //===----------------------------------------------------------------------===//
1238 // Basic SCEV Analysis and PHI Idiom Recognition Code
1241 /// deleteValueFromRecords - This method should be called by the
1242 /// client before it removes an instruction from the program, to make sure
1243 /// that no dangling references are left around.
1244 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1245 SmallVector<Value *, 16> Worklist;
1247 if (Scalars.erase(V)) {
1248 if (PHINode *PN = dyn_cast<PHINode>(V))
1249 ConstantEvolutionLoopExitValue.erase(PN);
1250 Worklist.push_back(V);
1253 while (!Worklist.empty()) {
1254 Value *VV = Worklist.back();
1255 Worklist.pop_back();
1257 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1259 Instruction *Inst = cast<Instruction>(*UI);
1260 if (Scalars.erase(Inst)) {
1261 if (PHINode *PN = dyn_cast<PHINode>(VV))
1262 ConstantEvolutionLoopExitValue.erase(PN);
1263 Worklist.push_back(Inst);
1270 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1271 /// expression and create a new one.
1272 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1273 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1275 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1276 if (I != Scalars.end()) return I->second;
1277 SCEVHandle S = createSCEV(V);
1278 Scalars.insert(std::make_pair(V, S));
1282 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1283 /// the specified instruction and replaces any references to the symbolic value
1284 /// SymName with the specified value. This is used during PHI resolution.
1285 void ScalarEvolutionsImpl::
1286 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1287 const SCEVHandle &NewVal) {
1288 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1289 if (SI == Scalars.end()) return;
1292 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1293 if (NV == SI->second) return; // No change.
1295 SI->second = NV; // Update the scalars map!
1297 // Any instruction values that use this instruction might also need to be
1299 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1301 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1304 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1305 /// a loop header, making it a potential recurrence, or it doesn't.
1307 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1308 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1309 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1310 if (L->getHeader() == PN->getParent()) {
1311 // If it lives in the loop header, it has two incoming values, one
1312 // from outside the loop, and one from inside.
1313 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1314 unsigned BackEdge = IncomingEdge^1;
1316 // While we are analyzing this PHI node, handle its value symbolically.
1317 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1318 assert(Scalars.find(PN) == Scalars.end() &&
1319 "PHI node already processed?");
1320 Scalars.insert(std::make_pair(PN, SymbolicName));
1322 // Using this symbolic name for the PHI, analyze the value coming around
1324 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1326 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1327 // has a special value for the first iteration of the loop.
1329 // If the value coming around the backedge is an add with the symbolic
1330 // value we just inserted, then we found a simple induction variable!
1331 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1332 // If there is a single occurrence of the symbolic value, replace it
1333 // with a recurrence.
1334 unsigned FoundIndex = Add->getNumOperands();
1335 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1336 if (Add->getOperand(i) == SymbolicName)
1337 if (FoundIndex == e) {
1342 if (FoundIndex != Add->getNumOperands()) {
1343 // Create an add with everything but the specified operand.
1344 std::vector<SCEVHandle> Ops;
1345 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1346 if (i != FoundIndex)
1347 Ops.push_back(Add->getOperand(i));
1348 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1350 // This is not a valid addrec if the step amount is varying each
1351 // loop iteration, but is not itself an addrec in this loop.
1352 if (Accum->isLoopInvariant(L) ||
1353 (isa<SCEVAddRecExpr>(Accum) &&
1354 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1355 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1356 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1358 // Okay, for the entire analysis of this edge we assumed the PHI
1359 // to be symbolic. We now need to go back and update all of the
1360 // entries for the scalars that use the PHI (except for the PHI
1361 // itself) to use the new analyzed value instead of the "symbolic"
1363 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1367 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1368 // Otherwise, this could be a loop like this:
1369 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1370 // In this case, j = {1,+,1} and BEValue is j.
1371 // Because the other in-value of i (0) fits the evolution of BEValue
1372 // i really is an addrec evolution.
1373 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1374 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1376 // If StartVal = j.start - j.stride, we can use StartVal as the
1377 // initial step of the addrec evolution.
1378 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1379 AddRec->getOperand(1))) {
1380 SCEVHandle PHISCEV =
1381 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1383 // Okay, for the entire analysis of this edge we assumed the PHI
1384 // to be symbolic. We now need to go back and update all of the
1385 // entries for the scalars that use the PHI (except for the PHI
1386 // itself) to use the new analyzed value instead of the "symbolic"
1388 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1394 return SymbolicName;
1397 // If it's not a loop phi, we can't handle it yet.
1398 return SCEVUnknown::get(PN);
1401 /// GetConstantFactor - Determine the largest constant factor that S has. For
1402 /// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
1403 static APInt GetConstantFactor(SCEVHandle S) {
1404 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
1405 const APInt& V = C->getValue()->getValue();
1406 if (!V.isMinValue())
1408 else // Zero is a multiple of everything.
1409 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1);
1412 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) {
1413 return GetConstantFactor(T->getOperand()).trunc(
1414 cast<IntegerType>(T->getType())->getBitWidth());
1416 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
1417 return GetConstantFactor(E->getOperand()).zext(
1418 cast<IntegerType>(E->getType())->getBitWidth());
1419 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S))
1420 return GetConstantFactor(E->getOperand()).sext(
1421 cast<IntegerType>(E->getType())->getBitWidth());
1423 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1424 // The result is the min of all operands.
1425 APInt Res(GetConstantFactor(A->getOperand(0)));
1426 for (unsigned i = 1, e = A->getNumOperands();
1427 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) {
1428 APInt Tmp(GetConstantFactor(A->getOperand(i)));
1429 Res = APIntOps::umin(Res, Tmp);
1434 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1435 // The result is the product of all the operands.
1436 APInt Res(GetConstantFactor(M->getOperand(0)));
1437 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) {
1438 APInt Tmp(GetConstantFactor(M->getOperand(i)));
1444 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1445 // For now, we just handle linear expressions.
1446 if (A->getNumOperands() == 2) {
1447 // We want the GCD between the start and the stride value.
1448 APInt Start(GetConstantFactor(A->getOperand(0)));
1451 APInt Stride(GetConstantFactor(A->getOperand(1)));
1452 return APIntOps::GreatestCommonDivisor(Start, Stride);
1456 // SCEVSDivExpr, SCEVUnknown.
1457 return APInt(S->getBitWidth(), 1);
1460 /// createSCEV - We know that there is no SCEV for the specified value.
1461 /// Analyze the expression.
1463 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1464 if (Instruction *I = dyn_cast<Instruction>(V)) {
1465 switch (I->getOpcode()) {
1466 case Instruction::Add:
1467 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1468 getSCEV(I->getOperand(1)));
1469 case Instruction::Mul:
1470 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1471 getSCEV(I->getOperand(1)));
1472 case Instruction::SDiv:
1473 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1474 getSCEV(I->getOperand(1)));
1477 case Instruction::Sub:
1478 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1479 getSCEV(I->getOperand(1)));
1480 case Instruction::Or:
1481 // If the RHS of the Or is a constant, we may have something like:
1482 // X*4+1 which got turned into X*4|1. Handle this as an add so loop
1483 // optimizations will transparently handle this case.
1484 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1485 SCEVHandle LHS = getSCEV(I->getOperand(0));
1486 APInt CommonFact(GetConstantFactor(LHS));
1487 assert(!CommonFact.isMinValue() &&
1488 "Common factor should at least be 1!");
1489 if (CommonFact.ugt(CI->getValue())) {
1490 // If the LHS is a multiple that is larger than the RHS, use +.
1491 return SCEVAddExpr::get(LHS,
1492 getSCEV(I->getOperand(1)));
1496 case Instruction::Xor:
1497 // If the RHS of the xor is a signbit, then this is just an add.
1498 // Instcombine turns add of signbit into xor as a strength reduction step.
1499 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1500 if (CI->getValue().isSignBit())
1501 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1502 getSCEV(I->getOperand(1)));
1506 case Instruction::Shl:
1507 // Turn shift left of a constant amount into a multiply.
1508 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1509 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1510 Constant *X = ConstantInt::get(
1511 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1512 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1516 case Instruction::Trunc:
1517 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
1519 case Instruction::ZExt:
1520 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1522 case Instruction::SExt:
1523 return SCEVSignExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1525 case Instruction::BitCast:
1526 // BitCasts are no-op casts so we just eliminate the cast.
1527 if (I->getType()->isInteger() &&
1528 I->getOperand(0)->getType()->isInteger())
1529 return getSCEV(I->getOperand(0));
1532 case Instruction::PHI:
1533 return createNodeForPHI(cast<PHINode>(I));
1535 default: // We cannot analyze this expression.
1540 return SCEVUnknown::get(V);
1545 //===----------------------------------------------------------------------===//
1546 // Iteration Count Computation Code
1549 /// getIterationCount - If the specified loop has a predictable iteration
1550 /// count, return it. Note that it is not valid to call this method on a
1551 /// loop without a loop-invariant iteration count.
1552 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1553 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1554 if (I == IterationCounts.end()) {
1555 SCEVHandle ItCount = ComputeIterationCount(L);
1556 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1557 if (ItCount != UnknownValue) {
1558 assert(ItCount->isLoopInvariant(L) &&
1559 "Computed trip count isn't loop invariant for loop!");
1560 ++NumTripCountsComputed;
1561 } else if (isa<PHINode>(L->getHeader()->begin())) {
1562 // Only count loops that have phi nodes as not being computable.
1563 ++NumTripCountsNotComputed;
1569 /// ComputeIterationCount - Compute the number of times the specified loop
1571 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1572 // If the loop has a non-one exit block count, we can't analyze it.
1573 SmallVector<BasicBlock*, 8> ExitBlocks;
1574 L->getExitBlocks(ExitBlocks);
1575 if (ExitBlocks.size() != 1) return UnknownValue;
1577 // Okay, there is one exit block. Try to find the condition that causes the
1578 // loop to be exited.
1579 BasicBlock *ExitBlock = ExitBlocks[0];
1581 BasicBlock *ExitingBlock = 0;
1582 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1584 if (L->contains(*PI)) {
1585 if (ExitingBlock == 0)
1588 return UnknownValue; // More than one block exiting!
1590 assert(ExitingBlock && "No exits from loop, something is broken!");
1592 // Okay, we've computed the exiting block. See what condition causes us to
1595 // FIXME: we should be able to handle switch instructions (with a single exit)
1596 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1597 if (ExitBr == 0) return UnknownValue;
1598 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1600 // At this point, we know we have a conditional branch that determines whether
1601 // the loop is exited. However, we don't know if the branch is executed each
1602 // time through the loop. If not, then the execution count of the branch will
1603 // not be equal to the trip count of the loop.
1605 // Currently we check for this by checking to see if the Exit branch goes to
1606 // the loop header. If so, we know it will always execute the same number of
1607 // times as the loop. We also handle the case where the exit block *is* the
1608 // loop header. This is common for un-rotated loops. More extensive analysis
1609 // could be done to handle more cases here.
1610 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1611 ExitBr->getSuccessor(1) != L->getHeader() &&
1612 ExitBr->getParent() != L->getHeader())
1613 return UnknownValue;
1615 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1617 // If its not an integer comparison then compute it the hard way.
1618 // Note that ICmpInst deals with pointer comparisons too so we must check
1619 // the type of the operand.
1620 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1621 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1622 ExitBr->getSuccessor(0) == ExitBlock);
1624 // If the condition was exit on true, convert the condition to exit on false
1625 ICmpInst::Predicate Cond;
1626 if (ExitBr->getSuccessor(1) == ExitBlock)
1627 Cond = ExitCond->getPredicate();
1629 Cond = ExitCond->getInversePredicate();
1631 // Handle common loops like: for (X = "string"; *X; ++X)
1632 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1633 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1635 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1636 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1639 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1640 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1642 // Try to evaluate any dependencies out of the loop.
1643 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1644 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1645 Tmp = getSCEVAtScope(RHS, L);
1646 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1648 // At this point, we would like to compute how many iterations of the
1649 // loop the predicate will return true for these inputs.
1650 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1651 // If there is a constant, force it into the RHS.
1652 std::swap(LHS, RHS);
1653 Cond = ICmpInst::getSwappedPredicate(Cond);
1656 // FIXME: think about handling pointer comparisons! i.e.:
1657 // while (P != P+100) ++P;
1659 // If we have a comparison of a chrec against a constant, try to use value
1660 // ranges to answer this query.
1661 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1662 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1663 if (AddRec->getLoop() == L) {
1664 // Form the comparison range using the constant of the correct type so
1665 // that the ConstantRange class knows to do a signed or unsigned
1667 ConstantInt *CompVal = RHSC->getValue();
1668 const Type *RealTy = ExitCond->getOperand(0)->getType();
1669 CompVal = dyn_cast<ConstantInt>(
1670 ConstantExpr::getBitCast(CompVal, RealTy));
1672 // Form the constant range.
1673 ConstantRange CompRange(
1674 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
1676 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
1677 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1682 case ICmpInst::ICMP_NE: { // while (X != Y)
1683 // Convert to: while (X-Y != 0)
1684 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1685 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1688 case ICmpInst::ICMP_EQ: {
1689 // Convert to: while (X-Y == 0) // while (X == Y)
1690 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1691 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1694 case ICmpInst::ICMP_SLT: {
1695 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, true);
1696 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1699 case ICmpInst::ICMP_SGT: {
1700 SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS),
1701 SCEV::getNegativeSCEV(RHS), L, true);
1702 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1705 case ICmpInst::ICMP_ULT: {
1706 SCEVHandle TC = HowManyLessThans(LHS, RHS, L, false);
1707 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1710 case ICmpInst::ICMP_UGT: {
1711 SCEVHandle TC = HowManyLessThans(SCEV::getNegativeSCEV(LHS),
1712 SCEV::getNegativeSCEV(RHS), L, false);
1713 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1718 cerr << "ComputeIterationCount ";
1719 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1720 cerr << "[unsigned] ";
1722 << Instruction::getOpcodeName(Instruction::ICmp)
1723 << " " << *RHS << "\n";
1727 return ComputeIterationCountExhaustively(L, ExitCond,
1728 ExitBr->getSuccessor(0) == ExitBlock);
1731 static ConstantInt *
1732 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C) {
1733 SCEVHandle InVal = SCEVConstant::get(C);
1734 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1735 assert(isa<SCEVConstant>(Val) &&
1736 "Evaluation of SCEV at constant didn't fold correctly?");
1737 return cast<SCEVConstant>(Val)->getValue();
1740 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1741 /// and a GEP expression (missing the pointer index) indexing into it, return
1742 /// the addressed element of the initializer or null if the index expression is
1745 GetAddressedElementFromGlobal(GlobalVariable *GV,
1746 const std::vector<ConstantInt*> &Indices) {
1747 Constant *Init = GV->getInitializer();
1748 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1749 uint64_t Idx = Indices[i]->getZExtValue();
1750 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1751 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1752 Init = cast<Constant>(CS->getOperand(Idx));
1753 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1754 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1755 Init = cast<Constant>(CA->getOperand(Idx));
1756 } else if (isa<ConstantAggregateZero>(Init)) {
1757 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1758 assert(Idx < STy->getNumElements() && "Bad struct index!");
1759 Init = Constant::getNullValue(STy->getElementType(Idx));
1760 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1761 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1762 Init = Constant::getNullValue(ATy->getElementType());
1764 assert(0 && "Unknown constant aggregate type!");
1768 return 0; // Unknown initializer type
1774 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1775 /// 'setcc load X, cst', try to se if we can compute the trip count.
1776 SCEVHandle ScalarEvolutionsImpl::
1777 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1779 ICmpInst::Predicate predicate) {
1780 if (LI->isVolatile()) return UnknownValue;
1782 // Check to see if the loaded pointer is a getelementptr of a global.
1783 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1784 if (!GEP) return UnknownValue;
1786 // Make sure that it is really a constant global we are gepping, with an
1787 // initializer, and make sure the first IDX is really 0.
1788 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1789 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1790 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1791 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1792 return UnknownValue;
1794 // Okay, we allow one non-constant index into the GEP instruction.
1796 std::vector<ConstantInt*> Indexes;
1797 unsigned VarIdxNum = 0;
1798 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1799 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1800 Indexes.push_back(CI);
1801 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1802 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1803 VarIdx = GEP->getOperand(i);
1805 Indexes.push_back(0);
1808 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1809 // Check to see if X is a loop variant variable value now.
1810 SCEVHandle Idx = getSCEV(VarIdx);
1811 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1812 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1814 // We can only recognize very limited forms of loop index expressions, in
1815 // particular, only affine AddRec's like {C1,+,C2}.
1816 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1817 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1818 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1819 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1820 return UnknownValue;
1822 unsigned MaxSteps = MaxBruteForceIterations;
1823 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1824 ConstantInt *ItCst =
1825 ConstantInt::get(IdxExpr->getType(), IterationNum);
1826 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1828 // Form the GEP offset.
1829 Indexes[VarIdxNum] = Val;
1831 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1832 if (Result == 0) break; // Cannot compute!
1834 // Evaluate the condition for this iteration.
1835 Result = ConstantExpr::getICmp(predicate, Result, RHS);
1836 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
1837 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
1839 cerr << "\n***\n*** Computed loop count " << *ItCst
1840 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1843 ++NumArrayLenItCounts;
1844 return SCEVConstant::get(ItCst); // Found terminating iteration!
1847 return UnknownValue;
1851 /// CanConstantFold - Return true if we can constant fold an instruction of the
1852 /// specified type, assuming that all operands were constants.
1853 static bool CanConstantFold(const Instruction *I) {
1854 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
1855 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1858 if (const CallInst *CI = dyn_cast<CallInst>(I))
1859 if (const Function *F = CI->getCalledFunction())
1860 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1864 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1865 /// in the loop that V is derived from. We allow arbitrary operations along the
1866 /// way, but the operands of an operation must either be constants or a value
1867 /// derived from a constant PHI. If this expression does not fit with these
1868 /// constraints, return null.
1869 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1870 // If this is not an instruction, or if this is an instruction outside of the
1871 // loop, it can't be derived from a loop PHI.
1872 Instruction *I = dyn_cast<Instruction>(V);
1873 if (I == 0 || !L->contains(I->getParent())) return 0;
1875 if (PHINode *PN = dyn_cast<PHINode>(I))
1876 if (L->getHeader() == I->getParent())
1879 // We don't currently keep track of the control flow needed to evaluate
1880 // PHIs, so we cannot handle PHIs inside of loops.
1883 // If we won't be able to constant fold this expression even if the operands
1884 // are constants, return early.
1885 if (!CanConstantFold(I)) return 0;
1887 // Otherwise, we can evaluate this instruction if all of its operands are
1888 // constant or derived from a PHI node themselves.
1890 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1891 if (!(isa<Constant>(I->getOperand(Op)) ||
1892 isa<GlobalValue>(I->getOperand(Op)))) {
1893 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1894 if (P == 0) return 0; // Not evolving from PHI
1898 return 0; // Evolving from multiple different PHIs.
1901 // This is a expression evolving from a constant PHI!
1905 /// EvaluateExpression - Given an expression that passes the
1906 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1907 /// in the loop has the value PHIVal. If we can't fold this expression for some
1908 /// reason, return null.
1909 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1910 if (isa<PHINode>(V)) return PHIVal;
1911 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1913 if (Constant *C = dyn_cast<Constant>(V)) return C;
1914 Instruction *I = cast<Instruction>(V);
1916 std::vector<Constant*> Operands;
1917 Operands.resize(I->getNumOperands());
1919 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1920 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1921 if (Operands[i] == 0) return 0;
1924 return ConstantFoldInstOperands(I, &Operands[0], Operands.size());
1927 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1928 /// in the header of its containing loop, we know the loop executes a
1929 /// constant number of times, and the PHI node is just a recurrence
1930 /// involving constants, fold it.
1931 Constant *ScalarEvolutionsImpl::
1932 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
1933 std::map<PHINode*, Constant*>::iterator I =
1934 ConstantEvolutionLoopExitValue.find(PN);
1935 if (I != ConstantEvolutionLoopExitValue.end())
1938 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
1939 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1941 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1943 // Since the loop is canonicalized, the PHI node must have two entries. One
1944 // entry must be a constant (coming in from outside of the loop), and the
1945 // second must be derived from the same PHI.
1946 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1947 Constant *StartCST =
1948 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1950 return RetVal = 0; // Must be a constant.
1952 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1953 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1955 return RetVal = 0; // Not derived from same PHI.
1957 // Execute the loop symbolically to determine the exit value.
1958 if (Its.getActiveBits() >= 32)
1959 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
1961 unsigned NumIterations = Its.getZExtValue(); // must be in range
1962 unsigned IterationNum = 0;
1963 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1964 if (IterationNum == NumIterations)
1965 return RetVal = PHIVal; // Got exit value!
1967 // Compute the value of the PHI node for the next iteration.
1968 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1969 if (NextPHI == PHIVal)
1970 return RetVal = NextPHI; // Stopped evolving!
1972 return 0; // Couldn't evaluate!
1977 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1978 /// constant number of times (the condition evolves only from constants),
1979 /// try to evaluate a few iterations of the loop until we get the exit
1980 /// condition gets a value of ExitWhen (true or false). If we cannot
1981 /// evaluate the trip count of the loop, return UnknownValue.
1982 SCEVHandle ScalarEvolutionsImpl::
1983 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1984 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1985 if (PN == 0) return UnknownValue;
1987 // Since the loop is canonicalized, the PHI node must have two entries. One
1988 // entry must be a constant (coming in from outside of the loop), and the
1989 // second must be derived from the same PHI.
1990 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1991 Constant *StartCST =
1992 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1993 if (StartCST == 0) return UnknownValue; // Must be a constant.
1995 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1996 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1997 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1999 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2000 // the loop symbolically to determine when the condition gets a value of
2002 unsigned IterationNum = 0;
2003 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2004 for (Constant *PHIVal = StartCST;
2005 IterationNum != MaxIterations; ++IterationNum) {
2006 ConstantInt *CondVal =
2007 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2009 // Couldn't symbolically evaluate.
2010 if (!CondVal) return UnknownValue;
2012 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2013 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2014 ++NumBruteForceTripCountsComputed;
2015 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
2018 // Compute the value of the PHI node for the next iteration.
2019 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2020 if (NextPHI == 0 || NextPHI == PHIVal)
2021 return UnknownValue; // Couldn't evaluate or not making progress...
2025 // Too many iterations were needed to evaluate.
2026 return UnknownValue;
2029 /// getSCEVAtScope - Compute the value of the specified expression within the
2030 /// indicated loop (which may be null to indicate in no loop). If the
2031 /// expression cannot be evaluated, return UnknownValue.
2032 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2033 // FIXME: this should be turned into a virtual method on SCEV!
2035 if (isa<SCEVConstant>(V)) return V;
2037 // If this instruction is evolves from a constant-evolving PHI, compute the
2038 // exit value from the loop without using SCEVs.
2039 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2040 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2041 const Loop *LI = this->LI[I->getParent()];
2042 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2043 if (PHINode *PN = dyn_cast<PHINode>(I))
2044 if (PN->getParent() == LI->getHeader()) {
2045 // Okay, there is no closed form solution for the PHI node. Check
2046 // to see if the loop that contains it has a known iteration count.
2047 // If so, we may be able to force computation of the exit value.
2048 SCEVHandle IterationCount = getIterationCount(LI);
2049 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
2050 // Okay, we know how many times the containing loop executes. If
2051 // this is a constant evolving PHI node, get the final value at
2052 // the specified iteration number.
2053 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2054 ICC->getValue()->getValue(),
2056 if (RV) return SCEVUnknown::get(RV);
2060 // Okay, this is an expression that we cannot symbolically evaluate
2061 // into a SCEV. Check to see if it's possible to symbolically evaluate
2062 // the arguments into constants, and if so, try to constant propagate the
2063 // result. This is particularly useful for computing loop exit values.
2064 if (CanConstantFold(I)) {
2065 std::vector<Constant*> Operands;
2066 Operands.reserve(I->getNumOperands());
2067 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2068 Value *Op = I->getOperand(i);
2069 if (Constant *C = dyn_cast<Constant>(Op)) {
2070 Operands.push_back(C);
2072 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2073 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2074 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2077 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2078 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2079 Operands.push_back(ConstantExpr::getIntegerCast(C,
2089 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
2090 return SCEVUnknown::get(C);
2094 // This is some other type of SCEVUnknown, just return it.
2098 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2099 // Avoid performing the look-up in the common case where the specified
2100 // expression has no loop-variant portions.
2101 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2102 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2103 if (OpAtScope != Comm->getOperand(i)) {
2104 if (OpAtScope == UnknownValue) return UnknownValue;
2105 // Okay, at least one of these operands is loop variant but might be
2106 // foldable. Build a new instance of the folded commutative expression.
2107 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2108 NewOps.push_back(OpAtScope);
2110 for (++i; i != e; ++i) {
2111 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2112 if (OpAtScope == UnknownValue) return UnknownValue;
2113 NewOps.push_back(OpAtScope);
2115 if (isa<SCEVAddExpr>(Comm))
2116 return SCEVAddExpr::get(NewOps);
2117 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2118 return SCEVMulExpr::get(NewOps);
2121 // If we got here, all operands are loop invariant.
2125 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2126 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2127 if (LHS == UnknownValue) return LHS;
2128 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2129 if (RHS == UnknownValue) return RHS;
2130 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2131 return Div; // must be loop invariant
2132 return SCEVSDivExpr::get(LHS, RHS);
2135 // If this is a loop recurrence for a loop that does not contain L, then we
2136 // are dealing with the final value computed by the loop.
2137 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2138 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2139 // To evaluate this recurrence, we need to know how many times the AddRec
2140 // loop iterates. Compute this now.
2141 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2142 if (IterationCount == UnknownValue) return UnknownValue;
2143 IterationCount = getTruncateOrZeroExtend(IterationCount,
2146 // If the value is affine, simplify the expression evaluation to just
2147 // Start + Step*IterationCount.
2148 if (AddRec->isAffine())
2149 return SCEVAddExpr::get(AddRec->getStart(),
2150 SCEVMulExpr::get(IterationCount,
2151 AddRec->getOperand(1)));
2153 // Otherwise, evaluate it the hard way.
2154 return AddRec->evaluateAtIteration(IterationCount);
2156 return UnknownValue;
2159 //assert(0 && "Unknown SCEV type!");
2160 return UnknownValue;
2164 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2165 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2166 /// might be the same) or two SCEVCouldNotCompute objects.
2168 static std::pair<SCEVHandle,SCEVHandle>
2169 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2170 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2171 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2172 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2173 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2175 // We currently can only solve this if the coefficients are constants.
2176 if (!LC || !MC || !NC) {
2177 SCEV *CNC = new SCEVCouldNotCompute();
2178 return std::make_pair(CNC, CNC);
2181 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2182 const APInt &L = LC->getValue()->getValue();
2183 const APInt &M = MC->getValue()->getValue();
2184 const APInt &N = NC->getValue()->getValue();
2185 APInt Two(BitWidth, 2);
2186 APInt Four(BitWidth, 4);
2189 using namespace APIntOps;
2191 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2192 // The B coefficient is M-N/2
2196 // The A coefficient is N/2
2197 APInt A(N.sdiv(Two));
2199 // Compute the B^2-4ac term.
2202 SqrtTerm -= Four * (A * C);
2204 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2205 // integer value or else APInt::sqrt() will assert.
2206 APInt SqrtVal(SqrtTerm.sqrt());
2208 // Compute the two solutions for the quadratic formula.
2209 // The divisions must be performed as signed divisions.
2211 APInt TwoA( A << 1 );
2212 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2213 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2215 return std::make_pair(SCEVConstant::get(Solution1),
2216 SCEVConstant::get(Solution2));
2217 } // end APIntOps namespace
2220 /// HowFarToZero - Return the number of times a backedge comparing the specified
2221 /// value to zero will execute. If not computable, return UnknownValue
2222 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2223 // If the value is a constant
2224 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2225 // If the value is already zero, the branch will execute zero times.
2226 if (C->getValue()->isZero()) return C;
2227 return UnknownValue; // Otherwise it will loop infinitely.
2230 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2231 if (!AddRec || AddRec->getLoop() != L)
2232 return UnknownValue;
2234 if (AddRec->isAffine()) {
2235 // If this is an affine expression the execution count of this branch is
2238 // (0 - Start/Step) iff Start % Step == 0
2240 // Get the initial value for the loop.
2241 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2242 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2243 SCEVHandle Step = AddRec->getOperand(1);
2245 Step = getSCEVAtScope(Step, L->getParentLoop());
2247 // Figure out if Start % Step == 0.
2248 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2249 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2250 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2251 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2252 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2253 return Start; // 0 - Start/-1 == Start
2255 // Check to see if Start is divisible by SC with no remainder.
2256 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2257 ConstantInt *StartCC = StartC->getValue();
2258 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2259 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2260 if (Rem->isNullValue()) {
2261 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2262 return SCEVUnknown::get(Result);
2266 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2267 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2268 // the quadratic equation to solve it.
2269 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2270 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2271 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2274 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2275 << " sol#2: " << *R2 << "\n";
2277 // Pick the smallest positive root value.
2278 if (ConstantInt *CB =
2279 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2280 R1->getValue(), R2->getValue()))) {
2281 if (CB->getZExtValue() == false)
2282 std::swap(R1, R2); // R1 is the minimum root now.
2284 // We can only use this value if the chrec ends up with an exact zero
2285 // value at this index. When solving for "X*X != 5", for example, we
2286 // should not accept a root of 2.
2287 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2288 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2289 if (EvalVal->getValue()->isZero())
2290 return R1; // We found a quadratic root!
2295 return UnknownValue;
2298 /// HowFarToNonZero - Return the number of times a backedge checking the
2299 /// specified value for nonzero will execute. If not computable, return
2301 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2302 // Loops that look like: while (X == 0) are very strange indeed. We don't
2303 // handle them yet except for the trivial case. This could be expanded in the
2304 // future as needed.
2306 // If the value is a constant, check to see if it is known to be non-zero
2307 // already. If so, the backedge will execute zero times.
2308 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2309 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2311 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2312 if (NonZero == ConstantInt::getTrue())
2313 return getSCEV(Zero);
2314 return UnknownValue; // Otherwise it will loop infinitely.
2317 // We could implement others, but I really doubt anyone writes loops like
2318 // this, and if they did, they would already be constant folded.
2319 return UnknownValue;
2322 /// HowManyLessThans - Return the number of times a backedge containing the
2323 /// specified less-than comparison will execute. If not computable, return
2325 SCEVHandle ScalarEvolutionsImpl::
2326 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
2327 // Only handle: "ADDREC < LoopInvariant".
2328 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2330 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2331 if (!AddRec || AddRec->getLoop() != L)
2332 return UnknownValue;
2334 if (AddRec->isAffine()) {
2335 // FORNOW: We only support unit strides.
2336 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2337 if (AddRec->getOperand(1) != One)
2338 return UnknownValue;
2340 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2341 // know that m is >= n on input to the loop. If it is, the condition return
2342 // true zero times. What we really should return, for full generality, is
2343 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2344 // canonical loop form: most do-loops will have a check that dominates the
2345 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2346 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2348 // Search for the check.
2349 BasicBlock *Preheader = L->getLoopPreheader();
2350 BasicBlock *PreheaderDest = L->getHeader();
2351 if (Preheader == 0) return UnknownValue;
2353 BranchInst *LoopEntryPredicate =
2354 dyn_cast<BranchInst>(Preheader->getTerminator());
2355 if (!LoopEntryPredicate) return UnknownValue;
2357 // This might be a critical edge broken out. If the loop preheader ends in
2358 // an unconditional branch to the loop, check to see if the preheader has a
2359 // single predecessor, and if so, look for its terminator.
2360 while (LoopEntryPredicate->isUnconditional()) {
2361 PreheaderDest = Preheader;
2362 Preheader = Preheader->getSinglePredecessor();
2363 if (!Preheader) return UnknownValue; // Multiple preds.
2365 LoopEntryPredicate =
2366 dyn_cast<BranchInst>(Preheader->getTerminator());
2367 if (!LoopEntryPredicate) return UnknownValue;
2370 // Now that we found a conditional branch that dominates the loop, check to
2371 // see if it is the comparison we are looking for.
2372 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2373 Value *PreCondLHS = ICI->getOperand(0);
2374 Value *PreCondRHS = ICI->getOperand(1);
2375 ICmpInst::Predicate Cond;
2376 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2377 Cond = ICI->getPredicate();
2379 Cond = ICI->getInversePredicate();
2382 case ICmpInst::ICMP_UGT:
2383 if (isSigned) return UnknownValue;
2384 std::swap(PreCondLHS, PreCondRHS);
2385 Cond = ICmpInst::ICMP_ULT;
2387 case ICmpInst::ICMP_SGT:
2388 if (!isSigned) return UnknownValue;
2389 std::swap(PreCondLHS, PreCondRHS);
2390 Cond = ICmpInst::ICMP_SLT;
2392 case ICmpInst::ICMP_ULT:
2393 if (isSigned) return UnknownValue;
2395 case ICmpInst::ICMP_SLT:
2396 if (!isSigned) return UnknownValue;
2399 return UnknownValue;
2402 if (PreCondLHS->getType()->isInteger()) {
2403 if (RHS != getSCEV(PreCondRHS))
2404 return UnknownValue; // Not a comparison against 'm'.
2406 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2407 != getSCEV(PreCondLHS))
2408 return UnknownValue; // Not a comparison against 'n-1'.
2410 else return UnknownValue;
2412 // cerr << "Computed Loop Trip Count as: "
2413 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2414 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2417 return UnknownValue;
2420 return UnknownValue;
2423 /// getNumIterationsInRange - Return the number of iterations of this loop that
2424 /// produce values in the specified constant range. Another way of looking at
2425 /// this is that it returns the first iteration number where the value is not in
2426 /// the condition, thus computing the exit count. If the iteration count can't
2427 /// be computed, an instance of SCEVCouldNotCompute is returned.
2428 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
2429 if (Range.isFullSet()) // Infinite loop.
2430 return new SCEVCouldNotCompute();
2432 // If the start is a non-zero constant, shift the range to simplify things.
2433 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2434 if (!SC->getValue()->isZero()) {
2435 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2436 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2437 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2438 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2439 return ShiftedAddRec->getNumIterationsInRange(
2440 Range.subtract(SC->getValue()->getValue()));
2441 // This is strange and shouldn't happen.
2442 return new SCEVCouldNotCompute();
2445 // The only time we can solve this is when we have all constant indices.
2446 // Otherwise, we cannot determine the overflow conditions.
2447 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2448 if (!isa<SCEVConstant>(getOperand(i)))
2449 return new SCEVCouldNotCompute();
2452 // Okay at this point we know that all elements of the chrec are constants and
2453 // that the start element is zero.
2455 // First check to see if the range contains zero. If not, the first
2457 if (!Range.contains(APInt(getBitWidth(),0)))
2458 return SCEVConstant::get(ConstantInt::get(getType(),0));
2461 // If this is an affine expression then we have this situation:
2462 // Solve {0,+,A} in Range === Ax in Range
2464 // We know that zero is in the range. If A is positive then we know that
2465 // the upper value of the range must be the first possible exit value.
2466 // If A is negative then the lower of the range is the last possible loop
2467 // value. Also note that we already checked for a full range.
2468 APInt One(getBitWidth(),1);
2469 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2470 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
2472 // The exit value should be (End+A)/A.
2473 APInt ExitVal = (End + A).udiv(A);
2474 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
2476 // Evaluate at the exit value. If we really did fall out of the valid
2477 // range, then we computed our trip count, otherwise wrap around or other
2478 // things must have happened.
2479 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2480 if (Range.contains(Val->getValue()))
2481 return new SCEVCouldNotCompute(); // Something strange happened
2483 // Ensure that the previous value is in the range. This is a sanity check.
2484 assert(Range.contains(
2485 EvaluateConstantChrecAtConstant(this,
2486 ConstantInt::get(ExitVal - One))->getValue()) &&
2487 "Linear scev computation is off in a bad way!");
2488 return SCEVConstant::get(ExitValue);
2489 } else if (isQuadratic()) {
2490 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2491 // quadratic equation to solve it. To do this, we must frame our problem in
2492 // terms of figuring out when zero is crossed, instead of when
2493 // Range.getUpper() is crossed.
2494 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2495 NewOps[0] = SCEV::getNegativeSCEV(SCEVConstant::get(Range.getUpper()));
2496 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2498 // Next, solve the constructed addrec
2499 std::pair<SCEVHandle,SCEVHandle> Roots =
2500 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2501 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2502 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2504 // Pick the smallest positive root value.
2505 if (ConstantInt *CB =
2506 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2507 R1->getValue(), R2->getValue()))) {
2508 if (CB->getZExtValue() == false)
2509 std::swap(R1, R2); // R1 is the minimum root now.
2511 // Make sure the root is not off by one. The returned iteration should
2512 // not be in the range, but the previous one should be. When solving
2513 // for "X*X < 5", for example, we should not return a root of 2.
2514 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2516 if (Range.contains(R1Val->getValue())) {
2517 // The next iteration must be out of the range...
2518 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
2520 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2521 if (!Range.contains(R1Val->getValue()))
2522 return SCEVConstant::get(NextVal);
2523 return new SCEVCouldNotCompute(); // Something strange happened
2526 // If R1 was not in the range, then it is a good return value. Make
2527 // sure that R1-1 WAS in the range though, just in case.
2528 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
2529 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2530 if (Range.contains(R1Val->getValue()))
2532 return new SCEVCouldNotCompute(); // Something strange happened
2537 // Fallback, if this is a general polynomial, figure out the progression
2538 // through brute force: evaluate until we find an iteration that fails the
2539 // test. This is likely to be slow, but getting an accurate trip count is
2540 // incredibly important, we will be able to simplify the exit test a lot, and
2541 // we are almost guaranteed to get a trip count in this case.
2542 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2543 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2545 ++NumBruteForceEvaluations;
2546 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2547 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2548 return new SCEVCouldNotCompute();
2550 // Check to see if we found the value!
2551 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
2552 return SCEVConstant::get(TestVal);
2554 // Increment to test the next index.
2555 TestVal = ConstantInt::get(TestVal->getValue()+1);
2556 } while (TestVal != EndVal);
2558 return new SCEVCouldNotCompute();
2563 //===----------------------------------------------------------------------===//
2564 // ScalarEvolution Class Implementation
2565 //===----------------------------------------------------------------------===//
2567 bool ScalarEvolution::runOnFunction(Function &F) {
2568 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2572 void ScalarEvolution::releaseMemory() {
2573 delete (ScalarEvolutionsImpl*)Impl;
2577 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2578 AU.setPreservesAll();
2579 AU.addRequiredTransitive<LoopInfo>();
2582 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2583 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2586 /// hasSCEV - Return true if the SCEV for this value has already been
2588 bool ScalarEvolution::hasSCEV(Value *V) const {
2589 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2593 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2594 /// the specified value.
2595 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2596 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2600 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2601 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2604 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2605 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2608 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2609 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2612 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
2613 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
2616 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2618 // Print all inner loops first
2619 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2620 PrintLoopInfo(OS, SE, *I);
2622 cerr << "Loop " << L->getHeader()->getName() << ": ";
2624 SmallVector<BasicBlock*, 8> ExitBlocks;
2625 L->getExitBlocks(ExitBlocks);
2626 if (ExitBlocks.size() != 1)
2627 cerr << "<multiple exits> ";
2629 if (SE->hasLoopInvariantIterationCount(L)) {
2630 cerr << *SE->getIterationCount(L) << " iterations! ";
2632 cerr << "Unpredictable iteration count. ";
2638 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2639 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2640 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2642 OS << "Classifying expressions for: " << F.getName() << "\n";
2643 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2644 if (I->getType()->isInteger()) {
2647 SCEVHandle SV = getSCEV(&*I);
2651 if ((*I).getType()->isInteger()) {
2652 ConstantRange Bounds = SV->getValueRange();
2653 if (!Bounds.isFullSet())
2654 OS << "Bounds: " << Bounds << " ";
2657 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2659 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2660 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2661 OS << "<<Unknown>>";
2671 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2672 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2673 PrintLoopInfo(OS, this, *I);