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/Support/Allocator.h"
29 #include "llvm/ADT/FoldingSet.h"
30 #include "llvm/ADT/DenseMap.h"
37 class ScalarEvolution;
41 /// SCEV - This class represents an analyzed expression in the program. These
42 /// are opaque objects that the client is not allowed to do much with
45 class SCEV : public FoldingSetNode {
46 const unsigned SCEVType; // The SCEV baseclass this node corresponds to
48 SCEV(const SCEV &); // DO NOT IMPLEMENT
49 void operator=(const SCEV &); // DO NOT IMPLEMENT
53 explicit SCEV(unsigned SCEVTy) :
56 virtual void Profile(FoldingSetNodeID &ID) const = 0;
58 unsigned getSCEVType() const { return SCEVType; }
60 /// isLoopInvariant - Return true if the value of this SCEV is unchanging in
61 /// the specified loop.
62 virtual bool isLoopInvariant(const Loop *L) const = 0;
64 /// hasComputableLoopEvolution - Return true if this SCEV changes value in a
65 /// known way in the specified loop. This property being true implies that
66 /// the value is variant in the loop AND that we can emit an expression to
67 /// compute the value of the expression at any particular loop iteration.
68 virtual bool hasComputableLoopEvolution(const Loop *L) const = 0;
70 /// getType - Return the LLVM type of this SCEV expression.
72 virtual const Type *getType() const = 0;
74 /// isZero - Return true if the expression is a constant zero.
78 /// isOne - Return true if the expression is a constant one.
82 /// isAllOnesValue - Return true if the expression is a constant
85 bool isAllOnesValue() const;
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 SCEV *Sym,
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();
131 // None of these methods are valid for this object.
132 virtual void Profile(FoldingSetNodeID &ID) const;
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 SCEV *Sym,
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 /// ScalarEvolution - This class is the main scalar evolution driver. Because
152 /// client code (intentionally) can't do much with the SCEV objects directly,
153 /// they must ask this class for services.
155 class ScalarEvolution : public FunctionPass {
156 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
157 /// notified whenever a Value is deleted.
158 class SCEVCallbackVH : public CallbackVH {
160 virtual void deleted();
161 virtual void allUsesReplacedWith(Value *New);
163 SCEVCallbackVH(Value *V, ScalarEvolution *SE = 0);
166 friend class SCEVCallbackVH;
167 friend class SCEVExpander;
169 /// F - The function we are analyzing.
173 /// LI - The loop information for the function we are currently analyzing.
177 /// TD - The target data information for the target we are targetting.
181 /// CouldNotCompute - This SCEV is used to represent unknown trip
182 /// counts and things.
183 SCEVCouldNotCompute CouldNotCompute;
185 /// Scalars - This is a cache of the scalars we have analyzed so far.
187 std::map<SCEVCallbackVH, const SCEV *> Scalars;
189 /// BackedgeTakenInfo - Information about the backedge-taken count
190 /// of a loop. This currently inclues an exact count and a maximum count.
192 struct BackedgeTakenInfo {
193 /// Exact - An expression indicating the exact backedge-taken count of
194 /// the loop if it is known, or a SCEVCouldNotCompute otherwise.
197 /// Max - An expression indicating the least maximum backedge-taken
198 /// count of the loop that is known, or a SCEVCouldNotCompute.
201 /*implicit*/ BackedgeTakenInfo(const SCEV *exact) :
202 Exact(exact), Max(exact) {}
204 BackedgeTakenInfo(const SCEV *exact, const SCEV *max) :
205 Exact(exact), Max(max) {}
207 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
208 /// computed information, or whether it's all SCEVCouldNotCompute
210 bool hasAnyInfo() const {
211 return !isa<SCEVCouldNotCompute>(Exact) ||
212 !isa<SCEVCouldNotCompute>(Max);
216 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
217 /// this function as they are computed.
218 std::map<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
220 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
221 /// the PHI instructions that we attempt to compute constant evolutions for.
222 /// This allows us to avoid potentially expensive recomputation of these
223 /// properties. An instruction maps to null if we are unable to compute its
225 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
227 /// ValuesAtScopes - This map contains entries for all the instructions
228 /// that we attempt to compute getSCEVAtScope information for without
229 /// using SCEV techniques, which can be expensive.
230 std::map<Instruction *, std::map<const Loop *, Constant *> > ValuesAtScopes;
232 /// createSCEV - We know that there is no SCEV for the specified value.
233 /// Analyze the expression.
234 const SCEV *createSCEV(Value *V);
236 /// createNodeForPHI - Provide the special handling we need to analyze PHI
238 const SCEV *createNodeForPHI(PHINode *PN);
240 /// createNodeForGEP - Provide the special handling we need to analyze GEP
242 const SCEV *createNodeForGEP(User *GEP);
244 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
245 /// for the specified instruction and replaces any references to the
246 /// symbolic value SymName with the specified value. This is used during
248 void ReplaceSymbolicValueWithConcrete(Instruction *I,
252 /// getBECount - Subtract the end and start values and divide by the step,
253 /// rounding up, to get the number of times the backedge is executed. Return
254 /// CouldNotCompute if an intermediate computation overflows.
255 const SCEV *getBECount(const SCEV *Start,
259 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
260 /// loop, lazily computing new values if the loop hasn't been analyzed
262 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
264 /// ComputeBackedgeTakenCount - Compute the number of times the specified
265 /// loop will iterate.
266 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
268 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the
269 /// backedge of the specified loop will execute if it exits via the
271 BackedgeTakenInfo ComputeBackedgeTakenCountFromExit(const Loop *L,
272 BasicBlock *ExitingBlock);
274 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
275 /// backedge of the specified loop will execute if its exit condition
276 /// were a conditional branch of ExitCond, TBB, and FBB.
278 ComputeBackedgeTakenCountFromExitCond(const Loop *L,
283 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of
284 /// times the backedge of the specified loop will execute if its exit
285 /// condition were a conditional branch of the ICmpInst ExitCond, TBB,
288 ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
293 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
294 /// of 'icmp op load X, cst', try to see if we can compute the trip count.
296 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
299 ICmpInst::Predicate p);
301 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute
302 /// a constant number of times (the condition evolves only from constants),
303 /// try to evaluate a few iterations of the loop until we get the exit
304 /// condition gets a value of ExitWhen (true or false). If we cannot
305 /// evaluate the trip count of the loop, return CouldNotCompute.
306 const SCEV *ComputeBackedgeTakenCountExhaustively(const Loop *L,
310 /// HowFarToZero - Return the number of times a backedge comparing the
311 /// specified value to zero will execute. If not computable, return
313 const SCEV *HowFarToZero(const SCEV *V, const Loop *L);
315 /// HowFarToNonZero - Return the number of times a backedge checking the
316 /// specified value for nonzero will execute. If not computable, return
318 const SCEV *HowFarToNonZero(const SCEV *V, const Loop *L);
320 /// HowManyLessThans - Return the number of times a backedge containing the
321 /// specified less-than comparison will execute. If not computable, return
322 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
323 BackedgeTakenInfo HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
324 const Loop *L, bool isSigned);
326 /// getLoopPredecessor - If the given loop's header has exactly one unique
327 /// predecessor outside the loop, return it. Otherwise return null.
328 BasicBlock *getLoopPredecessor(const Loop *L);
330 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
331 /// (which may not be an immediate predecessor) which has exactly one
332 /// successor from which BB is reachable, or null if no such block is
334 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
336 /// isNecessaryCond - Test whether the given CondValue value is a condition
337 /// which is at least as strict as the one described by Pred, LHS, and RHS.
338 bool isNecessaryCond(Value *Cond, ICmpInst::Predicate Pred,
339 const SCEV *LHS, const SCEV *RHS,
342 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
343 /// in the header of its containing loop, we know the loop executes a
344 /// constant number of times, and the PHI node is just a recurrence
345 /// involving constants, fold it.
346 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
350 static char ID; // Pass identification, replacement for typeid
353 LLVMContext *getContext() const { return Context; }
355 /// isSCEVable - Test if values of the given type are analyzable within
356 /// the SCEV framework. This primarily includes integer types, and it
357 /// can optionally include pointer types if the ScalarEvolution class
358 /// has access to target-specific information.
359 bool isSCEVable(const Type *Ty) const;
361 /// getTypeSizeInBits - Return the size in bits of the specified type,
362 /// for which isSCEVable must return true.
363 uint64_t getTypeSizeInBits(const Type *Ty) const;
365 /// getEffectiveSCEVType - Return a type with the same bitwidth as
366 /// the given type and which represents how SCEV will treat the given
367 /// type, for which isSCEVable must return true. For pointer types,
368 /// this is the pointer-sized integer type.
369 const Type *getEffectiveSCEVType(const Type *Ty) const;
371 /// getSCEV - Return a SCEV expression handle for the full generality of the
372 /// specified expression.
373 const SCEV *getSCEV(Value *V);
375 const SCEV *getConstant(ConstantInt *V);
376 const SCEV *getConstant(const APInt& Val);
377 const SCEV *getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
378 const SCEV *getTruncateExpr(const SCEV *Op, const Type *Ty);
379 const SCEV *getZeroExtendExpr(const SCEV *Op, const Type *Ty);
380 const SCEV *getSignExtendExpr(const SCEV *Op, const Type *Ty);
381 const SCEV *getAnyExtendExpr(const SCEV *Op, const Type *Ty);
382 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops);
383 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS) {
384 SmallVector<const SCEV *, 2> Ops;
387 return getAddExpr(Ops);
389 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1,
391 SmallVector<const SCEV *, 3> Ops;
395 return getAddExpr(Ops);
397 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops);
398 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS) {
399 SmallVector<const SCEV *, 2> Ops;
402 return getMulExpr(Ops);
404 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
405 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
407 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
409 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
411 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
412 return getAddRecExpr(NewOp, L);
414 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
415 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
416 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
417 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
418 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
419 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
420 const SCEV *getUnknown(Value *V);
421 const SCEV *getCouldNotCompute();
423 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
425 const SCEV *getNegativeSCEV(const SCEV *V);
427 /// getNotSCEV - Return the SCEV object corresponding to ~V.
429 const SCEV *getNotSCEV(const SCEV *V);
431 /// getMinusSCEV - Return LHS-RHS.
433 const SCEV *getMinusSCEV(const SCEV *LHS,
436 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
437 /// of the input value to the specified type. If the type must be
438 /// extended, it is zero extended.
439 const SCEV *getTruncateOrZeroExtend(const SCEV *V, const Type *Ty);
441 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
442 /// of the input value to the specified type. If the type must be
443 /// extended, it is sign extended.
444 const SCEV *getTruncateOrSignExtend(const SCEV *V, const Type *Ty);
446 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
447 /// the input value to the specified type. If the type must be extended,
448 /// it is zero extended. The conversion must not be narrowing.
449 const SCEV *getNoopOrZeroExtend(const SCEV *V, const Type *Ty);
451 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
452 /// the input value to the specified type. If the type must be extended,
453 /// it is sign extended. The conversion must not be narrowing.
454 const SCEV *getNoopOrSignExtend(const SCEV *V, const Type *Ty);
456 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
457 /// the input value to the specified type. If the type must be extended,
458 /// it is extended with unspecified bits. The conversion must not be
460 const SCEV *getNoopOrAnyExtend(const SCEV *V, const Type *Ty);
462 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
463 /// input value to the specified type. The conversion must not be
465 const SCEV *getTruncateOrNoop(const SCEV *V, const Type *Ty);
467 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
468 /// specified signed integer value and return a SCEV for the constant.
469 const SCEV *getIntegerSCEV(int Val, const Type *Ty);
471 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
472 /// the types using zero-extension, and then perform a umax operation
474 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
477 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
478 /// the types using zero-extension, and then perform a umin operation
480 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
483 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
484 /// at the specified scope in the program. The L value specifies a loop
485 /// nest to evaluate the expression at, where null is the top-level or a
486 /// specified loop is immediately inside of the loop.
488 /// This method can be used to compute the exit value for a variable defined
489 /// in a loop by querying what the value will hold in the parent loop.
491 /// In the case that a relevant loop exit value cannot be computed, the
492 /// original value V is returned.
493 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
495 /// getSCEVAtScope - This is a convenience function which does
496 /// getSCEVAtScope(getSCEV(V), L).
497 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
499 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
500 /// a conditional between LHS and RHS. This is used to help avoid max
501 /// expressions in loop trip counts.
502 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
503 const SCEV *LHS, const SCEV *RHS);
505 /// getBackedgeTakenCount - If the specified loop has a predictable
506 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
507 /// object. The backedge-taken count is the number of times the loop header
508 /// will be branched to from within the loop. This is one less than the
509 /// trip count of the loop, since it doesn't count the first iteration,
510 /// when the header is branched to from outside the loop.
512 /// Note that it is not valid to call this method on a loop without a
513 /// loop-invariant backedge-taken count (see
514 /// hasLoopInvariantBackedgeTakenCount).
516 const SCEV *getBackedgeTakenCount(const Loop *L);
518 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
519 /// return the least SCEV value that is known never to be less than the
520 /// actual backedge taken count.
521 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
523 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
524 /// has an analyzable loop-invariant backedge-taken count.
525 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
527 /// forgetLoopBackedgeTakenCount - This method should be called by the
528 /// client when it has changed a loop in a way that may effect
529 /// ScalarEvolution's ability to compute a trip count, or if the loop
531 void forgetLoopBackedgeTakenCount(const Loop *L);
533 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
534 /// is guaranteed to end in (at every loop iteration). It is, at the same
535 /// time, the minimum number of times S is divisible by 2. For example,
536 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
538 uint32_t GetMinTrailingZeros(const SCEV *S);
540 /// GetMinLeadingZeros - Determine the minimum number of zero bits that S is
541 /// guaranteed to begin with (at every loop iteration).
542 uint32_t GetMinLeadingZeros(const SCEV *S);
544 /// GetMinSignBits - Determine the minimum number of sign bits that S is
545 /// guaranteed to begin with.
546 uint32_t GetMinSignBits(const SCEV *S);
548 virtual bool runOnFunction(Function &F);
549 virtual void releaseMemory();
550 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
551 void print(raw_ostream &OS, const Module* = 0) const;
552 virtual void print(std::ostream &OS, const Module* = 0) const;
553 void print(std::ostream *OS, const Module* M = 0) const {
554 if (OS) print(*OS, M);
558 FoldingSet<SCEV> UniqueSCEVs;
559 BumpPtrAllocator SCEVAllocator;