1 //===- llvm/Analysis/ScalarEvolution.h - Scalar Evolution -------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // The ScalarEvolution class is an LLVM pass which can be used to analyze and
11 // catagorize scalar expressions in loops. It specializes in recognizing
12 // general induction variables, representing them with the abstract and opaque
13 // SCEV class. Given this analysis, trip counts of loops and other important
14 // properties can be obtained.
16 // This analysis is primarily useful for induction variable substitution and
17 // strength reduction.
19 //===----------------------------------------------------------------------===//
21 #ifndef LLVM_ANALYSIS_SCALAREVOLUTION_H
22 #define LLVM_ANALYSIS_SCALAREVOLUTION_H
24 #include "llvm/Pass.h"
25 #include "llvm/Analysis/LoopInfo.h"
26 #include "llvm/Support/DataTypes.h"
27 #include "llvm/Support/ValueHandle.h"
28 #include "llvm/ADT/DenseMap.h"
36 class ScalarEvolution;
38 template<> struct DenseMapInfo<SCEVHandle>;
40 /// SCEV - This class represents an analyzed expression in the program. These
41 /// are reference-counted opaque objects that the client is not allowed to
42 /// do much with directly.
45 const unsigned SCEVType; // The SCEV baseclass this node corresponds to
46 mutable unsigned RefCount;
48 friend class SCEVHandle;
49 friend class DenseMapInfo<SCEVHandle>;
50 void addRef() const { ++RefCount; }
51 void dropRef() const {
56 SCEV(const SCEV &); // DO NOT IMPLEMENT
57 void operator=(const SCEV &); // DO NOT IMPLEMENT
61 explicit SCEV(unsigned SCEVTy) : SCEVType(SCEVTy), RefCount(0) {}
63 unsigned getSCEVType() const { return SCEVType; }
65 /// isLoopInvariant - Return true if the value of this SCEV is unchanging in
66 /// the specified loop.
67 virtual bool isLoopInvariant(const Loop *L) const = 0;
69 /// hasComputableLoopEvolution - Return true if this SCEV changes value in a
70 /// known way in the specified loop. This property being true implies that
71 /// the value is variant in the loop AND that we can emit an expression to
72 /// compute the value of the expression at any particular loop iteration.
73 virtual bool hasComputableLoopEvolution(const Loop *L) const = 0;
75 /// getType - Return the LLVM type of this SCEV expression.
77 virtual const Type *getType() const = 0;
79 /// isZero - Return true if the expression is a constant zero.
83 /// isOne - Return true if the expression is a constant one.
87 /// replaceSymbolicValuesWithConcrete - If this SCEV internally references
88 /// the symbolic value "Sym", construct and return a new SCEV that produces
89 /// the same value, but which uses the concrete value Conc instead of the
90 /// symbolic value. If this SCEV does not use the symbolic value, it
93 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
94 const SCEVHandle &Conc,
95 ScalarEvolution &SE) const = 0;
97 /// dominates - Return true if elements that makes up this SCEV dominates
98 /// the specified basic block.
99 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const = 0;
101 /// print - Print out the internal representation of this scalar to the
102 /// specified stream. This should really only be used for debugging
104 virtual void print(raw_ostream &OS) const = 0;
105 void print(std::ostream &OS) const;
106 void print(std::ostream *OS) const { if (OS) print(*OS); }
108 /// dump - This method is used for debugging.
113 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
118 inline std::ostream &operator<<(std::ostream &OS, const SCEV &S) {
123 /// SCEVCouldNotCompute - An object of this class is returned by queries that
124 /// could not be answered. For example, if you ask for the number of
125 /// iterations of a linked-list traversal loop, you will get one of these.
126 /// None of the standard SCEV operations are valid on this class, it is just a
128 struct SCEVCouldNotCompute : public SCEV {
129 SCEVCouldNotCompute();
130 ~SCEVCouldNotCompute();
132 // None of these methods are valid for this object.
133 virtual bool isLoopInvariant(const Loop *L) const;
134 virtual const Type *getType() const;
135 virtual bool hasComputableLoopEvolution(const Loop *L) const;
136 virtual void print(raw_ostream &OS) const;
138 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
139 const SCEVHandle &Conc,
140 ScalarEvolution &SE) const;
142 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const {
146 /// Methods for support type inquiry through isa, cast, and dyn_cast:
147 static inline bool classof(const SCEVCouldNotCompute *S) { return true; }
148 static bool classof(const SCEV *S);
151 /// SCEVHandle - This class is used to maintain the SCEV object's refcounts,
152 /// freeing the objects when the last reference is dropped.
155 SCEVHandle(); // DO NOT IMPLEMENT
157 SCEVHandle(const SCEV *s) : S(s) {
158 assert(S && "Cannot create a handle to a null SCEV!");
161 SCEVHandle(const SCEVHandle &RHS) : S(RHS.S) {
164 ~SCEVHandle() { S->dropRef(); }
166 operator const SCEV*() const { return S; }
168 const SCEV &operator*() const { return *S; }
169 const SCEV *operator->() const { return S; }
171 bool operator==(const SCEV *RHS) const { return S == RHS; }
172 bool operator!=(const SCEV *RHS) const { return S != RHS; }
174 const SCEVHandle &operator=(SCEV *RHS) {
183 const SCEVHandle &operator=(const SCEVHandle &RHS) {
193 template<typename From> struct simplify_type;
194 template<> struct simplify_type<const SCEVHandle> {
195 typedef const SCEV* SimpleType;
196 static SimpleType getSimplifiedValue(const SCEVHandle &Node) {
200 template<> struct simplify_type<SCEVHandle>
201 : public simplify_type<const SCEVHandle> {};
203 // Specialize DenseMapInfo for SCEVHandle so that SCEVHandle may be used
204 // as a key in DenseMaps.
206 struct DenseMapInfo<SCEVHandle> {
207 static inline SCEVHandle getEmptyKey() {
208 static SCEVCouldNotCompute Empty;
209 if (Empty.RefCount == 0)
213 static inline SCEVHandle getTombstoneKey() {
214 static SCEVCouldNotCompute Tombstone;
215 if (Tombstone.RefCount == 0)
219 static unsigned getHashValue(const SCEVHandle &Val) {
220 return DenseMapInfo<const SCEV *>::getHashValue(Val);
222 static bool isEqual(const SCEVHandle &LHS, const SCEVHandle &RHS) {
225 static bool isPod() { return false; }
228 /// ScalarEvolution - This class is the main scalar evolution driver. Because
229 /// client code (intentionally) can't do much with the SCEV objects directly,
230 /// they must ask this class for services.
232 class ScalarEvolution : public FunctionPass {
233 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
234 /// notified whenever a Value is deleted.
235 class SCEVCallbackVH : public CallbackVH {
237 virtual void deleted();
238 virtual void allUsesReplacedWith(Value *New);
240 SCEVCallbackVH(Value *V, ScalarEvolution *SE = 0);
243 friend class SCEVCallbackVH;
244 friend class SCEVExpander;
246 /// F - The function we are analyzing.
250 /// LI - The loop information for the function we are currently analyzing.
254 /// TD - The target data information for the target we are targetting.
258 /// CouldNotCompute - This SCEV is used to represent unknown trip
259 /// counts and things.
260 SCEVHandle CouldNotCompute;
262 /// Scalars - This is a cache of the scalars we have analyzed so far.
264 std::map<SCEVCallbackVH, SCEVHandle> Scalars;
266 /// BackedgeTakenInfo - Information about the backedge-taken count
267 /// of a loop. This currently inclues an exact count and a maximum count.
269 struct BackedgeTakenInfo {
270 /// Exact - An expression indicating the exact backedge-taken count of
271 /// the loop if it is known, or a SCEVCouldNotCompute otherwise.
274 /// Exact - An expression indicating the least maximum backedge-taken
275 /// count of the loop that is known, or a SCEVCouldNotCompute.
278 /*implicit*/ BackedgeTakenInfo(SCEVHandle exact) :
279 Exact(exact), Max(exact) {}
281 /*implicit*/ BackedgeTakenInfo(const SCEV *exact) :
282 Exact(exact), Max(exact) {}
284 BackedgeTakenInfo(SCEVHandle exact, SCEVHandle max) :
285 Exact(exact), Max(max) {}
287 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
288 /// computed information, or whether it's all SCEVCouldNotCompute
290 bool hasAnyInfo() const {
291 return !isa<SCEVCouldNotCompute>(Exact) ||
292 !isa<SCEVCouldNotCompute>(Max);
296 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
297 /// this function as they are computed.
298 std::map<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
300 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
301 /// the PHI instructions that we attempt to compute constant evolutions for.
302 /// This allows us to avoid potentially expensive recomputation of these
303 /// properties. An instruction maps to null if we are unable to compute its
305 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
307 /// ValuesAtScopes - This map contains entries for all the instructions
308 /// that we attempt to compute getSCEVAtScope information for without
309 /// using SCEV techniques, which can be expensive.
310 std::map<Instruction *, std::map<const Loop *, Constant *> > ValuesAtScopes;
312 /// createSCEV - We know that there is no SCEV for the specified value.
313 /// Analyze the expression.
314 SCEVHandle createSCEV(Value *V);
316 /// createNodeForPHI - Provide the special handling we need to analyze PHI
318 SCEVHandle createNodeForPHI(PHINode *PN);
320 /// createNodeForGEP - Provide the special handling we need to analyze GEP
322 SCEVHandle createNodeForGEP(User *GEP);
324 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
325 /// for the specified instruction and replaces any references to the
326 /// symbolic value SymName with the specified value. This is used during
328 void ReplaceSymbolicValueWithConcrete(Instruction *I,
329 const SCEVHandle &SymName,
330 const SCEVHandle &NewVal);
332 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
333 /// loop, lazily computing new values if the loop hasn't been analyzed
335 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
337 /// ComputeBackedgeTakenCount - Compute the number of times the specified
338 /// loop will iterate.
339 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
341 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
342 /// of 'icmp op load X, cst', try to see if we can compute the trip count.
344 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
347 ICmpInst::Predicate p);
349 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute
350 /// a constant number of times (the condition evolves only from constants),
351 /// try to evaluate a few iterations of the loop until we get the exit
352 /// condition gets a value of ExitWhen (true or false). If we cannot
353 /// evaluate the trip count of the loop, return CouldNotCompute.
354 SCEVHandle ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond,
357 /// HowFarToZero - Return the number of times a backedge comparing the
358 /// specified value to zero will execute. If not computable, return
360 SCEVHandle HowFarToZero(const SCEV *V, const Loop *L);
362 /// HowFarToNonZero - Return the number of times a backedge checking the
363 /// specified value for nonzero will execute. If not computable, return
365 SCEVHandle HowFarToNonZero(const SCEV *V, const Loop *L);
367 /// HowManyLessThans - Return the number of times a backedge containing the
368 /// specified less-than comparison will execute. If not computable, return
369 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
370 BackedgeTakenInfo HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
371 const Loop *L, bool isSigned);
373 /// getLoopPredecessor - If the given loop's header has exactly one unique
374 /// predecessor outside the loop, return it. Otherwise return null.
375 BasicBlock *getLoopPredecessor(const Loop *L);
377 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
378 /// (which may not be an immediate predecessor) which has exactly one
379 /// successor from which BB is reachable, or null if no such block is
381 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
383 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
384 /// in the header of its containing loop, we know the loop executes a
385 /// constant number of times, and the PHI node is just a recurrence
386 /// involving constants, fold it.
387 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
390 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
391 /// PHI nodes in the given loop. This is used when the trip count of
392 /// the loop may have changed.
393 void forgetLoopPHIs(const Loop *L);
396 static char ID; // Pass identification, replacement for typeid
399 /// isSCEVable - Test if values of the given type are analyzable within
400 /// the SCEV framework. This primarily includes integer types, and it
401 /// can optionally include pointer types if the ScalarEvolution class
402 /// has access to target-specific information.
403 bool isSCEVable(const Type *Ty) const;
405 /// getTypeSizeInBits - Return the size in bits of the specified type,
406 /// for which isSCEVable must return true.
407 uint64_t getTypeSizeInBits(const Type *Ty) const;
409 /// getEffectiveSCEVType - Return a type with the same bitwidth as
410 /// the given type and which represents how SCEV will treat the given
411 /// type, for which isSCEVable must return true. For pointer types,
412 /// this is the pointer-sized integer type.
413 const Type *getEffectiveSCEVType(const Type *Ty) const;
415 /// getSCEV - Return a SCEV expression handle for the full generality of the
416 /// specified expression.
417 SCEVHandle getSCEV(Value *V);
419 SCEVHandle getConstant(ConstantInt *V);
420 SCEVHandle getConstant(const APInt& Val);
421 SCEVHandle getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
422 SCEVHandle getTruncateExpr(const SCEVHandle &Op, const Type *Ty);
423 SCEVHandle getZeroExtendExpr(const SCEVHandle &Op, const Type *Ty);
424 SCEVHandle getSignExtendExpr(const SCEVHandle &Op, const Type *Ty);
425 SCEVHandle getAnyExtendExpr(const SCEVHandle &Op, const Type *Ty);
426 SCEVHandle getAddExpr(SmallVectorImpl<SCEVHandle> &Ops);
427 SCEVHandle getAddExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
428 SmallVector<SCEVHandle, 2> Ops;
431 return getAddExpr(Ops);
433 SCEVHandle getAddExpr(const SCEVHandle &Op0, const SCEVHandle &Op1,
434 const SCEVHandle &Op2) {
435 SmallVector<SCEVHandle, 3> Ops;
439 return getAddExpr(Ops);
441 SCEVHandle getMulExpr(SmallVectorImpl<SCEVHandle> &Ops);
442 SCEVHandle getMulExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
443 SmallVector<SCEVHandle, 2> Ops;
446 return getMulExpr(Ops);
448 SCEVHandle getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS);
449 SCEVHandle getAddRecExpr(const SCEVHandle &Start, const SCEVHandle &Step,
451 SCEVHandle getAddRecExpr(SmallVectorImpl<SCEVHandle> &Operands,
453 SCEVHandle getAddRecExpr(const SmallVectorImpl<SCEVHandle> &Operands,
455 SmallVector<SCEVHandle, 4> NewOp(Operands.begin(), Operands.end());
456 return getAddRecExpr(NewOp, L);
458 SCEVHandle getSMaxExpr(const SCEVHandle &LHS, const SCEVHandle &RHS);
459 SCEVHandle getSMaxExpr(SmallVectorImpl<SCEVHandle> &Operands);
460 SCEVHandle getUMaxExpr(const SCEVHandle &LHS, const SCEVHandle &RHS);
461 SCEVHandle getUMaxExpr(SmallVectorImpl<SCEVHandle> &Operands);
462 SCEVHandle getUnknown(Value *V);
463 SCEVHandle getCouldNotCompute();
465 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
467 SCEVHandle getNegativeSCEV(const SCEVHandle &V);
469 /// getNotSCEV - Return the SCEV object corresponding to ~V.
471 SCEVHandle getNotSCEV(const SCEVHandle &V);
473 /// getMinusSCEV - Return LHS-RHS.
475 SCEVHandle getMinusSCEV(const SCEVHandle &LHS,
476 const SCEVHandle &RHS);
478 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
479 /// of the input value to the specified type. If the type must be
480 /// extended, it is zero extended.
481 SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty);
483 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
484 /// of the input value to the specified type. If the type must be
485 /// extended, it is sign extended.
486 SCEVHandle getTruncateOrSignExtend(const SCEVHandle &V, const Type *Ty);
488 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
489 /// the input value to the specified type. If the type must be extended,
490 /// it is zero extended. The conversion must not be narrowing.
491 SCEVHandle getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty);
493 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
494 /// the input value to the specified type. If the type must be extended,
495 /// it is sign extended. The conversion must not be narrowing.
496 SCEVHandle getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty);
498 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
499 /// the input value to the specified type. If the type must be extended,
500 /// it is extended with unspecified bits. The conversion must not be
502 SCEVHandle getNoopOrAnyExtend(const SCEVHandle &V, const Type *Ty);
504 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
505 /// input value to the specified type. The conversion must not be
507 SCEVHandle getTruncateOrNoop(const SCEVHandle &V, const Type *Ty);
509 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
510 /// specified signed integer value and return a SCEV for the constant.
511 SCEVHandle getIntegerSCEV(int Val, const Type *Ty);
513 /// hasSCEV - Return true if the SCEV for this value has already been
515 bool hasSCEV(Value *V) const;
517 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
518 /// the specified value.
519 void setSCEV(Value *V, const SCEVHandle &H);
521 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
522 /// at the specified scope in the program. The L value specifies a loop
523 /// nest to evaluate the expression at, where null is the top-level or a
524 /// specified loop is immediately inside of the loop.
526 /// This method can be used to compute the exit value for a variable defined
527 /// in a loop by querying what the value will hold in the parent loop.
529 /// In the case that a relevant loop exit value cannot be computed, the
530 /// original value V is returned.
531 SCEVHandle getSCEVAtScope(const SCEV *S, const Loop *L);
533 /// getSCEVAtScope - This is a convenience function which does
534 /// getSCEVAtScope(getSCEV(V), L).
535 SCEVHandle getSCEVAtScope(Value *V, const Loop *L);
537 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
538 /// a conditional between LHS and RHS. This is used to help avoid max
539 /// expressions in loop trip counts.
540 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
541 const SCEV *LHS, const SCEV *RHS);
543 /// getBackedgeTakenCount - If the specified loop has a predictable
544 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
545 /// object. The backedge-taken count is the number of times the loop header
546 /// will be branched to from within the loop. This is one less than the
547 /// trip count of the loop, since it doesn't count the first iteration,
548 /// when the header is branched to from outside the loop.
550 /// Note that it is not valid to call this method on a loop without a
551 /// loop-invariant backedge-taken count (see
552 /// hasLoopInvariantBackedgeTakenCount).
554 SCEVHandle getBackedgeTakenCount(const Loop *L);
556 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
557 /// return the least SCEV value that is known never to be less than the
558 /// actual backedge taken count.
559 SCEVHandle getMaxBackedgeTakenCount(const Loop *L);
561 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
562 /// has an analyzable loop-invariant backedge-taken count.
563 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
565 /// forgetLoopBackedgeTakenCount - This method should be called by the
566 /// client when it has changed a loop in a way that may effect
567 /// ScalarEvolution's ability to compute a trip count, or if the loop
569 void forgetLoopBackedgeTakenCount(const Loop *L);
571 virtual bool runOnFunction(Function &F);
572 virtual void releaseMemory();
573 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
574 void print(raw_ostream &OS, const Module* = 0) const;
575 virtual void print(std::ostream &OS, const Module* = 0) const;
576 void print(std::ostream *OS, const Module* M = 0) const {
577 if (OS) print(*OS, M);