1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by the LLVM research group and is distributed under
6 // the University of Illinois Open Source License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Assembly/Writer.h"
71 #include "llvm/Transforms/Scalar.h"
72 #include "llvm/Support/CFG.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/InstIterator.h"
77 #include "llvm/Support/ManagedStatic.h"
78 #include "llvm/Support/MathExtras.h"
79 #include "llvm/Support/Streams.h"
80 #include "llvm/ADT/Statistic.h"
86 STATISTIC(NumBruteForceEvaluations,
87 "Number of brute force evaluations needed to "
88 "calculate high-order polynomial exit values");
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant derived loop"),
105 RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis");
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
117 void SCEV::dump() const {
121 /// getValueRange - Return the tightest constant bounds that this value is
122 /// known to have. This method is only valid on integer SCEV objects.
123 ConstantRange SCEV::getValueRange() const {
124 const Type *Ty = getType();
125 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
126 // Default to a full range if no better information is available.
127 return ConstantRange(getBitWidth());
130 uint32_t SCEV::getBitWidth() const {
131 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
132 return ITy->getBitWidth();
137 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
139 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
144 const Type *SCEVCouldNotCompute::getType() const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
154 SCEVHandle SCEVCouldNotCompute::
155 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
156 const SCEVHandle &Conc) const {
160 void SCEVCouldNotCompute::print(std::ostream &OS) const {
161 OS << "***COULDNOTCOMPUTE***";
164 bool SCEVCouldNotCompute::classof(const SCEV *S) {
165 return S->getSCEVType() == scCouldNotCompute;
169 // SCEVConstants - Only allow the creation of one SCEVConstant for any
170 // particular value. Don't use a SCEVHandle here, or else the object will
172 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
175 SCEVConstant::~SCEVConstant() {
176 SCEVConstants->erase(V);
179 SCEVHandle SCEVConstant::get(ConstantInt *V) {
180 SCEVConstant *&R = (*SCEVConstants)[V];
181 if (R == 0) R = new SCEVConstant(V);
185 ConstantRange SCEVConstant::getValueRange() const {
186 return ConstantRange(V->getValue());
189 const Type *SCEVConstant::getType() const { return V->getType(); }
191 void SCEVConstant::print(std::ostream &OS) const {
192 WriteAsOperand(OS, V, false);
195 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
196 // particular input. Don't use a SCEVHandle here, or else the object will
198 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
199 SCEVTruncateExpr*> > SCEVTruncates;
201 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
202 : SCEV(scTruncate), Op(op), Ty(ty) {
203 assert(Op->getType()->isInteger() && Ty->isInteger() &&
204 "Cannot truncate non-integer value!");
205 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
206 && "This is not a truncating conversion!");
209 SCEVTruncateExpr::~SCEVTruncateExpr() {
210 SCEVTruncates->erase(std::make_pair(Op, Ty));
213 ConstantRange SCEVTruncateExpr::getValueRange() const {
214 return getOperand()->getValueRange().truncate(getBitWidth());
217 void SCEVTruncateExpr::print(std::ostream &OS) const {
218 OS << "(truncate " << *Op << " to " << *Ty << ")";
221 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
222 // particular input. Don't use a SCEVHandle here, or else the object will never
224 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
225 SCEVZeroExtendExpr*> > SCEVZeroExtends;
227 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
228 : SCEV(scZeroExtend), Op(op), Ty(ty) {
229 assert(Op->getType()->isInteger() && Ty->isInteger() &&
230 "Cannot zero extend non-integer value!");
231 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
232 && "This is not an extending conversion!");
235 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
236 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
239 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
240 return getOperand()->getValueRange().zeroExtend(getBitWidth());
243 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
244 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
247 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
248 // particular input. Don't use a SCEVHandle here, or else the object will never
250 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
251 SCEVCommutativeExpr*> > SCEVCommExprs;
253 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
254 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
255 std::vector<SCEV*>(Operands.begin(),
259 void SCEVCommutativeExpr::print(std::ostream &OS) const {
260 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
261 const char *OpStr = getOperationStr();
262 OS << "(" << *Operands[0];
263 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
264 OS << OpStr << *Operands[i];
268 SCEVHandle SCEVCommutativeExpr::
269 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
270 const SCEVHandle &Conc) const {
271 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
272 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
273 if (H != getOperand(i)) {
274 std::vector<SCEVHandle> NewOps;
275 NewOps.reserve(getNumOperands());
276 for (unsigned j = 0; j != i; ++j)
277 NewOps.push_back(getOperand(j));
279 for (++i; i != e; ++i)
280 NewOps.push_back(getOperand(i)->
281 replaceSymbolicValuesWithConcrete(Sym, Conc));
283 if (isa<SCEVAddExpr>(this))
284 return SCEVAddExpr::get(NewOps);
285 else if (isa<SCEVMulExpr>(this))
286 return SCEVMulExpr::get(NewOps);
288 assert(0 && "Unknown commutative expr!");
295 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
296 // input. Don't use a SCEVHandle here, or else the object will never be
298 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
299 SCEVSDivExpr*> > SCEVSDivs;
301 SCEVSDivExpr::~SCEVSDivExpr() {
302 SCEVSDivs->erase(std::make_pair(LHS, RHS));
305 void SCEVSDivExpr::print(std::ostream &OS) const {
306 OS << "(" << *LHS << " /s " << *RHS << ")";
309 const Type *SCEVSDivExpr::getType() const {
310 return LHS->getType();
313 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
314 // particular input. Don't use a SCEVHandle here, or else the object will never
316 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
317 SCEVAddRecExpr*> > SCEVAddRecExprs;
319 SCEVAddRecExpr::~SCEVAddRecExpr() {
320 SCEVAddRecExprs->erase(std::make_pair(L,
321 std::vector<SCEV*>(Operands.begin(),
325 SCEVHandle SCEVAddRecExpr::
326 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
327 const SCEVHandle &Conc) const {
328 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
329 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
330 if (H != getOperand(i)) {
331 std::vector<SCEVHandle> NewOps;
332 NewOps.reserve(getNumOperands());
333 for (unsigned j = 0; j != i; ++j)
334 NewOps.push_back(getOperand(j));
336 for (++i; i != e; ++i)
337 NewOps.push_back(getOperand(i)->
338 replaceSymbolicValuesWithConcrete(Sym, Conc));
340 return get(NewOps, L);
347 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
348 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
349 // contain L and if the start is invariant.
350 return !QueryLoop->contains(L->getHeader()) &&
351 getOperand(0)->isLoopInvariant(QueryLoop);
355 void SCEVAddRecExpr::print(std::ostream &OS) const {
356 OS << "{" << *Operands[0];
357 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
358 OS << ",+," << *Operands[i];
359 OS << "}<" << L->getHeader()->getName() + ">";
362 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
363 // value. Don't use a SCEVHandle here, or else the object will never be
365 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
367 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
369 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
370 // All non-instruction values are loop invariant. All instructions are loop
371 // invariant if they are not contained in the specified loop.
372 if (Instruction *I = dyn_cast<Instruction>(V))
373 return !L->contains(I->getParent());
377 const Type *SCEVUnknown::getType() const {
381 void SCEVUnknown::print(std::ostream &OS) const {
382 WriteAsOperand(OS, V, false);
385 //===----------------------------------------------------------------------===//
387 //===----------------------------------------------------------------------===//
390 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
391 /// than the complexity of the RHS. This comparator is used to canonicalize
393 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
394 bool operator()(SCEV *LHS, SCEV *RHS) {
395 return LHS->getSCEVType() < RHS->getSCEVType();
400 /// GroupByComplexity - Given a list of SCEV objects, order them by their
401 /// complexity, and group objects of the same complexity together by value.
402 /// When this routine is finished, we know that any duplicates in the vector are
403 /// consecutive and that complexity is monotonically increasing.
405 /// Note that we go take special precautions to ensure that we get determinstic
406 /// results from this routine. In other words, we don't want the results of
407 /// this to depend on where the addresses of various SCEV objects happened to
410 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
411 if (Ops.size() < 2) return; // Noop
412 if (Ops.size() == 2) {
413 // This is the common case, which also happens to be trivially simple.
415 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
416 std::swap(Ops[0], Ops[1]);
420 // Do the rough sort by complexity.
421 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
423 // Now that we are sorted by complexity, group elements of the same
424 // complexity. Note that this is, at worst, N^2, but the vector is likely to
425 // be extremely short in practice. Note that we take this approach because we
426 // do not want to depend on the addresses of the objects we are grouping.
427 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
429 unsigned Complexity = S->getSCEVType();
431 // If there are any objects of the same complexity and same value as this
433 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
434 if (Ops[j] == S) { // Found a duplicate.
435 // Move it to immediately after i'th element.
436 std::swap(Ops[i+1], Ops[j]);
437 ++i; // no need to rescan it.
438 if (i == e-2) return; // Done!
446 //===----------------------------------------------------------------------===//
447 // Simple SCEV method implementations
448 //===----------------------------------------------------------------------===//
450 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
451 /// specified signed integer value and return a SCEV for the constant.
452 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
455 C = Constant::getNullValue(Ty);
456 else if (Ty->isFloatingPoint())
457 C = ConstantFP::get(Ty, Val);
459 C = ConstantInt::get(Ty, Val);
460 return SCEVUnknown::get(C);
463 SCEVHandle SCEVUnknown::getIntegerSCEV(const APInt& Val) {
464 return SCEVUnknown::get(ConstantInt::get(Val));
467 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
468 /// input value to the specified type. If the type must be extended, it is zero
470 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
471 const Type *SrcTy = V->getType();
472 assert(SrcTy->isInteger() && Ty->isInteger() &&
473 "Cannot truncate or zero extend with non-integer arguments!");
474 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
475 return V; // No conversion
476 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
477 return SCEVTruncateExpr::get(V, Ty);
478 return SCEVZeroExtendExpr::get(V, Ty);
481 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
483 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
484 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
485 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
487 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
490 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
492 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
494 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
498 /// PartialFact - Compute V!/(V-NumSteps)!
499 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
500 // Handle this case efficiently, it is common to have constant iteration
501 // counts while computing loop exit values.
502 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
503 const APInt& Val = SC->getValue()->getValue();
504 APInt Result(Val.getBitWidth(), 1);
505 for (; NumSteps; --NumSteps)
506 Result *= Val-(NumSteps-1);
507 return SCEVUnknown::get(ConstantInt::get(Result));
510 const Type *Ty = V->getType();
512 return SCEVUnknown::getIntegerSCEV(1, Ty);
514 SCEVHandle Result = V;
515 for (unsigned i = 1; i != NumSteps; ++i)
516 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
517 SCEVUnknown::getIntegerSCEV(i, Ty)));
522 /// evaluateAtIteration - Return the value of this chain of recurrences at
523 /// the specified iteration number. We can evaluate this recurrence by
524 /// multiplying each element in the chain by the binomial coefficient
525 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
527 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
529 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
530 /// Is the binomial equation safe using modular arithmetic??
532 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
533 SCEVHandle Result = getStart();
535 const Type *Ty = It->getType();
536 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
537 SCEVHandle BC = PartialFact(It, i);
539 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
540 SCEVUnknown::getIntegerSCEV(Divisor,Ty));
541 Result = SCEVAddExpr::get(Result, Val);
547 //===----------------------------------------------------------------------===//
548 // SCEV Expression folder implementations
549 //===----------------------------------------------------------------------===//
551 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
552 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
553 return SCEVUnknown::get(
554 ConstantExpr::getTrunc(SC->getValue(), Ty));
556 // If the input value is a chrec scev made out of constants, truncate
557 // all of the constants.
558 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
559 std::vector<SCEVHandle> Operands;
560 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
561 // FIXME: This should allow truncation of other expression types!
562 if (isa<SCEVConstant>(AddRec->getOperand(i)))
563 Operands.push_back(get(AddRec->getOperand(i), Ty));
566 if (Operands.size() == AddRec->getNumOperands())
567 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
570 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
571 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
575 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
576 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
577 return SCEVUnknown::get(
578 ConstantExpr::getZExt(SC->getValue(), Ty));
580 // FIXME: If the input value is a chrec scev, and we can prove that the value
581 // did not overflow the old, smaller, value, we can zero extend all of the
582 // operands (often constants). This would allow analysis of something like
583 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
585 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
586 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
590 // get - Get a canonical add expression, or something simpler if possible.
591 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
592 assert(!Ops.empty() && "Cannot get empty add!");
593 if (Ops.size() == 1) return Ops[0];
595 // Sort by complexity, this groups all similar expression types together.
596 GroupByComplexity(Ops);
598 // If there are any constants, fold them together.
600 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
602 assert(Idx < Ops.size());
603 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
604 // We found two constants, fold them together!
605 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
606 RHSC->getValue()->getValue());
607 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
608 Ops[0] = SCEVConstant::get(CI);
609 Ops.erase(Ops.begin()+1); // Erase the folded element
610 if (Ops.size() == 1) return Ops[0];
611 LHSC = cast<SCEVConstant>(Ops[0]);
613 // If we couldn't fold the expression, move to the next constant. Note
614 // that this is impossible to happen in practice because we always
615 // constant fold constant ints to constant ints.
620 // If we are left with a constant zero being added, strip it off.
621 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
622 Ops.erase(Ops.begin());
627 if (Ops.size() == 1) return Ops[0];
629 // Okay, check to see if the same value occurs in the operand list twice. If
630 // so, merge them together into an multiply expression. Since we sorted the
631 // list, these values are required to be adjacent.
632 const Type *Ty = Ops[0]->getType();
633 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
634 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
635 // Found a match, merge the two values into a multiply, and add any
636 // remaining values to the result.
637 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
638 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
641 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
643 return SCEVAddExpr::get(Ops);
646 // Okay, now we know the first non-constant operand. If there are add
647 // operands they would be next.
648 if (Idx < Ops.size()) {
649 bool DeletedAdd = false;
650 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
651 // If we have an add, expand the add operands onto the end of the operands
653 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
654 Ops.erase(Ops.begin()+Idx);
658 // If we deleted at least one add, we added operands to the end of the list,
659 // and they are not necessarily sorted. Recurse to resort and resimplify
660 // any operands we just aquired.
665 // Skip over the add expression until we get to a multiply.
666 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
669 // If we are adding something to a multiply expression, make sure the
670 // something is not already an operand of the multiply. If so, merge it into
672 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
673 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
674 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
675 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
676 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
677 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
678 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
679 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
680 if (Mul->getNumOperands() != 2) {
681 // If the multiply has more than two operands, we must get the
683 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
684 MulOps.erase(MulOps.begin()+MulOp);
685 InnerMul = SCEVMulExpr::get(MulOps);
687 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
688 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
689 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
690 if (Ops.size() == 2) return OuterMul;
692 Ops.erase(Ops.begin()+AddOp);
693 Ops.erase(Ops.begin()+Idx-1);
695 Ops.erase(Ops.begin()+Idx);
696 Ops.erase(Ops.begin()+AddOp-1);
698 Ops.push_back(OuterMul);
699 return SCEVAddExpr::get(Ops);
702 // Check this multiply against other multiplies being added together.
703 for (unsigned OtherMulIdx = Idx+1;
704 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
706 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
707 // If MulOp occurs in OtherMul, we can fold the two multiplies
709 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
710 OMulOp != e; ++OMulOp)
711 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
712 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
713 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
714 if (Mul->getNumOperands() != 2) {
715 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
716 MulOps.erase(MulOps.begin()+MulOp);
717 InnerMul1 = SCEVMulExpr::get(MulOps);
719 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
720 if (OtherMul->getNumOperands() != 2) {
721 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
723 MulOps.erase(MulOps.begin()+OMulOp);
724 InnerMul2 = SCEVMulExpr::get(MulOps);
726 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
727 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
728 if (Ops.size() == 2) return OuterMul;
729 Ops.erase(Ops.begin()+Idx);
730 Ops.erase(Ops.begin()+OtherMulIdx-1);
731 Ops.push_back(OuterMul);
732 return SCEVAddExpr::get(Ops);
738 // If there are any add recurrences in the operands list, see if any other
739 // added values are loop invariant. If so, we can fold them into the
741 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
744 // Scan over all recurrences, trying to fold loop invariants into them.
745 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
746 // Scan all of the other operands to this add and add them to the vector if
747 // they are loop invariant w.r.t. the recurrence.
748 std::vector<SCEVHandle> LIOps;
749 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
750 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
751 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
752 LIOps.push_back(Ops[i]);
753 Ops.erase(Ops.begin()+i);
757 // If we found some loop invariants, fold them into the recurrence.
758 if (!LIOps.empty()) {
759 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
760 LIOps.push_back(AddRec->getStart());
762 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
763 AddRecOps[0] = SCEVAddExpr::get(LIOps);
765 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
766 // If all of the other operands were loop invariant, we are done.
767 if (Ops.size() == 1) return NewRec;
769 // Otherwise, add the folded AddRec by the non-liv parts.
770 for (unsigned i = 0;; ++i)
771 if (Ops[i] == AddRec) {
775 return SCEVAddExpr::get(Ops);
778 // Okay, if there weren't any loop invariants to be folded, check to see if
779 // there are multiple AddRec's with the same loop induction variable being
780 // added together. If so, we can fold them.
781 for (unsigned OtherIdx = Idx+1;
782 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
783 if (OtherIdx != Idx) {
784 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
785 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
786 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
787 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
788 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
789 if (i >= NewOps.size()) {
790 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
791 OtherAddRec->op_end());
794 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
796 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
798 if (Ops.size() == 2) return NewAddRec;
800 Ops.erase(Ops.begin()+Idx);
801 Ops.erase(Ops.begin()+OtherIdx-1);
802 Ops.push_back(NewAddRec);
803 return SCEVAddExpr::get(Ops);
807 // Otherwise couldn't fold anything into this recurrence. Move onto the
811 // Okay, it looks like we really DO need an add expr. Check to see if we
812 // already have one, otherwise create a new one.
813 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
814 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
816 if (Result == 0) Result = new SCEVAddExpr(Ops);
821 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
822 assert(!Ops.empty() && "Cannot get empty mul!");
824 // Sort by complexity, this groups all similar expression types together.
825 GroupByComplexity(Ops);
827 // If there are any constants, fold them together.
829 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
831 // C1*(C2+V) -> C1*C2 + C1*V
833 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
834 if (Add->getNumOperands() == 2 &&
835 isa<SCEVConstant>(Add->getOperand(0)))
836 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
837 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
841 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
842 // We found two constants, fold them together!
843 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
844 RHSC->getValue()->getValue());
845 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
846 Ops[0] = SCEVConstant::get(CI);
847 Ops.erase(Ops.begin()+1); // Erase the folded element
848 if (Ops.size() == 1) return Ops[0];
849 LHSC = cast<SCEVConstant>(Ops[0]);
851 // If we couldn't fold the expression, move to the next constant. Note
852 // that this is impossible to happen in practice because we always
853 // constant fold constant ints to constant ints.
858 // If we are left with a constant one being multiplied, strip it off.
859 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
860 Ops.erase(Ops.begin());
862 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
863 // If we have a multiply of zero, it will always be zero.
868 // Skip over the add expression until we get to a multiply.
869 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
875 // If there are mul operands inline them all into this expression.
876 if (Idx < Ops.size()) {
877 bool DeletedMul = false;
878 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
879 // If we have an mul, expand the mul operands onto the end of the operands
881 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
882 Ops.erase(Ops.begin()+Idx);
886 // If we deleted at least one mul, we added operands to the end of the list,
887 // and they are not necessarily sorted. Recurse to resort and resimplify
888 // any operands we just aquired.
893 // If there are any add recurrences in the operands list, see if any other
894 // added values are loop invariant. If so, we can fold them into the
896 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
899 // Scan over all recurrences, trying to fold loop invariants into them.
900 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
901 // Scan all of the other operands to this mul and add them to the vector if
902 // they are loop invariant w.r.t. the recurrence.
903 std::vector<SCEVHandle> LIOps;
904 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
905 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
906 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
907 LIOps.push_back(Ops[i]);
908 Ops.erase(Ops.begin()+i);
912 // If we found some loop invariants, fold them into the recurrence.
913 if (!LIOps.empty()) {
914 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
915 std::vector<SCEVHandle> NewOps;
916 NewOps.reserve(AddRec->getNumOperands());
917 if (LIOps.size() == 1) {
918 SCEV *Scale = LIOps[0];
919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
920 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
922 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
923 std::vector<SCEVHandle> MulOps(LIOps);
924 MulOps.push_back(AddRec->getOperand(i));
925 NewOps.push_back(SCEVMulExpr::get(MulOps));
929 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
931 // If all of the other operands were loop invariant, we are done.
932 if (Ops.size() == 1) return NewRec;
934 // Otherwise, multiply the folded AddRec by the non-liv parts.
935 for (unsigned i = 0;; ++i)
936 if (Ops[i] == AddRec) {
940 return SCEVMulExpr::get(Ops);
943 // Okay, if there weren't any loop invariants to be folded, check to see if
944 // there are multiple AddRec's with the same loop induction variable being
945 // multiplied together. If so, we can fold them.
946 for (unsigned OtherIdx = Idx+1;
947 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
948 if (OtherIdx != Idx) {
949 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
950 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
951 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
952 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
953 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
955 SCEVHandle B = F->getStepRecurrence();
956 SCEVHandle D = G->getStepRecurrence();
957 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
958 SCEVMulExpr::get(G, B),
959 SCEVMulExpr::get(B, D));
960 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
962 if (Ops.size() == 2) return NewAddRec;
964 Ops.erase(Ops.begin()+Idx);
965 Ops.erase(Ops.begin()+OtherIdx-1);
966 Ops.push_back(NewAddRec);
967 return SCEVMulExpr::get(Ops);
971 // Otherwise couldn't fold anything into this recurrence. Move onto the
975 // Okay, it looks like we really DO need an mul expr. Check to see if we
976 // already have one, otherwise create a new one.
977 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
978 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
981 Result = new SCEVMulExpr(Ops);
985 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
986 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
987 if (RHSC->getValue()->equalsInt(1))
988 return LHS; // X sdiv 1 --> x
989 if (RHSC->getValue()->isAllOnesValue())
990 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
992 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
993 Constant *LHSCV = LHSC->getValue();
994 Constant *RHSCV = RHSC->getValue();
995 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
999 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1001 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
1002 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
1007 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1008 /// specified loop. Simplify the expression as much as possible.
1009 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
1010 const SCEVHandle &Step, const Loop *L) {
1011 std::vector<SCEVHandle> Operands;
1012 Operands.push_back(Start);
1013 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1014 if (StepChrec->getLoop() == L) {
1015 Operands.insert(Operands.end(), StepChrec->op_begin(),
1016 StepChrec->op_end());
1017 return get(Operands, L);
1020 Operands.push_back(Step);
1021 return get(Operands, L);
1024 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1025 /// specified loop. Simplify the expression as much as possible.
1026 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1028 if (Operands.size() == 1) return Operands[0];
1030 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1031 if (StepC->getValue()->isZero()) {
1032 Operands.pop_back();
1033 return get(Operands, L); // { X,+,0 } --> X
1036 SCEVAddRecExpr *&Result =
1037 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1039 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1043 SCEVHandle SCEVUnknown::get(Value *V) {
1044 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1045 return SCEVConstant::get(CI);
1046 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1047 if (Result == 0) Result = new SCEVUnknown(V);
1052 //===----------------------------------------------------------------------===//
1053 // ScalarEvolutionsImpl Definition and Implementation
1054 //===----------------------------------------------------------------------===//
1056 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1060 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1061 /// F - The function we are analyzing.
1065 /// LI - The loop information for the function we are currently analyzing.
1069 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1071 SCEVHandle UnknownValue;
1073 /// Scalars - This is a cache of the scalars we have analyzed so far.
1075 std::map<Value*, SCEVHandle> Scalars;
1077 /// IterationCounts - Cache the iteration count of the loops for this
1078 /// function as they are computed.
1079 std::map<const Loop*, SCEVHandle> IterationCounts;
1081 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1082 /// the PHI instructions that we attempt to compute constant evolutions for.
1083 /// This allows us to avoid potentially expensive recomputation of these
1084 /// properties. An instruction maps to null if we are unable to compute its
1086 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1089 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1090 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1092 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1093 /// expression and create a new one.
1094 SCEVHandle getSCEV(Value *V);
1096 /// hasSCEV - Return true if the SCEV for this value has already been
1098 bool hasSCEV(Value *V) const {
1099 return Scalars.count(V);
1102 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1103 /// the specified value.
1104 void setSCEV(Value *V, const SCEVHandle &H) {
1105 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1106 assert(isNew && "This entry already existed!");
1110 /// getSCEVAtScope - Compute the value of the specified expression within
1111 /// the indicated loop (which may be null to indicate in no loop). If the
1112 /// expression cannot be evaluated, return UnknownValue itself.
1113 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1116 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1117 /// an analyzable loop-invariant iteration count.
1118 bool hasLoopInvariantIterationCount(const Loop *L);
1120 /// getIterationCount - If the specified loop has a predictable iteration
1121 /// count, return it. Note that it is not valid to call this method on a
1122 /// loop without a loop-invariant iteration count.
1123 SCEVHandle getIterationCount(const Loop *L);
1125 /// deleteInstructionFromRecords - This method should be called by the
1126 /// client before it removes an instruction from the program, to make sure
1127 /// that no dangling references are left around.
1128 void deleteInstructionFromRecords(Instruction *I);
1131 /// createSCEV - We know that there is no SCEV for the specified value.
1132 /// Analyze the expression.
1133 SCEVHandle createSCEV(Value *V);
1135 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1137 SCEVHandle createNodeForPHI(PHINode *PN);
1139 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1140 /// for the specified instruction and replaces any references to the
1141 /// symbolic value SymName with the specified value. This is used during
1143 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1144 const SCEVHandle &SymName,
1145 const SCEVHandle &NewVal);
1147 /// ComputeIterationCount - Compute the number of times the specified loop
1149 SCEVHandle ComputeIterationCount(const Loop *L);
1151 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1152 /// 'setcc load X, cst', try to see if we can compute the trip count.
1153 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1156 ICmpInst::Predicate p);
1158 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1159 /// constant number of times (the condition evolves only from constants),
1160 /// try to evaluate a few iterations of the loop until we get the exit
1161 /// condition gets a value of ExitWhen (true or false). If we cannot
1162 /// evaluate the trip count of the loop, return UnknownValue.
1163 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1166 /// HowFarToZero - Return the number of times a backedge comparing the
1167 /// specified value to zero will execute. If not computable, return
1169 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1171 /// HowFarToNonZero - Return the number of times a backedge checking the
1172 /// specified value for nonzero will execute. If not computable, return
1174 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1176 /// HowManyLessThans - Return the number of times a backedge containing the
1177 /// specified less-than comparison will execute. If not computable, return
1179 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
1181 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1182 /// in the header of its containing loop, we know the loop executes a
1183 /// constant number of times, and the PHI node is just a recurrence
1184 /// involving constants, fold it.
1185 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1190 //===----------------------------------------------------------------------===//
1191 // Basic SCEV Analysis and PHI Idiom Recognition Code
1194 /// deleteInstructionFromRecords - This method should be called by the
1195 /// client before it removes an instruction from the program, to make sure
1196 /// that no dangling references are left around.
1197 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
1199 if (PHINode *PN = dyn_cast<PHINode>(I))
1200 ConstantEvolutionLoopExitValue.erase(PN);
1204 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1205 /// expression and create a new one.
1206 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1207 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1209 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1210 if (I != Scalars.end()) return I->second;
1211 SCEVHandle S = createSCEV(V);
1212 Scalars.insert(std::make_pair(V, S));
1216 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1217 /// the specified instruction and replaces any references to the symbolic value
1218 /// SymName with the specified value. This is used during PHI resolution.
1219 void ScalarEvolutionsImpl::
1220 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1221 const SCEVHandle &NewVal) {
1222 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1223 if (SI == Scalars.end()) return;
1226 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1227 if (NV == SI->second) return; // No change.
1229 SI->second = NV; // Update the scalars map!
1231 // Any instruction values that use this instruction might also need to be
1233 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1235 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1238 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1239 /// a loop header, making it a potential recurrence, or it doesn't.
1241 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1242 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1243 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1244 if (L->getHeader() == PN->getParent()) {
1245 // If it lives in the loop header, it has two incoming values, one
1246 // from outside the loop, and one from inside.
1247 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1248 unsigned BackEdge = IncomingEdge^1;
1250 // While we are analyzing this PHI node, handle its value symbolically.
1251 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1252 assert(Scalars.find(PN) == Scalars.end() &&
1253 "PHI node already processed?");
1254 Scalars.insert(std::make_pair(PN, SymbolicName));
1256 // Using this symbolic name for the PHI, analyze the value coming around
1258 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1260 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1261 // has a special value for the first iteration of the loop.
1263 // If the value coming around the backedge is an add with the symbolic
1264 // value we just inserted, then we found a simple induction variable!
1265 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1266 // If there is a single occurrence of the symbolic value, replace it
1267 // with a recurrence.
1268 unsigned FoundIndex = Add->getNumOperands();
1269 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1270 if (Add->getOperand(i) == SymbolicName)
1271 if (FoundIndex == e) {
1276 if (FoundIndex != Add->getNumOperands()) {
1277 // Create an add with everything but the specified operand.
1278 std::vector<SCEVHandle> Ops;
1279 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1280 if (i != FoundIndex)
1281 Ops.push_back(Add->getOperand(i));
1282 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1284 // This is not a valid addrec if the step amount is varying each
1285 // loop iteration, but is not itself an addrec in this loop.
1286 if (Accum->isLoopInvariant(L) ||
1287 (isa<SCEVAddRecExpr>(Accum) &&
1288 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1289 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1290 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1292 // Okay, for the entire analysis of this edge we assumed the PHI
1293 // to be symbolic. We now need to go back and update all of the
1294 // entries for the scalars that use the PHI (except for the PHI
1295 // itself) to use the new analyzed value instead of the "symbolic"
1297 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1301 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1302 // Otherwise, this could be a loop like this:
1303 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1304 // In this case, j = {1,+,1} and BEValue is j.
1305 // Because the other in-value of i (0) fits the evolution of BEValue
1306 // i really is an addrec evolution.
1307 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1308 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1310 // If StartVal = j.start - j.stride, we can use StartVal as the
1311 // initial step of the addrec evolution.
1312 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1313 AddRec->getOperand(1))) {
1314 SCEVHandle PHISCEV =
1315 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1317 // Okay, for the entire analysis of this edge we assumed the PHI
1318 // to be symbolic. We now need to go back and update all of the
1319 // entries for the scalars that use the PHI (except for the PHI
1320 // itself) to use the new analyzed value instead of the "symbolic"
1322 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1328 return SymbolicName;
1331 // If it's not a loop phi, we can't handle it yet.
1332 return SCEVUnknown::get(PN);
1335 /// GetConstantFactor - Determine the largest constant factor that S has. For
1336 /// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
1337 static APInt GetConstantFactor(SCEVHandle S) {
1338 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
1339 const APInt& V = C->getValue()->getValue();
1340 if (!V.isMinValue())
1342 else // Zero is a multiple of everything.
1343 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1);
1346 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) {
1347 return GetConstantFactor(T->getOperand()).trunc(
1348 cast<IntegerType>(T->getType())->getBitWidth());
1350 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
1351 return GetConstantFactor(E->getOperand()).zext(
1352 cast<IntegerType>(E->getType())->getBitWidth());
1354 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1355 // The result is the min of all operands.
1356 APInt Res(GetConstantFactor(A->getOperand(0)));
1357 for (unsigned i = 1, e = A->getNumOperands();
1358 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) {
1359 APInt Tmp(GetConstantFactor(A->getOperand(i)));
1360 Res = APIntOps::umin(Res, Tmp);
1365 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1366 // The result is the product of all the operands.
1367 APInt Res(GetConstantFactor(M->getOperand(0)));
1368 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) {
1369 APInt Tmp(GetConstantFactor(M->getOperand(i)));
1375 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1376 // For now, we just handle linear expressions.
1377 if (A->getNumOperands() == 2) {
1378 // We want the GCD between the start and the stride value.
1379 APInt Start(GetConstantFactor(A->getOperand(0)));
1382 APInt Stride(GetConstantFactor(A->getOperand(1)));
1383 return APIntOps::GreatestCommonDivisor(Start, Stride);
1387 // SCEVSDivExpr, SCEVUnknown.
1388 return APInt(S->getBitWidth(), 1);
1391 /// createSCEV - We know that there is no SCEV for the specified value.
1392 /// Analyze the expression.
1394 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1395 if (Instruction *I = dyn_cast<Instruction>(V)) {
1396 switch (I->getOpcode()) {
1397 case Instruction::Add:
1398 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1399 getSCEV(I->getOperand(1)));
1400 case Instruction::Mul:
1401 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1402 getSCEV(I->getOperand(1)));
1403 case Instruction::SDiv:
1404 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1405 getSCEV(I->getOperand(1)));
1408 case Instruction::Sub:
1409 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1410 getSCEV(I->getOperand(1)));
1411 case Instruction::Or:
1412 // If the RHS of the Or is a constant, we may have something like:
1413 // X*4+1 which got turned into X*4|1. Handle this as an add so loop
1414 // optimizations will transparently handle this case.
1415 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1416 SCEVHandle LHS = getSCEV(I->getOperand(0));
1417 APInt CommonFact(GetConstantFactor(LHS));
1418 assert(!CommonFact.isMinValue() &&
1419 "Common factor should at least be 1!");
1420 if (CommonFact.ugt(CI->getValue())) {
1421 // If the LHS is a multiple that is larger than the RHS, use +.
1422 return SCEVAddExpr::get(LHS,
1423 getSCEV(I->getOperand(1)));
1427 case Instruction::Xor:
1428 // If the RHS of the xor is a signbit, then this is just an add.
1429 // Instcombine turns add of signbit into xor as a strength reduction step.
1430 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1431 if (CI->getValue().isSignBit())
1432 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1433 getSCEV(I->getOperand(1)));
1437 case Instruction::Shl:
1438 // Turn shift left of a constant amount into a multiply.
1439 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1440 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1441 Constant *X = ConstantInt::get(
1442 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1443 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1447 case Instruction::Trunc:
1448 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
1450 case Instruction::ZExt:
1451 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1453 case Instruction::BitCast:
1454 // BitCasts are no-op casts so we just eliminate the cast.
1455 if (I->getType()->isInteger() &&
1456 I->getOperand(0)->getType()->isInteger())
1457 return getSCEV(I->getOperand(0));
1460 case Instruction::PHI:
1461 return createNodeForPHI(cast<PHINode>(I));
1463 default: // We cannot analyze this expression.
1468 return SCEVUnknown::get(V);
1473 //===----------------------------------------------------------------------===//
1474 // Iteration Count Computation Code
1477 /// getIterationCount - If the specified loop has a predictable iteration
1478 /// count, return it. Note that it is not valid to call this method on a
1479 /// loop without a loop-invariant iteration count.
1480 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1481 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1482 if (I == IterationCounts.end()) {
1483 SCEVHandle ItCount = ComputeIterationCount(L);
1484 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1485 if (ItCount != UnknownValue) {
1486 assert(ItCount->isLoopInvariant(L) &&
1487 "Computed trip count isn't loop invariant for loop!");
1488 ++NumTripCountsComputed;
1489 } else if (isa<PHINode>(L->getHeader()->begin())) {
1490 // Only count loops that have phi nodes as not being computable.
1491 ++NumTripCountsNotComputed;
1497 /// ComputeIterationCount - Compute the number of times the specified loop
1499 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1500 // If the loop has a non-one exit block count, we can't analyze it.
1501 std::vector<BasicBlock*> ExitBlocks;
1502 L->getExitBlocks(ExitBlocks);
1503 if (ExitBlocks.size() != 1) return UnknownValue;
1505 // Okay, there is one exit block. Try to find the condition that causes the
1506 // loop to be exited.
1507 BasicBlock *ExitBlock = ExitBlocks[0];
1509 BasicBlock *ExitingBlock = 0;
1510 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1512 if (L->contains(*PI)) {
1513 if (ExitingBlock == 0)
1516 return UnknownValue; // More than one block exiting!
1518 assert(ExitingBlock && "No exits from loop, something is broken!");
1520 // Okay, we've computed the exiting block. See what condition causes us to
1523 // FIXME: we should be able to handle switch instructions (with a single exit)
1524 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1525 if (ExitBr == 0) return UnknownValue;
1526 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1528 // At this point, we know we have a conditional branch that determines whether
1529 // the loop is exited. However, we don't know if the branch is executed each
1530 // time through the loop. If not, then the execution count of the branch will
1531 // not be equal to the trip count of the loop.
1533 // Currently we check for this by checking to see if the Exit branch goes to
1534 // the loop header. If so, we know it will always execute the same number of
1535 // times as the loop. We also handle the case where the exit block *is* the
1536 // loop header. This is common for un-rotated loops. More extensive analysis
1537 // could be done to handle more cases here.
1538 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1539 ExitBr->getSuccessor(1) != L->getHeader() &&
1540 ExitBr->getParent() != L->getHeader())
1541 return UnknownValue;
1543 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1545 // If its not an integer comparison then compute it the hard way.
1546 // Note that ICmpInst deals with pointer comparisons too so we must check
1547 // the type of the operand.
1548 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1549 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1550 ExitBr->getSuccessor(0) == ExitBlock);
1552 // If the condition was exit on true, convert the condition to exit on false
1553 ICmpInst::Predicate Cond;
1554 if (ExitBr->getSuccessor(1) == ExitBlock)
1555 Cond = ExitCond->getPredicate();
1557 Cond = ExitCond->getInversePredicate();
1559 // Handle common loops like: for (X = "string"; *X; ++X)
1560 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1561 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1563 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1564 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1567 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1568 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1570 // Try to evaluate any dependencies out of the loop.
1571 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1572 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1573 Tmp = getSCEVAtScope(RHS, L);
1574 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1576 // At this point, we would like to compute how many iterations of the
1577 // loop the predicate will return true for these inputs.
1578 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1579 // If there is a constant, force it into the RHS.
1580 std::swap(LHS, RHS);
1581 Cond = ICmpInst::getSwappedPredicate(Cond);
1584 // FIXME: think about handling pointer comparisons! i.e.:
1585 // while (P != P+100) ++P;
1587 // If we have a comparison of a chrec against a constant, try to use value
1588 // ranges to answer this query.
1589 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1590 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1591 if (AddRec->getLoop() == L) {
1592 // Form the comparison range using the constant of the correct type so
1593 // that the ConstantRange class knows to do a signed or unsigned
1595 ConstantInt *CompVal = RHSC->getValue();
1596 const Type *RealTy = ExitCond->getOperand(0)->getType();
1597 CompVal = dyn_cast<ConstantInt>(
1598 ConstantExpr::getBitCast(CompVal, RealTy));
1600 // Form the constant range.
1601 ConstantRange CompRange(
1602 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
1604 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
1605 false /*Always treat as unsigned range*/);
1606 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1611 case ICmpInst::ICMP_NE: { // while (X != Y)
1612 // Convert to: while (X-Y != 0)
1613 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1614 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1617 case ICmpInst::ICMP_EQ: {
1618 // Convert to: while (X-Y == 0) // while (X == Y)
1619 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1620 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1623 case ICmpInst::ICMP_SLT: {
1624 SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1625 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1628 case ICmpInst::ICMP_SGT: {
1629 SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1630 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1635 cerr << "ComputeIterationCount ";
1636 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1637 cerr << "[unsigned] ";
1639 << Instruction::getOpcodeName(Instruction::ICmp)
1640 << " " << *RHS << "\n";
1644 return ComputeIterationCountExhaustively(L, ExitCond,
1645 ExitBr->getSuccessor(0) == ExitBlock);
1648 static ConstantInt *
1649 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1650 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1651 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1652 assert(isa<SCEVConstant>(Val) &&
1653 "Evaluation of SCEV at constant didn't fold correctly?");
1654 return cast<SCEVConstant>(Val)->getValue();
1657 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1658 /// and a GEP expression (missing the pointer index) indexing into it, return
1659 /// the addressed element of the initializer or null if the index expression is
1662 GetAddressedElementFromGlobal(GlobalVariable *GV,
1663 const std::vector<ConstantInt*> &Indices) {
1664 Constant *Init = GV->getInitializer();
1665 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1666 uint64_t Idx = Indices[i]->getZExtValue();
1667 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1668 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1669 Init = cast<Constant>(CS->getOperand(Idx));
1670 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1671 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1672 Init = cast<Constant>(CA->getOperand(Idx));
1673 } else if (isa<ConstantAggregateZero>(Init)) {
1674 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1675 assert(Idx < STy->getNumElements() && "Bad struct index!");
1676 Init = Constant::getNullValue(STy->getElementType(Idx));
1677 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1678 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1679 Init = Constant::getNullValue(ATy->getElementType());
1681 assert(0 && "Unknown constant aggregate type!");
1685 return 0; // Unknown initializer type
1691 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1692 /// 'setcc load X, cst', try to se if we can compute the trip count.
1693 SCEVHandle ScalarEvolutionsImpl::
1694 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1696 ICmpInst::Predicate predicate) {
1697 if (LI->isVolatile()) return UnknownValue;
1699 // Check to see if the loaded pointer is a getelementptr of a global.
1700 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1701 if (!GEP) return UnknownValue;
1703 // Make sure that it is really a constant global we are gepping, with an
1704 // initializer, and make sure the first IDX is really 0.
1705 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1706 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1707 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1708 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1709 return UnknownValue;
1711 // Okay, we allow one non-constant index into the GEP instruction.
1713 std::vector<ConstantInt*> Indexes;
1714 unsigned VarIdxNum = 0;
1715 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1716 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1717 Indexes.push_back(CI);
1718 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1719 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1720 VarIdx = GEP->getOperand(i);
1722 Indexes.push_back(0);
1725 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1726 // Check to see if X is a loop variant variable value now.
1727 SCEVHandle Idx = getSCEV(VarIdx);
1728 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1729 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1731 // We can only recognize very limited forms of loop index expressions, in
1732 // particular, only affine AddRec's like {C1,+,C2}.
1733 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1734 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1735 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1736 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1737 return UnknownValue;
1739 unsigned MaxSteps = MaxBruteForceIterations;
1740 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1741 ConstantInt *ItCst =
1742 ConstantInt::get(IdxExpr->getType(), IterationNum);
1743 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1745 // Form the GEP offset.
1746 Indexes[VarIdxNum] = Val;
1748 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1749 if (Result == 0) break; // Cannot compute!
1751 // Evaluate the condition for this iteration.
1752 Result = ConstantExpr::getICmp(predicate, Result, RHS);
1753 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
1754 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
1756 cerr << "\n***\n*** Computed loop count " << *ItCst
1757 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1760 ++NumArrayLenItCounts;
1761 return SCEVConstant::get(ItCst); // Found terminating iteration!
1764 return UnknownValue;
1768 /// CanConstantFold - Return true if we can constant fold an instruction of the
1769 /// specified type, assuming that all operands were constants.
1770 static bool CanConstantFold(const Instruction *I) {
1771 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
1772 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1775 if (const CallInst *CI = dyn_cast<CallInst>(I))
1776 if (const Function *F = CI->getCalledFunction())
1777 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1781 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1782 /// in the loop that V is derived from. We allow arbitrary operations along the
1783 /// way, but the operands of an operation must either be constants or a value
1784 /// derived from a constant PHI. If this expression does not fit with these
1785 /// constraints, return null.
1786 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1787 // If this is not an instruction, or if this is an instruction outside of the
1788 // loop, it can't be derived from a loop PHI.
1789 Instruction *I = dyn_cast<Instruction>(V);
1790 if (I == 0 || !L->contains(I->getParent())) return 0;
1792 if (PHINode *PN = dyn_cast<PHINode>(I))
1793 if (L->getHeader() == I->getParent())
1796 // We don't currently keep track of the control flow needed to evaluate
1797 // PHIs, so we cannot handle PHIs inside of loops.
1800 // If we won't be able to constant fold this expression even if the operands
1801 // are constants, return early.
1802 if (!CanConstantFold(I)) return 0;
1804 // Otherwise, we can evaluate this instruction if all of its operands are
1805 // constant or derived from a PHI node themselves.
1807 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1808 if (!(isa<Constant>(I->getOperand(Op)) ||
1809 isa<GlobalValue>(I->getOperand(Op)))) {
1810 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1811 if (P == 0) return 0; // Not evolving from PHI
1815 return 0; // Evolving from multiple different PHIs.
1818 // This is a expression evolving from a constant PHI!
1822 /// EvaluateExpression - Given an expression that passes the
1823 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1824 /// in the loop has the value PHIVal. If we can't fold this expression for some
1825 /// reason, return null.
1826 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1827 if (isa<PHINode>(V)) return PHIVal;
1828 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1830 if (Constant *C = dyn_cast<Constant>(V)) return C;
1831 Instruction *I = cast<Instruction>(V);
1833 std::vector<Constant*> Operands;
1834 Operands.resize(I->getNumOperands());
1836 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1837 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1838 if (Operands[i] == 0) return 0;
1841 return ConstantFoldInstOperands(I, &Operands[0], Operands.size());
1844 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1845 /// in the header of its containing loop, we know the loop executes a
1846 /// constant number of times, and the PHI node is just a recurrence
1847 /// involving constants, fold it.
1848 Constant *ScalarEvolutionsImpl::
1849 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
1850 std::map<PHINode*, Constant*>::iterator I =
1851 ConstantEvolutionLoopExitValue.find(PN);
1852 if (I != ConstantEvolutionLoopExitValue.end())
1855 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
1856 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1858 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1860 // Since the loop is canonicalized, the PHI node must have two entries. One
1861 // entry must be a constant (coming in from outside of the loop), and the
1862 // second must be derived from the same PHI.
1863 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1864 Constant *StartCST =
1865 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1867 return RetVal = 0; // Must be a constant.
1869 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1870 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1872 return RetVal = 0; // Not derived from same PHI.
1874 // Execute the loop symbolically to determine the exit value.
1875 if (Its.getActiveBits() >= 32)
1876 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
1878 unsigned NumIterations = Its.getZExtValue(); // must be in range
1879 unsigned IterationNum = 0;
1880 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1881 if (IterationNum == NumIterations)
1882 return RetVal = PHIVal; // Got exit value!
1884 // Compute the value of the PHI node for the next iteration.
1885 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1886 if (NextPHI == PHIVal)
1887 return RetVal = NextPHI; // Stopped evolving!
1889 return 0; // Couldn't evaluate!
1894 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1895 /// constant number of times (the condition evolves only from constants),
1896 /// try to evaluate a few iterations of the loop until we get the exit
1897 /// condition gets a value of ExitWhen (true or false). If we cannot
1898 /// evaluate the trip count of the loop, return UnknownValue.
1899 SCEVHandle ScalarEvolutionsImpl::
1900 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1901 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1902 if (PN == 0) return UnknownValue;
1904 // Since the loop is canonicalized, the PHI node must have two entries. One
1905 // entry must be a constant (coming in from outside of the loop), and the
1906 // second must be derived from the same PHI.
1907 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1908 Constant *StartCST =
1909 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1910 if (StartCST == 0) return UnknownValue; // Must be a constant.
1912 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1913 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1914 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1916 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1917 // the loop symbolically to determine when the condition gets a value of
1919 unsigned IterationNum = 0;
1920 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1921 for (Constant *PHIVal = StartCST;
1922 IterationNum != MaxIterations; ++IterationNum) {
1923 ConstantInt *CondVal =
1924 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
1926 // Couldn't symbolically evaluate.
1927 if (!CondVal) return UnknownValue;
1929 if (CondVal->getValue() == uint64_t(ExitWhen)) {
1930 ConstantEvolutionLoopExitValue[PN] = PHIVal;
1931 ++NumBruteForceTripCountsComputed;
1932 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
1935 // Compute the value of the PHI node for the next iteration.
1936 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1937 if (NextPHI == 0 || NextPHI == PHIVal)
1938 return UnknownValue; // Couldn't evaluate or not making progress...
1942 // Too many iterations were needed to evaluate.
1943 return UnknownValue;
1946 /// getSCEVAtScope - Compute the value of the specified expression within the
1947 /// indicated loop (which may be null to indicate in no loop). If the
1948 /// expression cannot be evaluated, return UnknownValue.
1949 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1950 // FIXME: this should be turned into a virtual method on SCEV!
1952 if (isa<SCEVConstant>(V)) return V;
1954 // If this instruction is evolves from a constant-evolving PHI, compute the
1955 // exit value from the loop without using SCEVs.
1956 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1957 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1958 const Loop *LI = this->LI[I->getParent()];
1959 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
1960 if (PHINode *PN = dyn_cast<PHINode>(I))
1961 if (PN->getParent() == LI->getHeader()) {
1962 // Okay, there is no closed form solution for the PHI node. Check
1963 // to see if the loop that contains it has a known iteration count.
1964 // If so, we may be able to force computation of the exit value.
1965 SCEVHandle IterationCount = getIterationCount(LI);
1966 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1967 // Okay, we know how many times the containing loop executes. If
1968 // this is a constant evolving PHI node, get the final value at
1969 // the specified iteration number.
1970 Constant *RV = getConstantEvolutionLoopExitValue(PN,
1971 ICC->getValue()->getValue(),
1973 if (RV) return SCEVUnknown::get(RV);
1977 // Okay, this is an expression that we cannot symbolically evaluate
1978 // into a SCEV. Check to see if it's possible to symbolically evaluate
1979 // the arguments into constants, and if so, try to constant propagate the
1980 // result. This is particularly useful for computing loop exit values.
1981 if (CanConstantFold(I)) {
1982 std::vector<Constant*> Operands;
1983 Operands.reserve(I->getNumOperands());
1984 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1985 Value *Op = I->getOperand(i);
1986 if (Constant *C = dyn_cast<Constant>(Op)) {
1987 Operands.push_back(C);
1989 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1990 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1991 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
1994 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
1995 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
1996 Operands.push_back(ConstantExpr::getIntegerCast(C,
2006 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
2007 return SCEVUnknown::get(C);
2011 // This is some other type of SCEVUnknown, just return it.
2015 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2016 // Avoid performing the look-up in the common case where the specified
2017 // expression has no loop-variant portions.
2018 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2019 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2020 if (OpAtScope != Comm->getOperand(i)) {
2021 if (OpAtScope == UnknownValue) return UnknownValue;
2022 // Okay, at least one of these operands is loop variant but might be
2023 // foldable. Build a new instance of the folded commutative expression.
2024 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2025 NewOps.push_back(OpAtScope);
2027 for (++i; i != e; ++i) {
2028 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2029 if (OpAtScope == UnknownValue) return UnknownValue;
2030 NewOps.push_back(OpAtScope);
2032 if (isa<SCEVAddExpr>(Comm))
2033 return SCEVAddExpr::get(NewOps);
2034 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2035 return SCEVMulExpr::get(NewOps);
2038 // If we got here, all operands are loop invariant.
2042 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2043 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2044 if (LHS == UnknownValue) return LHS;
2045 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2046 if (RHS == UnknownValue) return RHS;
2047 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2048 return Div; // must be loop invariant
2049 return SCEVSDivExpr::get(LHS, RHS);
2052 // If this is a loop recurrence for a loop that does not contain L, then we
2053 // are dealing with the final value computed by the loop.
2054 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2055 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2056 // To evaluate this recurrence, we need to know how many times the AddRec
2057 // loop iterates. Compute this now.
2058 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2059 if (IterationCount == UnknownValue) return UnknownValue;
2060 IterationCount = getTruncateOrZeroExtend(IterationCount,
2063 // If the value is affine, simplify the expression evaluation to just
2064 // Start + Step*IterationCount.
2065 if (AddRec->isAffine())
2066 return SCEVAddExpr::get(AddRec->getStart(),
2067 SCEVMulExpr::get(IterationCount,
2068 AddRec->getOperand(1)));
2070 // Otherwise, evaluate it the hard way.
2071 return AddRec->evaluateAtIteration(IterationCount);
2073 return UnknownValue;
2076 //assert(0 && "Unknown SCEV type!");
2077 return UnknownValue;
2081 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2082 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2083 /// might be the same) or two SCEVCouldNotCompute objects.
2085 static std::pair<SCEVHandle,SCEVHandle>
2086 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2087 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2088 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2089 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2090 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2092 // We currently can only solve this if the coefficients are constants.
2093 if (!LC || !MC || !NC) {
2094 SCEV *CNC = new SCEVCouldNotCompute();
2095 return std::make_pair(CNC, CNC);
2098 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2099 const APInt &L = LC->getValue()->getValue();
2100 const APInt &M = MC->getValue()->getValue();
2101 const APInt &N = NC->getValue()->getValue();
2102 APInt Two(BitWidth, 2);
2103 APInt Four(BitWidth, 4);
2106 using namespace APIntOps;
2108 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2109 // The B coefficient is M-N/2
2113 // The A coefficient is N/2
2114 APInt A(N.sdiv(Two));
2116 // Compute the B^2-4ac term.
2119 SqrtTerm -= Four * (A * C);
2121 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2122 // integer value or else APInt::sqrt() will assert.
2123 APInt SqrtVal(SqrtTerm.sqrt());
2125 // Compute the two solutions for the quadratic formula.
2126 // The divisions must be performed as signed divisions.
2128 APInt TwoA( A << 1 );
2129 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2130 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2132 return std::make_pair(SCEVUnknown::get(Solution1),
2133 SCEVUnknown::get(Solution2));
2134 } // end APIntOps namespace
2137 /// HowFarToZero - Return the number of times a backedge comparing the specified
2138 /// value to zero will execute. If not computable, return UnknownValue
2139 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2140 // If the value is a constant
2141 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2142 // If the value is already zero, the branch will execute zero times.
2143 if (C->getValue()->isZero()) return C;
2144 return UnknownValue; // Otherwise it will loop infinitely.
2147 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2148 if (!AddRec || AddRec->getLoop() != L)
2149 return UnknownValue;
2151 if (AddRec->isAffine()) {
2152 // If this is an affine expression the execution count of this branch is
2155 // (0 - Start/Step) iff Start % Step == 0
2157 // Get the initial value for the loop.
2158 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2159 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2160 SCEVHandle Step = AddRec->getOperand(1);
2162 Step = getSCEVAtScope(Step, L->getParentLoop());
2164 // Figure out if Start % Step == 0.
2165 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2166 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2167 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2168 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2169 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2170 return Start; // 0 - Start/-1 == Start
2172 // Check to see if Start is divisible by SC with no remainder.
2173 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2174 ConstantInt *StartCC = StartC->getValue();
2175 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2176 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2177 if (Rem->isNullValue()) {
2178 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2179 return SCEVUnknown::get(Result);
2183 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2184 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2185 // the quadratic equation to solve it.
2186 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2187 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2188 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2191 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2192 << " sol#2: " << *R2 << "\n";
2194 // Pick the smallest positive root value.
2195 if (ConstantInt *CB =
2196 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2197 R1->getValue(), R2->getValue()))) {
2198 if (CB->getZExtValue() == false)
2199 std::swap(R1, R2); // R1 is the minimum root now.
2201 // We can only use this value if the chrec ends up with an exact zero
2202 // value at this index. When solving for "X*X != 5", for example, we
2203 // should not accept a root of 2.
2204 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2205 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2206 if (EvalVal->getValue()->isZero())
2207 return R1; // We found a quadratic root!
2212 return UnknownValue;
2215 /// HowFarToNonZero - Return the number of times a backedge checking the
2216 /// specified value for nonzero will execute. If not computable, return
2218 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2219 // Loops that look like: while (X == 0) are very strange indeed. We don't
2220 // handle them yet except for the trivial case. This could be expanded in the
2221 // future as needed.
2223 // If the value is a constant, check to see if it is known to be non-zero
2224 // already. If so, the backedge will execute zero times.
2225 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2226 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2228 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2229 if (NonZero == ConstantInt::getTrue())
2230 return getSCEV(Zero);
2231 return UnknownValue; // Otherwise it will loop infinitely.
2234 // We could implement others, but I really doubt anyone writes loops like
2235 // this, and if they did, they would already be constant folded.
2236 return UnknownValue;
2239 /// HowManyLessThans - Return the number of times a backedge containing the
2240 /// specified less-than comparison will execute. If not computable, return
2242 SCEVHandle ScalarEvolutionsImpl::
2243 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2244 // Only handle: "ADDREC < LoopInvariant".
2245 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2247 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2248 if (!AddRec || AddRec->getLoop() != L)
2249 return UnknownValue;
2251 if (AddRec->isAffine()) {
2252 // FORNOW: We only support unit strides.
2253 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2254 if (AddRec->getOperand(1) != One)
2255 return UnknownValue;
2257 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2258 // know that m is >= n on input to the loop. If it is, the condition return
2259 // true zero times. What we really should return, for full generality, is
2260 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2261 // canonical loop form: most do-loops will have a check that dominates the
2262 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2263 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2265 // Search for the check.
2266 BasicBlock *Preheader = L->getLoopPreheader();
2267 BasicBlock *PreheaderDest = L->getHeader();
2268 if (Preheader == 0) return UnknownValue;
2270 BranchInst *LoopEntryPredicate =
2271 dyn_cast<BranchInst>(Preheader->getTerminator());
2272 if (!LoopEntryPredicate) return UnknownValue;
2274 // This might be a critical edge broken out. If the loop preheader ends in
2275 // an unconditional branch to the loop, check to see if the preheader has a
2276 // single predecessor, and if so, look for its terminator.
2277 while (LoopEntryPredicate->isUnconditional()) {
2278 PreheaderDest = Preheader;
2279 Preheader = Preheader->getSinglePredecessor();
2280 if (!Preheader) return UnknownValue; // Multiple preds.
2282 LoopEntryPredicate =
2283 dyn_cast<BranchInst>(Preheader->getTerminator());
2284 if (!LoopEntryPredicate) return UnknownValue;
2287 // Now that we found a conditional branch that dominates the loop, check to
2288 // see if it is the comparison we are looking for.
2289 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2290 Value *PreCondLHS = ICI->getOperand(0);
2291 Value *PreCondRHS = ICI->getOperand(1);
2292 ICmpInst::Predicate Cond;
2293 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2294 Cond = ICI->getPredicate();
2296 Cond = ICI->getInversePredicate();
2299 case ICmpInst::ICMP_UGT:
2300 std::swap(PreCondLHS, PreCondRHS);
2301 Cond = ICmpInst::ICMP_ULT;
2303 case ICmpInst::ICMP_SGT:
2304 std::swap(PreCondLHS, PreCondRHS);
2305 Cond = ICmpInst::ICMP_SLT;
2310 if (Cond == ICmpInst::ICMP_SLT) {
2311 if (PreCondLHS->getType()->isInteger()) {
2312 if (RHS != getSCEV(PreCondRHS))
2313 return UnknownValue; // Not a comparison against 'm'.
2315 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2316 != getSCEV(PreCondLHS))
2317 return UnknownValue; // Not a comparison against 'n-1'.
2319 else return UnknownValue;
2320 } else if (Cond == ICmpInst::ICMP_ULT)
2321 return UnknownValue;
2323 // cerr << "Computed Loop Trip Count as: "
2324 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2325 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2328 return UnknownValue;
2331 return UnknownValue;
2334 /// getNumIterationsInRange - Return the number of iterations of this loop that
2335 /// produce values in the specified constant range. Another way of looking at
2336 /// this is that it returns the first iteration number where the value is not in
2337 /// the condition, thus computing the exit count. If the iteration count can't
2338 /// be computed, an instance of SCEVCouldNotCompute is returned.
2339 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2340 bool isSigned) const {
2341 if (Range.isFullSet()) // Infinite loop.
2342 return new SCEVCouldNotCompute();
2344 // If the start is a non-zero constant, shift the range to simplify things.
2345 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2346 if (!SC->getValue()->isZero()) {
2347 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2348 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2349 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2350 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2351 return ShiftedAddRec->getNumIterationsInRange(
2352 Range.subtract(SC->getValue()->getValue()),isSigned);
2353 // This is strange and shouldn't happen.
2354 return new SCEVCouldNotCompute();
2357 // The only time we can solve this is when we have all constant indices.
2358 // Otherwise, we cannot determine the overflow conditions.
2359 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2360 if (!isa<SCEVConstant>(getOperand(i)))
2361 return new SCEVCouldNotCompute();
2364 // Okay at this point we know that all elements of the chrec are constants and
2365 // that the start element is zero.
2367 // First check to see if the range contains zero. If not, the first
2369 if (!Range.contains(APInt(getBitWidth(),0)))
2370 return SCEVConstant::get(ConstantInt::get(getType(),0));
2373 // If this is an affine expression then we have this situation:
2374 // Solve {0,+,A} in Range === Ax in Range
2376 // Since we know that zero is in the range, we know that the upper value of
2377 // the range must be the first possible exit value. Also note that we
2378 // already checked for a full range.
2379 const APInt &Upper = Range.getUpper();
2380 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2381 APInt One(getBitWidth(),1);
2383 // The exit value should be (Upper+A-1)/A.
2384 APInt ExitVal(Upper);
2386 ExitVal = (Upper + A - One).sdiv(A);
2387 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
2389 // Evaluate at the exit value. If we really did fall out of the valid
2390 // range, then we computed our trip count, otherwise wrap around or other
2391 // things must have happened.
2392 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2393 if (Range.contains(Val->getValue()))
2394 return new SCEVCouldNotCompute(); // Something strange happened
2396 // Ensure that the previous value is in the range. This is a sanity check.
2397 assert(Range.contains(
2398 EvaluateConstantChrecAtConstant(this,
2399 ConstantInt::get(ExitVal - One))->getValue()) &&
2400 "Linear scev computation is off in a bad way!");
2401 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2402 } else if (isQuadratic()) {
2403 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2404 // quadratic equation to solve it. To do this, we must frame our problem in
2405 // terms of figuring out when zero is crossed, instead of when
2406 // Range.getUpper() is crossed.
2407 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2408 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(
2409 ConstantInt::get(Range.getUpper())));
2410 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2412 // Next, solve the constructed addrec
2413 std::pair<SCEVHandle,SCEVHandle> Roots =
2414 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2415 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2416 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2418 // Pick the smallest positive root value.
2419 if (ConstantInt *CB =
2420 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2421 R1->getValue(), R2->getValue()))) {
2422 if (CB->getZExtValue() == false)
2423 std::swap(R1, R2); // R1 is the minimum root now.
2425 // Make sure the root is not off by one. The returned iteration should
2426 // not be in the range, but the previous one should be. When solving
2427 // for "X*X < 5", for example, we should not return a root of 2.
2428 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2430 if (Range.contains(R1Val->getValue())) {
2431 // The next iteration must be out of the range...
2432 Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
2434 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2435 if (!Range.contains(R1Val->getValue()))
2436 return SCEVUnknown::get(NextVal);
2437 return new SCEVCouldNotCompute(); // Something strange happened
2440 // If R1 was not in the range, then it is a good return value. Make
2441 // sure that R1-1 WAS in the range though, just in case.
2442 Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
2443 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2444 if (Range.contains(R1Val->getValue()))
2446 return new SCEVCouldNotCompute(); // Something strange happened
2451 // Fallback, if this is a general polynomial, figure out the progression
2452 // through brute force: evaluate until we find an iteration that fails the
2453 // test. This is likely to be slow, but getting an accurate trip count is
2454 // incredibly important, we will be able to simplify the exit test a lot, and
2455 // we are almost guaranteed to get a trip count in this case.
2456 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2457 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2459 ++NumBruteForceEvaluations;
2460 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2461 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2462 return new SCEVCouldNotCompute();
2464 // Check to see if we found the value!
2465 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
2466 return SCEVConstant::get(TestVal);
2468 // Increment to test the next index.
2469 TestVal = ConstantInt::get(TestVal->getValue()+1);
2470 } while (TestVal != EndVal);
2472 return new SCEVCouldNotCompute();
2477 //===----------------------------------------------------------------------===//
2478 // ScalarEvolution Class Implementation
2479 //===----------------------------------------------------------------------===//
2481 bool ScalarEvolution::runOnFunction(Function &F) {
2482 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2486 void ScalarEvolution::releaseMemory() {
2487 delete (ScalarEvolutionsImpl*)Impl;
2491 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2492 AU.setPreservesAll();
2493 AU.addRequiredTransitive<LoopInfo>();
2496 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2497 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2500 /// hasSCEV - Return true if the SCEV for this value has already been
2502 bool ScalarEvolution::hasSCEV(Value *V) const {
2503 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2507 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2508 /// the specified value.
2509 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2510 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2514 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2515 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2518 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2519 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2522 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2523 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2526 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2527 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2530 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2532 // Print all inner loops first
2533 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2534 PrintLoopInfo(OS, SE, *I);
2536 cerr << "Loop " << L->getHeader()->getName() << ": ";
2538 std::vector<BasicBlock*> ExitBlocks;
2539 L->getExitBlocks(ExitBlocks);
2540 if (ExitBlocks.size() != 1)
2541 cerr << "<multiple exits> ";
2543 if (SE->hasLoopInvariantIterationCount(L)) {
2544 cerr << *SE->getIterationCount(L) << " iterations! ";
2546 cerr << "Unpredictable iteration count. ";
2552 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2553 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2554 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2556 OS << "Classifying expressions for: " << F.getName() << "\n";
2557 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2558 if (I->getType()->isInteger()) {
2561 SCEVHandle SV = getSCEV(&*I);
2565 if ((*I).getType()->isInteger()) {
2566 ConstantRange Bounds = SV->getValueRange();
2567 if (!Bounds.isFullSet())
2568 OS << "Bounds: " << Bounds << " ";
2571 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2573 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2574 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2575 OS << "<<Unknown>>";
2585 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2586 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2587 PrintLoopInfo(OS, this, *I);