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/Instructions.h"
26 #include "llvm/Support/DataTypes.h"
27 #include "llvm/Support/ValueHandle.h"
28 #include "llvm/Support/Allocator.h"
29 #include "llvm/Support/ConstantRange.h"
30 #include "llvm/ADT/FoldingSet.h"
31 #include "llvm/ADT/DenseMap.h"
41 class ScalarEvolution;
48 /// SCEV - This class represents an analyzed expression in the program. These
49 /// are opaque objects that the client is not allowed to do much with
52 class SCEV : public FastFoldingSetNode {
53 const unsigned SCEVType; // The SCEV baseclass this node corresponds to
55 SCEV(const SCEV &); // DO NOT IMPLEMENT
56 void operator=(const SCEV &); // DO NOT IMPLEMENT
60 explicit SCEV(const FoldingSetNodeID &ID, unsigned SCEVTy) :
61 FastFoldingSetNode(ID), SCEVType(SCEVTy) {}
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 /// isAllOnesValue - Return true if the expression is a constant
90 bool isAllOnesValue() const;
92 /// replaceSymbolicValuesWithConcrete - If this SCEV internally references
93 /// the symbolic value "Sym", construct and return a new SCEV that produces
94 /// the same value, but which uses the concrete value Conc instead of the
95 /// symbolic value. If this SCEV does not use the symbolic value, it
98 replaceSymbolicValuesWithConcrete(const SCEV *Sym,
100 ScalarEvolution &SE) const = 0;
102 /// dominates - Return true if elements that makes up this SCEV dominates
103 /// the specified basic block.
104 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const = 0;
106 /// print - Print out the internal representation of this scalar to the
107 /// specified stream. This should really only be used for debugging
109 virtual void print(raw_ostream &OS) const = 0;
110 void print(std::ostream &OS) const;
111 void print(std::ostream *OS) const { if (OS) print(*OS); }
113 /// dump - This method is used for debugging.
118 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
123 inline std::ostream &operator<<(std::ostream &OS, const SCEV &S) {
128 /// SCEVCouldNotCompute - An object of this class is returned by queries that
129 /// could not be answered. For example, if you ask for the number of
130 /// iterations of a linked-list traversal loop, you will get one of these.
131 /// None of the standard SCEV operations are valid on this class, it is just a
133 struct SCEVCouldNotCompute : public SCEV {
134 SCEVCouldNotCompute();
136 // None of these methods are valid for this object.
137 virtual bool isLoopInvariant(const Loop *L) const;
138 virtual const Type *getType() const;
139 virtual bool hasComputableLoopEvolution(const Loop *L) const;
140 virtual void print(raw_ostream &OS) const;
142 replaceSymbolicValuesWithConcrete(const SCEV *Sym,
144 ScalarEvolution &SE) const;
146 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const {
150 /// Methods for support type inquiry through isa, cast, and dyn_cast:
151 static inline bool classof(const SCEVCouldNotCompute *S) { return true; }
152 static bool classof(const SCEV *S);
155 /// ScalarEvolution - This class is the main scalar evolution driver. Because
156 /// client code (intentionally) can't do much with the SCEV objects directly,
157 /// they must ask this class for services.
159 class ScalarEvolution : public FunctionPass {
160 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
161 /// notified whenever a Value is deleted.
162 class SCEVCallbackVH : public CallbackVH {
164 virtual void deleted();
165 virtual void allUsesReplacedWith(Value *New);
167 SCEVCallbackVH(Value *V, ScalarEvolution *SE = 0);
170 friend class SCEVCallbackVH;
171 friend struct SCEVExpander;
173 /// F - The function we are analyzing.
177 /// LI - The loop information for the function we are currently analyzing.
181 /// TD - The target data information for the target we are targetting.
185 /// CouldNotCompute - This SCEV is used to represent unknown trip
186 /// counts and things.
187 SCEVCouldNotCompute CouldNotCompute;
189 /// Scalars - This is a cache of the scalars we have analyzed so far.
191 std::map<SCEVCallbackVH, const SCEV *> Scalars;
193 /// BackedgeTakenInfo - Information about the backedge-taken count
194 /// of a loop. This currently inclues an exact count and a maximum count.
196 struct BackedgeTakenInfo {
197 /// Exact - An expression indicating the exact backedge-taken count of
198 /// the loop if it is known, or a SCEVCouldNotCompute otherwise.
201 /// Max - An expression indicating the least maximum backedge-taken
202 /// count of the loop that is known, or a SCEVCouldNotCompute.
205 /*implicit*/ BackedgeTakenInfo(const SCEV *exact) :
206 Exact(exact), Max(exact) {}
208 BackedgeTakenInfo(const SCEV *exact, const SCEV *max) :
209 Exact(exact), Max(max) {}
211 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
212 /// computed information, or whether it's all SCEVCouldNotCompute
214 bool hasAnyInfo() const {
215 return !isa<SCEVCouldNotCompute>(Exact) ||
216 !isa<SCEVCouldNotCompute>(Max);
220 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
221 /// this function as they are computed.
222 std::map<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
224 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
225 /// the PHI instructions that we attempt to compute constant evolutions for.
226 /// This allows us to avoid potentially expensive recomputation of these
227 /// properties. An instruction maps to null if we are unable to compute its
229 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
231 /// ValuesAtScopes - This map contains entries for all the instructions
232 /// that we attempt to compute getSCEVAtScope information for without
233 /// using SCEV techniques, which can be expensive.
234 std::map<Instruction *, std::map<const Loop *, Constant *> > ValuesAtScopes;
236 /// createSCEV - We know that there is no SCEV for the specified value.
237 /// Analyze the expression.
238 const SCEV *createSCEV(Value *V);
240 /// createNodeForPHI - Provide the special handling we need to analyze PHI
242 const SCEV *createNodeForPHI(PHINode *PN);
244 /// createNodeForGEP - Provide the special handling we need to analyze GEP
246 const SCEV *createNodeForGEP(Operator *GEP);
248 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
249 /// for the specified instruction and replaces any references to the
250 /// symbolic value SymName with the specified value. This is used during
252 void ReplaceSymbolicValueWithConcrete(Instruction *I,
256 /// getBECount - Subtract the end and start values and divide by the step,
257 /// rounding up, to get the number of times the backedge is executed. Return
258 /// CouldNotCompute if an intermediate computation overflows.
259 const SCEV *getBECount(const SCEV *Start,
263 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
264 /// loop, lazily computing new values if the loop hasn't been analyzed
266 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
268 /// ComputeBackedgeTakenCount - Compute the number of times the specified
269 /// loop will iterate.
270 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
272 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the
273 /// backedge of the specified loop will execute if it exits via the
275 BackedgeTakenInfo ComputeBackedgeTakenCountFromExit(const Loop *L,
276 BasicBlock *ExitingBlock);
278 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
279 /// backedge of the specified loop will execute if its exit condition
280 /// were a conditional branch of ExitCond, TBB, and FBB.
282 ComputeBackedgeTakenCountFromExitCond(const Loop *L,
287 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of
288 /// times the backedge of the specified loop will execute if its exit
289 /// condition were a conditional branch of the ICmpInst ExitCond, TBB,
292 ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
297 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
298 /// of 'icmp op load X, cst', try to see if we can compute the trip count.
300 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
303 ICmpInst::Predicate p);
305 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute
306 /// a constant number of times (the condition evolves only from constants),
307 /// try to evaluate a few iterations of the loop until we get the exit
308 /// condition gets a value of ExitWhen (true or false). If we cannot
309 /// evaluate the trip count of the loop, return CouldNotCompute.
310 const SCEV *ComputeBackedgeTakenCountExhaustively(const Loop *L,
314 /// HowFarToZero - Return the number of times a backedge comparing the
315 /// specified value to zero will execute. If not computable, return
317 const SCEV *HowFarToZero(const SCEV *V, const Loop *L);
319 /// HowFarToNonZero - Return the number of times a backedge checking the
320 /// specified value for nonzero will execute. If not computable, return
322 const SCEV *HowFarToNonZero(const SCEV *V, const Loop *L);
324 /// HowManyLessThans - Return the number of times a backedge containing the
325 /// specified less-than comparison will execute. If not computable, return
326 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
327 BackedgeTakenInfo HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
328 const Loop *L, bool isSigned);
330 /// getLoopPredecessor - If the given loop's header has exactly one unique
331 /// predecessor outside the loop, return it. Otherwise return null.
332 BasicBlock *getLoopPredecessor(const Loop *L);
334 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
335 /// (which may not be an immediate predecessor) which has exactly one
336 /// successor from which BB is reachable, or null if no such block is
338 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
340 /// isNecessaryCond - Test whether the condition described by Pred, LHS,
341 /// and RHS is a necessary condition for the given Cond value to evaluate
343 bool isNecessaryCond(Value *Cond, ICmpInst::Predicate Pred,
344 const SCEV *LHS, const SCEV *RHS,
347 /// isNecessaryCondOperands - Test whether the condition described by Pred,
348 /// LHS, and RHS is a necessary condition for the condition described by
349 /// Pred, FoundLHS, and FoundRHS to evaluate to true.
350 bool isNecessaryCondOperands(ICmpInst::Predicate Pred,
351 const SCEV *LHS, const SCEV *RHS,
352 const SCEV *FoundLHS, const SCEV *FoundRHS);
354 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
355 /// in the header of its containing loop, we know the loop executes a
356 /// constant number of times, and the PHI node is just a recurrence
357 /// involving constants, fold it.
358 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
362 static char ID; // Pass identification, replacement for typeid
365 LLVMContext *getContext() const { return Context; }
367 /// isSCEVable - Test if values of the given type are analyzable within
368 /// the SCEV framework. This primarily includes integer types, and it
369 /// can optionally include pointer types if the ScalarEvolution class
370 /// has access to target-specific information.
371 bool isSCEVable(const Type *Ty) const;
373 /// getTypeSizeInBits - Return the size in bits of the specified type,
374 /// for which isSCEVable must return true.
375 uint64_t getTypeSizeInBits(const Type *Ty) const;
377 /// getEffectiveSCEVType - Return a type with the same bitwidth as
378 /// the given type and which represents how SCEV will treat the given
379 /// type, for which isSCEVable must return true. For pointer types,
380 /// this is the pointer-sized integer type.
381 const Type *getEffectiveSCEVType(const Type *Ty) const;
383 /// getSCEV - Return a SCEV expression handle for the full generality of the
384 /// specified expression.
385 const SCEV *getSCEV(Value *V);
387 const SCEV *getConstant(ConstantInt *V);
388 const SCEV *getConstant(const APInt& Val);
389 const SCEV *getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
390 const SCEV *getTruncateExpr(const SCEV *Op, const Type *Ty);
391 const SCEV *getZeroExtendExpr(const SCEV *Op, const Type *Ty);
392 const SCEV *getSignExtendExpr(const SCEV *Op, const Type *Ty);
393 const SCEV *getAnyExtendExpr(const SCEV *Op, const Type *Ty);
394 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops);
395 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS) {
396 SmallVector<const SCEV *, 2> Ops;
399 return getAddExpr(Ops);
401 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1,
403 SmallVector<const SCEV *, 3> Ops;
407 return getAddExpr(Ops);
409 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops);
410 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS) {
411 SmallVector<const SCEV *, 2> Ops;
414 return getMulExpr(Ops);
416 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
417 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
419 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
421 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
423 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
424 return getAddRecExpr(NewOp, L);
426 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
427 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
428 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
429 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
430 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
431 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
432 const SCEV *getUnknown(Value *V);
433 const SCEV *getCouldNotCompute();
435 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
437 const SCEV *getNegativeSCEV(const SCEV *V);
439 /// getNotSCEV - Return the SCEV object corresponding to ~V.
441 const SCEV *getNotSCEV(const SCEV *V);
443 /// getMinusSCEV - Return LHS-RHS.
445 const SCEV *getMinusSCEV(const SCEV *LHS,
448 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
449 /// of the input value to the specified type. If the type must be
450 /// extended, it is zero extended.
451 const SCEV *getTruncateOrZeroExtend(const SCEV *V, const Type *Ty);
453 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
454 /// of the input value to the specified type. If the type must be
455 /// extended, it is sign extended.
456 const SCEV *getTruncateOrSignExtend(const SCEV *V, const Type *Ty);
458 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
459 /// the input value to the specified type. If the type must be extended,
460 /// it is zero extended. The conversion must not be narrowing.
461 const SCEV *getNoopOrZeroExtend(const SCEV *V, const Type *Ty);
463 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
464 /// the input value to the specified type. If the type must be extended,
465 /// it is sign extended. The conversion must not be narrowing.
466 const SCEV *getNoopOrSignExtend(const SCEV *V, const Type *Ty);
468 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
469 /// the input value to the specified type. If the type must be extended,
470 /// it is extended with unspecified bits. The conversion must not be
472 const SCEV *getNoopOrAnyExtend(const SCEV *V, const Type *Ty);
474 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
475 /// input value to the specified type. The conversion must not be
477 const SCEV *getTruncateOrNoop(const SCEV *V, const Type *Ty);
479 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
480 /// specified signed integer value and return a SCEV for the constant.
481 const SCEV *getIntegerSCEV(int Val, const Type *Ty);
483 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
484 /// the types using zero-extension, and then perform a umax operation
486 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
489 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
490 /// the types using zero-extension, and then perform a umin operation
492 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
495 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
496 /// at the specified scope in the program. The L value specifies a loop
497 /// nest to evaluate the expression at, where null is the top-level or a
498 /// specified loop is immediately inside of the loop.
500 /// This method can be used to compute the exit value for a variable defined
501 /// in a loop by querying what the value will hold in the parent loop.
503 /// In the case that a relevant loop exit value cannot be computed, the
504 /// original value V is returned.
505 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
507 /// getSCEVAtScope - This is a convenience function which does
508 /// getSCEVAtScope(getSCEV(V), L).
509 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
511 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
512 /// a conditional between LHS and RHS. This is used to help avoid max
513 /// expressions in loop trip counts, and to eliminate casts.
514 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
515 const SCEV *LHS, const SCEV *RHS);
517 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
518 /// protected by a conditional between LHS and RHS. This is used to
519 /// to eliminate casts.
520 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
521 const SCEV *LHS, const SCEV *RHS);
523 /// getBackedgeTakenCount - If the specified loop has a predictable
524 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
525 /// object. The backedge-taken count is the number of times the loop header
526 /// will be branched to from within the loop. This is one less than the
527 /// trip count of the loop, since it doesn't count the first iteration,
528 /// when the header is branched to from outside the loop.
530 /// Note that it is not valid to call this method on a loop without a
531 /// loop-invariant backedge-taken count (see
532 /// hasLoopInvariantBackedgeTakenCount).
534 const SCEV *getBackedgeTakenCount(const Loop *L);
536 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
537 /// return the least SCEV value that is known never to be less than the
538 /// actual backedge taken count.
539 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
541 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
542 /// has an analyzable loop-invariant backedge-taken count.
543 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
545 /// forgetLoopBackedgeTakenCount - This method should be called by the
546 /// client when it has changed a loop in a way that may effect
547 /// ScalarEvolution's ability to compute a trip count, or if the loop
549 void forgetLoopBackedgeTakenCount(const Loop *L);
551 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
552 /// is guaranteed to end in (at every loop iteration). It is, at the same
553 /// time, the minimum number of times S is divisible by 2. For example,
554 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
556 uint32_t GetMinTrailingZeros(const SCEV *S);
558 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
560 ConstantRange getUnsignedRange(const SCEV *S);
562 /// getSignedRange - Determine the signed range for a particular SCEV.
564 ConstantRange getSignedRange(const SCEV *S);
566 /// isKnownNegative - Test if the given expression is known to be negative.
568 bool isKnownNegative(const SCEV *S);
570 /// isKnownPositive - Test if the given expression is known to be positive.
572 bool isKnownPositive(const SCEV *S);
574 /// isKnownNonNegative - Test if the given expression is known to be
577 bool isKnownNonNegative(const SCEV *S);
579 /// isKnownNonPositive - Test if the given expression is known to be
582 bool isKnownNonPositive(const SCEV *S);
584 /// isKnownNonZero - Test if the given expression is known to be
587 bool isKnownNonZero(const SCEV *S);
589 /// isKnownNonZero - Test if the given expression is known to satisfy
590 /// the condition described by Pred, LHS, and RHS.
592 bool isKnownPredicate(ICmpInst::Predicate Pred,
593 const SCEV *LHS, const SCEV *RHS);
595 virtual bool runOnFunction(Function &F);
596 virtual void releaseMemory();
597 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
598 void print(raw_ostream &OS, const Module* = 0) const;
599 virtual void print(std::ostream &OS, const Module* = 0) const;
600 void print(std::ostream *OS, const Module* M = 0) const {
601 if (OS) print(*OS, M);
605 FoldingSet<SCEV> UniqueSCEVs;
606 BumpPtrAllocator SCEVAllocator;