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. We also handle the case where the exit block *is* the
1510 // loop header. This is common for un-rotated loops. More extensive analysis
1511 // could be done to handle more cases here.
1512 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1513 ExitBr->getSuccessor(1) != L->getHeader() &&
1514 ExitBr->getParent() != L->getHeader())
1515 return UnknownValue;
1517 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1519 // If its not an integer comparison then compute it the hard way.
1520 // Note that ICmpInst deals with pointer comparisons too so we must check
1521 // the type of the operand.
1522 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1523 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1524 ExitBr->getSuccessor(0) == ExitBlock);
1526 // If the condition was exit on true, convert the condition to exit on false
1527 ICmpInst::Predicate Cond;
1528 if (ExitBr->getSuccessor(1) == ExitBlock)
1529 Cond = ExitCond->getPredicate();
1531 Cond = ExitCond->getInversePredicate();
1533 // Handle common loops like: for (X = "string"; *X; ++X)
1534 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1535 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1537 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1538 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1541 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1542 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1544 // Try to evaluate any dependencies out of the loop.
1545 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1546 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1547 Tmp = getSCEVAtScope(RHS, L);
1548 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1550 // At this point, we would like to compute how many iterations of the
1551 // loop the predicate will return true for these inputs.
1552 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1553 // If there is a constant, force it into the RHS.
1554 std::swap(LHS, RHS);
1555 Cond = ICmpInst::getSwappedPredicate(Cond);
1558 // FIXME: think about handling pointer comparisons! i.e.:
1559 // while (P != P+100) ++P;
1561 // If we have a comparison of a chrec against a constant, try to use value
1562 // ranges to answer this query.
1563 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1564 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1565 if (AddRec->getLoop() == L) {
1566 // Form the comparison range using the constant of the correct type so
1567 // that the ConstantRange class knows to do a signed or unsigned
1569 ConstantInt *CompVal = RHSC->getValue();
1570 const Type *RealTy = ExitCond->getOperand(0)->getType();
1571 CompVal = dyn_cast<ConstantInt>(
1572 ConstantExpr::getBitCast(CompVal, RealTy));
1574 // Form the constant range.
1575 ConstantRange CompRange(Cond, CompVal);
1577 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
1578 false /*Always treat as unsigned range*/);
1579 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1584 case ICmpInst::ICMP_NE: { // while (X != Y)
1585 // Convert to: while (X-Y != 0)
1586 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1587 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1590 case ICmpInst::ICMP_EQ: {
1591 // Convert to: while (X-Y == 0) // while (X == Y)
1592 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1593 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1596 case ICmpInst::ICMP_SLT: {
1597 SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1598 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1601 case ICmpInst::ICMP_SGT: {
1602 SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1603 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1608 cerr << "ComputeIterationCount ";
1609 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1610 cerr << "[unsigned] ";
1612 << Instruction::getOpcodeName(Instruction::ICmp)
1613 << " " << *RHS << "\n";
1617 return ComputeIterationCountExhaustively(L, ExitCond,
1618 ExitBr->getSuccessor(0) == ExitBlock);
1621 static ConstantInt *
1622 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1623 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1624 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1625 assert(isa<SCEVConstant>(Val) &&
1626 "Evaluation of SCEV at constant didn't fold correctly?");
1627 return cast<SCEVConstant>(Val)->getValue();
1630 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1631 /// and a GEP expression (missing the pointer index) indexing into it, return
1632 /// the addressed element of the initializer or null if the index expression is
1635 GetAddressedElementFromGlobal(GlobalVariable *GV,
1636 const std::vector<ConstantInt*> &Indices) {
1637 Constant *Init = GV->getInitializer();
1638 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1639 uint64_t Idx = Indices[i]->getZExtValue();
1640 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1641 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1642 Init = cast<Constant>(CS->getOperand(Idx));
1643 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1644 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1645 Init = cast<Constant>(CA->getOperand(Idx));
1646 } else if (isa<ConstantAggregateZero>(Init)) {
1647 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1648 assert(Idx < STy->getNumElements() && "Bad struct index!");
1649 Init = Constant::getNullValue(STy->getElementType(Idx));
1650 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1651 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1652 Init = Constant::getNullValue(ATy->getElementType());
1654 assert(0 && "Unknown constant aggregate type!");
1658 return 0; // Unknown initializer type
1664 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1665 /// 'setcc load X, cst', try to se if we can compute the trip count.
1666 SCEVHandle ScalarEvolutionsImpl::
1667 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1669 ICmpInst::Predicate predicate) {
1670 if (LI->isVolatile()) return UnknownValue;
1672 // Check to see if the loaded pointer is a getelementptr of a global.
1673 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1674 if (!GEP) return UnknownValue;
1676 // Make sure that it is really a constant global we are gepping, with an
1677 // initializer, and make sure the first IDX is really 0.
1678 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1679 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1680 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1681 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1682 return UnknownValue;
1684 // Okay, we allow one non-constant index into the GEP instruction.
1686 std::vector<ConstantInt*> Indexes;
1687 unsigned VarIdxNum = 0;
1688 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1689 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1690 Indexes.push_back(CI);
1691 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1692 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1693 VarIdx = GEP->getOperand(i);
1695 Indexes.push_back(0);
1698 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1699 // Check to see if X is a loop variant variable value now.
1700 SCEVHandle Idx = getSCEV(VarIdx);
1701 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1702 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1704 // We can only recognize very limited forms of loop index expressions, in
1705 // particular, only affine AddRec's like {C1,+,C2}.
1706 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1707 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1708 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1709 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1710 return UnknownValue;
1712 unsigned MaxSteps = MaxBruteForceIterations;
1713 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1714 ConstantInt *ItCst =
1715 ConstantInt::get(IdxExpr->getType(), IterationNum);
1716 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1718 // Form the GEP offset.
1719 Indexes[VarIdxNum] = Val;
1721 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1722 if (Result == 0) break; // Cannot compute!
1724 // Evaluate the condition for this iteration.
1725 Result = ConstantExpr::getICmp(predicate, Result, RHS);
1726 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
1727 if (cast<ConstantInt>(Result)->getZExtValue() == false) {
1729 cerr << "\n***\n*** Computed loop count " << *ItCst
1730 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1733 ++NumArrayLenItCounts;
1734 return SCEVConstant::get(ItCst); // Found terminating iteration!
1737 return UnknownValue;
1741 /// CanConstantFold - Return true if we can constant fold an instruction of the
1742 /// specified type, assuming that all operands were constants.
1743 static bool CanConstantFold(const Instruction *I) {
1744 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) || isa<CmpInst>(I) ||
1745 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1748 if (const CallInst *CI = dyn_cast<CallInst>(I))
1749 if (const Function *F = CI->getCalledFunction())
1750 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1754 /// ConstantFold - Constant fold an instruction of the specified type with the
1755 /// specified constant operands. This function may modify the operands vector.
1756 static Constant *ConstantFold(const Instruction *I,
1757 std::vector<Constant*> &Operands) {
1758 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
1759 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
1761 if (isa<CastInst>(I))
1762 return ConstantExpr::getCast(I->getOpcode(), Operands[0], I->getType());
1764 switch (I->getOpcode()) {
1765 case Instruction::Select:
1766 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
1767 case Instruction::Call:
1768 if (Function *GV = dyn_cast<Function>(Operands[0])) {
1769 Operands.erase(Operands.begin());
1770 return ConstantFoldCall(cast<Function>(GV), Operands);
1773 case Instruction::GetElementPtr: {
1774 Constant *Base = Operands[0];
1775 Operands.erase(Operands.begin());
1776 return ConstantExpr::getGetElementPtr(Base, Operands);
1778 case Instruction::ICmp:
1779 return ConstantExpr::getICmp(
1780 cast<ICmpInst>(I)->getPredicate(), Operands[0], Operands[1]);
1781 case Instruction::FCmp:
1782 return ConstantExpr::getFCmp(
1783 cast<FCmpInst>(I)->getPredicate(), Operands[0], Operands[1]);
1789 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1790 /// in the loop that V is derived from. We allow arbitrary operations along the
1791 /// way, but the operands of an operation must either be constants or a value
1792 /// derived from a constant PHI. If this expression does not fit with these
1793 /// constraints, return null.
1794 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1795 // If this is not an instruction, or if this is an instruction outside of the
1796 // loop, it can't be derived from a loop PHI.
1797 Instruction *I = dyn_cast<Instruction>(V);
1798 if (I == 0 || !L->contains(I->getParent())) return 0;
1800 if (PHINode *PN = dyn_cast<PHINode>(I))
1801 if (L->getHeader() == I->getParent())
1804 // We don't currently keep track of the control flow needed to evaluate
1805 // PHIs, so we cannot handle PHIs inside of loops.
1808 // If we won't be able to constant fold this expression even if the operands
1809 // are constants, return early.
1810 if (!CanConstantFold(I)) return 0;
1812 // Otherwise, we can evaluate this instruction if all of its operands are
1813 // constant or derived from a PHI node themselves.
1815 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1816 if (!(isa<Constant>(I->getOperand(Op)) ||
1817 isa<GlobalValue>(I->getOperand(Op)))) {
1818 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1819 if (P == 0) return 0; // Not evolving from PHI
1823 return 0; // Evolving from multiple different PHIs.
1826 // This is a expression evolving from a constant PHI!
1830 /// EvaluateExpression - Given an expression that passes the
1831 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1832 /// in the loop has the value PHIVal. If we can't fold this expression for some
1833 /// reason, return null.
1834 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1835 if (isa<PHINode>(V)) return PHIVal;
1836 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1838 if (Constant *C = dyn_cast<Constant>(V)) return C;
1839 Instruction *I = cast<Instruction>(V);
1841 std::vector<Constant*> Operands;
1842 Operands.resize(I->getNumOperands());
1844 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1845 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1846 if (Operands[i] == 0) return 0;
1849 return ConstantFold(I, Operands);
1852 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1853 /// in the header of its containing loop, we know the loop executes a
1854 /// constant number of times, and the PHI node is just a recurrence
1855 /// involving constants, fold it.
1856 Constant *ScalarEvolutionsImpl::
1857 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
1858 std::map<PHINode*, Constant*>::iterator I =
1859 ConstantEvolutionLoopExitValue.find(PN);
1860 if (I != ConstantEvolutionLoopExitValue.end())
1863 if (Its > MaxBruteForceIterations)
1864 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1866 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1868 // Since the loop is canonicalized, the PHI node must have two entries. One
1869 // entry must be a constant (coming in from outside of the loop), and the
1870 // second must be derived from the same PHI.
1871 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1872 Constant *StartCST =
1873 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1875 return RetVal = 0; // Must be a constant.
1877 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1878 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1880 return RetVal = 0; // Not derived from same PHI.
1882 // Execute the loop symbolically to determine the exit value.
1883 unsigned IterationNum = 0;
1884 unsigned NumIterations = Its;
1885 if (NumIterations != Its)
1886 return RetVal = 0; // More than 2^32 iterations??
1888 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1889 if (IterationNum == NumIterations)
1890 return RetVal = PHIVal; // Got exit value!
1892 // Compute the value of the PHI node for the next iteration.
1893 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1894 if (NextPHI == PHIVal)
1895 return RetVal = NextPHI; // Stopped evolving!
1897 return 0; // Couldn't evaluate!
1902 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1903 /// constant number of times (the condition evolves only from constants),
1904 /// try to evaluate a few iterations of the loop until we get the exit
1905 /// condition gets a value of ExitWhen (true or false). If we cannot
1906 /// evaluate the trip count of the loop, return UnknownValue.
1907 SCEVHandle ScalarEvolutionsImpl::
1908 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1909 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1910 if (PN == 0) return UnknownValue;
1912 // Since the loop is canonicalized, the PHI node must have two entries. One
1913 // entry must be a constant (coming in from outside of the loop), and the
1914 // second must be derived from the same PHI.
1915 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1916 Constant *StartCST =
1917 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1918 if (StartCST == 0) return UnknownValue; // Must be a constant.
1920 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1921 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1922 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1924 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1925 // the loop symbolically to determine when the condition gets a value of
1927 unsigned IterationNum = 0;
1928 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1929 for (Constant *PHIVal = StartCST;
1930 IterationNum != MaxIterations; ++IterationNum) {
1931 ConstantInt *CondVal =
1932 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
1934 // Couldn't symbolically evaluate.
1935 if (!CondVal) return UnknownValue;
1937 if (CondVal->getZExtValue() == ExitWhen) {
1938 ConstantEvolutionLoopExitValue[PN] = PHIVal;
1939 ++NumBruteForceTripCountsComputed;
1940 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
1943 // Compute the value of the PHI node for the next iteration.
1944 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1945 if (NextPHI == 0 || NextPHI == PHIVal)
1946 return UnknownValue; // Couldn't evaluate or not making progress...
1950 // Too many iterations were needed to evaluate.
1951 return UnknownValue;
1954 /// getSCEVAtScope - Compute the value of the specified expression within the
1955 /// indicated loop (which may be null to indicate in no loop). If the
1956 /// expression cannot be evaluated, return UnknownValue.
1957 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1958 // FIXME: this should be turned into a virtual method on SCEV!
1960 if (isa<SCEVConstant>(V)) return V;
1962 // If this instruction is evolves from a constant-evolving PHI, compute the
1963 // exit value from the loop without using SCEVs.
1964 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1965 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1966 const Loop *LI = this->LI[I->getParent()];
1967 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
1968 if (PHINode *PN = dyn_cast<PHINode>(I))
1969 if (PN->getParent() == LI->getHeader()) {
1970 // Okay, there is no closed form solution for the PHI node. Check
1971 // to see if the loop that contains it has a known iteration count.
1972 // If so, we may be able to force computation of the exit value.
1973 SCEVHandle IterationCount = getIterationCount(LI);
1974 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1975 // Okay, we know how many times the containing loop executes. If
1976 // this is a constant evolving PHI node, get the final value at
1977 // the specified iteration number.
1978 Constant *RV = getConstantEvolutionLoopExitValue(PN,
1979 ICC->getValue()->getZExtValue(),
1981 if (RV) return SCEVUnknown::get(RV);
1985 // Okay, this is an expression that we cannot symbolically evaluate
1986 // into a SCEV. Check to see if it's possible to symbolically evaluate
1987 // the arguments into constants, and if so, try to constant propagate the
1988 // result. This is particularly useful for computing loop exit values.
1989 if (CanConstantFold(I)) {
1990 std::vector<Constant*> Operands;
1991 Operands.reserve(I->getNumOperands());
1992 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1993 Value *Op = I->getOperand(i);
1994 if (Constant *C = dyn_cast<Constant>(Op)) {
1995 Operands.push_back(C);
1997 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1998 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1999 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2002 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2003 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2004 Operands.push_back(ConstantExpr::getIntegerCast(C,
2014 return SCEVUnknown::get(ConstantFold(I, Operands));
2018 // This is some other type of SCEVUnknown, just return it.
2022 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2023 // Avoid performing the look-up in the common case where the specified
2024 // expression has no loop-variant portions.
2025 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2026 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2027 if (OpAtScope != Comm->getOperand(i)) {
2028 if (OpAtScope == UnknownValue) return UnknownValue;
2029 // Okay, at least one of these operands is loop variant but might be
2030 // foldable. Build a new instance of the folded commutative expression.
2031 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2032 NewOps.push_back(OpAtScope);
2034 for (++i; i != e; ++i) {
2035 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2036 if (OpAtScope == UnknownValue) return UnknownValue;
2037 NewOps.push_back(OpAtScope);
2039 if (isa<SCEVAddExpr>(Comm))
2040 return SCEVAddExpr::get(NewOps);
2041 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2042 return SCEVMulExpr::get(NewOps);
2045 // If we got here, all operands are loop invariant.
2049 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2050 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2051 if (LHS == UnknownValue) return LHS;
2052 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2053 if (RHS == UnknownValue) return RHS;
2054 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2055 return Div; // must be loop invariant
2056 return SCEVSDivExpr::get(LHS, RHS);
2059 // If this is a loop recurrence for a loop that does not contain L, then we
2060 // are dealing with the final value computed by the loop.
2061 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2062 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2063 // To evaluate this recurrence, we need to know how many times the AddRec
2064 // loop iterates. Compute this now.
2065 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2066 if (IterationCount == UnknownValue) return UnknownValue;
2067 IterationCount = getTruncateOrZeroExtend(IterationCount,
2070 // If the value is affine, simplify the expression evaluation to just
2071 // Start + Step*IterationCount.
2072 if (AddRec->isAffine())
2073 return SCEVAddExpr::get(AddRec->getStart(),
2074 SCEVMulExpr::get(IterationCount,
2075 AddRec->getOperand(1)));
2077 // Otherwise, evaluate it the hard way.
2078 return AddRec->evaluateAtIteration(IterationCount);
2080 return UnknownValue;
2083 //assert(0 && "Unknown SCEV type!");
2084 return UnknownValue;
2088 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2089 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2090 /// might be the same) or two SCEVCouldNotCompute objects.
2092 static std::pair<SCEVHandle,SCEVHandle>
2093 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2094 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2095 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2096 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2097 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2099 // We currently can only solve this if the coefficients are constants.
2100 if (!L || !M || !N) {
2101 SCEV *CNC = new SCEVCouldNotCompute();
2102 return std::make_pair(CNC, CNC);
2105 Constant *C = L->getValue();
2106 Constant *Two = ConstantInt::get(C->getType(), 2);
2108 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2109 // The B coefficient is M-N/2
2110 Constant *B = ConstantExpr::getSub(M->getValue(),
2111 ConstantExpr::getSDiv(N->getValue(),
2113 // The A coefficient is N/2
2114 Constant *A = ConstantExpr::getSDiv(N->getValue(), Two);
2116 // Compute the B^2-4ac term.
2117 Constant *SqrtTerm =
2118 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
2119 ConstantExpr::getMul(A, C));
2120 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
2122 // Compute floor(sqrt(B^2-4ac))
2123 uint64_t SqrtValV = cast<ConstantInt>(SqrtTerm)->getZExtValue();
2124 uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
2125 // The square root might not be precise for arbitrary 64-bit integer
2126 // values. Do some sanity checks to ensure it's correct.
2127 if (SqrtValV2*SqrtValV2 > SqrtValV ||
2128 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
2129 SCEV *CNC = new SCEVCouldNotCompute();
2130 return std::make_pair(CNC, CNC);
2133 ConstantInt *SqrtVal = ConstantInt::get(Type::Int64Ty, SqrtValV2);
2134 SqrtTerm = ConstantExpr::getTruncOrBitCast(SqrtVal, SqrtTerm->getType());
2136 Constant *NegB = ConstantExpr::getNeg(B);
2137 Constant *TwoA = ConstantExpr::getMul(A, Two);
2139 // The divisions must be performed as signed divisions.
2140 Constant *Solution1 =
2141 ConstantExpr::getSDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
2142 Constant *Solution2 =
2143 ConstantExpr::getSDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
2144 return std::make_pair(SCEVUnknown::get(Solution1),
2145 SCEVUnknown::get(Solution2));
2148 /// HowFarToZero - Return the number of times a backedge comparing the specified
2149 /// value to zero will execute. If not computable, return UnknownValue
2150 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2151 // If the value is a constant
2152 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2153 // If the value is already zero, the branch will execute zero times.
2154 if (C->getValue()->isNullValue()) return C;
2155 return UnknownValue; // Otherwise it will loop infinitely.
2158 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2159 if (!AddRec || AddRec->getLoop() != L)
2160 return UnknownValue;
2162 if (AddRec->isAffine()) {
2163 // If this is an affine expression the execution count of this branch is
2166 // (0 - Start/Step) iff Start % Step == 0
2168 // Get the initial value for the loop.
2169 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2170 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2171 SCEVHandle Step = AddRec->getOperand(1);
2173 Step = getSCEVAtScope(Step, L->getParentLoop());
2175 // Figure out if Start % Step == 0.
2176 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2177 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2178 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2179 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2180 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2181 return Start; // 0 - Start/-1 == Start
2183 // Check to see if Start is divisible by SC with no remainder.
2184 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2185 ConstantInt *StartCC = StartC->getValue();
2186 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2187 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2188 if (Rem->isNullValue()) {
2189 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2190 return SCEVUnknown::get(Result);
2194 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2195 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2196 // the quadratic equation to solve it.
2197 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2198 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2199 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2202 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2203 << " sol#2: " << *R2 << "\n";
2205 // Pick the smallest positive root value.
2206 if (ConstantInt *CB =
2207 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2208 R1->getValue(), R2->getValue()))) {
2209 if (CB->getZExtValue() == false)
2210 std::swap(R1, R2); // R1 is the minimum root now.
2212 // We can only use this value if the chrec ends up with an exact zero
2213 // value at this index. When solving for "X*X != 5", for example, we
2214 // should not accept a root of 2.
2215 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2216 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2217 if (EvalVal->getValue()->isNullValue())
2218 return R1; // We found a quadratic root!
2223 return UnknownValue;
2226 /// HowFarToNonZero - Return the number of times a backedge checking the
2227 /// specified value for nonzero will execute. If not computable, return
2229 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2230 // Loops that look like: while (X == 0) are very strange indeed. We don't
2231 // handle them yet except for the trivial case. This could be expanded in the
2232 // future as needed.
2234 // If the value is a constant, check to see if it is known to be non-zero
2235 // already. If so, the backedge will execute zero times.
2236 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2237 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2239 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2240 if (NonZero == ConstantInt::getTrue())
2241 return getSCEV(Zero);
2242 return UnknownValue; // Otherwise it will loop infinitely.
2245 // We could implement others, but I really doubt anyone writes loops like
2246 // this, and if they did, they would already be constant folded.
2247 return UnknownValue;
2250 /// HowManyLessThans - Return the number of times a backedge containing the
2251 /// specified less-than comparison will execute. If not computable, return
2253 SCEVHandle ScalarEvolutionsImpl::
2254 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2255 // Only handle: "ADDREC < LoopInvariant".
2256 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2258 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2259 if (!AddRec || AddRec->getLoop() != L)
2260 return UnknownValue;
2262 if (AddRec->isAffine()) {
2263 // FORNOW: We only support unit strides.
2264 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2265 if (AddRec->getOperand(1) != One)
2266 return UnknownValue;
2268 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2269 // know that m is >= n on input to the loop. If it is, the condition return
2270 // true zero times. What we really should return, for full generality, is
2271 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2272 // canonical loop form: most do-loops will have a check that dominates the
2273 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2274 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2276 // Search for the check.
2277 BasicBlock *Preheader = L->getLoopPreheader();
2278 BasicBlock *PreheaderDest = L->getHeader();
2279 if (Preheader == 0) return UnknownValue;
2281 BranchInst *LoopEntryPredicate =
2282 dyn_cast<BranchInst>(Preheader->getTerminator());
2283 if (!LoopEntryPredicate) return UnknownValue;
2285 // This might be a critical edge broken out. If the loop preheader ends in
2286 // an unconditional branch to the loop, check to see if the preheader has a
2287 // single predecessor, and if so, look for its terminator.
2288 while (LoopEntryPredicate->isUnconditional()) {
2289 PreheaderDest = Preheader;
2290 Preheader = Preheader->getSinglePredecessor();
2291 if (!Preheader) return UnknownValue; // Multiple preds.
2293 LoopEntryPredicate =
2294 dyn_cast<BranchInst>(Preheader->getTerminator());
2295 if (!LoopEntryPredicate) return UnknownValue;
2298 // Now that we found a conditional branch that dominates the loop, check to
2299 // see if it is the comparison we are looking for.
2300 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2301 Value *PreCondLHS = ICI->getOperand(0);
2302 Value *PreCondRHS = ICI->getOperand(1);
2303 ICmpInst::Predicate Cond;
2304 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2305 Cond = ICI->getPredicate();
2307 Cond = ICI->getInversePredicate();
2310 case ICmpInst::ICMP_UGT:
2311 std::swap(PreCondLHS, PreCondRHS);
2312 Cond = ICmpInst::ICMP_ULT;
2314 case ICmpInst::ICMP_SGT:
2315 std::swap(PreCondLHS, PreCondRHS);
2316 Cond = ICmpInst::ICMP_SLT;
2321 if (Cond == ICmpInst::ICMP_SLT) {
2322 if (PreCondLHS->getType()->isInteger()) {
2323 if (RHS != getSCEV(PreCondRHS))
2324 return UnknownValue; // Not a comparison against 'm'.
2326 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2327 != getSCEV(PreCondLHS))
2328 return UnknownValue; // Not a comparison against 'n-1'.
2330 else return UnknownValue;
2331 } else if (Cond == ICmpInst::ICMP_ULT)
2332 return UnknownValue;
2334 // cerr << "Computed Loop Trip Count as: "
2335 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2336 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2339 return UnknownValue;
2342 return UnknownValue;
2345 /// getNumIterationsInRange - Return the number of iterations of this loop that
2346 /// produce values in the specified constant range. Another way of looking at
2347 /// this is that it returns the first iteration number where the value is not in
2348 /// the condition, thus computing the exit count. If the iteration count can't
2349 /// be computed, an instance of SCEVCouldNotCompute is returned.
2350 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2351 bool isSigned) const {
2352 if (Range.isFullSet()) // Infinite loop.
2353 return new SCEVCouldNotCompute();
2355 // If the start is a non-zero constant, shift the range to simplify things.
2356 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2357 if (!SC->getValue()->isNullValue()) {
2358 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2359 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2360 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2361 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2362 return ShiftedAddRec->getNumIterationsInRange(
2363 Range.subtract(SC->getValue()),isSigned);
2364 // This is strange and shouldn't happen.
2365 return new SCEVCouldNotCompute();
2368 // The only time we can solve this is when we have all constant indices.
2369 // Otherwise, we cannot determine the overflow conditions.
2370 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2371 if (!isa<SCEVConstant>(getOperand(i)))
2372 return new SCEVCouldNotCompute();
2375 // Okay at this point we know that all elements of the chrec are constants and
2376 // that the start element is zero.
2378 // First check to see if the range contains zero. If not, the first
2380 ConstantInt *Zero = ConstantInt::get(getType(), 0);
2381 if (!Range.contains(Zero, isSigned)) return SCEVConstant::get(Zero);
2384 // If this is an affine expression then we have this situation:
2385 // Solve {0,+,A} in Range === Ax in Range
2387 // Since we know that zero is in the range, we know that the upper value of
2388 // the range must be the first possible exit value. Also note that we
2389 // already checked for a full range.
2390 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
2391 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
2392 ConstantInt *One = ConstantInt::get(getType(), 1);
2394 // The exit value should be (Upper+A-1)/A.
2395 Constant *ExitValue = Upper;
2397 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
2398 ExitValue = ConstantExpr::getSDiv(ExitValue, A);
2400 assert(isa<ConstantInt>(ExitValue) &&
2401 "Constant folding of integers not implemented?");
2403 // Evaluate at the exit value. If we really did fall out of the valid
2404 // range, then we computed our trip count, otherwise wrap around or other
2405 // things must have happened.
2406 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2407 if (Range.contains(Val, isSigned))
2408 return new SCEVCouldNotCompute(); // Something strange happened
2410 // Ensure that the previous value is in the range. This is a sanity check.
2411 assert(Range.contains(EvaluateConstantChrecAtConstant(this,
2412 ConstantExpr::getSub(ExitValue, One)), isSigned) &&
2413 "Linear scev computation is off in a bad way!");
2414 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2415 } else if (isQuadratic()) {
2416 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2417 // quadratic equation to solve it. To do this, we must frame our problem in
2418 // terms of figuring out when zero is crossed, instead of when
2419 // Range.getUpper() is crossed.
2420 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2421 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
2422 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2424 // Next, solve the constructed addrec
2425 std::pair<SCEVHandle,SCEVHandle> Roots =
2426 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2427 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2428 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2430 // Pick the smallest positive root value.
2431 if (ConstantInt *CB =
2432 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2433 R1->getValue(), R2->getValue()))) {
2434 if (CB->getZExtValue() == false)
2435 std::swap(R1, R2); // R1 is the minimum root now.
2437 // Make sure the root is not off by one. The returned iteration should
2438 // not be in the range, but the previous one should be. When solving
2439 // for "X*X < 5", for example, we should not return a root of 2.
2440 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2442 if (Range.contains(R1Val, isSigned)) {
2443 // The next iteration must be out of the range...
2445 ConstantExpr::getAdd(R1->getValue(),
2446 ConstantInt::get(R1->getType(), 1));
2448 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2449 if (!Range.contains(R1Val, isSigned))
2450 return SCEVUnknown::get(NextVal);
2451 return new SCEVCouldNotCompute(); // Something strange happened
2454 // If R1 was not in the range, then it is a good return value. Make
2455 // sure that R1-1 WAS in the range though, just in case.
2457 ConstantExpr::getSub(R1->getValue(),
2458 ConstantInt::get(R1->getType(), 1));
2459 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2460 if (Range.contains(R1Val, isSigned))
2462 return new SCEVCouldNotCompute(); // Something strange happened
2467 // Fallback, if this is a general polynomial, figure out the progression
2468 // through brute force: evaluate until we find an iteration that fails the
2469 // test. This is likely to be slow, but getting an accurate trip count is
2470 // incredibly important, we will be able to simplify the exit test a lot, and
2471 // we are almost guaranteed to get a trip count in this case.
2472 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2473 ConstantInt *One = ConstantInt::get(getType(), 1);
2474 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2476 ++NumBruteForceEvaluations;
2477 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2478 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2479 return new SCEVCouldNotCompute();
2481 // Check to see if we found the value!
2482 if (!Range.contains(cast<SCEVConstant>(Val)->getValue(), isSigned))
2483 return SCEVConstant::get(TestVal);
2485 // Increment to test the next index.
2486 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
2487 } while (TestVal != EndVal);
2489 return new SCEVCouldNotCompute();
2494 //===----------------------------------------------------------------------===//
2495 // ScalarEvolution Class Implementation
2496 //===----------------------------------------------------------------------===//
2498 bool ScalarEvolution::runOnFunction(Function &F) {
2499 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2503 void ScalarEvolution::releaseMemory() {
2504 delete (ScalarEvolutionsImpl*)Impl;
2508 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2509 AU.setPreservesAll();
2510 AU.addRequiredTransitive<LoopInfo>();
2513 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2514 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2517 /// hasSCEV - Return true if the SCEV for this value has already been
2519 bool ScalarEvolution::hasSCEV(Value *V) const {
2520 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2524 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2525 /// the specified value.
2526 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2527 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2531 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2532 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2535 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2536 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2539 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2540 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2543 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2544 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2547 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2549 // Print all inner loops first
2550 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2551 PrintLoopInfo(OS, SE, *I);
2553 cerr << "Loop " << L->getHeader()->getName() << ": ";
2555 std::vector<BasicBlock*> ExitBlocks;
2556 L->getExitBlocks(ExitBlocks);
2557 if (ExitBlocks.size() != 1)
2558 cerr << "<multiple exits> ";
2560 if (SE->hasLoopInvariantIterationCount(L)) {
2561 cerr << *SE->getIterationCount(L) << " iterations! ";
2563 cerr << "Unpredictable iteration count. ";
2569 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2570 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2571 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2573 OS << "Classifying expressions for: " << F.getName() << "\n";
2574 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2575 if (I->getType()->isInteger()) {
2578 SCEVHandle SV = getSCEV(&*I);
2582 if ((*I).getType()->isIntegral()) {
2583 ConstantRange Bounds = SV->getValueRange();
2584 if (!Bounds.isFullSet())
2585 OS << "Bounds: " << Bounds << " ";
2588 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2590 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2591 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2592 OS << "<<Unknown>>";
2602 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2603 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2604 PrintLoopInfo(OS, this, *I);