1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by the LLVM research group and is distributed under
6 // the University of Illinois Open Source License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Assembly/Writer.h"
71 #include "llvm/Transforms/Scalar.h"
72 #include "llvm/Support/CFG.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/InstIterator.h"
77 #include "llvm/Support/ManagedStatic.h"
78 #include "llvm/Support/MathExtras.h"
79 #include "llvm/Support/Streams.h"
80 #include "llvm/ADT/Statistic.h"
86 STATISTIC(NumBruteForceEvaluations,
87 "Number of brute force evaluations needed to "
88 "calculate high-order polynomial exit values");
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant derived loop"),
105 RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis");
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
118 void SCEV::dump() const {
122 /// getValueRange - Return the tightest constant bounds that this value is
123 /// known to have. This method is only valid on integer SCEV objects.
124 ConstantRange SCEV::getValueRange() const {
125 const Type *Ty = getType();
126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
127 // Default to a full range if no better information is available.
128 return ConstantRange(getBitWidth());
131 uint32_t SCEV::getBitWidth() const {
132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
133 return ITy->getBitWidth();
138 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
140 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 const Type *SCEVCouldNotCompute::getType() const {
146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
155 SCEVHandle SCEVCouldNotCompute::
156 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
157 const SCEVHandle &Conc) const {
161 void SCEVCouldNotCompute::print(std::ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
165 bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
170 // SCEVConstants - Only allow the creation of one SCEVConstant for any
171 // particular value. Don't use a SCEVHandle here, or else the object will
173 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
176 SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
180 SCEVHandle SCEVConstant::get(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
186 ConstantRange SCEVConstant::getValueRange() const {
187 return ConstantRange(V->getValue());
190 const Type *SCEVConstant::getType() const { return V->getType(); }
192 void SCEVConstant::print(std::ostream &OS) const {
193 WriteAsOperand(OS, V, false);
196 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
197 // particular input. Don't use a SCEVHandle here, or else the object will
199 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
200 SCEVTruncateExpr*> > SCEVTruncates;
202 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
203 : SCEV(scTruncate), Op(op), Ty(ty) {
204 assert(Op->getType()->isInteger() && Ty->isInteger() &&
205 "Cannot truncate non-integer value!");
206 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
207 && "This is not a truncating conversion!");
210 SCEVTruncateExpr::~SCEVTruncateExpr() {
211 SCEVTruncates->erase(std::make_pair(Op, Ty));
214 ConstantRange SCEVTruncateExpr::getValueRange() const {
215 return getOperand()->getValueRange().truncate(getBitWidth());
218 void SCEVTruncateExpr::print(std::ostream &OS) const {
219 OS << "(truncate " << *Op << " to " << *Ty << ")";
222 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
223 // particular input. Don't use a SCEVHandle here, or else the object will never
225 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
226 SCEVZeroExtendExpr*> > SCEVZeroExtends;
228 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
229 : SCEV(scZeroExtend), Op(op), Ty(ty) {
230 assert(Op->getType()->isInteger() && Ty->isInteger() &&
231 "Cannot zero extend non-integer value!");
232 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
233 && "This is not an extending conversion!");
236 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
237 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
240 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
241 return getOperand()->getValueRange().zeroExtend(getBitWidth());
244 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
245 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
248 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
249 // particular input. Don't use a SCEVHandle here, or else the object will never
251 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
252 SCEVCommutativeExpr*> > SCEVCommExprs;
254 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
255 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
256 std::vector<SCEV*>(Operands.begin(),
260 void SCEVCommutativeExpr::print(std::ostream &OS) const {
261 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
262 const char *OpStr = getOperationStr();
263 OS << "(" << *Operands[0];
264 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
265 OS << OpStr << *Operands[i];
269 SCEVHandle SCEVCommutativeExpr::
270 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
271 const SCEVHandle &Conc) const {
272 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
273 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
274 if (H != getOperand(i)) {
275 std::vector<SCEVHandle> NewOps;
276 NewOps.reserve(getNumOperands());
277 for (unsigned j = 0; j != i; ++j)
278 NewOps.push_back(getOperand(j));
280 for (++i; i != e; ++i)
281 NewOps.push_back(getOperand(i)->
282 replaceSymbolicValuesWithConcrete(Sym, Conc));
284 if (isa<SCEVAddExpr>(this))
285 return SCEVAddExpr::get(NewOps);
286 else if (isa<SCEVMulExpr>(this))
287 return SCEVMulExpr::get(NewOps);
289 assert(0 && "Unknown commutative expr!");
296 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
297 // input. Don't use a SCEVHandle here, or else the object will never be
299 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
300 SCEVSDivExpr*> > SCEVSDivs;
302 SCEVSDivExpr::~SCEVSDivExpr() {
303 SCEVSDivs->erase(std::make_pair(LHS, RHS));
306 void SCEVSDivExpr::print(std::ostream &OS) const {
307 OS << "(" << *LHS << " /s " << *RHS << ")";
310 const Type *SCEVSDivExpr::getType() const {
311 return LHS->getType();
314 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
315 // particular input. Don't use a SCEVHandle here, or else the object will never
317 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
318 SCEVAddRecExpr*> > SCEVAddRecExprs;
320 SCEVAddRecExpr::~SCEVAddRecExpr() {
321 SCEVAddRecExprs->erase(std::make_pair(L,
322 std::vector<SCEV*>(Operands.begin(),
326 SCEVHandle SCEVAddRecExpr::
327 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
328 const SCEVHandle &Conc) const {
329 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
330 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
331 if (H != getOperand(i)) {
332 std::vector<SCEVHandle> NewOps;
333 NewOps.reserve(getNumOperands());
334 for (unsigned j = 0; j != i; ++j)
335 NewOps.push_back(getOperand(j));
337 for (++i; i != e; ++i)
338 NewOps.push_back(getOperand(i)->
339 replaceSymbolicValuesWithConcrete(Sym, Conc));
341 return get(NewOps, L);
348 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
349 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
350 // contain L and if the start is invariant.
351 return !QueryLoop->contains(L->getHeader()) &&
352 getOperand(0)->isLoopInvariant(QueryLoop);
356 void SCEVAddRecExpr::print(std::ostream &OS) const {
357 OS << "{" << *Operands[0];
358 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
359 OS << ",+," << *Operands[i];
360 OS << "}<" << L->getHeader()->getName() + ">";
363 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
364 // value. Don't use a SCEVHandle here, or else the object will never be
366 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
368 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
370 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
371 // All non-instruction values are loop invariant. All instructions are loop
372 // invariant if they are not contained in the specified loop.
373 if (Instruction *I = dyn_cast<Instruction>(V))
374 return !L->contains(I->getParent());
378 const Type *SCEVUnknown::getType() const {
382 void SCEVUnknown::print(std::ostream &OS) const {
383 WriteAsOperand(OS, V, false);
386 //===----------------------------------------------------------------------===//
388 //===----------------------------------------------------------------------===//
391 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
392 /// than the complexity of the RHS. This comparator is used to canonicalize
394 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
395 bool operator()(SCEV *LHS, SCEV *RHS) {
396 return LHS->getSCEVType() < RHS->getSCEVType();
401 /// GroupByComplexity - Given a list of SCEV objects, order them by their
402 /// complexity, and group objects of the same complexity together by value.
403 /// When this routine is finished, we know that any duplicates in the vector are
404 /// consecutive and that complexity is monotonically increasing.
406 /// Note that we go take special precautions to ensure that we get determinstic
407 /// results from this routine. In other words, we don't want the results of
408 /// this to depend on where the addresses of various SCEV objects happened to
411 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
412 if (Ops.size() < 2) return; // Noop
413 if (Ops.size() == 2) {
414 // This is the common case, which also happens to be trivially simple.
416 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
417 std::swap(Ops[0], Ops[1]);
421 // Do the rough sort by complexity.
422 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
424 // Now that we are sorted by complexity, group elements of the same
425 // complexity. Note that this is, at worst, N^2, but the vector is likely to
426 // be extremely short in practice. Note that we take this approach because we
427 // do not want to depend on the addresses of the objects we are grouping.
428 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
430 unsigned Complexity = S->getSCEVType();
432 // If there are any objects of the same complexity and same value as this
434 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
435 if (Ops[j] == S) { // Found a duplicate.
436 // Move it to immediately after i'th element.
437 std::swap(Ops[i+1], Ops[j]);
438 ++i; // no need to rescan it.
439 if (i == e-2) return; // Done!
447 //===----------------------------------------------------------------------===//
448 // Simple SCEV method implementations
449 //===----------------------------------------------------------------------===//
451 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
452 /// specified signed integer value and return a SCEV for the constant.
453 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
456 C = Constant::getNullValue(Ty);
457 else if (Ty->isFloatingPoint())
458 C = ConstantFP::get(Ty, Val);
460 C = ConstantInt::get(Ty, Val);
461 return SCEVUnknown::get(C);
464 SCEVHandle SCEVUnknown::getIntegerSCEV(const APInt& Val) {
465 return SCEVUnknown::get(ConstantInt::get(Val));
468 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
469 /// input value to the specified type. If the type must be extended, it is zero
471 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
472 const Type *SrcTy = V->getType();
473 assert(SrcTy->isInteger() && Ty->isInteger() &&
474 "Cannot truncate or zero extend with non-integer arguments!");
475 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
476 return V; // No conversion
477 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
478 return SCEVTruncateExpr::get(V, Ty);
479 return SCEVZeroExtendExpr::get(V, Ty);
482 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
484 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
485 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
486 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
488 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
491 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
493 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
495 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
499 /// PartialFact - Compute V!/(V-NumSteps)!
500 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
501 // Handle this case efficiently, it is common to have constant iteration
502 // counts while computing loop exit values.
503 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
504 const APInt& Val = SC->getValue()->getValue();
505 APInt Result(Val.getBitWidth(), 1);
506 for (; NumSteps; --NumSteps)
507 Result *= Val-(NumSteps-1);
508 return SCEVUnknown::get(ConstantInt::get(Result));
511 const Type *Ty = V->getType();
513 return SCEVUnknown::getIntegerSCEV(1, Ty);
515 SCEVHandle Result = V;
516 for (unsigned i = 1; i != NumSteps; ++i)
517 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
518 SCEVUnknown::getIntegerSCEV(i, Ty)));
523 /// evaluateAtIteration - Return the value of this chain of recurrences at
524 /// the specified iteration number. We can evaluate this recurrence by
525 /// multiplying each element in the chain by the binomial coefficient
526 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
528 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
530 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
531 /// Is the binomial equation safe using modular arithmetic??
533 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
534 SCEVHandle Result = getStart();
536 const Type *Ty = It->getType();
537 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
538 SCEVHandle BC = PartialFact(It, i);
540 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
541 SCEVUnknown::getIntegerSCEV(Divisor,Ty));
542 Result = SCEVAddExpr::get(Result, Val);
548 //===----------------------------------------------------------------------===//
549 // SCEV Expression folder implementations
550 //===----------------------------------------------------------------------===//
552 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
553 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
554 return SCEVUnknown::get(
555 ConstantExpr::getTrunc(SC->getValue(), Ty));
557 // If the input value is a chrec scev made out of constants, truncate
558 // all of the constants.
559 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
560 std::vector<SCEVHandle> Operands;
561 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
562 // FIXME: This should allow truncation of other expression types!
563 if (isa<SCEVConstant>(AddRec->getOperand(i)))
564 Operands.push_back(get(AddRec->getOperand(i), Ty));
567 if (Operands.size() == AddRec->getNumOperands())
568 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
571 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
572 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
576 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
577 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
578 return SCEVUnknown::get(
579 ConstantExpr::getZExt(SC->getValue(), Ty));
581 // FIXME: If the input value is a chrec scev, and we can prove that the value
582 // did not overflow the old, smaller, value, we can zero extend all of the
583 // operands (often constants). This would allow analysis of something like
584 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
586 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
587 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
591 // get - Get a canonical add expression, or something simpler if possible.
592 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
593 assert(!Ops.empty() && "Cannot get empty add!");
594 if (Ops.size() == 1) return Ops[0];
596 // Sort by complexity, this groups all similar expression types together.
597 GroupByComplexity(Ops);
599 // If there are any constants, fold them together.
601 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
603 assert(Idx < Ops.size());
604 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
605 // We found two constants, fold them together!
606 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
607 RHSC->getValue()->getValue());
608 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
609 Ops[0] = SCEVConstant::get(CI);
610 Ops.erase(Ops.begin()+1); // Erase the folded element
611 if (Ops.size() == 1) return Ops[0];
612 LHSC = cast<SCEVConstant>(Ops[0]);
614 // If we couldn't fold the expression, move to the next constant. Note
615 // that this is impossible to happen in practice because we always
616 // constant fold constant ints to constant ints.
621 // If we are left with a constant zero being added, strip it off.
622 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
623 Ops.erase(Ops.begin());
628 if (Ops.size() == 1) return Ops[0];
630 // Okay, check to see if the same value occurs in the operand list twice. If
631 // so, merge them together into an multiply expression. Since we sorted the
632 // list, these values are required to be adjacent.
633 const Type *Ty = Ops[0]->getType();
634 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
635 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
636 // Found a match, merge the two values into a multiply, and add any
637 // remaining values to the result.
638 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
639 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
642 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
644 return SCEVAddExpr::get(Ops);
647 // Okay, now we know the first non-constant operand. If there are add
648 // operands they would be next.
649 if (Idx < Ops.size()) {
650 bool DeletedAdd = false;
651 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
652 // If we have an add, expand the add operands onto the end of the operands
654 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
655 Ops.erase(Ops.begin()+Idx);
659 // If we deleted at least one add, we added operands to the end of the list,
660 // and they are not necessarily sorted. Recurse to resort and resimplify
661 // any operands we just aquired.
666 // Skip over the add expression until we get to a multiply.
667 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
670 // If we are adding something to a multiply expression, make sure the
671 // something is not already an operand of the multiply. If so, merge it into
673 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
674 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
675 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
676 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
677 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
678 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
679 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
680 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
681 if (Mul->getNumOperands() != 2) {
682 // If the multiply has more than two operands, we must get the
684 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
685 MulOps.erase(MulOps.begin()+MulOp);
686 InnerMul = SCEVMulExpr::get(MulOps);
688 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
689 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
690 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
691 if (Ops.size() == 2) return OuterMul;
693 Ops.erase(Ops.begin()+AddOp);
694 Ops.erase(Ops.begin()+Idx-1);
696 Ops.erase(Ops.begin()+Idx);
697 Ops.erase(Ops.begin()+AddOp-1);
699 Ops.push_back(OuterMul);
700 return SCEVAddExpr::get(Ops);
703 // Check this multiply against other multiplies being added together.
704 for (unsigned OtherMulIdx = Idx+1;
705 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
707 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
708 // If MulOp occurs in OtherMul, we can fold the two multiplies
710 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
711 OMulOp != e; ++OMulOp)
712 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
713 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
714 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
715 if (Mul->getNumOperands() != 2) {
716 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
717 MulOps.erase(MulOps.begin()+MulOp);
718 InnerMul1 = SCEVMulExpr::get(MulOps);
720 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
721 if (OtherMul->getNumOperands() != 2) {
722 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
724 MulOps.erase(MulOps.begin()+OMulOp);
725 InnerMul2 = SCEVMulExpr::get(MulOps);
727 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
728 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
729 if (Ops.size() == 2) return OuterMul;
730 Ops.erase(Ops.begin()+Idx);
731 Ops.erase(Ops.begin()+OtherMulIdx-1);
732 Ops.push_back(OuterMul);
733 return SCEVAddExpr::get(Ops);
739 // If there are any add recurrences in the operands list, see if any other
740 // added values are loop invariant. If so, we can fold them into the
742 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
745 // Scan over all recurrences, trying to fold loop invariants into them.
746 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
747 // Scan all of the other operands to this add and add them to the vector if
748 // they are loop invariant w.r.t. the recurrence.
749 std::vector<SCEVHandle> LIOps;
750 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
751 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
752 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
753 LIOps.push_back(Ops[i]);
754 Ops.erase(Ops.begin()+i);
758 // If we found some loop invariants, fold them into the recurrence.
759 if (!LIOps.empty()) {
760 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
761 LIOps.push_back(AddRec->getStart());
763 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
764 AddRecOps[0] = SCEVAddExpr::get(LIOps);
766 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
767 // If all of the other operands were loop invariant, we are done.
768 if (Ops.size() == 1) return NewRec;
770 // Otherwise, add the folded AddRec by the non-liv parts.
771 for (unsigned i = 0;; ++i)
772 if (Ops[i] == AddRec) {
776 return SCEVAddExpr::get(Ops);
779 // Okay, if there weren't any loop invariants to be folded, check to see if
780 // there are multiple AddRec's with the same loop induction variable being
781 // added together. If so, we can fold them.
782 for (unsigned OtherIdx = Idx+1;
783 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
784 if (OtherIdx != Idx) {
785 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
786 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
787 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
788 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
789 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
790 if (i >= NewOps.size()) {
791 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
792 OtherAddRec->op_end());
795 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
797 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
799 if (Ops.size() == 2) return NewAddRec;
801 Ops.erase(Ops.begin()+Idx);
802 Ops.erase(Ops.begin()+OtherIdx-1);
803 Ops.push_back(NewAddRec);
804 return SCEVAddExpr::get(Ops);
808 // Otherwise couldn't fold anything into this recurrence. Move onto the
812 // Okay, it looks like we really DO need an add expr. Check to see if we
813 // already have one, otherwise create a new one.
814 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
815 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
817 if (Result == 0) Result = new SCEVAddExpr(Ops);
822 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
823 assert(!Ops.empty() && "Cannot get empty mul!");
825 // Sort by complexity, this groups all similar expression types together.
826 GroupByComplexity(Ops);
828 // If there are any constants, fold them together.
830 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
832 // C1*(C2+V) -> C1*C2 + C1*V
834 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
835 if (Add->getNumOperands() == 2 &&
836 isa<SCEVConstant>(Add->getOperand(0)))
837 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
838 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
842 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
843 // We found two constants, fold them together!
844 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
845 RHSC->getValue()->getValue());
846 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
847 Ops[0] = SCEVConstant::get(CI);
848 Ops.erase(Ops.begin()+1); // Erase the folded element
849 if (Ops.size() == 1) return Ops[0];
850 LHSC = cast<SCEVConstant>(Ops[0]);
852 // If we couldn't fold the expression, move to the next constant. Note
853 // that this is impossible to happen in practice because we always
854 // constant fold constant ints to constant ints.
859 // If we are left with a constant one being multiplied, strip it off.
860 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
861 Ops.erase(Ops.begin());
863 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
864 // If we have a multiply of zero, it will always be zero.
869 // Skip over the add expression until we get to a multiply.
870 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
876 // If there are mul operands inline them all into this expression.
877 if (Idx < Ops.size()) {
878 bool DeletedMul = false;
879 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
880 // If we have an mul, expand the mul operands onto the end of the operands
882 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
883 Ops.erase(Ops.begin()+Idx);
887 // If we deleted at least one mul, we added operands to the end of the list,
888 // and they are not necessarily sorted. Recurse to resort and resimplify
889 // any operands we just aquired.
894 // If there are any add recurrences in the operands list, see if any other
895 // added values are loop invariant. If so, we can fold them into the
897 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
900 // Scan over all recurrences, trying to fold loop invariants into them.
901 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
902 // Scan all of the other operands to this mul and add them to the vector if
903 // they are loop invariant w.r.t. the recurrence.
904 std::vector<SCEVHandle> LIOps;
905 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
906 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
907 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
908 LIOps.push_back(Ops[i]);
909 Ops.erase(Ops.begin()+i);
913 // If we found some loop invariants, fold them into the recurrence.
914 if (!LIOps.empty()) {
915 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
916 std::vector<SCEVHandle> NewOps;
917 NewOps.reserve(AddRec->getNumOperands());
918 if (LIOps.size() == 1) {
919 SCEV *Scale = LIOps[0];
920 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
921 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
923 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
924 std::vector<SCEVHandle> MulOps(LIOps);
925 MulOps.push_back(AddRec->getOperand(i));
926 NewOps.push_back(SCEVMulExpr::get(MulOps));
930 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
932 // If all of the other operands were loop invariant, we are done.
933 if (Ops.size() == 1) return NewRec;
935 // Otherwise, multiply the folded AddRec by the non-liv parts.
936 for (unsigned i = 0;; ++i)
937 if (Ops[i] == AddRec) {
941 return SCEVMulExpr::get(Ops);
944 // Okay, if there weren't any loop invariants to be folded, check to see if
945 // there are multiple AddRec's with the same loop induction variable being
946 // multiplied together. If so, we can fold them.
947 for (unsigned OtherIdx = Idx+1;
948 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
949 if (OtherIdx != Idx) {
950 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
951 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
952 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
953 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
954 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
956 SCEVHandle B = F->getStepRecurrence();
957 SCEVHandle D = G->getStepRecurrence();
958 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
959 SCEVMulExpr::get(G, B),
960 SCEVMulExpr::get(B, D));
961 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
963 if (Ops.size() == 2) return NewAddRec;
965 Ops.erase(Ops.begin()+Idx);
966 Ops.erase(Ops.begin()+OtherIdx-1);
967 Ops.push_back(NewAddRec);
968 return SCEVMulExpr::get(Ops);
972 // Otherwise couldn't fold anything into this recurrence. Move onto the
976 // Okay, it looks like we really DO need an mul expr. Check to see if we
977 // already have one, otherwise create a new one.
978 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
979 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
982 Result = new SCEVMulExpr(Ops);
986 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
987 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
988 if (RHSC->getValue()->equalsInt(1))
989 return LHS; // X sdiv 1 --> x
990 if (RHSC->getValue()->isAllOnesValue())
991 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
993 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
994 Constant *LHSCV = LHSC->getValue();
995 Constant *RHSCV = RHSC->getValue();
996 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
1000 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1002 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
1003 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
1008 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1009 /// specified loop. Simplify the expression as much as possible.
1010 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
1011 const SCEVHandle &Step, const Loop *L) {
1012 std::vector<SCEVHandle> Operands;
1013 Operands.push_back(Start);
1014 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1015 if (StepChrec->getLoop() == L) {
1016 Operands.insert(Operands.end(), StepChrec->op_begin(),
1017 StepChrec->op_end());
1018 return get(Operands, L);
1021 Operands.push_back(Step);
1022 return get(Operands, L);
1025 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1026 /// specified loop. Simplify the expression as much as possible.
1027 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1029 if (Operands.size() == 1) return Operands[0];
1031 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1032 if (StepC->getValue()->isZero()) {
1033 Operands.pop_back();
1034 return get(Operands, L); // { X,+,0 } --> X
1037 SCEVAddRecExpr *&Result =
1038 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1040 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1044 SCEVHandle SCEVUnknown::get(Value *V) {
1045 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1046 return SCEVConstant::get(CI);
1047 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1048 if (Result == 0) Result = new SCEVUnknown(V);
1053 //===----------------------------------------------------------------------===//
1054 // ScalarEvolutionsImpl Definition and Implementation
1055 //===----------------------------------------------------------------------===//
1057 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1061 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1062 /// F - The function we are analyzing.
1066 /// LI - The loop information for the function we are currently analyzing.
1070 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1072 SCEVHandle UnknownValue;
1074 /// Scalars - This is a cache of the scalars we have analyzed so far.
1076 std::map<Value*, SCEVHandle> Scalars;
1078 /// IterationCounts - Cache the iteration count of the loops for this
1079 /// function as they are computed.
1080 std::map<const Loop*, SCEVHandle> IterationCounts;
1082 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1083 /// the PHI instructions that we attempt to compute constant evolutions for.
1084 /// This allows us to avoid potentially expensive recomputation of these
1085 /// properties. An instruction maps to null if we are unable to compute its
1087 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1090 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1091 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1093 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1094 /// expression and create a new one.
1095 SCEVHandle getSCEV(Value *V);
1097 /// hasSCEV - Return true if the SCEV for this value has already been
1099 bool hasSCEV(Value *V) const {
1100 return Scalars.count(V);
1103 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1104 /// the specified value.
1105 void setSCEV(Value *V, const SCEVHandle &H) {
1106 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1107 assert(isNew && "This entry already existed!");
1111 /// getSCEVAtScope - Compute the value of the specified expression within
1112 /// the indicated loop (which may be null to indicate in no loop). If the
1113 /// expression cannot be evaluated, return UnknownValue itself.
1114 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1117 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1118 /// an analyzable loop-invariant iteration count.
1119 bool hasLoopInvariantIterationCount(const Loop *L);
1121 /// getIterationCount - If the specified loop has a predictable iteration
1122 /// count, return it. Note that it is not valid to call this method on a
1123 /// loop without a loop-invariant iteration count.
1124 SCEVHandle getIterationCount(const Loop *L);
1126 /// deleteInstructionFromRecords - This method should be called by the
1127 /// client before it removes an instruction from the program, to make sure
1128 /// that no dangling references are left around.
1129 void deleteInstructionFromRecords(Instruction *I);
1132 /// createSCEV - We know that there is no SCEV for the specified value.
1133 /// Analyze the expression.
1134 SCEVHandle createSCEV(Value *V);
1136 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1138 SCEVHandle createNodeForPHI(PHINode *PN);
1140 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1141 /// for the specified instruction and replaces any references to the
1142 /// symbolic value SymName with the specified value. This is used during
1144 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1145 const SCEVHandle &SymName,
1146 const SCEVHandle &NewVal);
1148 /// ComputeIterationCount - Compute the number of times the specified loop
1150 SCEVHandle ComputeIterationCount(const Loop *L);
1152 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1153 /// 'setcc load X, cst', try to see if we can compute the trip count.
1154 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1157 ICmpInst::Predicate p);
1159 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1160 /// constant number of times (the condition evolves only from constants),
1161 /// try to evaluate a few iterations of the loop until we get the exit
1162 /// condition gets a value of ExitWhen (true or false). If we cannot
1163 /// evaluate the trip count of the loop, return UnknownValue.
1164 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1167 /// HowFarToZero - Return the number of times a backedge comparing the
1168 /// specified value to zero will execute. If not computable, return
1170 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1172 /// HowFarToNonZero - Return the number of times a backedge checking the
1173 /// specified value for nonzero will execute. If not computable, return
1175 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1177 /// HowManyLessThans - Return the number of times a backedge containing the
1178 /// specified less-than comparison will execute. If not computable, return
1180 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
1182 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1183 /// in the header of its containing loop, we know the loop executes a
1184 /// constant number of times, and the PHI node is just a recurrence
1185 /// involving constants, fold it.
1186 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1191 //===----------------------------------------------------------------------===//
1192 // Basic SCEV Analysis and PHI Idiom Recognition Code
1195 /// deleteInstructionFromRecords - This method should be called by the
1196 /// client before it removes an instruction from the program, to make sure
1197 /// that no dangling references are left around.
1198 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
1200 if (PHINode *PN = dyn_cast<PHINode>(I))
1201 ConstantEvolutionLoopExitValue.erase(PN);
1205 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1206 /// expression and create a new one.
1207 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1208 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1210 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1211 if (I != Scalars.end()) return I->second;
1212 SCEVHandle S = createSCEV(V);
1213 Scalars.insert(std::make_pair(V, S));
1217 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1218 /// the specified instruction and replaces any references to the symbolic value
1219 /// SymName with the specified value. This is used during PHI resolution.
1220 void ScalarEvolutionsImpl::
1221 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1222 const SCEVHandle &NewVal) {
1223 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1224 if (SI == Scalars.end()) return;
1227 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1228 if (NV == SI->second) return; // No change.
1230 SI->second = NV; // Update the scalars map!
1232 // Any instruction values that use this instruction might also need to be
1234 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1236 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1239 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1240 /// a loop header, making it a potential recurrence, or it doesn't.
1242 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1243 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1244 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1245 if (L->getHeader() == PN->getParent()) {
1246 // If it lives in the loop header, it has two incoming values, one
1247 // from outside the loop, and one from inside.
1248 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1249 unsigned BackEdge = IncomingEdge^1;
1251 // While we are analyzing this PHI node, handle its value symbolically.
1252 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1253 assert(Scalars.find(PN) == Scalars.end() &&
1254 "PHI node already processed?");
1255 Scalars.insert(std::make_pair(PN, SymbolicName));
1257 // Using this symbolic name for the PHI, analyze the value coming around
1259 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1261 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1262 // has a special value for the first iteration of the loop.
1264 // If the value coming around the backedge is an add with the symbolic
1265 // value we just inserted, then we found a simple induction variable!
1266 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1267 // If there is a single occurrence of the symbolic value, replace it
1268 // with a recurrence.
1269 unsigned FoundIndex = Add->getNumOperands();
1270 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1271 if (Add->getOperand(i) == SymbolicName)
1272 if (FoundIndex == e) {
1277 if (FoundIndex != Add->getNumOperands()) {
1278 // Create an add with everything but the specified operand.
1279 std::vector<SCEVHandle> Ops;
1280 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1281 if (i != FoundIndex)
1282 Ops.push_back(Add->getOperand(i));
1283 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1285 // This is not a valid addrec if the step amount is varying each
1286 // loop iteration, but is not itself an addrec in this loop.
1287 if (Accum->isLoopInvariant(L) ||
1288 (isa<SCEVAddRecExpr>(Accum) &&
1289 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1290 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1291 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1293 // Okay, for the entire analysis of this edge we assumed the PHI
1294 // to be symbolic. We now need to go back and update all of the
1295 // entries for the scalars that use the PHI (except for the PHI
1296 // itself) to use the new analyzed value instead of the "symbolic"
1298 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1302 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1303 // Otherwise, this could be a loop like this:
1304 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1305 // In this case, j = {1,+,1} and BEValue is j.
1306 // Because the other in-value of i (0) fits the evolution of BEValue
1307 // i really is an addrec evolution.
1308 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1309 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1311 // If StartVal = j.start - j.stride, we can use StartVal as the
1312 // initial step of the addrec evolution.
1313 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1314 AddRec->getOperand(1))) {
1315 SCEVHandle PHISCEV =
1316 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1318 // Okay, for the entire analysis of this edge we assumed the PHI
1319 // to be symbolic. We now need to go back and update all of the
1320 // entries for the scalars that use the PHI (except for the PHI
1321 // itself) to use the new analyzed value instead of the "symbolic"
1323 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1329 return SymbolicName;
1332 // If it's not a loop phi, we can't handle it yet.
1333 return SCEVUnknown::get(PN);
1336 /// GetConstantFactor - Determine the largest constant factor that S has. For
1337 /// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
1338 static APInt GetConstantFactor(SCEVHandle S) {
1339 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
1340 const APInt& V = C->getValue()->getValue();
1341 if (!V.isMinValue())
1343 else // Zero is a multiple of everything.
1344 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1);
1347 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) {
1348 return GetConstantFactor(T->getOperand()).trunc(
1349 cast<IntegerType>(T->getType())->getBitWidth());
1351 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
1352 return GetConstantFactor(E->getOperand()).zext(
1353 cast<IntegerType>(E->getType())->getBitWidth());
1355 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1356 // The result is the min of all operands.
1357 APInt Res(GetConstantFactor(A->getOperand(0)));
1358 for (unsigned i = 1, e = A->getNumOperands();
1359 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) {
1360 APInt Tmp(GetConstantFactor(A->getOperand(i)));
1361 Res = APIntOps::umin(Res, Tmp);
1366 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1367 // The result is the product of all the operands.
1368 APInt Res(GetConstantFactor(M->getOperand(0)));
1369 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) {
1370 APInt Tmp(GetConstantFactor(M->getOperand(i)));
1376 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1377 // For now, we just handle linear expressions.
1378 if (A->getNumOperands() == 2) {
1379 // We want the GCD between the start and the stride value.
1380 APInt Start(GetConstantFactor(A->getOperand(0)));
1383 APInt Stride(GetConstantFactor(A->getOperand(1)));
1384 return APIntOps::GreatestCommonDivisor(Start, Stride);
1388 // SCEVSDivExpr, SCEVUnknown.
1389 return APInt(S->getBitWidth(), 1);
1392 /// createSCEV - We know that there is no SCEV for the specified value.
1393 /// Analyze the expression.
1395 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1396 if (Instruction *I = dyn_cast<Instruction>(V)) {
1397 switch (I->getOpcode()) {
1398 case Instruction::Add:
1399 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1400 getSCEV(I->getOperand(1)));
1401 case Instruction::Mul:
1402 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1403 getSCEV(I->getOperand(1)));
1404 case Instruction::SDiv:
1405 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1406 getSCEV(I->getOperand(1)));
1409 case Instruction::Sub:
1410 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1411 getSCEV(I->getOperand(1)));
1412 case Instruction::Or:
1413 // If the RHS of the Or is a constant, we may have something like:
1414 // X*4+1 which got turned into X*4|1. Handle this as an add so loop
1415 // optimizations will transparently handle this case.
1416 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1417 SCEVHandle LHS = getSCEV(I->getOperand(0));
1418 APInt CommonFact(GetConstantFactor(LHS));
1419 assert(!CommonFact.isMinValue() &&
1420 "Common factor should at least be 1!");
1421 if (CommonFact.ugt(CI->getValue())) {
1422 // If the LHS is a multiple that is larger than the RHS, use +.
1423 return SCEVAddExpr::get(LHS,
1424 getSCEV(I->getOperand(1)));
1428 case Instruction::Xor:
1429 // If the RHS of the xor is a signbit, then this is just an add.
1430 // Instcombine turns add of signbit into xor as a strength reduction step.
1431 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1432 if (CI->getValue().isSignBit())
1433 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1434 getSCEV(I->getOperand(1)));
1438 case Instruction::Shl:
1439 // Turn shift left of a constant amount into a multiply.
1440 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1441 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1442 Constant *X = ConstantInt::get(
1443 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1444 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1448 case Instruction::Trunc:
1449 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
1451 case Instruction::ZExt:
1452 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1454 case Instruction::BitCast:
1455 // BitCasts are no-op casts so we just eliminate the cast.
1456 if (I->getType()->isInteger() &&
1457 I->getOperand(0)->getType()->isInteger())
1458 return getSCEV(I->getOperand(0));
1461 case Instruction::PHI:
1462 return createNodeForPHI(cast<PHINode>(I));
1464 default: // We cannot analyze this expression.
1469 return SCEVUnknown::get(V);
1474 //===----------------------------------------------------------------------===//
1475 // Iteration Count Computation Code
1478 /// getIterationCount - If the specified loop has a predictable iteration
1479 /// count, return it. Note that it is not valid to call this method on a
1480 /// loop without a loop-invariant iteration count.
1481 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1482 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1483 if (I == IterationCounts.end()) {
1484 SCEVHandle ItCount = ComputeIterationCount(L);
1485 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1486 if (ItCount != UnknownValue) {
1487 assert(ItCount->isLoopInvariant(L) &&
1488 "Computed trip count isn't loop invariant for loop!");
1489 ++NumTripCountsComputed;
1490 } else if (isa<PHINode>(L->getHeader()->begin())) {
1491 // Only count loops that have phi nodes as not being computable.
1492 ++NumTripCountsNotComputed;
1498 /// ComputeIterationCount - Compute the number of times the specified loop
1500 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1501 // If the loop has a non-one exit block count, we can't analyze it.
1502 std::vector<BasicBlock*> ExitBlocks;
1503 L->getExitBlocks(ExitBlocks);
1504 if (ExitBlocks.size() != 1) return UnknownValue;
1506 // Okay, there is one exit block. Try to find the condition that causes the
1507 // loop to be exited.
1508 BasicBlock *ExitBlock = ExitBlocks[0];
1510 BasicBlock *ExitingBlock = 0;
1511 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1513 if (L->contains(*PI)) {
1514 if (ExitingBlock == 0)
1517 return UnknownValue; // More than one block exiting!
1519 assert(ExitingBlock && "No exits from loop, something is broken!");
1521 // Okay, we've computed the exiting block. See what condition causes us to
1524 // FIXME: we should be able to handle switch instructions (with a single exit)
1525 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1526 if (ExitBr == 0) return UnknownValue;
1527 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1529 // At this point, we know we have a conditional branch that determines whether
1530 // the loop is exited. However, we don't know if the branch is executed each
1531 // time through the loop. If not, then the execution count of the branch will
1532 // not be equal to the trip count of the loop.
1534 // Currently we check for this by checking to see if the Exit branch goes to
1535 // the loop header. If so, we know it will always execute the same number of
1536 // times as the loop. We also handle the case where the exit block *is* the
1537 // loop header. This is common for un-rotated loops. More extensive analysis
1538 // could be done to handle more cases here.
1539 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1540 ExitBr->getSuccessor(1) != L->getHeader() &&
1541 ExitBr->getParent() != L->getHeader())
1542 return UnknownValue;
1544 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1546 // If its not an integer comparison then compute it the hard way.
1547 // Note that ICmpInst deals with pointer comparisons too so we must check
1548 // the type of the operand.
1549 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1550 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1551 ExitBr->getSuccessor(0) == ExitBlock);
1553 // If the condition was exit on true, convert the condition to exit on false
1554 ICmpInst::Predicate Cond;
1555 if (ExitBr->getSuccessor(1) == ExitBlock)
1556 Cond = ExitCond->getPredicate();
1558 Cond = ExitCond->getInversePredicate();
1560 // Handle common loops like: for (X = "string"; *X; ++X)
1561 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1562 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1564 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1565 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1568 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1569 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1571 // Try to evaluate any dependencies out of the loop.
1572 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1573 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1574 Tmp = getSCEVAtScope(RHS, L);
1575 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1577 // At this point, we would like to compute how many iterations of the
1578 // loop the predicate will return true for these inputs.
1579 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1580 // If there is a constant, force it into the RHS.
1581 std::swap(LHS, RHS);
1582 Cond = ICmpInst::getSwappedPredicate(Cond);
1585 // FIXME: think about handling pointer comparisons! i.e.:
1586 // while (P != P+100) ++P;
1588 // If we have a comparison of a chrec against a constant, try to use value
1589 // ranges to answer this query.
1590 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1591 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1592 if (AddRec->getLoop() == L) {
1593 // Form the comparison range using the constant of the correct type so
1594 // that the ConstantRange class knows to do a signed or unsigned
1596 ConstantInt *CompVal = RHSC->getValue();
1597 const Type *RealTy = ExitCond->getOperand(0)->getType();
1598 CompVal = dyn_cast<ConstantInt>(
1599 ConstantExpr::getBitCast(CompVal, RealTy));
1601 // Form the constant range.
1602 ConstantRange CompRange(
1603 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
1605 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
1606 false /*Always treat as unsigned range*/);
1607 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1612 case ICmpInst::ICMP_NE: { // while (X != Y)
1613 // Convert to: while (X-Y != 0)
1614 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1615 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1618 case ICmpInst::ICMP_EQ: {
1619 // Convert to: while (X-Y == 0) // while (X == Y)
1620 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1621 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1624 case ICmpInst::ICMP_SLT: {
1625 SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1626 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1629 case ICmpInst::ICMP_SGT: {
1630 SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1631 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1636 cerr << "ComputeIterationCount ";
1637 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1638 cerr << "[unsigned] ";
1640 << Instruction::getOpcodeName(Instruction::ICmp)
1641 << " " << *RHS << "\n";
1645 return ComputeIterationCountExhaustively(L, ExitCond,
1646 ExitBr->getSuccessor(0) == ExitBlock);
1649 static ConstantInt *
1650 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1651 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1652 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1653 assert(isa<SCEVConstant>(Val) &&
1654 "Evaluation of SCEV at constant didn't fold correctly?");
1655 return cast<SCEVConstant>(Val)->getValue();
1658 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1659 /// and a GEP expression (missing the pointer index) indexing into it, return
1660 /// the addressed element of the initializer or null if the index expression is
1663 GetAddressedElementFromGlobal(GlobalVariable *GV,
1664 const std::vector<ConstantInt*> &Indices) {
1665 Constant *Init = GV->getInitializer();
1666 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1667 uint64_t Idx = Indices[i]->getZExtValue();
1668 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1669 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1670 Init = cast<Constant>(CS->getOperand(Idx));
1671 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1672 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1673 Init = cast<Constant>(CA->getOperand(Idx));
1674 } else if (isa<ConstantAggregateZero>(Init)) {
1675 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1676 assert(Idx < STy->getNumElements() && "Bad struct index!");
1677 Init = Constant::getNullValue(STy->getElementType(Idx));
1678 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1679 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1680 Init = Constant::getNullValue(ATy->getElementType());
1682 assert(0 && "Unknown constant aggregate type!");
1686 return 0; // Unknown initializer type
1692 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1693 /// 'setcc load X, cst', try to se if we can compute the trip count.
1694 SCEVHandle ScalarEvolutionsImpl::
1695 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1697 ICmpInst::Predicate predicate) {
1698 if (LI->isVolatile()) return UnknownValue;
1700 // Check to see if the loaded pointer is a getelementptr of a global.
1701 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1702 if (!GEP) return UnknownValue;
1704 // Make sure that it is really a constant global we are gepping, with an
1705 // initializer, and make sure the first IDX is really 0.
1706 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1707 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1708 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1709 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1710 return UnknownValue;
1712 // Okay, we allow one non-constant index into the GEP instruction.
1714 std::vector<ConstantInt*> Indexes;
1715 unsigned VarIdxNum = 0;
1716 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1717 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1718 Indexes.push_back(CI);
1719 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1720 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1721 VarIdx = GEP->getOperand(i);
1723 Indexes.push_back(0);
1726 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1727 // Check to see if X is a loop variant variable value now.
1728 SCEVHandle Idx = getSCEV(VarIdx);
1729 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1730 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1732 // We can only recognize very limited forms of loop index expressions, in
1733 // particular, only affine AddRec's like {C1,+,C2}.
1734 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1735 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1736 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1737 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1738 return UnknownValue;
1740 unsigned MaxSteps = MaxBruteForceIterations;
1741 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1742 ConstantInt *ItCst =
1743 ConstantInt::get(IdxExpr->getType(), IterationNum);
1744 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1746 // Form the GEP offset.
1747 Indexes[VarIdxNum] = Val;
1749 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1750 if (Result == 0) break; // Cannot compute!
1752 // Evaluate the condition for this iteration.
1753 Result = ConstantExpr::getICmp(predicate, Result, RHS);
1754 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
1755 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
1757 cerr << "\n***\n*** Computed loop count " << *ItCst
1758 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1761 ++NumArrayLenItCounts;
1762 return SCEVConstant::get(ItCst); // Found terminating iteration!
1765 return UnknownValue;
1769 /// CanConstantFold - Return true if we can constant fold an instruction of the
1770 /// specified type, assuming that all operands were constants.
1771 static bool CanConstantFold(const Instruction *I) {
1772 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
1773 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1776 if (const CallInst *CI = dyn_cast<CallInst>(I))
1777 if (const Function *F = CI->getCalledFunction())
1778 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1782 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1783 /// in the loop that V is derived from. We allow arbitrary operations along the
1784 /// way, but the operands of an operation must either be constants or a value
1785 /// derived from a constant PHI. If this expression does not fit with these
1786 /// constraints, return null.
1787 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1788 // If this is not an instruction, or if this is an instruction outside of the
1789 // loop, it can't be derived from a loop PHI.
1790 Instruction *I = dyn_cast<Instruction>(V);
1791 if (I == 0 || !L->contains(I->getParent())) return 0;
1793 if (PHINode *PN = dyn_cast<PHINode>(I))
1794 if (L->getHeader() == I->getParent())
1797 // We don't currently keep track of the control flow needed to evaluate
1798 // PHIs, so we cannot handle PHIs inside of loops.
1801 // If we won't be able to constant fold this expression even if the operands
1802 // are constants, return early.
1803 if (!CanConstantFold(I)) return 0;
1805 // Otherwise, we can evaluate this instruction if all of its operands are
1806 // constant or derived from a PHI node themselves.
1808 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1809 if (!(isa<Constant>(I->getOperand(Op)) ||
1810 isa<GlobalValue>(I->getOperand(Op)))) {
1811 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1812 if (P == 0) return 0; // Not evolving from PHI
1816 return 0; // Evolving from multiple different PHIs.
1819 // This is a expression evolving from a constant PHI!
1823 /// EvaluateExpression - Given an expression that passes the
1824 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1825 /// in the loop has the value PHIVal. If we can't fold this expression for some
1826 /// reason, return null.
1827 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1828 if (isa<PHINode>(V)) return PHIVal;
1829 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1831 if (Constant *C = dyn_cast<Constant>(V)) return C;
1832 Instruction *I = cast<Instruction>(V);
1834 std::vector<Constant*> Operands;
1835 Operands.resize(I->getNumOperands());
1837 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1838 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1839 if (Operands[i] == 0) return 0;
1842 return ConstantFoldInstOperands(I, &Operands[0], Operands.size());
1845 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1846 /// in the header of its containing loop, we know the loop executes a
1847 /// constant number of times, and the PHI node is just a recurrence
1848 /// involving constants, fold it.
1849 Constant *ScalarEvolutionsImpl::
1850 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
1851 std::map<PHINode*, Constant*>::iterator I =
1852 ConstantEvolutionLoopExitValue.find(PN);
1853 if (I != ConstantEvolutionLoopExitValue.end())
1856 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
1857 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1859 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1861 // Since the loop is canonicalized, the PHI node must have two entries. One
1862 // entry must be a constant (coming in from outside of the loop), and the
1863 // second must be derived from the same PHI.
1864 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1865 Constant *StartCST =
1866 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1868 return RetVal = 0; // Must be a constant.
1870 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1871 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1873 return RetVal = 0; // Not derived from same PHI.
1875 // Execute the loop symbolically to determine the exit value.
1876 if (Its.getActiveBits() >= 32)
1877 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
1879 unsigned NumIterations = Its.getZExtValue(); // must be in range
1880 unsigned IterationNum = 0;
1881 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1882 if (IterationNum == NumIterations)
1883 return RetVal = PHIVal; // Got exit value!
1885 // Compute the value of the PHI node for the next iteration.
1886 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1887 if (NextPHI == PHIVal)
1888 return RetVal = NextPHI; // Stopped evolving!
1890 return 0; // Couldn't evaluate!
1895 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1896 /// constant number of times (the condition evolves only from constants),
1897 /// try to evaluate a few iterations of the loop until we get the exit
1898 /// condition gets a value of ExitWhen (true or false). If we cannot
1899 /// evaluate the trip count of the loop, return UnknownValue.
1900 SCEVHandle ScalarEvolutionsImpl::
1901 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1902 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1903 if (PN == 0) return UnknownValue;
1905 // Since the loop is canonicalized, the PHI node must have two entries. One
1906 // entry must be a constant (coming in from outside of the loop), and the
1907 // second must be derived from the same PHI.
1908 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1909 Constant *StartCST =
1910 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1911 if (StartCST == 0) return UnknownValue; // Must be a constant.
1913 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1914 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1915 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1917 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1918 // the loop symbolically to determine when the condition gets a value of
1920 unsigned IterationNum = 0;
1921 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1922 for (Constant *PHIVal = StartCST;
1923 IterationNum != MaxIterations; ++IterationNum) {
1924 ConstantInt *CondVal =
1925 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
1927 // Couldn't symbolically evaluate.
1928 if (!CondVal) return UnknownValue;
1930 if (CondVal->getValue() == uint64_t(ExitWhen)) {
1931 ConstantEvolutionLoopExitValue[PN] = PHIVal;
1932 ++NumBruteForceTripCountsComputed;
1933 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
1936 // Compute the value of the PHI node for the next iteration.
1937 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1938 if (NextPHI == 0 || NextPHI == PHIVal)
1939 return UnknownValue; // Couldn't evaluate or not making progress...
1943 // Too many iterations were needed to evaluate.
1944 return UnknownValue;
1947 /// getSCEVAtScope - Compute the value of the specified expression within the
1948 /// indicated loop (which may be null to indicate in no loop). If the
1949 /// expression cannot be evaluated, return UnknownValue.
1950 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1951 // FIXME: this should be turned into a virtual method on SCEV!
1953 if (isa<SCEVConstant>(V)) return V;
1955 // If this instruction is evolves from a constant-evolving PHI, compute the
1956 // exit value from the loop without using SCEVs.
1957 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1958 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1959 const Loop *LI = this->LI[I->getParent()];
1960 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
1961 if (PHINode *PN = dyn_cast<PHINode>(I))
1962 if (PN->getParent() == LI->getHeader()) {
1963 // Okay, there is no closed form solution for the PHI node. Check
1964 // to see if the loop that contains it has a known iteration count.
1965 // If so, we may be able to force computation of the exit value.
1966 SCEVHandle IterationCount = getIterationCount(LI);
1967 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1968 // Okay, we know how many times the containing loop executes. If
1969 // this is a constant evolving PHI node, get the final value at
1970 // the specified iteration number.
1971 Constant *RV = getConstantEvolutionLoopExitValue(PN,
1972 ICC->getValue()->getValue(),
1974 if (RV) return SCEVUnknown::get(RV);
1978 // Okay, this is an expression that we cannot symbolically evaluate
1979 // into a SCEV. Check to see if it's possible to symbolically evaluate
1980 // the arguments into constants, and if so, try to constant propagate the
1981 // result. This is particularly useful for computing loop exit values.
1982 if (CanConstantFold(I)) {
1983 std::vector<Constant*> Operands;
1984 Operands.reserve(I->getNumOperands());
1985 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1986 Value *Op = I->getOperand(i);
1987 if (Constant *C = dyn_cast<Constant>(Op)) {
1988 Operands.push_back(C);
1990 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1991 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1992 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
1995 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
1996 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
1997 Operands.push_back(ConstantExpr::getIntegerCast(C,
2007 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
2008 return SCEVUnknown::get(C);
2012 // This is some other type of SCEVUnknown, just return it.
2016 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2017 // Avoid performing the look-up in the common case where the specified
2018 // expression has no loop-variant portions.
2019 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2020 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2021 if (OpAtScope != Comm->getOperand(i)) {
2022 if (OpAtScope == UnknownValue) return UnknownValue;
2023 // Okay, at least one of these operands is loop variant but might be
2024 // foldable. Build a new instance of the folded commutative expression.
2025 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2026 NewOps.push_back(OpAtScope);
2028 for (++i; i != e; ++i) {
2029 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2030 if (OpAtScope == UnknownValue) return UnknownValue;
2031 NewOps.push_back(OpAtScope);
2033 if (isa<SCEVAddExpr>(Comm))
2034 return SCEVAddExpr::get(NewOps);
2035 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2036 return SCEVMulExpr::get(NewOps);
2039 // If we got here, all operands are loop invariant.
2043 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2044 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2045 if (LHS == UnknownValue) return LHS;
2046 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2047 if (RHS == UnknownValue) return RHS;
2048 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2049 return Div; // must be loop invariant
2050 return SCEVSDivExpr::get(LHS, RHS);
2053 // If this is a loop recurrence for a loop that does not contain L, then we
2054 // are dealing with the final value computed by the loop.
2055 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2056 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2057 // To evaluate this recurrence, we need to know how many times the AddRec
2058 // loop iterates. Compute this now.
2059 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2060 if (IterationCount == UnknownValue) return UnknownValue;
2061 IterationCount = getTruncateOrZeroExtend(IterationCount,
2064 // If the value is affine, simplify the expression evaluation to just
2065 // Start + Step*IterationCount.
2066 if (AddRec->isAffine())
2067 return SCEVAddExpr::get(AddRec->getStart(),
2068 SCEVMulExpr::get(IterationCount,
2069 AddRec->getOperand(1)));
2071 // Otherwise, evaluate it the hard way.
2072 return AddRec->evaluateAtIteration(IterationCount);
2074 return UnknownValue;
2077 //assert(0 && "Unknown SCEV type!");
2078 return UnknownValue;
2082 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2083 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2084 /// might be the same) or two SCEVCouldNotCompute objects.
2086 static std::pair<SCEVHandle,SCEVHandle>
2087 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2088 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2089 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2090 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2091 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2093 // We currently can only solve this if the coefficients are constants.
2094 if (!LC || !MC || !NC) {
2095 SCEV *CNC = new SCEVCouldNotCompute();
2096 return std::make_pair(CNC, CNC);
2099 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2100 const APInt &L = LC->getValue()->getValue();
2101 const APInt &M = MC->getValue()->getValue();
2102 const APInt &N = NC->getValue()->getValue();
2103 APInt Two(BitWidth, 2);
2104 APInt Four(BitWidth, 4);
2107 using namespace APIntOps;
2109 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2110 // The B coefficient is M-N/2
2114 // The A coefficient is N/2
2115 APInt A(N.sdiv(Two));
2117 // Compute the B^2-4ac term.
2120 SqrtTerm -= Four * (A * C);
2122 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2123 // integer value or else APInt::sqrt() will assert.
2124 APInt SqrtVal(SqrtTerm.sqrt());
2126 // Compute the two solutions for the quadratic formula.
2127 // The divisions must be performed as signed divisions.
2129 APInt TwoA( A << 1 );
2130 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2131 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2133 return std::make_pair(SCEVUnknown::get(Solution1),
2134 SCEVUnknown::get(Solution2));
2135 } // end APIntOps namespace
2138 /// HowFarToZero - Return the number of times a backedge comparing the specified
2139 /// value to zero will execute. If not computable, return UnknownValue
2140 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2141 // If the value is a constant
2142 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2143 // If the value is already zero, the branch will execute zero times.
2144 if (C->getValue()->isZero()) return C;
2145 return UnknownValue; // Otherwise it will loop infinitely.
2148 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2149 if (!AddRec || AddRec->getLoop() != L)
2150 return UnknownValue;
2152 if (AddRec->isAffine()) {
2153 // If this is an affine expression the execution count of this branch is
2156 // (0 - Start/Step) iff Start % Step == 0
2158 // Get the initial value for the loop.
2159 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2160 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2161 SCEVHandle Step = AddRec->getOperand(1);
2163 Step = getSCEVAtScope(Step, L->getParentLoop());
2165 // Figure out if Start % Step == 0.
2166 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2167 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2168 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2169 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2170 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2171 return Start; // 0 - Start/-1 == Start
2173 // Check to see if Start is divisible by SC with no remainder.
2174 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2175 ConstantInt *StartCC = StartC->getValue();
2176 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2177 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2178 if (Rem->isNullValue()) {
2179 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2180 return SCEVUnknown::get(Result);
2184 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2185 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2186 // the quadratic equation to solve it.
2187 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2188 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2189 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2192 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2193 << " sol#2: " << *R2 << "\n";
2195 // Pick the smallest positive root value.
2196 if (ConstantInt *CB =
2197 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2198 R1->getValue(), R2->getValue()))) {
2199 if (CB->getZExtValue() == false)
2200 std::swap(R1, R2); // R1 is the minimum root now.
2202 // We can only use this value if the chrec ends up with an exact zero
2203 // value at this index. When solving for "X*X != 5", for example, we
2204 // should not accept a root of 2.
2205 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2206 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2207 if (EvalVal->getValue()->isZero())
2208 return R1; // We found a quadratic root!
2213 return UnknownValue;
2216 /// HowFarToNonZero - Return the number of times a backedge checking the
2217 /// specified value for nonzero will execute. If not computable, return
2219 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2220 // Loops that look like: while (X == 0) are very strange indeed. We don't
2221 // handle them yet except for the trivial case. This could be expanded in the
2222 // future as needed.
2224 // If the value is a constant, check to see if it is known to be non-zero
2225 // already. If so, the backedge will execute zero times.
2226 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2227 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2229 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2230 if (NonZero == ConstantInt::getTrue())
2231 return getSCEV(Zero);
2232 return UnknownValue; // Otherwise it will loop infinitely.
2235 // We could implement others, but I really doubt anyone writes loops like
2236 // this, and if they did, they would already be constant folded.
2237 return UnknownValue;
2240 /// HowManyLessThans - Return the number of times a backedge containing the
2241 /// specified less-than comparison will execute. If not computable, return
2243 SCEVHandle ScalarEvolutionsImpl::
2244 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2245 // Only handle: "ADDREC < LoopInvariant".
2246 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2248 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2249 if (!AddRec || AddRec->getLoop() != L)
2250 return UnknownValue;
2252 if (AddRec->isAffine()) {
2253 // FORNOW: We only support unit strides.
2254 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2255 if (AddRec->getOperand(1) != One)
2256 return UnknownValue;
2258 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2259 // know that m is >= n on input to the loop. If it is, the condition return
2260 // true zero times. What we really should return, for full generality, is
2261 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2262 // canonical loop form: most do-loops will have a check that dominates the
2263 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2264 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2266 // Search for the check.
2267 BasicBlock *Preheader = L->getLoopPreheader();
2268 BasicBlock *PreheaderDest = L->getHeader();
2269 if (Preheader == 0) return UnknownValue;
2271 BranchInst *LoopEntryPredicate =
2272 dyn_cast<BranchInst>(Preheader->getTerminator());
2273 if (!LoopEntryPredicate) return UnknownValue;
2275 // This might be a critical edge broken out. If the loop preheader ends in
2276 // an unconditional branch to the loop, check to see if the preheader has a
2277 // single predecessor, and if so, look for its terminator.
2278 while (LoopEntryPredicate->isUnconditional()) {
2279 PreheaderDest = Preheader;
2280 Preheader = Preheader->getSinglePredecessor();
2281 if (!Preheader) return UnknownValue; // Multiple preds.
2283 LoopEntryPredicate =
2284 dyn_cast<BranchInst>(Preheader->getTerminator());
2285 if (!LoopEntryPredicate) return UnknownValue;
2288 // Now that we found a conditional branch that dominates the loop, check to
2289 // see if it is the comparison we are looking for.
2290 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2291 Value *PreCondLHS = ICI->getOperand(0);
2292 Value *PreCondRHS = ICI->getOperand(1);
2293 ICmpInst::Predicate Cond;
2294 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2295 Cond = ICI->getPredicate();
2297 Cond = ICI->getInversePredicate();
2300 case ICmpInst::ICMP_UGT:
2301 std::swap(PreCondLHS, PreCondRHS);
2302 Cond = ICmpInst::ICMP_ULT;
2304 case ICmpInst::ICMP_SGT:
2305 std::swap(PreCondLHS, PreCondRHS);
2306 Cond = ICmpInst::ICMP_SLT;
2311 if (Cond == ICmpInst::ICMP_SLT) {
2312 if (PreCondLHS->getType()->isInteger()) {
2313 if (RHS != getSCEV(PreCondRHS))
2314 return UnknownValue; // Not a comparison against 'm'.
2316 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2317 != getSCEV(PreCondLHS))
2318 return UnknownValue; // Not a comparison against 'n-1'.
2320 else return UnknownValue;
2321 } else if (Cond == ICmpInst::ICMP_ULT)
2322 return UnknownValue;
2324 // cerr << "Computed Loop Trip Count as: "
2325 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2326 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2329 return UnknownValue;
2332 return UnknownValue;
2335 /// getNumIterationsInRange - Return the number of iterations of this loop that
2336 /// produce values in the specified constant range. Another way of looking at
2337 /// this is that it returns the first iteration number where the value is not in
2338 /// the condition, thus computing the exit count. If the iteration count can't
2339 /// be computed, an instance of SCEVCouldNotCompute is returned.
2340 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2341 bool isSigned) const {
2342 if (Range.isFullSet()) // Infinite loop.
2343 return new SCEVCouldNotCompute();
2345 // If the start is a non-zero constant, shift the range to simplify things.
2346 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2347 if (!SC->getValue()->isZero()) {
2348 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2349 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2350 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2351 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2352 return ShiftedAddRec->getNumIterationsInRange(
2353 Range.subtract(SC->getValue()->getValue()),isSigned);
2354 // This is strange and shouldn't happen.
2355 return new SCEVCouldNotCompute();
2358 // The only time we can solve this is when we have all constant indices.
2359 // Otherwise, we cannot determine the overflow conditions.
2360 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2361 if (!isa<SCEVConstant>(getOperand(i)))
2362 return new SCEVCouldNotCompute();
2365 // Okay at this point we know that all elements of the chrec are constants and
2366 // that the start element is zero.
2368 // First check to see if the range contains zero. If not, the first
2370 if (!Range.contains(APInt(getBitWidth(),0)))
2371 return SCEVConstant::get(ConstantInt::get(getType(),0));
2374 // If this is an affine expression then we have this situation:
2375 // Solve {0,+,A} in Range === Ax in Range
2377 // Since we know that zero is in the range, we know that the upper value of
2378 // the range must be the first possible exit value. Also note that we
2379 // already checked for a full range.
2380 const APInt &Upper = Range.getUpper();
2381 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2382 APInt One(getBitWidth(),1);
2384 // The exit value should be (Upper+A-1)/A.
2385 APInt ExitVal(Upper);
2387 ExitVal = (Upper + A - One).sdiv(A);
2388 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
2390 // Evaluate at the exit value. If we really did fall out of the valid
2391 // range, then we computed our trip count, otherwise wrap around or other
2392 // things must have happened.
2393 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2394 if (Range.contains(Val->getValue()))
2395 return new SCEVCouldNotCompute(); // Something strange happened
2397 // Ensure that the previous value is in the range. This is a sanity check.
2398 assert(Range.contains(
2399 EvaluateConstantChrecAtConstant(this,
2400 ConstantInt::get(ExitVal - One))->getValue()) &&
2401 "Linear scev computation is off in a bad way!");
2402 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2403 } else if (isQuadratic()) {
2404 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2405 // quadratic equation to solve it. To do this, we must frame our problem in
2406 // terms of figuring out when zero is crossed, instead of when
2407 // Range.getUpper() is crossed.
2408 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2409 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(
2410 ConstantInt::get(Range.getUpper())));
2411 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2413 // Next, solve the constructed addrec
2414 std::pair<SCEVHandle,SCEVHandle> Roots =
2415 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2416 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2417 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2419 // Pick the smallest positive root value.
2420 if (ConstantInt *CB =
2421 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2422 R1->getValue(), R2->getValue()))) {
2423 if (CB->getZExtValue() == false)
2424 std::swap(R1, R2); // R1 is the minimum root now.
2426 // Make sure the root is not off by one. The returned iteration should
2427 // not be in the range, but the previous one should be. When solving
2428 // for "X*X < 5", for example, we should not return a root of 2.
2429 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2431 if (Range.contains(R1Val->getValue())) {
2432 // The next iteration must be out of the range...
2433 Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
2435 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2436 if (!Range.contains(R1Val->getValue()))
2437 return SCEVUnknown::get(NextVal);
2438 return new SCEVCouldNotCompute(); // Something strange happened
2441 // If R1 was not in the range, then it is a good return value. Make
2442 // sure that R1-1 WAS in the range though, just in case.
2443 Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
2444 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2445 if (Range.contains(R1Val->getValue()))
2447 return new SCEVCouldNotCompute(); // Something strange happened
2452 // Fallback, if this is a general polynomial, figure out the progression
2453 // through brute force: evaluate until we find an iteration that fails the
2454 // test. This is likely to be slow, but getting an accurate trip count is
2455 // incredibly important, we will be able to simplify the exit test a lot, and
2456 // we are almost guaranteed to get a trip count in this case.
2457 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2458 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2460 ++NumBruteForceEvaluations;
2461 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2462 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2463 return new SCEVCouldNotCompute();
2465 // Check to see if we found the value!
2466 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
2467 return SCEVConstant::get(TestVal);
2469 // Increment to test the next index.
2470 TestVal = ConstantInt::get(TestVal->getValue()+1);
2471 } while (TestVal != EndVal);
2473 return new SCEVCouldNotCompute();
2478 //===----------------------------------------------------------------------===//
2479 // ScalarEvolution Class Implementation
2480 //===----------------------------------------------------------------------===//
2482 bool ScalarEvolution::runOnFunction(Function &F) {
2483 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2487 void ScalarEvolution::releaseMemory() {
2488 delete (ScalarEvolutionsImpl*)Impl;
2492 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2493 AU.setPreservesAll();
2494 AU.addRequiredTransitive<LoopInfo>();
2497 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2498 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2501 /// hasSCEV - Return true if the SCEV for this value has already been
2503 bool ScalarEvolution::hasSCEV(Value *V) const {
2504 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2508 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2509 /// the specified value.
2510 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2511 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2515 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2516 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2519 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2520 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2523 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2524 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2527 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2528 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2531 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2533 // Print all inner loops first
2534 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2535 PrintLoopInfo(OS, SE, *I);
2537 cerr << "Loop " << L->getHeader()->getName() << ": ";
2539 std::vector<BasicBlock*> ExitBlocks;
2540 L->getExitBlocks(ExitBlocks);
2541 if (ExitBlocks.size() != 1)
2542 cerr << "<multiple exits> ";
2544 if (SE->hasLoopInvariantIterationCount(L)) {
2545 cerr << *SE->getIterationCount(L) << " iterations! ";
2547 cerr << "Unpredictable iteration count. ";
2553 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2554 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2555 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2557 OS << "Classifying expressions for: " << F.getName() << "\n";
2558 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2559 if (I->getType()->isInteger()) {
2562 SCEVHandle SV = getSCEV(&*I);
2566 if ((*I).getType()->isInteger()) {
2567 ConstantRange Bounds = SV->getValueRange();
2568 if (!Bounds.isFullSet())
2569 OS << "Bounds: " << Bounds << " ";
2572 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2574 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2575 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2576 OS << "<<Unknown>>";
2586 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2587 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2588 PrintLoopInfo(OS, this, *I);