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");
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
117 void SCEV::dump() const {
121 /// getValueRange - Return the tightest constant bounds that this value is
122 /// known to have. This method is only valid on integer SCEV objects.
123 ConstantRange SCEV::getValueRange() const {
124 const Type *Ty = getType();
125 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
126 // Default to a full range if no better information is available.
127 return ConstantRange(getType());
131 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
133 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
134 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
138 const Type *SCEVCouldNotCompute::getType() const {
139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
143 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
144 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
148 SCEVHandle SCEVCouldNotCompute::
149 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
150 const SCEVHandle &Conc) const {
154 void SCEVCouldNotCompute::print(std::ostream &OS) const {
155 OS << "***COULDNOTCOMPUTE***";
158 bool SCEVCouldNotCompute::classof(const SCEV *S) {
159 return S->getSCEVType() == scCouldNotCompute;
163 // SCEVConstants - Only allow the creation of one SCEVConstant for any
164 // particular value. Don't use a SCEVHandle here, or else the object will
166 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
169 SCEVConstant::~SCEVConstant() {
170 SCEVConstants->erase(V);
173 SCEVHandle SCEVConstant::get(ConstantInt *V) {
174 SCEVConstant *&R = (*SCEVConstants)[V];
175 if (R == 0) R = new SCEVConstant(V);
179 ConstantRange SCEVConstant::getValueRange() const {
180 return ConstantRange(V);
183 const Type *SCEVConstant::getType() const { return V->getType(); }
185 void SCEVConstant::print(std::ostream &OS) const {
186 WriteAsOperand(OS, V, false);
189 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
190 // particular input. Don't use a SCEVHandle here, or else the object will
192 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
193 SCEVTruncateExpr*> > SCEVTruncates;
195 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
196 : SCEV(scTruncate), Op(op), Ty(ty) {
197 assert(Op->getType()->isInteger() && Ty->isInteger() &&
198 "Cannot truncate non-integer value!");
199 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
200 && "This is not a truncating conversion!");
203 SCEVTruncateExpr::~SCEVTruncateExpr() {
204 SCEVTruncates->erase(std::make_pair(Op, Ty));
207 ConstantRange SCEVTruncateExpr::getValueRange() const {
208 return getOperand()->getValueRange().truncate(getType());
211 void SCEVTruncateExpr::print(std::ostream &OS) const {
212 OS << "(truncate " << *Op << " to " << *Ty << ")";
215 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
216 // particular input. Don't use a SCEVHandle here, or else the object will never
218 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
219 SCEVZeroExtendExpr*> > SCEVZeroExtends;
221 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
222 : SCEV(scZeroExtend), Op(op), Ty(ty) {
223 assert(Op->getType()->isInteger() && Ty->isInteger() &&
224 "Cannot zero extend non-integer value!");
225 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
226 && "This is not an extending conversion!");
229 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
230 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
233 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
234 return getOperand()->getValueRange().zeroExtend(getType());
237 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
238 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
241 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
242 // particular input. Don't use a SCEVHandle here, or else the object will never
244 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
245 SCEVCommutativeExpr*> > SCEVCommExprs;
247 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
248 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
249 std::vector<SCEV*>(Operands.begin(),
253 void SCEVCommutativeExpr::print(std::ostream &OS) const {
254 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
255 const char *OpStr = getOperationStr();
256 OS << "(" << *Operands[0];
257 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
258 OS << OpStr << *Operands[i];
262 SCEVHandle SCEVCommutativeExpr::
263 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
264 const SCEVHandle &Conc) const {
265 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
266 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
267 if (H != getOperand(i)) {
268 std::vector<SCEVHandle> NewOps;
269 NewOps.reserve(getNumOperands());
270 for (unsigned j = 0; j != i; ++j)
271 NewOps.push_back(getOperand(j));
273 for (++i; i != e; ++i)
274 NewOps.push_back(getOperand(i)->
275 replaceSymbolicValuesWithConcrete(Sym, Conc));
277 if (isa<SCEVAddExpr>(this))
278 return SCEVAddExpr::get(NewOps);
279 else if (isa<SCEVMulExpr>(this))
280 return SCEVMulExpr::get(NewOps);
282 assert(0 && "Unknown commutative expr!");
289 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
290 // input. Don't use a SCEVHandle here, or else the object will never be
292 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
293 SCEVSDivExpr*> > SCEVSDivs;
295 SCEVSDivExpr::~SCEVSDivExpr() {
296 SCEVSDivs->erase(std::make_pair(LHS, RHS));
299 void SCEVSDivExpr::print(std::ostream &OS) const {
300 OS << "(" << *LHS << " /s " << *RHS << ")";
303 const Type *SCEVSDivExpr::getType() const {
304 return LHS->getType();
307 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
308 // particular input. Don't use a SCEVHandle here, or else the object will never
310 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
311 SCEVAddRecExpr*> > SCEVAddRecExprs;
313 SCEVAddRecExpr::~SCEVAddRecExpr() {
314 SCEVAddRecExprs->erase(std::make_pair(L,
315 std::vector<SCEV*>(Operands.begin(),
319 SCEVHandle SCEVAddRecExpr::
320 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
321 const SCEVHandle &Conc) const {
322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
324 if (H != getOperand(i)) {
325 std::vector<SCEVHandle> NewOps;
326 NewOps.reserve(getNumOperands());
327 for (unsigned j = 0; j != i; ++j)
328 NewOps.push_back(getOperand(j));
330 for (++i; i != e; ++i)
331 NewOps.push_back(getOperand(i)->
332 replaceSymbolicValuesWithConcrete(Sym, Conc));
334 return get(NewOps, L);
341 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
342 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
343 // contain L and if the start is invariant.
344 return !QueryLoop->contains(L->getHeader()) &&
345 getOperand(0)->isLoopInvariant(QueryLoop);
349 void SCEVAddRecExpr::print(std::ostream &OS) const {
350 OS << "{" << *Operands[0];
351 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
352 OS << ",+," << *Operands[i];
353 OS << "}<" << L->getHeader()->getName() + ">";
356 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
357 // value. Don't use a SCEVHandle here, or else the object will never be
359 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
361 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
363 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
364 // All non-instruction values are loop invariant. All instructions are loop
365 // invariant if they are not contained in the specified loop.
366 if (Instruction *I = dyn_cast<Instruction>(V))
367 return !L->contains(I->getParent());
371 const Type *SCEVUnknown::getType() const {
375 void SCEVUnknown::print(std::ostream &OS) const {
376 WriteAsOperand(OS, V, false);
379 //===----------------------------------------------------------------------===//
381 //===----------------------------------------------------------------------===//
384 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
385 /// than the complexity of the RHS. This comparator is used to canonicalize
387 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
388 bool operator()(SCEV *LHS, SCEV *RHS) {
389 return LHS->getSCEVType() < RHS->getSCEVType();
394 /// GroupByComplexity - Given a list of SCEV objects, order them by their
395 /// complexity, and group objects of the same complexity together by value.
396 /// When this routine is finished, we know that any duplicates in the vector are
397 /// consecutive and that complexity is monotonically increasing.
399 /// Note that we go take special precautions to ensure that we get determinstic
400 /// results from this routine. In other words, we don't want the results of
401 /// this to depend on where the addresses of various SCEV objects happened to
404 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
405 if (Ops.size() < 2) return; // Noop
406 if (Ops.size() == 2) {
407 // This is the common case, which also happens to be trivially simple.
409 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
410 std::swap(Ops[0], Ops[1]);
414 // Do the rough sort by complexity.
415 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
417 // Now that we are sorted by complexity, group elements of the same
418 // complexity. Note that this is, at worst, N^2, but the vector is likely to
419 // be extremely short in practice. Note that we take this approach because we
420 // do not want to depend on the addresses of the objects we are grouping.
421 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
423 unsigned Complexity = S->getSCEVType();
425 // If there are any objects of the same complexity and same value as this
427 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
428 if (Ops[j] == S) { // Found a duplicate.
429 // Move it to immediately after i'th element.
430 std::swap(Ops[i+1], Ops[j]);
431 ++i; // no need to rescan it.
432 if (i == e-2) return; // Done!
440 //===----------------------------------------------------------------------===//
441 // Simple SCEV method implementations
442 //===----------------------------------------------------------------------===//
444 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
445 /// specified signed integer value and return a SCEV for the constant.
446 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
449 C = Constant::getNullValue(Ty);
450 else if (Ty->isFloatingPoint())
451 C = ConstantFP::get(Ty, Val);
453 C = ConstantInt::get(Ty, Val);
454 return SCEVUnknown::get(C);
457 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
458 /// input value to the specified type. If the type must be extended, it is zero
460 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
461 const Type *SrcTy = V->getType();
462 assert(SrcTy->isInteger() && Ty->isInteger() &&
463 "Cannot truncate or zero extend with non-integer arguments!");
464 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
465 return V; // No conversion
466 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
467 return SCEVTruncateExpr::get(V, Ty);
468 return SCEVZeroExtendExpr::get(V, Ty);
471 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
473 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
474 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
475 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
477 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
480 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
482 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
484 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
488 /// PartialFact - Compute V!/(V-NumSteps)!
489 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
490 // Handle this case efficiently, it is common to have constant iteration
491 // counts while computing loop exit values.
492 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
493 uint64_t Val = SC->getValue()->getZExtValue();
495 for (; NumSteps; --NumSteps)
496 Result *= Val-(NumSteps-1);
497 Constant *Res = ConstantInt::get(Type::Int64Ty, Result);
498 return SCEVUnknown::get(ConstantExpr::getTruncOrBitCast(Res, V->getType()));
501 const Type *Ty = V->getType();
503 return SCEVUnknown::getIntegerSCEV(1, Ty);
505 SCEVHandle Result = V;
506 for (unsigned i = 1; i != NumSteps; ++i)
507 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
508 SCEVUnknown::getIntegerSCEV(i, Ty)));
513 /// evaluateAtIteration - Return the value of this chain of recurrences at
514 /// the specified iteration number. We can evaluate this recurrence by
515 /// multiplying each element in the chain by the binomial coefficient
516 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
518 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
520 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
521 /// Is the binomial equation safe using modular arithmetic??
523 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
524 SCEVHandle Result = getStart();
526 const Type *Ty = It->getType();
527 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
528 SCEVHandle BC = PartialFact(It, i);
530 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
531 SCEVUnknown::getIntegerSCEV(Divisor,Ty));
532 Result = SCEVAddExpr::get(Result, Val);
538 //===----------------------------------------------------------------------===//
539 // SCEV Expression folder implementations
540 //===----------------------------------------------------------------------===//
542 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
543 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
544 return SCEVUnknown::get(
545 ConstantExpr::getTrunc(SC->getValue(), Ty));
547 // If the input value is a chrec scev made out of constants, truncate
548 // all of the constants.
549 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
550 std::vector<SCEVHandle> Operands;
551 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
552 // FIXME: This should allow truncation of other expression types!
553 if (isa<SCEVConstant>(AddRec->getOperand(i)))
554 Operands.push_back(get(AddRec->getOperand(i), Ty));
557 if (Operands.size() == AddRec->getNumOperands())
558 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
561 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
562 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
566 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
567 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
568 return SCEVUnknown::get(
569 ConstantExpr::getZExt(SC->getValue(), Ty));
571 // FIXME: If the input value is a chrec scev, and we can prove that the value
572 // did not overflow the old, smaller, value, we can zero extend all of the
573 // operands (often constants). This would allow analysis of something like
574 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
576 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
577 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
581 // get - Get a canonical add expression, or something simpler if possible.
582 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
583 assert(!Ops.empty() && "Cannot get empty add!");
584 if (Ops.size() == 1) return Ops[0];
586 // Sort by complexity, this groups all similar expression types together.
587 GroupByComplexity(Ops);
589 // If there are any constants, fold them together.
591 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
593 assert(Idx < Ops.size());
594 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
595 // We found two constants, fold them together!
596 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
597 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
598 Ops[0] = SCEVConstant::get(CI);
599 Ops.erase(Ops.begin()+1); // Erase the folded element
600 if (Ops.size() == 1) return Ops[0];
601 LHSC = cast<SCEVConstant>(Ops[0]);
603 // If we couldn't fold the expression, move to the next constant. Note
604 // that this is impossible to happen in practice because we always
605 // constant fold constant ints to constant ints.
610 // If we are left with a constant zero being added, strip it off.
611 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
612 Ops.erase(Ops.begin());
617 if (Ops.size() == 1) return Ops[0];
619 // Okay, check to see if the same value occurs in the operand list twice. If
620 // so, merge them together into an multiply expression. Since we sorted the
621 // list, these values are required to be adjacent.
622 const Type *Ty = Ops[0]->getType();
623 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
624 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
625 // Found a match, merge the two values into a multiply, and add any
626 // remaining values to the result.
627 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
628 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
631 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
633 return SCEVAddExpr::get(Ops);
636 // Okay, now we know the first non-constant operand. If there are add
637 // operands they would be next.
638 if (Idx < Ops.size()) {
639 bool DeletedAdd = false;
640 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
641 // If we have an add, expand the add operands onto the end of the operands
643 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
644 Ops.erase(Ops.begin()+Idx);
648 // If we deleted at least one add, we added operands to the end of the list,
649 // and they are not necessarily sorted. Recurse to resort and resimplify
650 // any operands we just aquired.
655 // Skip over the add expression until we get to a multiply.
656 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
659 // If we are adding something to a multiply expression, make sure the
660 // something is not already an operand of the multiply. If so, merge it into
662 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
663 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
664 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
665 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
666 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
667 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
668 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
669 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
670 if (Mul->getNumOperands() != 2) {
671 // If the multiply has more than two operands, we must get the
673 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
674 MulOps.erase(MulOps.begin()+MulOp);
675 InnerMul = SCEVMulExpr::get(MulOps);
677 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
678 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
679 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
680 if (Ops.size() == 2) return OuterMul;
682 Ops.erase(Ops.begin()+AddOp);
683 Ops.erase(Ops.begin()+Idx-1);
685 Ops.erase(Ops.begin()+Idx);
686 Ops.erase(Ops.begin()+AddOp-1);
688 Ops.push_back(OuterMul);
689 return SCEVAddExpr::get(Ops);
692 // Check this multiply against other multiplies being added together.
693 for (unsigned OtherMulIdx = Idx+1;
694 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
696 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
697 // If MulOp occurs in OtherMul, we can fold the two multiplies
699 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
700 OMulOp != e; ++OMulOp)
701 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
702 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
703 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
704 if (Mul->getNumOperands() != 2) {
705 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
706 MulOps.erase(MulOps.begin()+MulOp);
707 InnerMul1 = SCEVMulExpr::get(MulOps);
709 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
710 if (OtherMul->getNumOperands() != 2) {
711 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
713 MulOps.erase(MulOps.begin()+OMulOp);
714 InnerMul2 = SCEVMulExpr::get(MulOps);
716 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
717 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
718 if (Ops.size() == 2) return OuterMul;
719 Ops.erase(Ops.begin()+Idx);
720 Ops.erase(Ops.begin()+OtherMulIdx-1);
721 Ops.push_back(OuterMul);
722 return SCEVAddExpr::get(Ops);
728 // If there are any add recurrences in the operands list, see if any other
729 // added values are loop invariant. If so, we can fold them into the
731 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
734 // Scan over all recurrences, trying to fold loop invariants into them.
735 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
736 // Scan all of the other operands to this add and add them to the vector if
737 // they are loop invariant w.r.t. the recurrence.
738 std::vector<SCEVHandle> LIOps;
739 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
740 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
741 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
742 LIOps.push_back(Ops[i]);
743 Ops.erase(Ops.begin()+i);
747 // If we found some loop invariants, fold them into the recurrence.
748 if (!LIOps.empty()) {
749 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
750 LIOps.push_back(AddRec->getStart());
752 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
753 AddRecOps[0] = SCEVAddExpr::get(LIOps);
755 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
756 // If all of the other operands were loop invariant, we are done.
757 if (Ops.size() == 1) return NewRec;
759 // Otherwise, add the folded AddRec by the non-liv parts.
760 for (unsigned i = 0;; ++i)
761 if (Ops[i] == AddRec) {
765 return SCEVAddExpr::get(Ops);
768 // Okay, if there weren't any loop invariants to be folded, check to see if
769 // there are multiple AddRec's with the same loop induction variable being
770 // added together. If so, we can fold them.
771 for (unsigned OtherIdx = Idx+1;
772 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
773 if (OtherIdx != Idx) {
774 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
775 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
776 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
777 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
778 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
779 if (i >= NewOps.size()) {
780 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
781 OtherAddRec->op_end());
784 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
786 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
788 if (Ops.size() == 2) return NewAddRec;
790 Ops.erase(Ops.begin()+Idx);
791 Ops.erase(Ops.begin()+OtherIdx-1);
792 Ops.push_back(NewAddRec);
793 return SCEVAddExpr::get(Ops);
797 // Otherwise couldn't fold anything into this recurrence. Move onto the
801 // Okay, it looks like we really DO need an add expr. Check to see if we
802 // already have one, otherwise create a new one.
803 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
804 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
806 if (Result == 0) Result = new SCEVAddExpr(Ops);
811 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
812 assert(!Ops.empty() && "Cannot get empty mul!");
814 // Sort by complexity, this groups all similar expression types together.
815 GroupByComplexity(Ops);
817 // If there are any constants, fold them together.
819 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
821 // C1*(C2+V) -> C1*C2 + C1*V
823 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
824 if (Add->getNumOperands() == 2 &&
825 isa<SCEVConstant>(Add->getOperand(0)))
826 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
827 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
831 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
832 // We found two constants, fold them together!
833 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
834 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
835 Ops[0] = SCEVConstant::get(CI);
836 Ops.erase(Ops.begin()+1); // Erase the folded element
837 if (Ops.size() == 1) return Ops[0];
838 LHSC = cast<SCEVConstant>(Ops[0]);
840 // If we couldn't fold the expression, move to the next constant. Note
841 // that this is impossible to happen in practice because we always
842 // constant fold constant ints to constant ints.
847 // If we are left with a constant one being multiplied, strip it off.
848 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
849 Ops.erase(Ops.begin());
851 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
852 // If we have a multiply of zero, it will always be zero.
857 // Skip over the add expression until we get to a multiply.
858 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
864 // If there are mul operands inline them all into this expression.
865 if (Idx < Ops.size()) {
866 bool DeletedMul = false;
867 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
868 // If we have an mul, expand the mul operands onto the end of the operands
870 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
871 Ops.erase(Ops.begin()+Idx);
875 // If we deleted at least one mul, we added operands to the end of the list,
876 // and they are not necessarily sorted. Recurse to resort and resimplify
877 // any operands we just aquired.
882 // If there are any add recurrences in the operands list, see if any other
883 // added values are loop invariant. If so, we can fold them into the
885 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
888 // Scan over all recurrences, trying to fold loop invariants into them.
889 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
890 // Scan all of the other operands to this mul and add them to the vector if
891 // they are loop invariant w.r.t. the recurrence.
892 std::vector<SCEVHandle> LIOps;
893 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
894 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
895 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
896 LIOps.push_back(Ops[i]);
897 Ops.erase(Ops.begin()+i);
901 // If we found some loop invariants, fold them into the recurrence.
902 if (!LIOps.empty()) {
903 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
904 std::vector<SCEVHandle> NewOps;
905 NewOps.reserve(AddRec->getNumOperands());
906 if (LIOps.size() == 1) {
907 SCEV *Scale = LIOps[0];
908 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
909 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
911 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
912 std::vector<SCEVHandle> MulOps(LIOps);
913 MulOps.push_back(AddRec->getOperand(i));
914 NewOps.push_back(SCEVMulExpr::get(MulOps));
918 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
920 // If all of the other operands were loop invariant, we are done.
921 if (Ops.size() == 1) return NewRec;
923 // Otherwise, multiply the folded AddRec by the non-liv parts.
924 for (unsigned i = 0;; ++i)
925 if (Ops[i] == AddRec) {
929 return SCEVMulExpr::get(Ops);
932 // Okay, if there weren't any loop invariants to be folded, check to see if
933 // there are multiple AddRec's with the same loop induction variable being
934 // multiplied together. If so, we can fold them.
935 for (unsigned OtherIdx = Idx+1;
936 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
937 if (OtherIdx != Idx) {
938 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
939 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
940 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
941 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
942 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
944 SCEVHandle B = F->getStepRecurrence();
945 SCEVHandle D = G->getStepRecurrence();
946 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
947 SCEVMulExpr::get(G, B),
948 SCEVMulExpr::get(B, D));
949 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
951 if (Ops.size() == 2) return NewAddRec;
953 Ops.erase(Ops.begin()+Idx);
954 Ops.erase(Ops.begin()+OtherIdx-1);
955 Ops.push_back(NewAddRec);
956 return SCEVMulExpr::get(Ops);
960 // Otherwise couldn't fold anything into this recurrence. Move onto the
964 // Okay, it looks like we really DO need an mul expr. Check to see if we
965 // already have one, otherwise create a new one.
966 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
967 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
970 Result = new SCEVMulExpr(Ops);
974 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
975 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
976 if (RHSC->getValue()->equalsInt(1))
977 return LHS; // X sdiv 1 --> x
978 if (RHSC->getValue()->isAllOnesValue())
979 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
981 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
982 Constant *LHSCV = LHSC->getValue();
983 Constant *RHSCV = RHSC->getValue();
984 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
988 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
990 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
991 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
996 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
997 /// specified loop. Simplify the expression as much as possible.
998 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
999 const SCEVHandle &Step, const Loop *L) {
1000 std::vector<SCEVHandle> Operands;
1001 Operands.push_back(Start);
1002 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1003 if (StepChrec->getLoop() == L) {
1004 Operands.insert(Operands.end(), StepChrec->op_begin(),
1005 StepChrec->op_end());
1006 return get(Operands, L);
1009 Operands.push_back(Step);
1010 return get(Operands, L);
1013 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1014 /// specified loop. Simplify the expression as much as possible.
1015 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1017 if (Operands.size() == 1) return Operands[0];
1019 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1020 if (StepC->getValue()->isNullValue()) {
1021 Operands.pop_back();
1022 return get(Operands, L); // { X,+,0 } --> X
1025 SCEVAddRecExpr *&Result =
1026 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1028 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1032 SCEVHandle SCEVUnknown::get(Value *V) {
1033 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1034 return SCEVConstant::get(CI);
1035 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1036 if (Result == 0) Result = new SCEVUnknown(V);
1041 //===----------------------------------------------------------------------===//
1042 // ScalarEvolutionsImpl Definition and Implementation
1043 //===----------------------------------------------------------------------===//
1045 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1049 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1050 /// F - The function we are analyzing.
1054 /// LI - The loop information for the function we are currently analyzing.
1058 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1060 SCEVHandle UnknownValue;
1062 /// Scalars - This is a cache of the scalars we have analyzed so far.
1064 std::map<Value*, SCEVHandle> Scalars;
1066 /// IterationCounts - Cache the iteration count of the loops for this
1067 /// function as they are computed.
1068 std::map<const Loop*, SCEVHandle> IterationCounts;
1070 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1071 /// the PHI instructions that we attempt to compute constant evolutions for.
1072 /// This allows us to avoid potentially expensive recomputation of these
1073 /// properties. An instruction maps to null if we are unable to compute its
1075 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1078 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1079 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1081 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1082 /// expression and create a new one.
1083 SCEVHandle getSCEV(Value *V);
1085 /// hasSCEV - Return true if the SCEV for this value has already been
1087 bool hasSCEV(Value *V) const {
1088 return Scalars.count(V);
1091 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1092 /// the specified value.
1093 void setSCEV(Value *V, const SCEVHandle &H) {
1094 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1095 assert(isNew && "This entry already existed!");
1099 /// getSCEVAtScope - Compute the value of the specified expression within
1100 /// the indicated loop (which may be null to indicate in no loop). If the
1101 /// expression cannot be evaluated, return UnknownValue itself.
1102 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1105 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1106 /// an analyzable loop-invariant iteration count.
1107 bool hasLoopInvariantIterationCount(const Loop *L);
1109 /// getIterationCount - If the specified loop has a predictable iteration
1110 /// count, return it. Note that it is not valid to call this method on a
1111 /// loop without a loop-invariant iteration count.
1112 SCEVHandle getIterationCount(const Loop *L);
1114 /// deleteInstructionFromRecords - This method should be called by the
1115 /// client before it removes an instruction from the program, to make sure
1116 /// that no dangling references are left around.
1117 void deleteInstructionFromRecords(Instruction *I);
1120 /// createSCEV - We know that there is no SCEV for the specified value.
1121 /// Analyze the expression.
1122 SCEVHandle createSCEV(Value *V);
1124 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1126 SCEVHandle createNodeForPHI(PHINode *PN);
1128 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1129 /// for the specified instruction and replaces any references to the
1130 /// symbolic value SymName with the specified value. This is used during
1132 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1133 const SCEVHandle &SymName,
1134 const SCEVHandle &NewVal);
1136 /// ComputeIterationCount - Compute the number of times the specified loop
1138 SCEVHandle ComputeIterationCount(const Loop *L);
1140 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1141 /// 'setcc load X, cst', try to se if we can compute the trip count.
1142 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1145 ICmpInst::Predicate p);
1147 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1148 /// constant number of times (the condition evolves only from constants),
1149 /// try to evaluate a few iterations of the loop until we get the exit
1150 /// condition gets a value of ExitWhen (true or false). If we cannot
1151 /// evaluate the trip count of the loop, return UnknownValue.
1152 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1155 /// HowFarToZero - Return the number of times a backedge comparing the
1156 /// specified value to zero will execute. If not computable, return
1158 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1160 /// HowFarToNonZero - Return the number of times a backedge checking the
1161 /// specified value for nonzero will execute. If not computable, return
1163 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1165 /// HowManyLessThans - Return the number of times a backedge containing the
1166 /// specified less-than comparison will execute. If not computable, return
1168 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
1170 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1171 /// in the header of its containing loop, we know the loop executes a
1172 /// constant number of times, and the PHI node is just a recurrence
1173 /// involving constants, fold it.
1174 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
1179 //===----------------------------------------------------------------------===//
1180 // Basic SCEV Analysis and PHI Idiom Recognition Code
1183 /// deleteInstructionFromRecords - This method should be called by the
1184 /// client before it removes an instruction from the program, to make sure
1185 /// that no dangling references are left around.
1186 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
1188 if (PHINode *PN = dyn_cast<PHINode>(I))
1189 ConstantEvolutionLoopExitValue.erase(PN);
1193 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1194 /// expression and create a new one.
1195 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1196 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1198 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1199 if (I != Scalars.end()) return I->second;
1200 SCEVHandle S = createSCEV(V);
1201 Scalars.insert(std::make_pair(V, S));
1205 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1206 /// the specified instruction and replaces any references to the symbolic value
1207 /// SymName with the specified value. This is used during PHI resolution.
1208 void ScalarEvolutionsImpl::
1209 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1210 const SCEVHandle &NewVal) {
1211 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1212 if (SI == Scalars.end()) return;
1215 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1216 if (NV == SI->second) return; // No change.
1218 SI->second = NV; // Update the scalars map!
1220 // Any instruction values that use this instruction might also need to be
1222 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1224 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1227 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1228 /// a loop header, making it a potential recurrence, or it doesn't.
1230 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1231 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1232 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1233 if (L->getHeader() == PN->getParent()) {
1234 // If it lives in the loop header, it has two incoming values, one
1235 // from outside the loop, and one from inside.
1236 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1237 unsigned BackEdge = IncomingEdge^1;
1239 // While we are analyzing this PHI node, handle its value symbolically.
1240 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1241 assert(Scalars.find(PN) == Scalars.end() &&
1242 "PHI node already processed?");
1243 Scalars.insert(std::make_pair(PN, SymbolicName));
1245 // Using this symbolic name for the PHI, analyze the value coming around
1247 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1249 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1250 // has a special value for the first iteration of the loop.
1252 // If the value coming around the backedge is an add with the symbolic
1253 // value we just inserted, then we found a simple induction variable!
1254 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1255 // If there is a single occurrence of the symbolic value, replace it
1256 // with a recurrence.
1257 unsigned FoundIndex = Add->getNumOperands();
1258 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1259 if (Add->getOperand(i) == SymbolicName)
1260 if (FoundIndex == e) {
1265 if (FoundIndex != Add->getNumOperands()) {
1266 // Create an add with everything but the specified operand.
1267 std::vector<SCEVHandle> Ops;
1268 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1269 if (i != FoundIndex)
1270 Ops.push_back(Add->getOperand(i));
1271 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1273 // This is not a valid addrec if the step amount is varying each
1274 // loop iteration, but is not itself an addrec in this loop.
1275 if (Accum->isLoopInvariant(L) ||
1276 (isa<SCEVAddRecExpr>(Accum) &&
1277 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1278 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1279 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1281 // Okay, for the entire analysis of this edge we assumed the PHI
1282 // to be symbolic. We now need to go back and update all of the
1283 // entries for the scalars that use the PHI (except for the PHI
1284 // itself) to use the new analyzed value instead of the "symbolic"
1286 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1290 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1291 // Otherwise, this could be a loop like this:
1292 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1293 // In this case, j = {1,+,1} and BEValue is j.
1294 // Because the other in-value of i (0) fits the evolution of BEValue
1295 // i really is an addrec evolution.
1296 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1297 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1299 // If StartVal = j.start - j.stride, we can use StartVal as the
1300 // initial step of the addrec evolution.
1301 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1302 AddRec->getOperand(1))) {
1303 SCEVHandle PHISCEV =
1304 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1306 // Okay, for the entire analysis of this edge we assumed the PHI
1307 // to be symbolic. We now need to go back and update all of the
1308 // entries for the scalars that use the PHI (except for the PHI
1309 // itself) to use the new analyzed value instead of the "symbolic"
1311 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1317 return SymbolicName;
1320 // If it's not a loop phi, we can't handle it yet.
1321 return SCEVUnknown::get(PN);
1324 /// GetConstantFactor - Determine the largest constant factor that S has. For
1325 /// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
1326 static uint64_t GetConstantFactor(SCEVHandle S) {
1327 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
1328 if (uint64_t V = C->getValue()->getZExtValue())
1330 else // Zero is a multiple of everything.
1331 return 1ULL << (S->getType()->getPrimitiveSizeInBits()-1);
1334 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1335 return GetConstantFactor(T->getOperand()) &
1336 T->getType()->getIntegralTypeMask();
1337 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
1338 return GetConstantFactor(E->getOperand());
1340 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1341 // The result is the min of all operands.
1342 uint64_t Res = GetConstantFactor(A->getOperand(0));
1343 for (unsigned i = 1, e = A->getNumOperands(); i != e && Res > 1; ++i)
1344 Res = std::min(Res, GetConstantFactor(A->getOperand(i)));
1348 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1349 // The result is the product of all the operands.
1350 uint64_t Res = GetConstantFactor(M->getOperand(0));
1351 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i)
1352 Res *= GetConstantFactor(M->getOperand(i));
1356 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1357 // For now, we just handle linear expressions.
1358 if (A->getNumOperands() == 2) {
1359 // We want the GCD between the start and the stride value.
1360 uint64_t Start = GetConstantFactor(A->getOperand(0));
1361 if (Start == 1) return 1;
1362 uint64_t Stride = GetConstantFactor(A->getOperand(1));
1363 return GreatestCommonDivisor64(Start, Stride);
1367 // SCEVSDivExpr, SCEVUnknown.
1371 /// createSCEV - We know that there is no SCEV for the specified value.
1372 /// Analyze the expression.
1374 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1375 if (Instruction *I = dyn_cast<Instruction>(V)) {
1376 switch (I->getOpcode()) {
1377 case Instruction::Add:
1378 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1379 getSCEV(I->getOperand(1)));
1380 case Instruction::Mul:
1381 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1382 getSCEV(I->getOperand(1)));
1383 case Instruction::SDiv:
1384 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1385 getSCEV(I->getOperand(1)));
1388 case Instruction::Sub:
1389 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1390 getSCEV(I->getOperand(1)));
1391 case Instruction::Or:
1392 // If the RHS of the Or is a constant, we may have something like:
1393 // X*4+1 which got turned into X*4|1. Handle this as an add so loop
1394 // optimizations will transparently handle this case.
1395 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1396 SCEVHandle LHS = getSCEV(I->getOperand(0));
1397 uint64_t CommonFact = GetConstantFactor(LHS);
1398 assert(CommonFact && "Common factor should at least be 1!");
1399 if (CommonFact > CI->getZExtValue()) {
1400 // If the LHS is a multiple that is larger than the RHS, use +.
1401 return SCEVAddExpr::get(LHS,
1402 getSCEV(I->getOperand(1)));
1407 case Instruction::Shl:
1408 // Turn shift left of a constant amount into a multiply.
1409 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1410 Constant *X = ConstantInt::get(V->getType(), 1);
1411 X = ConstantExpr::getShl(X, SA);
1412 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1416 case Instruction::Trunc:
1417 // We don't handle trunc to bool yet.
1418 if (I->getType()->isInteger())
1419 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
1422 case Instruction::ZExt:
1423 // We don't handle zext from bool yet.
1424 if (I->getOperand(0)->getType()->isInteger())
1425 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1428 case Instruction::BitCast:
1429 // BitCasts are no-op casts so we just eliminate the cast.
1430 if (I->getType()->isInteger() && I->getOperand(0)->getType()->isInteger())
1431 return getSCEV(I->getOperand(0));
1434 case Instruction::PHI:
1435 return createNodeForPHI(cast<PHINode>(I));
1437 default: // We cannot analyze this expression.
1442 return SCEVUnknown::get(V);
1447 //===----------------------------------------------------------------------===//
1448 // Iteration Count Computation Code
1451 /// getIterationCount - If the specified loop has a predictable iteration
1452 /// count, return it. Note that it is not valid to call this method on a
1453 /// loop without a loop-invariant iteration count.
1454 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1455 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1456 if (I == IterationCounts.end()) {
1457 SCEVHandle ItCount = ComputeIterationCount(L);
1458 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1459 if (ItCount != UnknownValue) {
1460 assert(ItCount->isLoopInvariant(L) &&
1461 "Computed trip count isn't loop invariant for loop!");
1462 ++NumTripCountsComputed;
1463 } else if (isa<PHINode>(L->getHeader()->begin())) {
1464 // Only count loops that have phi nodes as not being computable.
1465 ++NumTripCountsNotComputed;
1471 /// ComputeIterationCount - Compute the number of times the specified loop
1473 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1474 // If the loop has a non-one exit block count, we can't analyze it.
1475 std::vector<BasicBlock*> ExitBlocks;
1476 L->getExitBlocks(ExitBlocks);
1477 if (ExitBlocks.size() != 1) return UnknownValue;
1479 // Okay, there is one exit block. Try to find the condition that causes the
1480 // loop to be exited.
1481 BasicBlock *ExitBlock = ExitBlocks[0];
1483 BasicBlock *ExitingBlock = 0;
1484 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1486 if (L->contains(*PI)) {
1487 if (ExitingBlock == 0)
1490 return UnknownValue; // More than one block exiting!
1492 assert(ExitingBlock && "No exits from loop, something is broken!");
1494 // Okay, we've computed the exiting block. See what condition causes us to
1497 // FIXME: we should be able to handle switch instructions (with a single exit)
1498 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1499 if (ExitBr == 0) return UnknownValue;
1500 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1502 // At this point, we know we have a conditional branch that determines whether
1503 // the loop is exited. However, we don't know if the branch is executed each
1504 // time through the loop. If not, then the execution count of the branch will
1505 // not be equal to the trip count of the loop.
1507 // Currently we check for this by checking to see if the Exit branch goes to
1508 // the loop header. If so, we know it will always execute the same number of
1509 // times as the loop. More extensive analysis could be done to handle more
1511 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1512 ExitBr->getSuccessor(1) != L->getHeader())
1513 return UnknownValue;
1515 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1517 // If its not an integer comparison then compute it the hard way.
1518 // Note that ICmpInst deals with pointer comparisons too so we must check
1519 // the type of the operand.
1520 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1521 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1522 ExitBr->getSuccessor(0) == ExitBlock);
1524 // If the condition was exit on true, convert the condition to exit on false
1525 ICmpInst::Predicate Cond;
1526 if (ExitBr->getSuccessor(1) == ExitBlock)
1527 Cond = ExitCond->getPredicate();
1529 Cond = ExitCond->getInversePredicate();
1531 // Handle common loops like: for (X = "string"; *X; ++X)
1532 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1533 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1535 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1536 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1539 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1540 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1542 // Try to evaluate any dependencies out of the loop.
1543 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1544 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1545 Tmp = getSCEVAtScope(RHS, L);
1546 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1548 // At this point, we would like to compute how many iterations of the
1549 // loop the predicate will return true for these inputs.
1550 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1551 // If there is a constant, force it into the RHS.
1552 std::swap(LHS, RHS);
1553 Cond = ICmpInst::getSwappedPredicate(Cond);
1556 // FIXME: think about handling pointer comparisons! i.e.:
1557 // while (P != P+100) ++P;
1559 // If we have a comparison of a chrec against a constant, try to use value
1560 // ranges to answer this query.
1561 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1562 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1563 if (AddRec->getLoop() == L) {
1564 // Form the comparison range using the constant of the correct type so
1565 // that the ConstantRange class knows to do a signed or unsigned
1567 ConstantInt *CompVal = RHSC->getValue();
1568 const Type *RealTy = ExitCond->getOperand(0)->getType();
1569 CompVal = dyn_cast<ConstantInt>(
1570 ConstantExpr::getBitCast(CompVal, RealTy));
1572 // Form the constant range.
1573 ConstantRange CompRange(Cond, CompVal);
1575 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
1576 false /*Always treat as unsigned range*/);
1577 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1582 case ICmpInst::ICMP_NE: { // while (X != Y)
1583 // Convert to: while (X-Y != 0)
1584 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1585 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1588 case ICmpInst::ICMP_EQ: {
1589 // Convert to: while (X-Y == 0) // while (X == Y)
1590 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1591 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1594 case ICmpInst::ICMP_SLT: {
1595 SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1596 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1599 case ICmpInst::ICMP_SGT: {
1600 SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1601 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1606 cerr << "ComputeIterationCount ";
1607 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1608 cerr << "[unsigned] ";
1610 << Instruction::getOpcodeName(Instruction::ICmp)
1611 << " " << *RHS << "\n";
1615 return ComputeIterationCountExhaustively(L, ExitCond,
1616 ExitBr->getSuccessor(0) == ExitBlock);
1619 static ConstantInt *
1620 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1621 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1622 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1623 assert(isa<SCEVConstant>(Val) &&
1624 "Evaluation of SCEV at constant didn't fold correctly?");
1625 return cast<SCEVConstant>(Val)->getValue();
1628 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1629 /// and a GEP expression (missing the pointer index) indexing into it, return
1630 /// the addressed element of the initializer or null if the index expression is
1633 GetAddressedElementFromGlobal(GlobalVariable *GV,
1634 const std::vector<ConstantInt*> &Indices) {
1635 Constant *Init = GV->getInitializer();
1636 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1637 uint64_t Idx = Indices[i]->getZExtValue();
1638 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1639 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1640 Init = cast<Constant>(CS->getOperand(Idx));
1641 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1642 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1643 Init = cast<Constant>(CA->getOperand(Idx));
1644 } else if (isa<ConstantAggregateZero>(Init)) {
1645 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1646 assert(Idx < STy->getNumElements() && "Bad struct index!");
1647 Init = Constant::getNullValue(STy->getElementType(Idx));
1648 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1649 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1650 Init = Constant::getNullValue(ATy->getElementType());
1652 assert(0 && "Unknown constant aggregate type!");
1656 return 0; // Unknown initializer type
1662 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1663 /// 'setcc load X, cst', try to se if we can compute the trip count.
1664 SCEVHandle ScalarEvolutionsImpl::
1665 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1667 ICmpInst::Predicate predicate) {
1668 if (LI->isVolatile()) return UnknownValue;
1670 // Check to see if the loaded pointer is a getelementptr of a global.
1671 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1672 if (!GEP) return UnknownValue;
1674 // Make sure that it is really a constant global we are gepping, with an
1675 // initializer, and make sure the first IDX is really 0.
1676 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1677 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1678 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1679 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1680 return UnknownValue;
1682 // Okay, we allow one non-constant index into the GEP instruction.
1684 std::vector<ConstantInt*> Indexes;
1685 unsigned VarIdxNum = 0;
1686 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1687 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1688 Indexes.push_back(CI);
1689 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1690 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1691 VarIdx = GEP->getOperand(i);
1693 Indexes.push_back(0);
1696 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1697 // Check to see if X is a loop variant variable value now.
1698 SCEVHandle Idx = getSCEV(VarIdx);
1699 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1700 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1702 // We can only recognize very limited forms of loop index expressions, in
1703 // particular, only affine AddRec's like {C1,+,C2}.
1704 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1705 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1706 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1707 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1708 return UnknownValue;
1710 unsigned MaxSteps = MaxBruteForceIterations;
1711 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1712 ConstantInt *ItCst =
1713 ConstantInt::get(IdxExpr->getType(), IterationNum);
1714 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1716 // Form the GEP offset.
1717 Indexes[VarIdxNum] = Val;
1719 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1720 if (Result == 0) break; // Cannot compute!
1722 // Evaluate the condition for this iteration.
1723 Result = ConstantExpr::getICmp(predicate, Result, RHS);
1724 if (!isa<ConstantBool>(Result)) break; // Couldn't decide for sure
1725 if (cast<ConstantBool>(Result)->getValue() == false) {
1727 cerr << "\n***\n*** Computed loop count " << *ItCst
1728 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1731 ++NumArrayLenItCounts;
1732 return SCEVConstant::get(ItCst); // Found terminating iteration!
1735 return UnknownValue;
1739 /// CanConstantFold - Return true if we can constant fold an instruction of the
1740 /// specified type, assuming that all operands were constants.
1741 static bool CanConstantFold(const Instruction *I) {
1742 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || isa<CmpInst>(I) ||
1743 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1746 if (const CallInst *CI = dyn_cast<CallInst>(I))
1747 if (const Function *F = CI->getCalledFunction())
1748 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1752 /// ConstantFold - Constant fold an instruction of the specified type with the
1753 /// specified constant operands. This function may modify the operands vector.
1754 static Constant *ConstantFold(const Instruction *I,
1755 std::vector<Constant*> &Operands) {
1756 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
1757 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
1759 if (isa<CastInst>(I))
1760 return ConstantExpr::getCast(I->getOpcode(), Operands[0], I->getType());
1762 switch (I->getOpcode()) {
1763 case Instruction::Select:
1764 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
1765 case Instruction::Call:
1766 if (Function *GV = dyn_cast<Function>(Operands[0])) {
1767 Operands.erase(Operands.begin());
1768 return ConstantFoldCall(cast<Function>(GV), Operands);
1771 case Instruction::GetElementPtr: {
1772 Constant *Base = Operands[0];
1773 Operands.erase(Operands.begin());
1774 return ConstantExpr::getGetElementPtr(Base, Operands);
1776 case Instruction::ICmp:
1777 return ConstantExpr::getICmp(
1778 cast<ICmpInst>(I)->getPredicate(), Operands[0], Operands[1]);
1779 case Instruction::FCmp:
1780 return ConstantExpr::getFCmp(
1781 cast<FCmpInst>(I)->getPredicate(), Operands[0], Operands[1]);
1787 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1788 /// in the loop that V is derived from. We allow arbitrary operations along the
1789 /// way, but the operands of an operation must either be constants or a value
1790 /// derived from a constant PHI. If this expression does not fit with these
1791 /// constraints, return null.
1792 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1793 // If this is not an instruction, or if this is an instruction outside of the
1794 // loop, it can't be derived from a loop PHI.
1795 Instruction *I = dyn_cast<Instruction>(V);
1796 if (I == 0 || !L->contains(I->getParent())) return 0;
1798 if (PHINode *PN = dyn_cast<PHINode>(I))
1799 if (L->getHeader() == I->getParent())
1802 // We don't currently keep track of the control flow needed to evaluate
1803 // PHIs, so we cannot handle PHIs inside of loops.
1806 // If we won't be able to constant fold this expression even if the operands
1807 // are constants, return early.
1808 if (!CanConstantFold(I)) return 0;
1810 // Otherwise, we can evaluate this instruction if all of its operands are
1811 // constant or derived from a PHI node themselves.
1813 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1814 if (!(isa<Constant>(I->getOperand(Op)) ||
1815 isa<GlobalValue>(I->getOperand(Op)))) {
1816 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1817 if (P == 0) return 0; // Not evolving from PHI
1821 return 0; // Evolving from multiple different PHIs.
1824 // This is a expression evolving from a constant PHI!
1828 /// EvaluateExpression - Given an expression that passes the
1829 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1830 /// in the loop has the value PHIVal. If we can't fold this expression for some
1831 /// reason, return null.
1832 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1833 if (isa<PHINode>(V)) return PHIVal;
1834 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1836 if (Constant *C = dyn_cast<Constant>(V)) return C;
1837 Instruction *I = cast<Instruction>(V);
1839 std::vector<Constant*> Operands;
1840 Operands.resize(I->getNumOperands());
1842 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1843 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1844 if (Operands[i] == 0) return 0;
1847 return ConstantFold(I, Operands);
1850 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1851 /// in the header of its containing loop, we know the loop executes a
1852 /// constant number of times, and the PHI node is just a recurrence
1853 /// involving constants, fold it.
1854 Constant *ScalarEvolutionsImpl::
1855 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
1856 std::map<PHINode*, Constant*>::iterator I =
1857 ConstantEvolutionLoopExitValue.find(PN);
1858 if (I != ConstantEvolutionLoopExitValue.end())
1861 if (Its > MaxBruteForceIterations)
1862 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1864 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1866 // Since the loop is canonicalized, the PHI node must have two entries. One
1867 // entry must be a constant (coming in from outside of the loop), and the
1868 // second must be derived from the same PHI.
1869 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1870 Constant *StartCST =
1871 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1873 return RetVal = 0; // Must be a constant.
1875 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1876 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1878 return RetVal = 0; // Not derived from same PHI.
1880 // Execute the loop symbolically to determine the exit value.
1881 unsigned IterationNum = 0;
1882 unsigned NumIterations = Its;
1883 if (NumIterations != Its)
1884 return RetVal = 0; // More than 2^32 iterations??
1886 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1887 if (IterationNum == NumIterations)
1888 return RetVal = PHIVal; // Got exit value!
1890 // Compute the value of the PHI node for the next iteration.
1891 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1892 if (NextPHI == PHIVal)
1893 return RetVal = NextPHI; // Stopped evolving!
1895 return 0; // Couldn't evaluate!
1900 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1901 /// constant number of times (the condition evolves only from constants),
1902 /// try to evaluate a few iterations of the loop until we get the exit
1903 /// condition gets a value of ExitWhen (true or false). If we cannot
1904 /// evaluate the trip count of the loop, return UnknownValue.
1905 SCEVHandle ScalarEvolutionsImpl::
1906 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1907 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1908 if (PN == 0) return UnknownValue;
1910 // Since the loop is canonicalized, the PHI node must have two entries. One
1911 // entry must be a constant (coming in from outside of the loop), and the
1912 // second must be derived from the same PHI.
1913 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1914 Constant *StartCST =
1915 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1916 if (StartCST == 0) return UnknownValue; // Must be a constant.
1918 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1919 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1920 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1922 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1923 // the loop symbolically to determine when the condition gets a value of
1925 unsigned IterationNum = 0;
1926 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1927 for (Constant *PHIVal = StartCST;
1928 IterationNum != MaxIterations; ++IterationNum) {
1929 ConstantBool *CondVal =
1930 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
1931 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate.
1933 if (CondVal->getValue() == ExitWhen) {
1934 ConstantEvolutionLoopExitValue[PN] = PHIVal;
1935 ++NumBruteForceTripCountsComputed;
1936 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
1939 // Compute the value of the PHI node for the next iteration.
1940 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1941 if (NextPHI == 0 || NextPHI == PHIVal)
1942 return UnknownValue; // Couldn't evaluate or not making progress...
1946 // Too many iterations were needed to evaluate.
1947 return UnknownValue;
1950 /// getSCEVAtScope - Compute the value of the specified expression within the
1951 /// indicated loop (which may be null to indicate in no loop). If the
1952 /// expression cannot be evaluated, return UnknownValue.
1953 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1954 // FIXME: this should be turned into a virtual method on SCEV!
1956 if (isa<SCEVConstant>(V)) return V;
1958 // If this instruction is evolves from a constant-evolving PHI, compute the
1959 // exit value from the loop without using SCEVs.
1960 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1961 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1962 const Loop *LI = this->LI[I->getParent()];
1963 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
1964 if (PHINode *PN = dyn_cast<PHINode>(I))
1965 if (PN->getParent() == LI->getHeader()) {
1966 // Okay, there is no closed form solution for the PHI node. Check
1967 // to see if the loop that contains it has a known iteration count.
1968 // If so, we may be able to force computation of the exit value.
1969 SCEVHandle IterationCount = getIterationCount(LI);
1970 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1971 // Okay, we know how many times the containing loop executes. If
1972 // this is a constant evolving PHI node, get the final value at
1973 // the specified iteration number.
1974 Constant *RV = getConstantEvolutionLoopExitValue(PN,
1975 ICC->getValue()->getZExtValue(),
1977 if (RV) return SCEVUnknown::get(RV);
1981 // Okay, this is an expression that we cannot symbolically evaluate
1982 // into a SCEV. Check to see if it's possible to symbolically evaluate
1983 // the arguments into constants, and if so, try to constant propagate the
1984 // result. This is particularly useful for computing loop exit values.
1985 if (CanConstantFold(I)) {
1986 std::vector<Constant*> Operands;
1987 Operands.reserve(I->getNumOperands());
1988 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1989 Value *Op = I->getOperand(i);
1990 if (Constant *C = dyn_cast<Constant>(Op)) {
1991 Operands.push_back(C);
1993 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1994 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1995 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
1998 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
1999 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2000 Operands.push_back(ConstantExpr::getIntegerCast(C,
2010 return SCEVUnknown::get(ConstantFold(I, Operands));
2014 // This is some other type of SCEVUnknown, just return it.
2018 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2019 // Avoid performing the look-up in the common case where the specified
2020 // expression has no loop-variant portions.
2021 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2022 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2023 if (OpAtScope != Comm->getOperand(i)) {
2024 if (OpAtScope == UnknownValue) return UnknownValue;
2025 // Okay, at least one of these operands is loop variant but might be
2026 // foldable. Build a new instance of the folded commutative expression.
2027 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2028 NewOps.push_back(OpAtScope);
2030 for (++i; i != e; ++i) {
2031 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2032 if (OpAtScope == UnknownValue) return UnknownValue;
2033 NewOps.push_back(OpAtScope);
2035 if (isa<SCEVAddExpr>(Comm))
2036 return SCEVAddExpr::get(NewOps);
2037 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2038 return SCEVMulExpr::get(NewOps);
2041 // If we got here, all operands are loop invariant.
2045 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2046 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2047 if (LHS == UnknownValue) return LHS;
2048 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2049 if (RHS == UnknownValue) return RHS;
2050 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2051 return Div; // must be loop invariant
2052 return SCEVSDivExpr::get(LHS, RHS);
2055 // If this is a loop recurrence for a loop that does not contain L, then we
2056 // are dealing with the final value computed by the loop.
2057 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2058 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2059 // To evaluate this recurrence, we need to know how many times the AddRec
2060 // loop iterates. Compute this now.
2061 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2062 if (IterationCount == UnknownValue) return UnknownValue;
2063 IterationCount = getTruncateOrZeroExtend(IterationCount,
2066 // If the value is affine, simplify the expression evaluation to just
2067 // Start + Step*IterationCount.
2068 if (AddRec->isAffine())
2069 return SCEVAddExpr::get(AddRec->getStart(),
2070 SCEVMulExpr::get(IterationCount,
2071 AddRec->getOperand(1)));
2073 // Otherwise, evaluate it the hard way.
2074 return AddRec->evaluateAtIteration(IterationCount);
2076 return UnknownValue;
2079 //assert(0 && "Unknown SCEV type!");
2080 return UnknownValue;
2084 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2085 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2086 /// might be the same) or two SCEVCouldNotCompute objects.
2088 static std::pair<SCEVHandle,SCEVHandle>
2089 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2090 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2091 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2092 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2093 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2095 // We currently can only solve this if the coefficients are constants.
2096 if (!L || !M || !N) {
2097 SCEV *CNC = new SCEVCouldNotCompute();
2098 return std::make_pair(CNC, CNC);
2101 Constant *C = L->getValue();
2102 Constant *Two = ConstantInt::get(C->getType(), 2);
2104 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2105 // The B coefficient is M-N/2
2106 Constant *B = ConstantExpr::getSub(M->getValue(),
2107 ConstantExpr::getSDiv(N->getValue(),
2109 // The A coefficient is N/2
2110 Constant *A = ConstantExpr::getSDiv(N->getValue(), Two);
2112 // Compute the B^2-4ac term.
2113 Constant *SqrtTerm =
2114 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
2115 ConstantExpr::getMul(A, C));
2116 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
2118 // Compute floor(sqrt(B^2-4ac))
2119 uint64_t SqrtValV = cast<ConstantInt>(SqrtTerm)->getZExtValue();
2120 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
2121 // The square root might not be precise for arbitrary 64-bit integer
2122 // values. Do some sanity checks to ensure it's correct.
2123 if (SqrtValV2*SqrtValV2 > SqrtValV ||
2124 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
2125 SCEV *CNC = new SCEVCouldNotCompute();
2126 return std::make_pair(CNC, CNC);
2129 ConstantInt *SqrtVal = ConstantInt::get(Type::Int64Ty, SqrtValV2);
2130 SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType());
2132 Constant *NegB = ConstantExpr::getNeg(B);
2133 Constant *TwoA = ConstantExpr::getMul(A, Two);
2135 // The divisions must be performed as signed divisions.
2136 Constant *Solution1 =
2137 ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
2138 Constant *Solution2 =
2139 ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
2140 return std::make_pair(SCEVUnknown::get(Solution1),
2141 SCEVUnknown::get(Solution2));
2144 /// HowFarToZero - Return the number of times a backedge comparing the specified
2145 /// value to zero will execute. If not computable, return UnknownValue
2146 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2147 // If the value is a constant
2148 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2149 // If the value is already zero, the branch will execute zero times.
2150 if (C->getValue()->isNullValue()) return C;
2151 return UnknownValue; // Otherwise it will loop infinitely.
2154 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2155 if (!AddRec || AddRec->getLoop() != L)
2156 return UnknownValue;
2158 if (AddRec->isAffine()) {
2159 // If this is an affine expression the execution count of this branch is
2162 // (0 - Start/Step) iff Start % Step == 0
2164 // Get the initial value for the loop.
2165 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2166 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2167 SCEVHandle Step = AddRec->getOperand(1);
2169 Step = getSCEVAtScope(Step, L->getParentLoop());
2171 // Figure out if Start % Step == 0.
2172 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2173 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2174 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2175 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2176 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2177 return Start; // 0 - Start/-1 == Start
2179 // Check to see if Start is divisible by SC with no remainder.
2180 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2181 ConstantInt *StartCC = StartC->getValue();
2182 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2183 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2184 if (Rem->isNullValue()) {
2185 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2186 return SCEVUnknown::get(Result);
2190 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2191 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2192 // the quadratic equation to solve it.
2193 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2194 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2195 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2198 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2199 << " sol#2: " << *R2 << "\n";
2201 // Pick the smallest positive root value.
2202 if (ConstantBool *CB =
2203 dyn_cast<ConstantBool>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2204 R1->getValue(), R2->getValue()))) {
2205 if (CB->getValue() == false)
2206 std::swap(R1, R2); // R1 is the minimum root now.
2208 // We can only use this value if the chrec ends up with an exact zero
2209 // value at this index. When solving for "X*X != 5", for example, we
2210 // should not accept a root of 2.
2211 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2212 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2213 if (EvalVal->getValue()->isNullValue())
2214 return R1; // We found a quadratic root!
2219 return UnknownValue;
2222 /// HowFarToNonZero - Return the number of times a backedge checking the
2223 /// specified value for nonzero will execute. If not computable, return
2225 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2226 // Loops that look like: while (X == 0) are very strange indeed. We don't
2227 // handle them yet except for the trivial case. This could be expanded in the
2228 // future as needed.
2230 // If the value is a constant, check to see if it is known to be non-zero
2231 // already. If so, the backedge will execute zero times.
2232 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2233 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2235 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2236 if (NonZero == ConstantBool::getTrue())
2237 return getSCEV(Zero);
2238 return UnknownValue; // Otherwise it will loop infinitely.
2241 // We could implement others, but I really doubt anyone writes loops like
2242 // this, and if they did, they would already be constant folded.
2243 return UnknownValue;
2246 /// HowManyLessThans - Return the number of times a backedge containing the
2247 /// specified less-than comparison will execute. If not computable, return
2249 SCEVHandle ScalarEvolutionsImpl::
2250 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2251 // Only handle: "ADDREC < LoopInvariant".
2252 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2254 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2255 if (!AddRec || AddRec->getLoop() != L)
2256 return UnknownValue;
2258 if (AddRec->isAffine()) {
2259 // FORNOW: We only support unit strides.
2260 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2261 if (AddRec->getOperand(1) != One)
2262 return UnknownValue;
2264 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2265 // know that m is >= n on input to the loop. If it is, the condition return
2266 // true zero times. What we really should return, for full generality, is
2267 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2268 // canonical loop form: most do-loops will have a check that dominates the
2269 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2270 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2272 // Search for the check.
2273 BasicBlock *Preheader = L->getLoopPreheader();
2274 BasicBlock *PreheaderDest = L->getHeader();
2275 if (Preheader == 0) return UnknownValue;
2277 BranchInst *LoopEntryPredicate =
2278 dyn_cast<BranchInst>(Preheader->getTerminator());
2279 if (!LoopEntryPredicate) return UnknownValue;
2281 // This might be a critical edge broken out. If the loop preheader ends in
2282 // an unconditional branch to the loop, check to see if the preheader has a
2283 // single predecessor, and if so, look for its terminator.
2284 while (LoopEntryPredicate->isUnconditional()) {
2285 PreheaderDest = Preheader;
2286 Preheader = Preheader->getSinglePredecessor();
2287 if (!Preheader) return UnknownValue; // Multiple preds.
2289 LoopEntryPredicate =
2290 dyn_cast<BranchInst>(Preheader->getTerminator());
2291 if (!LoopEntryPredicate) return UnknownValue;
2294 // Now that we found a conditional branch that dominates the loop, check to
2295 // see if it is the comparison we are looking for.
2296 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2297 Value *PreCondLHS = ICI->getOperand(0);
2298 Value *PreCondRHS = ICI->getOperand(1);
2299 ICmpInst::Predicate Cond;
2300 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2301 Cond = ICI->getPredicate();
2303 Cond = ICI->getInversePredicate();
2306 case ICmpInst::ICMP_UGT:
2307 std::swap(PreCondLHS, PreCondRHS);
2308 Cond = ICmpInst::ICMP_ULT;
2310 case ICmpInst::ICMP_SGT:
2311 std::swap(PreCondLHS, PreCondRHS);
2312 Cond = ICmpInst::ICMP_SLT;
2317 if (Cond == ICmpInst::ICMP_SLT) {
2318 if (PreCondLHS->getType()->isInteger()) {
2319 if (RHS != getSCEV(PreCondRHS))
2320 return UnknownValue; // Not a comparison against 'm'.
2322 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2323 != getSCEV(PreCondLHS))
2324 return UnknownValue; // Not a comparison against 'n-1'.
2326 else return UnknownValue;
2327 } else if (Cond == ICmpInst::ICMP_ULT)
2328 return UnknownValue;
2330 // cerr << "Computed Loop Trip Count as: "
2331 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2332 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2335 return UnknownValue;
2338 return UnknownValue;
2341 /// getNumIterationsInRange - Return the number of iterations of this loop that
2342 /// produce values in the specified constant range. Another way of looking at
2343 /// this is that it returns the first iteration number where the value is not in
2344 /// the condition, thus computing the exit count. If the iteration count can't
2345 /// be computed, an instance of SCEVCouldNotCompute is returned.
2346 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2347 bool isSigned) const {
2348 if (Range.isFullSet()) // Infinite loop.
2349 return new SCEVCouldNotCompute();
2351 // If the start is a non-zero constant, shift the range to simplify things.
2352 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2353 if (!SC->getValue()->isNullValue()) {
2354 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2355 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2356 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2357 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2358 return ShiftedAddRec->getNumIterationsInRange(
2359 Range.subtract(SC->getValue()),isSigned);
2360 // This is strange and shouldn't happen.
2361 return new SCEVCouldNotCompute();
2364 // The only time we can solve this is when we have all constant indices.
2365 // Otherwise, we cannot determine the overflow conditions.
2366 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2367 if (!isa<SCEVConstant>(getOperand(i)))
2368 return new SCEVCouldNotCompute();
2371 // Okay at this point we know that all elements of the chrec are constants and
2372 // that the start element is zero.
2374 // First check to see if the range contains zero. If not, the first
2376 ConstantInt *Zero = ConstantInt::get(getType(), 0);
2377 if (!Range.contains(Zero, isSigned)) return SCEVConstant::get(Zero);
2380 // If this is an affine expression then we have this situation:
2381 // Solve {0,+,A} in Range === Ax in Range
2383 // Since we know that zero is in the range, we know that the upper value of
2384 // the range must be the first possible exit value. Also note that we
2385 // already checked for a full range.
2386 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
2387 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
2388 ConstantInt *One = ConstantInt::get(getType(), 1);
2390 // The exit value should be (Upper+A-1)/A.
2391 Constant *ExitValue = Upper;
2393 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
2394 ExitValue = ConstantExpr::getSDiv(ExitValue, A);
2396 assert(isa<ConstantInt>(ExitValue) &&
2397 "Constant folding of integers not implemented?");
2399 // Evaluate at the exit value. If we really did fall out of the valid
2400 // range, then we computed our trip count, otherwise wrap around or other
2401 // things must have happened.
2402 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2403 if (Range.contains(Val, isSigned))
2404 return new SCEVCouldNotCompute(); // Something strange happened
2406 // Ensure that the previous value is in the range. This is a sanity check.
2407 assert(Range.contains(EvaluateConstantChrecAtConstant(this,
2408 ConstantExpr::getSub(ExitValue, One)), isSigned) &&
2409 "Linear scev computation is off in a bad way!");
2410 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2411 } else if (isQuadratic()) {
2412 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2413 // quadratic equation to solve it. To do this, we must frame our problem in
2414 // terms of figuring out when zero is crossed, instead of when
2415 // Range.getUpper() is crossed.
2416 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2417 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
2418 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2420 // Next, solve the constructed addrec
2421 std::pair<SCEVHandle,SCEVHandle> Roots =
2422 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2423 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2424 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2426 // Pick the smallest positive root value.
2427 if (ConstantBool *CB =
2428 dyn_cast<ConstantBool>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2429 R1->getValue(), R2->getValue()))) {
2430 if (CB->getValue() == false)
2431 std::swap(R1, R2); // R1 is the minimum root now.
2433 // Make sure the root is not off by one. The returned iteration should
2434 // not be in the range, but the previous one should be. When solving
2435 // for "X*X < 5", for example, we should not return a root of 2.
2436 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2438 if (Range.contains(R1Val, isSigned)) {
2439 // The next iteration must be out of the range...
2441 ConstantExpr::getAdd(R1->getValue(),
2442 ConstantInt::get(R1->getType(), 1));
2444 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2445 if (!Range.contains(R1Val, isSigned))
2446 return SCEVUnknown::get(NextVal);
2447 return new SCEVCouldNotCompute(); // Something strange happened
2450 // If R1 was not in the range, then it is a good return value. Make
2451 // sure that R1-1 WAS in the range though, just in case.
2453 ConstantExpr::getSub(R1->getValue(),
2454 ConstantInt::get(R1->getType(), 1));
2455 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2456 if (Range.contains(R1Val, isSigned))
2458 return new SCEVCouldNotCompute(); // Something strange happened
2463 // Fallback, if this is a general polynomial, figure out the progression
2464 // through brute force: evaluate until we find an iteration that fails the
2465 // test. This is likely to be slow, but getting an accurate trip count is
2466 // incredibly important, we will be able to simplify the exit test a lot, and
2467 // we are almost guaranteed to get a trip count in this case.
2468 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2469 ConstantInt *One = ConstantInt::get(getType(), 1);
2470 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2472 ++NumBruteForceEvaluations;
2473 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2474 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2475 return new SCEVCouldNotCompute();
2477 // Check to see if we found the value!
2478 if (!Range.contains(cast<SCEVConstant>(Val)->getValue(), isSigned))
2479 return SCEVConstant::get(TestVal);
2481 // Increment to test the next index.
2482 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
2483 } while (TestVal != EndVal);
2485 return new SCEVCouldNotCompute();
2490 //===----------------------------------------------------------------------===//
2491 // ScalarEvolution Class Implementation
2492 //===----------------------------------------------------------------------===//
2494 bool ScalarEvolution::runOnFunction(Function &F) {
2495 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2499 void ScalarEvolution::releaseMemory() {
2500 delete (ScalarEvolutionsImpl*)Impl;
2504 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2505 AU.setPreservesAll();
2506 AU.addRequiredTransitive<LoopInfo>();
2509 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2510 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2513 /// hasSCEV - Return true if the SCEV for this value has already been
2515 bool ScalarEvolution::hasSCEV(Value *V) const {
2516 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2520 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2521 /// the specified value.
2522 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2523 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2527 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2528 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2531 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2532 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2535 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2536 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2539 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2540 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2543 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2545 // Print all inner loops first
2546 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2547 PrintLoopInfo(OS, SE, *I);
2549 cerr << "Loop " << L->getHeader()->getName() << ": ";
2551 std::vector<BasicBlock*> ExitBlocks;
2552 L->getExitBlocks(ExitBlocks);
2553 if (ExitBlocks.size() != 1)
2554 cerr << "<multiple exits> ";
2556 if (SE->hasLoopInvariantIterationCount(L)) {
2557 cerr << *SE->getIterationCount(L) << " iterations! ";
2559 cerr << "Unpredictable iteration count. ";
2565 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2566 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2567 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2569 OS << "Classifying expressions for: " << F.getName() << "\n";
2570 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2571 if (I->getType()->isInteger()) {
2574 SCEVHandle SV = getSCEV(&*I);
2578 if ((*I).getType()->isIntegral()) {
2579 ConstantRange Bounds = SV->getValueRange();
2580 if (!Bounds.isFullSet())
2581 OS << "Bounds: " << Bounds << " ";
2584 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2586 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2587 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2588 OS << "<<Unknown>>";
2598 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2599 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2600 PrintLoopInfo(OS, this, *I);