1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by the LLVM research group and is distributed under
6 // the University of Illinois Open Source License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/LoopInfo.h"
70 #include "llvm/Assembly/Writer.h"
71 #include "llvm/Transforms/Scalar.h"
72 #include "llvm/Support/CFG.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/InstIterator.h"
77 #include "llvm/Support/ManagedStatic.h"
78 #include "llvm/Support/MathExtras.h"
79 #include "llvm/Support/Streams.h"
80 #include "llvm/ADT/Statistic.h"
86 STATISTIC(NumBruteForceEvaluations,
87 "Number of brute force evaluations needed to "
88 "calculate high-order polynomial exit values");
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant derived loop"),
105 RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis");
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
118 void SCEV::dump() const {
122 /// getValueRange - Return the tightest constant bounds that this value is
123 /// known to have. This method is only valid on integer SCEV objects.
124 ConstantRange SCEV::getValueRange() const {
125 const Type *Ty = getType();
126 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
127 // Default to a full range if no better information is available.
128 return ConstantRange(getBitWidth());
131 uint32_t SCEV::getBitWidth() const {
132 if (const IntegerType* ITy = dyn_cast<IntegerType>(getType()))
133 return ITy->getBitWidth();
138 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
140 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 const Type *SCEVCouldNotCompute::getType() const {
146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
155 SCEVHandle SCEVCouldNotCompute::
156 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
157 const SCEVHandle &Conc) const {
161 void SCEVCouldNotCompute::print(std::ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
165 bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
170 // SCEVConstants - Only allow the creation of one SCEVConstant for any
171 // particular value. Don't use a SCEVHandle here, or else the object will
173 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
176 SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
180 SCEVHandle SCEVConstant::get(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
186 ConstantRange SCEVConstant::getValueRange() const {
187 return ConstantRange(V->getValue());
190 const Type *SCEVConstant::getType() const { return V->getType(); }
192 void SCEVConstant::print(std::ostream &OS) const {
193 WriteAsOperand(OS, V, false);
196 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
197 // particular input. Don't use a SCEVHandle here, or else the object will
199 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
200 SCEVTruncateExpr*> > SCEVTruncates;
202 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
203 : SCEV(scTruncate), Op(op), Ty(ty) {
204 assert(Op->getType()->isInteger() && Ty->isInteger() &&
205 "Cannot truncate non-integer value!");
206 assert(Op->getType()->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits()
207 && "This is not a truncating conversion!");
210 SCEVTruncateExpr::~SCEVTruncateExpr() {
211 SCEVTruncates->erase(std::make_pair(Op, Ty));
214 ConstantRange SCEVTruncateExpr::getValueRange() const {
215 return getOperand()->getValueRange().truncate(getBitWidth());
218 void SCEVTruncateExpr::print(std::ostream &OS) const {
219 OS << "(truncate " << *Op << " to " << *Ty << ")";
222 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
223 // particular input. Don't use a SCEVHandle here, or else the object will never
225 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
226 SCEVZeroExtendExpr*> > SCEVZeroExtends;
228 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
229 : SCEV(scZeroExtend), Op(op), Ty(ty) {
230 assert(Op->getType()->isInteger() && Ty->isInteger() &&
231 "Cannot zero extend non-integer value!");
232 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
233 && "This is not an extending conversion!");
236 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
237 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
240 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
241 return getOperand()->getValueRange().zeroExtend(getBitWidth());
244 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
245 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
248 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
249 // particular input. Don't use a SCEVHandle here, or else the object will never
251 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
252 SCEVSignExtendExpr*> > SCEVSignExtends;
254 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
255 : SCEV(scSignExtend), Op(op), Ty(ty) {
256 assert(Op->getType()->isInteger() && Ty->isInteger() &&
257 "Cannot sign extend non-integer value!");
258 assert(Op->getType()->getPrimitiveSizeInBits() < Ty->getPrimitiveSizeInBits()
259 && "This is not an extending conversion!");
262 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
263 SCEVSignExtends->erase(std::make_pair(Op, Ty));
266 ConstantRange SCEVSignExtendExpr::getValueRange() const {
267 return getOperand()->getValueRange().signExtend(getBitWidth());
270 void SCEVSignExtendExpr::print(std::ostream &OS) const {
271 OS << "(signextend " << *Op << " to " << *Ty << ")";
274 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
275 // particular input. Don't use a SCEVHandle here, or else the object will never
277 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
278 SCEVCommutativeExpr*> > SCEVCommExprs;
280 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
281 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
282 std::vector<SCEV*>(Operands.begin(),
286 void SCEVCommutativeExpr::print(std::ostream &OS) const {
287 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
288 const char *OpStr = getOperationStr();
289 OS << "(" << *Operands[0];
290 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
291 OS << OpStr << *Operands[i];
295 SCEVHandle SCEVCommutativeExpr::
296 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
297 const SCEVHandle &Conc) const {
298 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
299 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
300 if (H != getOperand(i)) {
301 std::vector<SCEVHandle> NewOps;
302 NewOps.reserve(getNumOperands());
303 for (unsigned j = 0; j != i; ++j)
304 NewOps.push_back(getOperand(j));
306 for (++i; i != e; ++i)
307 NewOps.push_back(getOperand(i)->
308 replaceSymbolicValuesWithConcrete(Sym, Conc));
310 if (isa<SCEVAddExpr>(this))
311 return SCEVAddExpr::get(NewOps);
312 else if (isa<SCEVMulExpr>(this))
313 return SCEVMulExpr::get(NewOps);
315 assert(0 && "Unknown commutative expr!");
322 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
323 // input. Don't use a SCEVHandle here, or else the object will never be
325 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
326 SCEVSDivExpr*> > SCEVSDivs;
328 SCEVSDivExpr::~SCEVSDivExpr() {
329 SCEVSDivs->erase(std::make_pair(LHS, RHS));
332 void SCEVSDivExpr::print(std::ostream &OS) const {
333 OS << "(" << *LHS << " /s " << *RHS << ")";
336 const Type *SCEVSDivExpr::getType() const {
337 return LHS->getType();
340 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
341 // particular input. Don't use a SCEVHandle here, or else the object will never
343 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
344 SCEVAddRecExpr*> > SCEVAddRecExprs;
346 SCEVAddRecExpr::~SCEVAddRecExpr() {
347 SCEVAddRecExprs->erase(std::make_pair(L,
348 std::vector<SCEV*>(Operands.begin(),
352 SCEVHandle SCEVAddRecExpr::
353 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
354 const SCEVHandle &Conc) const {
355 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
356 SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
357 if (H != getOperand(i)) {
358 std::vector<SCEVHandle> NewOps;
359 NewOps.reserve(getNumOperands());
360 for (unsigned j = 0; j != i; ++j)
361 NewOps.push_back(getOperand(j));
363 for (++i; i != e; ++i)
364 NewOps.push_back(getOperand(i)->
365 replaceSymbolicValuesWithConcrete(Sym, Conc));
367 return get(NewOps, L);
374 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
375 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
376 // contain L and if the start is invariant.
377 return !QueryLoop->contains(L->getHeader()) &&
378 getOperand(0)->isLoopInvariant(QueryLoop);
382 void SCEVAddRecExpr::print(std::ostream &OS) const {
383 OS << "{" << *Operands[0];
384 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
385 OS << ",+," << *Operands[i];
386 OS << "}<" << L->getHeader()->getName() + ">";
389 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
390 // value. Don't use a SCEVHandle here, or else the object will never be
392 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
394 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
396 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
397 // All non-instruction values are loop invariant. All instructions are loop
398 // invariant if they are not contained in the specified loop.
399 if (Instruction *I = dyn_cast<Instruction>(V))
400 return !L->contains(I->getParent());
404 const Type *SCEVUnknown::getType() const {
408 void SCEVUnknown::print(std::ostream &OS) const {
409 WriteAsOperand(OS, V, false);
412 //===----------------------------------------------------------------------===//
414 //===----------------------------------------------------------------------===//
417 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
418 /// than the complexity of the RHS. This comparator is used to canonicalize
420 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
421 bool operator()(SCEV *LHS, SCEV *RHS) {
422 return LHS->getSCEVType() < RHS->getSCEVType();
427 /// GroupByComplexity - Given a list of SCEV objects, order them by their
428 /// complexity, and group objects of the same complexity together by value.
429 /// When this routine is finished, we know that any duplicates in the vector are
430 /// consecutive and that complexity is monotonically increasing.
432 /// Note that we go take special precautions to ensure that we get determinstic
433 /// results from this routine. In other words, we don't want the results of
434 /// this to depend on where the addresses of various SCEV objects happened to
437 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
438 if (Ops.size() < 2) return; // Noop
439 if (Ops.size() == 2) {
440 // This is the common case, which also happens to be trivially simple.
442 if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
443 std::swap(Ops[0], Ops[1]);
447 // Do the rough sort by complexity.
448 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
450 // Now that we are sorted by complexity, group elements of the same
451 // complexity. Note that this is, at worst, N^2, but the vector is likely to
452 // be extremely short in practice. Note that we take this approach because we
453 // do not want to depend on the addresses of the objects we are grouping.
454 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
456 unsigned Complexity = S->getSCEVType();
458 // If there are any objects of the same complexity and same value as this
460 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
461 if (Ops[j] == S) { // Found a duplicate.
462 // Move it to immediately after i'th element.
463 std::swap(Ops[i+1], Ops[j]);
464 ++i; // no need to rescan it.
465 if (i == e-2) return; // Done!
473 //===----------------------------------------------------------------------===//
474 // Simple SCEV method implementations
475 //===----------------------------------------------------------------------===//
477 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
478 /// specified signed integer value and return a SCEV for the constant.
479 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
482 C = Constant::getNullValue(Ty);
483 else if (Ty->isFloatingPoint())
484 C = ConstantFP::get(Ty, Val);
486 C = ConstantInt::get(Ty, Val);
487 return SCEVUnknown::get(C);
490 SCEVHandle SCEVUnknown::getIntegerSCEV(const APInt& Val) {
491 return SCEVUnknown::get(ConstantInt::get(Val));
494 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
495 /// input value to the specified type. If the type must be extended, it is zero
497 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
498 const Type *SrcTy = V->getType();
499 assert(SrcTy->isInteger() && Ty->isInteger() &&
500 "Cannot truncate or zero extend with non-integer arguments!");
501 if (SrcTy->getPrimitiveSizeInBits() == Ty->getPrimitiveSizeInBits())
502 return V; // No conversion
503 if (SrcTy->getPrimitiveSizeInBits() > Ty->getPrimitiveSizeInBits())
504 return SCEVTruncateExpr::get(V, Ty);
505 return SCEVZeroExtendExpr::get(V, Ty);
508 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
510 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
511 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
512 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
514 return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
517 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
519 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
521 return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
525 /// PartialFact - Compute V!/(V-NumSteps)!
526 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
527 // Handle this case efficiently, it is common to have constant iteration
528 // counts while computing loop exit values.
529 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
530 const APInt& Val = SC->getValue()->getValue();
531 APInt Result(Val.getBitWidth(), 1);
532 for (; NumSteps; --NumSteps)
533 Result *= Val-(NumSteps-1);
534 return SCEVUnknown::get(ConstantInt::get(Result));
537 const Type *Ty = V->getType();
539 return SCEVUnknown::getIntegerSCEV(1, Ty);
541 SCEVHandle Result = V;
542 for (unsigned i = 1; i != NumSteps; ++i)
543 Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
544 SCEVUnknown::getIntegerSCEV(i, Ty)));
549 /// evaluateAtIteration - Return the value of this chain of recurrences at
550 /// the specified iteration number. We can evaluate this recurrence by
551 /// multiplying each element in the chain by the binomial coefficient
552 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
554 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
556 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
557 /// Is the binomial equation safe using modular arithmetic??
559 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
560 SCEVHandle Result = getStart();
562 const Type *Ty = It->getType();
563 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
564 SCEVHandle BC = PartialFact(It, i);
566 SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
567 SCEVUnknown::getIntegerSCEV(Divisor,Ty));
568 Result = SCEVAddExpr::get(Result, Val);
574 //===----------------------------------------------------------------------===//
575 // SCEV Expression folder implementations
576 //===----------------------------------------------------------------------===//
578 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
579 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
580 return SCEVUnknown::get(
581 ConstantExpr::getTrunc(SC->getValue(), Ty));
583 // If the input value is a chrec scev made out of constants, truncate
584 // all of the constants.
585 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
586 std::vector<SCEVHandle> Operands;
587 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
588 // FIXME: This should allow truncation of other expression types!
589 if (isa<SCEVConstant>(AddRec->getOperand(i)))
590 Operands.push_back(get(AddRec->getOperand(i), Ty));
593 if (Operands.size() == AddRec->getNumOperands())
594 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
597 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
598 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
602 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
603 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
604 return SCEVUnknown::get(
605 ConstantExpr::getZExt(SC->getValue(), Ty));
607 // FIXME: If the input value is a chrec scev, and we can prove that the value
608 // did not overflow the old, smaller, value, we can zero extend all of the
609 // operands (often constants). This would allow analysis of something like
610 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
612 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
613 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
617 SCEVHandle SCEVSignExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
618 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
619 return SCEVUnknown::get(
620 ConstantExpr::getSExt(SC->getValue(), Ty));
622 // FIXME: If the input value is a chrec scev, and we can prove that the value
623 // did not overflow the old, smaller, value, we can sign extend all of the
624 // operands (often constants). This would allow analysis of something like
625 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
627 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
628 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
632 // get - Get a canonical add expression, or something simpler if possible.
633 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
634 assert(!Ops.empty() && "Cannot get empty add!");
635 if (Ops.size() == 1) return Ops[0];
637 // Sort by complexity, this groups all similar expression types together.
638 GroupByComplexity(Ops);
640 // If there are any constants, fold them together.
642 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
644 assert(Idx < Ops.size());
645 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
646 // We found two constants, fold them together!
647 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
648 RHSC->getValue()->getValue());
649 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
650 Ops[0] = SCEVConstant::get(CI);
651 Ops.erase(Ops.begin()+1); // Erase the folded element
652 if (Ops.size() == 1) return Ops[0];
653 LHSC = cast<SCEVConstant>(Ops[0]);
655 // If we couldn't fold the expression, move to the next constant. Note
656 // that this is impossible to happen in practice because we always
657 // constant fold constant ints to constant ints.
662 // If we are left with a constant zero being added, strip it off.
663 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
664 Ops.erase(Ops.begin());
669 if (Ops.size() == 1) return Ops[0];
671 // Okay, check to see if the same value occurs in the operand list twice. If
672 // so, merge them together into an multiply expression. Since we sorted the
673 // list, these values are required to be adjacent.
674 const Type *Ty = Ops[0]->getType();
675 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
676 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
677 // Found a match, merge the two values into a multiply, and add any
678 // remaining values to the result.
679 SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
680 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
683 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
685 return SCEVAddExpr::get(Ops);
688 // Now we know the first non-constant operand. Skip past any cast SCEVs.
689 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
692 // If there are add operands they would be next.
693 if (Idx < Ops.size()) {
694 bool DeletedAdd = false;
695 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
696 // If we have an add, expand the add operands onto the end of the operands
698 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
699 Ops.erase(Ops.begin()+Idx);
703 // If we deleted at least one add, we added operands to the end of the list,
704 // and they are not necessarily sorted. Recurse to resort and resimplify
705 // any operands we just aquired.
710 // Skip over the add expression until we get to a multiply.
711 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
714 // If we are adding something to a multiply expression, make sure the
715 // something is not already an operand of the multiply. If so, merge it into
717 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
718 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
719 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
720 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
721 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
722 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
723 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
724 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
725 if (Mul->getNumOperands() != 2) {
726 // If the multiply has more than two operands, we must get the
728 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
729 MulOps.erase(MulOps.begin()+MulOp);
730 InnerMul = SCEVMulExpr::get(MulOps);
732 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
733 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
734 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
735 if (Ops.size() == 2) return OuterMul;
737 Ops.erase(Ops.begin()+AddOp);
738 Ops.erase(Ops.begin()+Idx-1);
740 Ops.erase(Ops.begin()+Idx);
741 Ops.erase(Ops.begin()+AddOp-1);
743 Ops.push_back(OuterMul);
744 return SCEVAddExpr::get(Ops);
747 // Check this multiply against other multiplies being added together.
748 for (unsigned OtherMulIdx = Idx+1;
749 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
751 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
752 // If MulOp occurs in OtherMul, we can fold the two multiplies
754 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
755 OMulOp != e; ++OMulOp)
756 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
757 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
758 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
759 if (Mul->getNumOperands() != 2) {
760 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
761 MulOps.erase(MulOps.begin()+MulOp);
762 InnerMul1 = SCEVMulExpr::get(MulOps);
764 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
765 if (OtherMul->getNumOperands() != 2) {
766 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
768 MulOps.erase(MulOps.begin()+OMulOp);
769 InnerMul2 = SCEVMulExpr::get(MulOps);
771 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
772 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
773 if (Ops.size() == 2) return OuterMul;
774 Ops.erase(Ops.begin()+Idx);
775 Ops.erase(Ops.begin()+OtherMulIdx-1);
776 Ops.push_back(OuterMul);
777 return SCEVAddExpr::get(Ops);
783 // If there are any add recurrences in the operands list, see if any other
784 // added values are loop invariant. If so, we can fold them into the
786 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
789 // Scan over all recurrences, trying to fold loop invariants into them.
790 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
791 // Scan all of the other operands to this add and add them to the vector if
792 // they are loop invariant w.r.t. the recurrence.
793 std::vector<SCEVHandle> LIOps;
794 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
795 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
796 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
797 LIOps.push_back(Ops[i]);
798 Ops.erase(Ops.begin()+i);
802 // If we found some loop invariants, fold them into the recurrence.
803 if (!LIOps.empty()) {
804 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
805 LIOps.push_back(AddRec->getStart());
807 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
808 AddRecOps[0] = SCEVAddExpr::get(LIOps);
810 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
811 // If all of the other operands were loop invariant, we are done.
812 if (Ops.size() == 1) return NewRec;
814 // Otherwise, add the folded AddRec by the non-liv parts.
815 for (unsigned i = 0;; ++i)
816 if (Ops[i] == AddRec) {
820 return SCEVAddExpr::get(Ops);
823 // Okay, if there weren't any loop invariants to be folded, check to see if
824 // there are multiple AddRec's with the same loop induction variable being
825 // added together. If so, we can fold them.
826 for (unsigned OtherIdx = Idx+1;
827 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
828 if (OtherIdx != Idx) {
829 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
830 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
831 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
832 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
833 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
834 if (i >= NewOps.size()) {
835 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
836 OtherAddRec->op_end());
839 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
841 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
843 if (Ops.size() == 2) return NewAddRec;
845 Ops.erase(Ops.begin()+Idx);
846 Ops.erase(Ops.begin()+OtherIdx-1);
847 Ops.push_back(NewAddRec);
848 return SCEVAddExpr::get(Ops);
852 // Otherwise couldn't fold anything into this recurrence. Move onto the
856 // Okay, it looks like we really DO need an add expr. Check to see if we
857 // already have one, otherwise create a new one.
858 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
859 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
861 if (Result == 0) Result = new SCEVAddExpr(Ops);
866 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
867 assert(!Ops.empty() && "Cannot get empty mul!");
869 // Sort by complexity, this groups all similar expression types together.
870 GroupByComplexity(Ops);
872 // If there are any constants, fold them together.
874 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
876 // C1*(C2+V) -> C1*C2 + C1*V
878 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
879 if (Add->getNumOperands() == 2 &&
880 isa<SCEVConstant>(Add->getOperand(0)))
881 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
882 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
886 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
887 // We found two constants, fold them together!
888 Constant *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
889 RHSC->getValue()->getValue());
890 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
891 Ops[0] = SCEVConstant::get(CI);
892 Ops.erase(Ops.begin()+1); // Erase the folded element
893 if (Ops.size() == 1) return Ops[0];
894 LHSC = cast<SCEVConstant>(Ops[0]);
896 // If we couldn't fold the expression, move to the next constant. Note
897 // that this is impossible to happen in practice because we always
898 // constant fold constant ints to constant ints.
903 // If we are left with a constant one being multiplied, strip it off.
904 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
905 Ops.erase(Ops.begin());
907 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
908 // If we have a multiply of zero, it will always be zero.
913 // Skip over the add expression until we get to a multiply.
914 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
920 // If there are mul operands inline them all into this expression.
921 if (Idx < Ops.size()) {
922 bool DeletedMul = false;
923 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
924 // If we have an mul, expand the mul operands onto the end of the operands
926 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
927 Ops.erase(Ops.begin()+Idx);
931 // If we deleted at least one mul, we added operands to the end of the list,
932 // and they are not necessarily sorted. Recurse to resort and resimplify
933 // any operands we just aquired.
938 // If there are any add recurrences in the operands list, see if any other
939 // added values are loop invariant. If so, we can fold them into the
941 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
944 // Scan over all recurrences, trying to fold loop invariants into them.
945 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
946 // Scan all of the other operands to this mul and add them to the vector if
947 // they are loop invariant w.r.t. the recurrence.
948 std::vector<SCEVHandle> LIOps;
949 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
950 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
951 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
952 LIOps.push_back(Ops[i]);
953 Ops.erase(Ops.begin()+i);
957 // If we found some loop invariants, fold them into the recurrence.
958 if (!LIOps.empty()) {
959 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
960 std::vector<SCEVHandle> NewOps;
961 NewOps.reserve(AddRec->getNumOperands());
962 if (LIOps.size() == 1) {
963 SCEV *Scale = LIOps[0];
964 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
965 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
967 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
968 std::vector<SCEVHandle> MulOps(LIOps);
969 MulOps.push_back(AddRec->getOperand(i));
970 NewOps.push_back(SCEVMulExpr::get(MulOps));
974 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
976 // If all of the other operands were loop invariant, we are done.
977 if (Ops.size() == 1) return NewRec;
979 // Otherwise, multiply the folded AddRec by the non-liv parts.
980 for (unsigned i = 0;; ++i)
981 if (Ops[i] == AddRec) {
985 return SCEVMulExpr::get(Ops);
988 // Okay, if there weren't any loop invariants to be folded, check to see if
989 // there are multiple AddRec's with the same loop induction variable being
990 // multiplied together. If so, we can fold them.
991 for (unsigned OtherIdx = Idx+1;
992 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
993 if (OtherIdx != Idx) {
994 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
995 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
996 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
997 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
998 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
1000 SCEVHandle B = F->getStepRecurrence();
1001 SCEVHandle D = G->getStepRecurrence();
1002 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
1003 SCEVMulExpr::get(G, B),
1004 SCEVMulExpr::get(B, D));
1005 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
1007 if (Ops.size() == 2) return NewAddRec;
1009 Ops.erase(Ops.begin()+Idx);
1010 Ops.erase(Ops.begin()+OtherIdx-1);
1011 Ops.push_back(NewAddRec);
1012 return SCEVMulExpr::get(Ops);
1016 // Otherwise couldn't fold anything into this recurrence. Move onto the
1020 // Okay, it looks like we really DO need an mul expr. Check to see if we
1021 // already have one, otherwise create a new one.
1022 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1023 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1026 Result = new SCEVMulExpr(Ops);
1030 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1031 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1032 if (RHSC->getValue()->equalsInt(1))
1033 return LHS; // X sdiv 1 --> x
1034 if (RHSC->getValue()->isAllOnesValue())
1035 return SCEV::getNegativeSCEV(LHS); // X sdiv -1 --> -x
1037 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1038 Constant *LHSCV = LHSC->getValue();
1039 Constant *RHSCV = RHSC->getValue();
1040 return SCEVUnknown::get(ConstantExpr::getSDiv(LHSCV, RHSCV));
1044 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1046 SCEVSDivExpr *&Result = (*SCEVSDivs)[std::make_pair(LHS, RHS)];
1047 if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
1052 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1053 /// specified loop. Simplify the expression as much as possible.
1054 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
1055 const SCEVHandle &Step, const Loop *L) {
1056 std::vector<SCEVHandle> Operands;
1057 Operands.push_back(Start);
1058 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1059 if (StepChrec->getLoop() == L) {
1060 Operands.insert(Operands.end(), StepChrec->op_begin(),
1061 StepChrec->op_end());
1062 return get(Operands, L);
1065 Operands.push_back(Step);
1066 return get(Operands, L);
1069 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1070 /// specified loop. Simplify the expression as much as possible.
1071 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
1073 if (Operands.size() == 1) return Operands[0];
1075 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
1076 if (StepC->getValue()->isZero()) {
1077 Operands.pop_back();
1078 return get(Operands, L); // { X,+,0 } --> X
1081 SCEVAddRecExpr *&Result =
1082 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1084 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1088 SCEVHandle SCEVUnknown::get(Value *V) {
1089 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1090 return SCEVConstant::get(CI);
1091 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1092 if (Result == 0) Result = new SCEVUnknown(V);
1097 //===----------------------------------------------------------------------===//
1098 // ScalarEvolutionsImpl Definition and Implementation
1099 //===----------------------------------------------------------------------===//
1101 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1105 struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
1106 /// F - The function we are analyzing.
1110 /// LI - The loop information for the function we are currently analyzing.
1114 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1116 SCEVHandle UnknownValue;
1118 /// Scalars - This is a cache of the scalars we have analyzed so far.
1120 std::map<Value*, SCEVHandle> Scalars;
1122 /// IterationCounts - Cache the iteration count of the loops for this
1123 /// function as they are computed.
1124 std::map<const Loop*, SCEVHandle> IterationCounts;
1126 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1127 /// the PHI instructions that we attempt to compute constant evolutions for.
1128 /// This allows us to avoid potentially expensive recomputation of these
1129 /// properties. An instruction maps to null if we are unable to compute its
1131 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1134 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1135 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1137 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1138 /// expression and create a new one.
1139 SCEVHandle getSCEV(Value *V);
1141 /// hasSCEV - Return true if the SCEV for this value has already been
1143 bool hasSCEV(Value *V) const {
1144 return Scalars.count(V);
1147 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
1148 /// the specified value.
1149 void setSCEV(Value *V, const SCEVHandle &H) {
1150 bool isNew = Scalars.insert(std::make_pair(V, H)).second;
1151 assert(isNew && "This entry already existed!");
1155 /// getSCEVAtScope - Compute the value of the specified expression within
1156 /// the indicated loop (which may be null to indicate in no loop). If the
1157 /// expression cannot be evaluated, return UnknownValue itself.
1158 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1161 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1162 /// an analyzable loop-invariant iteration count.
1163 bool hasLoopInvariantIterationCount(const Loop *L);
1165 /// getIterationCount - If the specified loop has a predictable iteration
1166 /// count, return it. Note that it is not valid to call this method on a
1167 /// loop without a loop-invariant iteration count.
1168 SCEVHandle getIterationCount(const Loop *L);
1170 /// deleteValueFromRecords - This method should be called by the
1171 /// client before it removes a value from the program, to make sure
1172 /// that no dangling references are left around.
1173 void deleteValueFromRecords(Value *V);
1176 /// createSCEV - We know that there is no SCEV for the specified value.
1177 /// Analyze the expression.
1178 SCEVHandle createSCEV(Value *V);
1180 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1182 SCEVHandle createNodeForPHI(PHINode *PN);
1184 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
1185 /// for the specified instruction and replaces any references to the
1186 /// symbolic value SymName with the specified value. This is used during
1188 void ReplaceSymbolicValueWithConcrete(Instruction *I,
1189 const SCEVHandle &SymName,
1190 const SCEVHandle &NewVal);
1192 /// ComputeIterationCount - Compute the number of times the specified loop
1194 SCEVHandle ComputeIterationCount(const Loop *L);
1196 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1197 /// 'setcc load X, cst', try to see if we can compute the trip count.
1198 SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
1201 ICmpInst::Predicate p);
1203 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1204 /// constant number of times (the condition evolves only from constants),
1205 /// try to evaluate a few iterations of the loop until we get the exit
1206 /// condition gets a value of ExitWhen (true or false). If we cannot
1207 /// evaluate the trip count of the loop, return UnknownValue.
1208 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1211 /// HowFarToZero - Return the number of times a backedge comparing the
1212 /// specified value to zero will execute. If not computable, return
1214 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1216 /// HowFarToNonZero - Return the number of times a backedge checking the
1217 /// specified value for nonzero will execute. If not computable, return
1219 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1221 /// HowManyLessThans - Return the number of times a backedge containing the
1222 /// specified less-than comparison will execute. If not computable, return
1224 SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
1226 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1227 /// in the header of its containing loop, we know the loop executes a
1228 /// constant number of times, and the PHI node is just a recurrence
1229 /// involving constants, fold it.
1230 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its,
1235 //===----------------------------------------------------------------------===//
1236 // Basic SCEV Analysis and PHI Idiom Recognition Code
1239 /// deleteValueFromRecords - This method should be called by the
1240 /// client before it removes an instruction from the program, to make sure
1241 /// that no dangling references are left around.
1242 void ScalarEvolutionsImpl::deleteValueFromRecords(Value *V) {
1243 SmallVector<Value *, 16> Worklist;
1245 if (Scalars.erase(V)) {
1246 if (PHINode *PN = dyn_cast<PHINode>(V))
1247 ConstantEvolutionLoopExitValue.erase(PN);
1248 Worklist.push_back(V);
1251 while (!Worklist.empty()) {
1252 Value *VV = Worklist.back();
1253 Worklist.pop_back();
1255 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1257 Instruction *Inst = cast<Instruction>(*UI);
1258 if (Scalars.erase(Inst)) {
1259 if (PHINode *PN = dyn_cast<PHINode>(VV))
1260 ConstantEvolutionLoopExitValue.erase(PN);
1261 Worklist.push_back(Inst);
1268 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1269 /// expression and create a new one.
1270 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1271 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1273 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1274 if (I != Scalars.end()) return I->second;
1275 SCEVHandle S = createSCEV(V);
1276 Scalars.insert(std::make_pair(V, S));
1280 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1281 /// the specified instruction and replaces any references to the symbolic value
1282 /// SymName with the specified value. This is used during PHI resolution.
1283 void ScalarEvolutionsImpl::
1284 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1285 const SCEVHandle &NewVal) {
1286 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1287 if (SI == Scalars.end()) return;
1290 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
1291 if (NV == SI->second) return; // No change.
1293 SI->second = NV; // Update the scalars map!
1295 // Any instruction values that use this instruction might also need to be
1297 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1299 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1302 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1303 /// a loop header, making it a potential recurrence, or it doesn't.
1305 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1306 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1307 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1308 if (L->getHeader() == PN->getParent()) {
1309 // If it lives in the loop header, it has two incoming values, one
1310 // from outside the loop, and one from inside.
1311 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1312 unsigned BackEdge = IncomingEdge^1;
1314 // While we are analyzing this PHI node, handle its value symbolically.
1315 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1316 assert(Scalars.find(PN) == Scalars.end() &&
1317 "PHI node already processed?");
1318 Scalars.insert(std::make_pair(PN, SymbolicName));
1320 // Using this symbolic name for the PHI, analyze the value coming around
1322 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1324 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1325 // has a special value for the first iteration of the loop.
1327 // If the value coming around the backedge is an add with the symbolic
1328 // value we just inserted, then we found a simple induction variable!
1329 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1330 // If there is a single occurrence of the symbolic value, replace it
1331 // with a recurrence.
1332 unsigned FoundIndex = Add->getNumOperands();
1333 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1334 if (Add->getOperand(i) == SymbolicName)
1335 if (FoundIndex == e) {
1340 if (FoundIndex != Add->getNumOperands()) {
1341 // Create an add with everything but the specified operand.
1342 std::vector<SCEVHandle> Ops;
1343 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1344 if (i != FoundIndex)
1345 Ops.push_back(Add->getOperand(i));
1346 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1348 // This is not a valid addrec if the step amount is varying each
1349 // loop iteration, but is not itself an addrec in this loop.
1350 if (Accum->isLoopInvariant(L) ||
1351 (isa<SCEVAddRecExpr>(Accum) &&
1352 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1353 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1354 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1356 // Okay, for the entire analysis of this edge we assumed the PHI
1357 // to be symbolic. We now need to go back and update all of the
1358 // entries for the scalars that use the PHI (except for the PHI
1359 // itself) to use the new analyzed value instead of the "symbolic"
1361 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1365 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1366 // Otherwise, this could be a loop like this:
1367 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1368 // In this case, j = {1,+,1} and BEValue is j.
1369 // Because the other in-value of i (0) fits the evolution of BEValue
1370 // i really is an addrec evolution.
1371 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1372 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1374 // If StartVal = j.start - j.stride, we can use StartVal as the
1375 // initial step of the addrec evolution.
1376 if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
1377 AddRec->getOperand(1))) {
1378 SCEVHandle PHISCEV =
1379 SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
1381 // Okay, for the entire analysis of this edge we assumed the PHI
1382 // to be symbolic. We now need to go back and update all of the
1383 // entries for the scalars that use the PHI (except for the PHI
1384 // itself) to use the new analyzed value instead of the "symbolic"
1386 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1392 return SymbolicName;
1395 // If it's not a loop phi, we can't handle it yet.
1396 return SCEVUnknown::get(PN);
1399 /// GetConstantFactor - Determine the largest constant factor that S has. For
1400 /// example, turn {4,+,8} -> 4. (S umod result) should always equal zero.
1401 static APInt GetConstantFactor(SCEVHandle S) {
1402 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
1403 const APInt& V = C->getValue()->getValue();
1404 if (!V.isMinValue())
1406 else // Zero is a multiple of everything.
1407 return APInt(C->getBitWidth(), 1).shl(C->getBitWidth()-1);
1410 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S)) {
1411 return GetConstantFactor(T->getOperand()).trunc(
1412 cast<IntegerType>(T->getType())->getBitWidth());
1414 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S))
1415 return GetConstantFactor(E->getOperand()).zext(
1416 cast<IntegerType>(E->getType())->getBitWidth());
1417 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S))
1418 return GetConstantFactor(E->getOperand()).sext(
1419 cast<IntegerType>(E->getType())->getBitWidth());
1421 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1422 // The result is the min of all operands.
1423 APInt Res(GetConstantFactor(A->getOperand(0)));
1424 for (unsigned i = 1, e = A->getNumOperands();
1425 i != e && Res.ugt(APInt(Res.getBitWidth(),1)); ++i) {
1426 APInt Tmp(GetConstantFactor(A->getOperand(i)));
1427 Res = APIntOps::umin(Res, Tmp);
1432 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1433 // The result is the product of all the operands.
1434 APInt Res(GetConstantFactor(M->getOperand(0)));
1435 for (unsigned i = 1, e = M->getNumOperands(); i != e; ++i) {
1436 APInt Tmp(GetConstantFactor(M->getOperand(i)));
1442 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1443 // For now, we just handle linear expressions.
1444 if (A->getNumOperands() == 2) {
1445 // We want the GCD between the start and the stride value.
1446 APInt Start(GetConstantFactor(A->getOperand(0)));
1449 APInt Stride(GetConstantFactor(A->getOperand(1)));
1450 return APIntOps::GreatestCommonDivisor(Start, Stride);
1454 // SCEVSDivExpr, SCEVUnknown.
1455 return APInt(S->getBitWidth(), 1);
1458 /// createSCEV - We know that there is no SCEV for the specified value.
1459 /// Analyze the expression.
1461 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1462 if (Instruction *I = dyn_cast<Instruction>(V)) {
1463 switch (I->getOpcode()) {
1464 case Instruction::Add:
1465 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1466 getSCEV(I->getOperand(1)));
1467 case Instruction::Mul:
1468 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1469 getSCEV(I->getOperand(1)));
1470 case Instruction::SDiv:
1471 return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
1472 getSCEV(I->getOperand(1)));
1475 case Instruction::Sub:
1476 return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
1477 getSCEV(I->getOperand(1)));
1478 case Instruction::Or:
1479 // If the RHS of the Or is a constant, we may have something like:
1480 // X*4+1 which got turned into X*4|1. Handle this as an add so loop
1481 // optimizations will transparently handle this case.
1482 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1483 SCEVHandle LHS = getSCEV(I->getOperand(0));
1484 APInt CommonFact(GetConstantFactor(LHS));
1485 assert(!CommonFact.isMinValue() &&
1486 "Common factor should at least be 1!");
1487 if (CommonFact.ugt(CI->getValue())) {
1488 // If the LHS is a multiple that is larger than the RHS, use +.
1489 return SCEVAddExpr::get(LHS,
1490 getSCEV(I->getOperand(1)));
1494 case Instruction::Xor:
1495 // If the RHS of the xor is a signbit, then this is just an add.
1496 // Instcombine turns add of signbit into xor as a strength reduction step.
1497 if (ConstantInt *CI = dyn_cast<ConstantInt>(I->getOperand(1))) {
1498 if (CI->getValue().isSignBit())
1499 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1500 getSCEV(I->getOperand(1)));
1504 case Instruction::Shl:
1505 // Turn shift left of a constant amount into a multiply.
1506 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1507 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1508 Constant *X = ConstantInt::get(
1509 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1510 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1514 case Instruction::Trunc:
1515 return SCEVTruncateExpr::get(getSCEV(I->getOperand(0)), I->getType());
1517 case Instruction::ZExt:
1518 return SCEVZeroExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1520 case Instruction::SExt:
1521 return SCEVSignExtendExpr::get(getSCEV(I->getOperand(0)), I->getType());
1523 case Instruction::BitCast:
1524 // BitCasts are no-op casts so we just eliminate the cast.
1525 if (I->getType()->isInteger() &&
1526 I->getOperand(0)->getType()->isInteger())
1527 return getSCEV(I->getOperand(0));
1530 case Instruction::PHI:
1531 return createNodeForPHI(cast<PHINode>(I));
1533 default: // We cannot analyze this expression.
1538 return SCEVUnknown::get(V);
1543 //===----------------------------------------------------------------------===//
1544 // Iteration Count Computation Code
1547 /// getIterationCount - If the specified loop has a predictable iteration
1548 /// count, return it. Note that it is not valid to call this method on a
1549 /// loop without a loop-invariant iteration count.
1550 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1551 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1552 if (I == IterationCounts.end()) {
1553 SCEVHandle ItCount = ComputeIterationCount(L);
1554 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1555 if (ItCount != UnknownValue) {
1556 assert(ItCount->isLoopInvariant(L) &&
1557 "Computed trip count isn't loop invariant for loop!");
1558 ++NumTripCountsComputed;
1559 } else if (isa<PHINode>(L->getHeader()->begin())) {
1560 // Only count loops that have phi nodes as not being computable.
1561 ++NumTripCountsNotComputed;
1567 /// ComputeIterationCount - Compute the number of times the specified loop
1569 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1570 // If the loop has a non-one exit block count, we can't analyze it.
1571 std::vector<BasicBlock*> ExitBlocks;
1572 L->getExitBlocks(ExitBlocks);
1573 if (ExitBlocks.size() != 1) return UnknownValue;
1575 // Okay, there is one exit block. Try to find the condition that causes the
1576 // loop to be exited.
1577 BasicBlock *ExitBlock = ExitBlocks[0];
1579 BasicBlock *ExitingBlock = 0;
1580 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1582 if (L->contains(*PI)) {
1583 if (ExitingBlock == 0)
1586 return UnknownValue; // More than one block exiting!
1588 assert(ExitingBlock && "No exits from loop, something is broken!");
1590 // Okay, we've computed the exiting block. See what condition causes us to
1593 // FIXME: we should be able to handle switch instructions (with a single exit)
1594 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1595 if (ExitBr == 0) return UnknownValue;
1596 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1598 // At this point, we know we have a conditional branch that determines whether
1599 // the loop is exited. However, we don't know if the branch is executed each
1600 // time through the loop. If not, then the execution count of the branch will
1601 // not be equal to the trip count of the loop.
1603 // Currently we check for this by checking to see if the Exit branch goes to
1604 // the loop header. If so, we know it will always execute the same number of
1605 // times as the loop. We also handle the case where the exit block *is* the
1606 // loop header. This is common for un-rotated loops. More extensive analysis
1607 // could be done to handle more cases here.
1608 if (ExitBr->getSuccessor(0) != L->getHeader() &&
1609 ExitBr->getSuccessor(1) != L->getHeader() &&
1610 ExitBr->getParent() != L->getHeader())
1611 return UnknownValue;
1613 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
1615 // If its not an integer comparison then compute it the hard way.
1616 // Note that ICmpInst deals with pointer comparisons too so we must check
1617 // the type of the operand.
1618 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
1619 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1620 ExitBr->getSuccessor(0) == ExitBlock);
1622 // If the condition was exit on true, convert the condition to exit on false
1623 ICmpInst::Predicate Cond;
1624 if (ExitBr->getSuccessor(1) == ExitBlock)
1625 Cond = ExitCond->getPredicate();
1627 Cond = ExitCond->getInversePredicate();
1629 // Handle common loops like: for (X = "string"; *X; ++X)
1630 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
1631 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
1633 ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
1634 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
1637 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1638 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1640 // Try to evaluate any dependencies out of the loop.
1641 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1642 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1643 Tmp = getSCEVAtScope(RHS, L);
1644 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1646 // At this point, we would like to compute how many iterations of the
1647 // loop the predicate will return true for these inputs.
1648 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1649 // If there is a constant, force it into the RHS.
1650 std::swap(LHS, RHS);
1651 Cond = ICmpInst::getSwappedPredicate(Cond);
1654 // FIXME: think about handling pointer comparisons! i.e.:
1655 // while (P != P+100) ++P;
1657 // If we have a comparison of a chrec against a constant, try to use value
1658 // ranges to answer this query.
1659 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1660 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1661 if (AddRec->getLoop() == L) {
1662 // Form the comparison range using the constant of the correct type so
1663 // that the ConstantRange class knows to do a signed or unsigned
1665 ConstantInt *CompVal = RHSC->getValue();
1666 const Type *RealTy = ExitCond->getOperand(0)->getType();
1667 CompVal = dyn_cast<ConstantInt>(
1668 ConstantExpr::getBitCast(CompVal, RealTy));
1670 // Form the constant range.
1671 ConstantRange CompRange(
1672 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
1674 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange,
1675 false /*Always treat as unsigned range*/);
1676 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1681 case ICmpInst::ICMP_NE: { // while (X != Y)
1682 // Convert to: while (X-Y != 0)
1683 SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
1684 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1687 case ICmpInst::ICMP_EQ: {
1688 // Convert to: while (X-Y == 0) // while (X == Y)
1689 SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
1690 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1693 case ICmpInst::ICMP_SLT: {
1694 SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
1695 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1698 case ICmpInst::ICMP_SGT: {
1699 SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
1700 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1705 cerr << "ComputeIterationCount ";
1706 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1707 cerr << "[unsigned] ";
1709 << Instruction::getOpcodeName(Instruction::ICmp)
1710 << " " << *RHS << "\n";
1714 return ComputeIterationCountExhaustively(L, ExitCond,
1715 ExitBr->getSuccessor(0) == ExitBlock);
1718 static ConstantInt *
1719 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
1720 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
1721 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
1722 assert(isa<SCEVConstant>(Val) &&
1723 "Evaluation of SCEV at constant didn't fold correctly?");
1724 return cast<SCEVConstant>(Val)->getValue();
1727 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
1728 /// and a GEP expression (missing the pointer index) indexing into it, return
1729 /// the addressed element of the initializer or null if the index expression is
1732 GetAddressedElementFromGlobal(GlobalVariable *GV,
1733 const std::vector<ConstantInt*> &Indices) {
1734 Constant *Init = GV->getInitializer();
1735 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
1736 uint64_t Idx = Indices[i]->getZExtValue();
1737 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
1738 assert(Idx < CS->getNumOperands() && "Bad struct index!");
1739 Init = cast<Constant>(CS->getOperand(Idx));
1740 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
1741 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
1742 Init = cast<Constant>(CA->getOperand(Idx));
1743 } else if (isa<ConstantAggregateZero>(Init)) {
1744 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
1745 assert(Idx < STy->getNumElements() && "Bad struct index!");
1746 Init = Constant::getNullValue(STy->getElementType(Idx));
1747 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
1748 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
1749 Init = Constant::getNullValue(ATy->getElementType());
1751 assert(0 && "Unknown constant aggregate type!");
1755 return 0; // Unknown initializer type
1761 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
1762 /// 'setcc load X, cst', try to se if we can compute the trip count.
1763 SCEVHandle ScalarEvolutionsImpl::
1764 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
1766 ICmpInst::Predicate predicate) {
1767 if (LI->isVolatile()) return UnknownValue;
1769 // Check to see if the loaded pointer is a getelementptr of a global.
1770 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
1771 if (!GEP) return UnknownValue;
1773 // Make sure that it is really a constant global we are gepping, with an
1774 // initializer, and make sure the first IDX is really 0.
1775 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
1776 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
1777 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
1778 !cast<Constant>(GEP->getOperand(1))->isNullValue())
1779 return UnknownValue;
1781 // Okay, we allow one non-constant index into the GEP instruction.
1783 std::vector<ConstantInt*> Indexes;
1784 unsigned VarIdxNum = 0;
1785 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
1786 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
1787 Indexes.push_back(CI);
1788 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
1789 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
1790 VarIdx = GEP->getOperand(i);
1792 Indexes.push_back(0);
1795 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
1796 // Check to see if X is a loop variant variable value now.
1797 SCEVHandle Idx = getSCEV(VarIdx);
1798 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
1799 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
1801 // We can only recognize very limited forms of loop index expressions, in
1802 // particular, only affine AddRec's like {C1,+,C2}.
1803 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
1804 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
1805 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
1806 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
1807 return UnknownValue;
1809 unsigned MaxSteps = MaxBruteForceIterations;
1810 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
1811 ConstantInt *ItCst =
1812 ConstantInt::get(IdxExpr->getType(), IterationNum);
1813 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
1815 // Form the GEP offset.
1816 Indexes[VarIdxNum] = Val;
1818 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
1819 if (Result == 0) break; // Cannot compute!
1821 // Evaluate the condition for this iteration.
1822 Result = ConstantExpr::getICmp(predicate, Result, RHS);
1823 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
1824 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
1826 cerr << "\n***\n*** Computed loop count " << *ItCst
1827 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
1830 ++NumArrayLenItCounts;
1831 return SCEVConstant::get(ItCst); // Found terminating iteration!
1834 return UnknownValue;
1838 /// CanConstantFold - Return true if we can constant fold an instruction of the
1839 /// specified type, assuming that all operands were constants.
1840 static bool CanConstantFold(const Instruction *I) {
1841 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
1842 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1845 if (const CallInst *CI = dyn_cast<CallInst>(I))
1846 if (const Function *F = CI->getCalledFunction())
1847 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1851 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1852 /// in the loop that V is derived from. We allow arbitrary operations along the
1853 /// way, but the operands of an operation must either be constants or a value
1854 /// derived from a constant PHI. If this expression does not fit with these
1855 /// constraints, return null.
1856 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1857 // If this is not an instruction, or if this is an instruction outside of the
1858 // loop, it can't be derived from a loop PHI.
1859 Instruction *I = dyn_cast<Instruction>(V);
1860 if (I == 0 || !L->contains(I->getParent())) return 0;
1862 if (PHINode *PN = dyn_cast<PHINode>(I))
1863 if (L->getHeader() == I->getParent())
1866 // We don't currently keep track of the control flow needed to evaluate
1867 // PHIs, so we cannot handle PHIs inside of loops.
1870 // If we won't be able to constant fold this expression even if the operands
1871 // are constants, return early.
1872 if (!CanConstantFold(I)) return 0;
1874 // Otherwise, we can evaluate this instruction if all of its operands are
1875 // constant or derived from a PHI node themselves.
1877 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1878 if (!(isa<Constant>(I->getOperand(Op)) ||
1879 isa<GlobalValue>(I->getOperand(Op)))) {
1880 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1881 if (P == 0) return 0; // Not evolving from PHI
1885 return 0; // Evolving from multiple different PHIs.
1888 // This is a expression evolving from a constant PHI!
1892 /// EvaluateExpression - Given an expression that passes the
1893 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1894 /// in the loop has the value PHIVal. If we can't fold this expression for some
1895 /// reason, return null.
1896 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1897 if (isa<PHINode>(V)) return PHIVal;
1898 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1900 if (Constant *C = dyn_cast<Constant>(V)) return C;
1901 Instruction *I = cast<Instruction>(V);
1903 std::vector<Constant*> Operands;
1904 Operands.resize(I->getNumOperands());
1906 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1907 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1908 if (Operands[i] == 0) return 0;
1911 return ConstantFoldInstOperands(I, &Operands[0], Operands.size());
1914 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1915 /// in the header of its containing loop, we know the loop executes a
1916 /// constant number of times, and the PHI node is just a recurrence
1917 /// involving constants, fold it.
1918 Constant *ScalarEvolutionsImpl::
1919 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& Its, const Loop *L){
1920 std::map<PHINode*, Constant*>::iterator I =
1921 ConstantEvolutionLoopExitValue.find(PN);
1922 if (I != ConstantEvolutionLoopExitValue.end())
1925 if (Its.ugt(APInt(Its.getBitWidth(),MaxBruteForceIterations)))
1926 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1928 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1930 // Since the loop is canonicalized, the PHI node must have two entries. One
1931 // entry must be a constant (coming in from outside of the loop), and the
1932 // second must be derived from the same PHI.
1933 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1934 Constant *StartCST =
1935 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1937 return RetVal = 0; // Must be a constant.
1939 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1940 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1942 return RetVal = 0; // Not derived from same PHI.
1944 // Execute the loop symbolically to determine the exit value.
1945 if (Its.getActiveBits() >= 32)
1946 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
1948 unsigned NumIterations = Its.getZExtValue(); // must be in range
1949 unsigned IterationNum = 0;
1950 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1951 if (IterationNum == NumIterations)
1952 return RetVal = PHIVal; // Got exit value!
1954 // Compute the value of the PHI node for the next iteration.
1955 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1956 if (NextPHI == PHIVal)
1957 return RetVal = NextPHI; // Stopped evolving!
1959 return 0; // Couldn't evaluate!
1964 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1965 /// constant number of times (the condition evolves only from constants),
1966 /// try to evaluate a few iterations of the loop until we get the exit
1967 /// condition gets a value of ExitWhen (true or false). If we cannot
1968 /// evaluate the trip count of the loop, return UnknownValue.
1969 SCEVHandle ScalarEvolutionsImpl::
1970 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1971 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1972 if (PN == 0) return UnknownValue;
1974 // Since the loop is canonicalized, the PHI node must have two entries. One
1975 // entry must be a constant (coming in from outside of the loop), and the
1976 // second must be derived from the same PHI.
1977 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1978 Constant *StartCST =
1979 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1980 if (StartCST == 0) return UnknownValue; // Must be a constant.
1982 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1983 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1984 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1986 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1987 // the loop symbolically to determine when the condition gets a value of
1989 unsigned IterationNum = 0;
1990 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1991 for (Constant *PHIVal = StartCST;
1992 IterationNum != MaxIterations; ++IterationNum) {
1993 ConstantInt *CondVal =
1994 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
1996 // Couldn't symbolically evaluate.
1997 if (!CondVal) return UnknownValue;
1999 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2000 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2001 ++NumBruteForceTripCountsComputed;
2002 return SCEVConstant::get(ConstantInt::get(Type::Int32Ty, IterationNum));
2005 // Compute the value of the PHI node for the next iteration.
2006 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2007 if (NextPHI == 0 || NextPHI == PHIVal)
2008 return UnknownValue; // Couldn't evaluate or not making progress...
2012 // Too many iterations were needed to evaluate.
2013 return UnknownValue;
2016 /// getSCEVAtScope - Compute the value of the specified expression within the
2017 /// indicated loop (which may be null to indicate in no loop). If the
2018 /// expression cannot be evaluated, return UnknownValue.
2019 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
2020 // FIXME: this should be turned into a virtual method on SCEV!
2022 if (isa<SCEVConstant>(V)) return V;
2024 // If this instruction is evolves from a constant-evolving PHI, compute the
2025 // exit value from the loop without using SCEVs.
2026 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2027 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2028 const Loop *LI = this->LI[I->getParent()];
2029 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2030 if (PHINode *PN = dyn_cast<PHINode>(I))
2031 if (PN->getParent() == LI->getHeader()) {
2032 // Okay, there is no closed form solution for the PHI node. Check
2033 // to see if the loop that contains it has a known iteration count.
2034 // If so, we may be able to force computation of the exit value.
2035 SCEVHandle IterationCount = getIterationCount(LI);
2036 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
2037 // Okay, we know how many times the containing loop executes. If
2038 // this is a constant evolving PHI node, get the final value at
2039 // the specified iteration number.
2040 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2041 ICC->getValue()->getValue(),
2043 if (RV) return SCEVUnknown::get(RV);
2047 // Okay, this is an expression that we cannot symbolically evaluate
2048 // into a SCEV. Check to see if it's possible to symbolically evaluate
2049 // the arguments into constants, and if so, try to constant propagate the
2050 // result. This is particularly useful for computing loop exit values.
2051 if (CanConstantFold(I)) {
2052 std::vector<Constant*> Operands;
2053 Operands.reserve(I->getNumOperands());
2054 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2055 Value *Op = I->getOperand(i);
2056 if (Constant *C = dyn_cast<Constant>(Op)) {
2057 Operands.push_back(C);
2059 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2060 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
2061 Operands.push_back(ConstantExpr::getIntegerCast(SC->getValue(),
2064 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2065 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
2066 Operands.push_back(ConstantExpr::getIntegerCast(C,
2076 Constant *C =ConstantFoldInstOperands(I, &Operands[0], Operands.size());
2077 return SCEVUnknown::get(C);
2081 // This is some other type of SCEVUnknown, just return it.
2085 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2086 // Avoid performing the look-up in the common case where the specified
2087 // expression has no loop-variant portions.
2088 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2089 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2090 if (OpAtScope != Comm->getOperand(i)) {
2091 if (OpAtScope == UnknownValue) return UnknownValue;
2092 // Okay, at least one of these operands is loop variant but might be
2093 // foldable. Build a new instance of the folded commutative expression.
2094 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2095 NewOps.push_back(OpAtScope);
2097 for (++i; i != e; ++i) {
2098 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2099 if (OpAtScope == UnknownValue) return UnknownValue;
2100 NewOps.push_back(OpAtScope);
2102 if (isa<SCEVAddExpr>(Comm))
2103 return SCEVAddExpr::get(NewOps);
2104 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
2105 return SCEVMulExpr::get(NewOps);
2108 // If we got here, all operands are loop invariant.
2112 if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
2113 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2114 if (LHS == UnknownValue) return LHS;
2115 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2116 if (RHS == UnknownValue) return RHS;
2117 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2118 return Div; // must be loop invariant
2119 return SCEVSDivExpr::get(LHS, RHS);
2122 // If this is a loop recurrence for a loop that does not contain L, then we
2123 // are dealing with the final value computed by the loop.
2124 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2125 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2126 // To evaluate this recurrence, we need to know how many times the AddRec
2127 // loop iterates. Compute this now.
2128 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
2129 if (IterationCount == UnknownValue) return UnknownValue;
2130 IterationCount = getTruncateOrZeroExtend(IterationCount,
2133 // If the value is affine, simplify the expression evaluation to just
2134 // Start + Step*IterationCount.
2135 if (AddRec->isAffine())
2136 return SCEVAddExpr::get(AddRec->getStart(),
2137 SCEVMulExpr::get(IterationCount,
2138 AddRec->getOperand(1)));
2140 // Otherwise, evaluate it the hard way.
2141 return AddRec->evaluateAtIteration(IterationCount);
2143 return UnknownValue;
2146 //assert(0 && "Unknown SCEV type!");
2147 return UnknownValue;
2151 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2152 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2153 /// might be the same) or two SCEVCouldNotCompute objects.
2155 static std::pair<SCEVHandle,SCEVHandle>
2156 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
2157 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2158 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2159 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2160 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2162 // We currently can only solve this if the coefficients are constants.
2163 if (!LC || !MC || !NC) {
2164 SCEV *CNC = new SCEVCouldNotCompute();
2165 return std::make_pair(CNC, CNC);
2168 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2169 const APInt &L = LC->getValue()->getValue();
2170 const APInt &M = MC->getValue()->getValue();
2171 const APInt &N = NC->getValue()->getValue();
2172 APInt Two(BitWidth, 2);
2173 APInt Four(BitWidth, 4);
2176 using namespace APIntOps;
2178 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2179 // The B coefficient is M-N/2
2183 // The A coefficient is N/2
2184 APInt A(N.sdiv(Two));
2186 // Compute the B^2-4ac term.
2189 SqrtTerm -= Four * (A * C);
2191 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2192 // integer value or else APInt::sqrt() will assert.
2193 APInt SqrtVal(SqrtTerm.sqrt());
2195 // Compute the two solutions for the quadratic formula.
2196 // The divisions must be performed as signed divisions.
2198 APInt TwoA( A << 1 );
2199 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2200 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2202 return std::make_pair(SCEVUnknown::get(Solution1),
2203 SCEVUnknown::get(Solution2));
2204 } // end APIntOps namespace
2207 /// HowFarToZero - Return the number of times a backedge comparing the specified
2208 /// value to zero will execute. If not computable, return UnknownValue
2209 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
2210 // If the value is a constant
2211 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2212 // If the value is already zero, the branch will execute zero times.
2213 if (C->getValue()->isZero()) return C;
2214 return UnknownValue; // Otherwise it will loop infinitely.
2217 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2218 if (!AddRec || AddRec->getLoop() != L)
2219 return UnknownValue;
2221 if (AddRec->isAffine()) {
2222 // If this is an affine expression the execution count of this branch is
2225 // (0 - Start/Step) iff Start % Step == 0
2227 // Get the initial value for the loop.
2228 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2229 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2230 SCEVHandle Step = AddRec->getOperand(1);
2232 Step = getSCEVAtScope(Step, L->getParentLoop());
2234 // Figure out if Start % Step == 0.
2235 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2236 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2237 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2238 return SCEV::getNegativeSCEV(Start); // 0 - Start/1 == -Start
2239 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2240 return Start; // 0 - Start/-1 == Start
2242 // Check to see if Start is divisible by SC with no remainder.
2243 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2244 ConstantInt *StartCC = StartC->getValue();
2245 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2246 Constant *Rem = ConstantExpr::getSRem(StartNegC, StepC->getValue());
2247 if (Rem->isNullValue()) {
2248 Constant *Result =ConstantExpr::getSDiv(StartNegC,StepC->getValue());
2249 return SCEVUnknown::get(Result);
2253 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2254 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2255 // the quadratic equation to solve it.
2256 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2257 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2258 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2261 cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2262 << " sol#2: " << *R2 << "\n";
2264 // Pick the smallest positive root value.
2265 if (ConstantInt *CB =
2266 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2267 R1->getValue(), R2->getValue()))) {
2268 if (CB->getZExtValue() == false)
2269 std::swap(R1, R2); // R1 is the minimum root now.
2271 // We can only use this value if the chrec ends up with an exact zero
2272 // value at this index. When solving for "X*X != 5", for example, we
2273 // should not accept a root of 2.
2274 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2275 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2276 if (EvalVal->getValue()->isZero())
2277 return R1; // We found a quadratic root!
2282 return UnknownValue;
2285 /// HowFarToNonZero - Return the number of times a backedge checking the
2286 /// specified value for nonzero will execute. If not computable, return
2288 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2289 // Loops that look like: while (X == 0) are very strange indeed. We don't
2290 // handle them yet except for the trivial case. This could be expanded in the
2291 // future as needed.
2293 // If the value is a constant, check to see if it is known to be non-zero
2294 // already. If so, the backedge will execute zero times.
2295 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2296 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2298 ConstantExpr::getICmp(ICmpInst::ICMP_NE, C->getValue(), Zero);
2299 if (NonZero == ConstantInt::getTrue())
2300 return getSCEV(Zero);
2301 return UnknownValue; // Otherwise it will loop infinitely.
2304 // We could implement others, but I really doubt anyone writes loops like
2305 // this, and if they did, they would already be constant folded.
2306 return UnknownValue;
2309 /// HowManyLessThans - Return the number of times a backedge containing the
2310 /// specified less-than comparison will execute. If not computable, return
2312 SCEVHandle ScalarEvolutionsImpl::
2313 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
2314 // Only handle: "ADDREC < LoopInvariant".
2315 if (!RHS->isLoopInvariant(L)) return UnknownValue;
2317 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
2318 if (!AddRec || AddRec->getLoop() != L)
2319 return UnknownValue;
2321 if (AddRec->isAffine()) {
2322 // FORNOW: We only support unit strides.
2323 SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
2324 if (AddRec->getOperand(1) != One)
2325 return UnknownValue;
2327 // The number of iterations for "[n,+,1] < m", is m-n. However, we don't
2328 // know that m is >= n on input to the loop. If it is, the condition return
2329 // true zero times. What we really should return, for full generality, is
2330 // SMAX(0, m-n). Since we cannot check this, we will instead check for a
2331 // canonical loop form: most do-loops will have a check that dominates the
2332 // loop, that only enters the loop if [n-1]<m. If we can find this check,
2333 // we know that the SMAX will evaluate to m-n, because we know that m >= n.
2335 // Search for the check.
2336 BasicBlock *Preheader = L->getLoopPreheader();
2337 BasicBlock *PreheaderDest = L->getHeader();
2338 if (Preheader == 0) return UnknownValue;
2340 BranchInst *LoopEntryPredicate =
2341 dyn_cast<BranchInst>(Preheader->getTerminator());
2342 if (!LoopEntryPredicate) return UnknownValue;
2344 // This might be a critical edge broken out. If the loop preheader ends in
2345 // an unconditional branch to the loop, check to see if the preheader has a
2346 // single predecessor, and if so, look for its terminator.
2347 while (LoopEntryPredicate->isUnconditional()) {
2348 PreheaderDest = Preheader;
2349 Preheader = Preheader->getSinglePredecessor();
2350 if (!Preheader) return UnknownValue; // Multiple preds.
2352 LoopEntryPredicate =
2353 dyn_cast<BranchInst>(Preheader->getTerminator());
2354 if (!LoopEntryPredicate) return UnknownValue;
2357 // Now that we found a conditional branch that dominates the loop, check to
2358 // see if it is the comparison we are looking for.
2359 if (ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition())){
2360 Value *PreCondLHS = ICI->getOperand(0);
2361 Value *PreCondRHS = ICI->getOperand(1);
2362 ICmpInst::Predicate Cond;
2363 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
2364 Cond = ICI->getPredicate();
2366 Cond = ICI->getInversePredicate();
2369 case ICmpInst::ICMP_UGT:
2370 std::swap(PreCondLHS, PreCondRHS);
2371 Cond = ICmpInst::ICMP_ULT;
2373 case ICmpInst::ICMP_SGT:
2374 std::swap(PreCondLHS, PreCondRHS);
2375 Cond = ICmpInst::ICMP_SLT;
2380 if (Cond == ICmpInst::ICMP_SLT) {
2381 if (PreCondLHS->getType()->isInteger()) {
2382 if (RHS != getSCEV(PreCondRHS))
2383 return UnknownValue; // Not a comparison against 'm'.
2385 if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
2386 != getSCEV(PreCondLHS))
2387 return UnknownValue; // Not a comparison against 'n-1'.
2389 else return UnknownValue;
2390 } else if (Cond == ICmpInst::ICMP_ULT)
2391 return UnknownValue;
2393 // cerr << "Computed Loop Trip Count as: "
2394 // << // *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
2395 return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
2398 return UnknownValue;
2401 return UnknownValue;
2404 /// getNumIterationsInRange - Return the number of iterations of this loop that
2405 /// produce values in the specified constant range. Another way of looking at
2406 /// this is that it returns the first iteration number where the value is not in
2407 /// the condition, thus computing the exit count. If the iteration count can't
2408 /// be computed, an instance of SCEVCouldNotCompute is returned.
2409 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
2410 bool isSigned) const {
2411 if (Range.isFullSet()) // Infinite loop.
2412 return new SCEVCouldNotCompute();
2414 // If the start is a non-zero constant, shift the range to simplify things.
2415 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2416 if (!SC->getValue()->isZero()) {
2417 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2418 Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
2419 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2420 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2421 return ShiftedAddRec->getNumIterationsInRange(
2422 Range.subtract(SC->getValue()->getValue()),isSigned);
2423 // This is strange and shouldn't happen.
2424 return new SCEVCouldNotCompute();
2427 // The only time we can solve this is when we have all constant indices.
2428 // Otherwise, we cannot determine the overflow conditions.
2429 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2430 if (!isa<SCEVConstant>(getOperand(i)))
2431 return new SCEVCouldNotCompute();
2434 // Okay at this point we know that all elements of the chrec are constants and
2435 // that the start element is zero.
2437 // First check to see if the range contains zero. If not, the first
2439 if (!Range.contains(APInt(getBitWidth(),0)))
2440 return SCEVConstant::get(ConstantInt::get(getType(),0));
2443 // If this is an affine expression then we have this situation:
2444 // Solve {0,+,A} in Range === Ax in Range
2446 // Since we know that zero is in the range, we know that the upper value of
2447 // the range must be the first possible exit value. Also note that we
2448 // already checked for a full range.
2449 const APInt &Upper = Range.getUpper();
2450 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
2451 APInt One(getBitWidth(),1);
2453 // The exit value should be (Upper+A-1)/A.
2454 APInt ExitVal(Upper);
2456 ExitVal = (Upper + A - One).sdiv(A);
2457 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
2459 // Evaluate at the exit value. If we really did fall out of the valid
2460 // range, then we computed our trip count, otherwise wrap around or other
2461 // things must have happened.
2462 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2463 if (Range.contains(Val->getValue()))
2464 return new SCEVCouldNotCompute(); // Something strange happened
2466 // Ensure that the previous value is in the range. This is a sanity check.
2467 assert(Range.contains(
2468 EvaluateConstantChrecAtConstant(this,
2469 ConstantInt::get(ExitVal - One))->getValue()) &&
2470 "Linear scev computation is off in a bad way!");
2471 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2472 } else if (isQuadratic()) {
2473 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2474 // quadratic equation to solve it. To do this, we must frame our problem in
2475 // terms of figuring out when zero is crossed, instead of when
2476 // Range.getUpper() is crossed.
2477 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2478 NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(
2479 ConstantInt::get(Range.getUpper())));
2480 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2482 // Next, solve the constructed addrec
2483 std::pair<SCEVHandle,SCEVHandle> Roots =
2484 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2485 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2486 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2488 // Pick the smallest positive root value.
2489 if (ConstantInt *CB =
2490 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2491 R1->getValue(), R2->getValue()))) {
2492 if (CB->getZExtValue() == false)
2493 std::swap(R1, R2); // R1 is the minimum root now.
2495 // Make sure the root is not off by one. The returned iteration should
2496 // not be in the range, but the previous one should be. When solving
2497 // for "X*X < 5", for example, we should not return a root of 2.
2498 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2500 if (Range.contains(R1Val->getValue())) {
2501 // The next iteration must be out of the range...
2502 Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
2504 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2505 if (!Range.contains(R1Val->getValue()))
2506 return SCEVUnknown::get(NextVal);
2507 return new SCEVCouldNotCompute(); // Something strange happened
2510 // If R1 was not in the range, then it is a good return value. Make
2511 // sure that R1-1 WAS in the range though, just in case.
2512 Constant *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
2513 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2514 if (Range.contains(R1Val->getValue()))
2516 return new SCEVCouldNotCompute(); // Something strange happened
2521 // Fallback, if this is a general polynomial, figure out the progression
2522 // through brute force: evaluate until we find an iteration that fails the
2523 // test. This is likely to be slow, but getting an accurate trip count is
2524 // incredibly important, we will be able to simplify the exit test a lot, and
2525 // we are almost guaranteed to get a trip count in this case.
2526 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2527 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2529 ++NumBruteForceEvaluations;
2530 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2531 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2532 return new SCEVCouldNotCompute();
2534 // Check to see if we found the value!
2535 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()->getValue()))
2536 return SCEVConstant::get(TestVal);
2538 // Increment to test the next index.
2539 TestVal = ConstantInt::get(TestVal->getValue()+1);
2540 } while (TestVal != EndVal);
2542 return new SCEVCouldNotCompute();
2547 //===----------------------------------------------------------------------===//
2548 // ScalarEvolution Class Implementation
2549 //===----------------------------------------------------------------------===//
2551 bool ScalarEvolution::runOnFunction(Function &F) {
2552 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2556 void ScalarEvolution::releaseMemory() {
2557 delete (ScalarEvolutionsImpl*)Impl;
2561 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2562 AU.setPreservesAll();
2563 AU.addRequiredTransitive<LoopInfo>();
2566 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2567 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2570 /// hasSCEV - Return true if the SCEV for this value has already been
2572 bool ScalarEvolution::hasSCEV(Value *V) const {
2573 return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
2577 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
2578 /// the specified value.
2579 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
2580 ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
2584 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2585 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2588 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2589 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2592 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2593 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2596 void ScalarEvolution::deleteValueFromRecords(Value *V) const {
2597 return ((ScalarEvolutionsImpl*)Impl)->deleteValueFromRecords(V);
2600 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2602 // Print all inner loops first
2603 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2604 PrintLoopInfo(OS, SE, *I);
2606 cerr << "Loop " << L->getHeader()->getName() << ": ";
2608 std::vector<BasicBlock*> ExitBlocks;
2609 L->getExitBlocks(ExitBlocks);
2610 if (ExitBlocks.size() != 1)
2611 cerr << "<multiple exits> ";
2613 if (SE->hasLoopInvariantIterationCount(L)) {
2614 cerr << *SE->getIterationCount(L) << " iterations! ";
2616 cerr << "Unpredictable iteration count. ";
2622 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
2623 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2624 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2626 OS << "Classifying expressions for: " << F.getName() << "\n";
2627 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2628 if (I->getType()->isInteger()) {
2631 SCEVHandle SV = getSCEV(&*I);
2635 if ((*I).getType()->isInteger()) {
2636 ConstantRange Bounds = SV->getValueRange();
2637 if (!Bounds.isFullSet())
2638 OS << "Bounds: " << Bounds << " ";
2641 if (const Loop *L = LI.getLoopFor((*I).getParent())) {
2643 SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
2644 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2645 OS << "<<Unknown>>";
2655 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2656 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2657 PrintLoopInfo(OS, this, *I);