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"
35 class ScalarEvolution;
38 class SCEVTruncateExpr;
39 class SCEVZeroExtendExpr;
40 class SCEVCommutativeExpr;
42 class SCEVSignExtendExpr;
46 /// SCEV - This class represents an analyzed expression in the program. These
47 /// are reference-counted opaque objects that the client is not allowed to
48 /// do much with directly.
51 const unsigned SCEVType; // The SCEV baseclass this node corresponds to
53 SCEV(const SCEV &); // DO NOT IMPLEMENT
54 void operator=(const SCEV &); // DO NOT IMPLEMENT
58 explicit SCEV(unsigned SCEVTy) :
61 unsigned getSCEVType() const { return SCEVType; }
63 /// isLoopInvariant - Return true if the value of this SCEV is unchanging in
64 /// the specified loop.
65 virtual bool isLoopInvariant(const Loop *L) const = 0;
67 /// hasComputableLoopEvolution - Return true if this SCEV changes value in a
68 /// known way in the specified loop. This property being true implies that
69 /// the value is variant in the loop AND that we can emit an expression to
70 /// compute the value of the expression at any particular loop iteration.
71 virtual bool hasComputableLoopEvolution(const Loop *L) const = 0;
73 /// getType - Return the LLVM type of this SCEV expression.
75 virtual const Type *getType() const = 0;
77 /// isZero - Return true if the expression is a constant zero.
81 /// isOne - Return true if the expression is a constant one.
85 /// isAllOnesValue - Return true if the expression is a constant
88 bool isAllOnesValue() const;
90 /// replaceSymbolicValuesWithConcrete - If this SCEV internally references
91 /// the symbolic value "Sym", construct and return a new SCEV that produces
92 /// the same value, but which uses the concrete value Conc instead of the
93 /// symbolic value. If this SCEV does not use the symbolic value, it
96 replaceSymbolicValuesWithConcrete(const SCEV* Sym,
98 ScalarEvolution &SE) const = 0;
100 /// dominates - Return true if elements that makes up this SCEV dominates
101 /// the specified basic block.
102 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const = 0;
104 /// print - Print out the internal representation of this scalar to the
105 /// specified stream. This should really only be used for debugging
107 virtual void print(raw_ostream &OS) const = 0;
108 void print(std::ostream &OS) const;
109 void print(std::ostream *OS) const { if (OS) print(*OS); }
111 /// dump - This method is used for debugging.
116 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
121 inline std::ostream &operator<<(std::ostream &OS, const SCEV &S) {
126 /// SCEVCouldNotCompute - An object of this class is returned by queries that
127 /// could not be answered. For example, if you ask for the number of
128 /// iterations of a linked-list traversal loop, you will get one of these.
129 /// None of the standard SCEV operations are valid on this class, it is just a
131 struct SCEVCouldNotCompute : public SCEV {
132 SCEVCouldNotCompute();
134 // None of these methods are valid for this object.
135 virtual bool isLoopInvariant(const Loop *L) const;
136 virtual const Type *getType() const;
137 virtual bool hasComputableLoopEvolution(const Loop *L) const;
138 virtual void print(raw_ostream &OS) const;
140 replaceSymbolicValuesWithConcrete(const SCEV* Sym,
142 ScalarEvolution &SE) const;
144 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const {
148 /// Methods for support type inquiry through isa, cast, and dyn_cast:
149 static inline bool classof(const SCEVCouldNotCompute *S) { return true; }
150 static bool classof(const SCEV *S);
153 /// ScalarEvolution - This class is the main scalar evolution driver. Because
154 /// client code (intentionally) can't do much with the SCEV objects directly,
155 /// they must ask this class for services.
157 class ScalarEvolution : public FunctionPass {
158 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
159 /// notified whenever a Value is deleted.
160 class SCEVCallbackVH : public CallbackVH {
162 virtual void deleted();
163 virtual void allUsesReplacedWith(Value *New);
165 SCEVCallbackVH(Value *V, ScalarEvolution *SE = 0);
168 friend class SCEVCallbackVH;
169 friend class SCEVExpander;
171 /// F - The function we are analyzing.
175 /// LI - The loop information for the function we are currently analyzing.
179 /// TD - The target data information for the target we are targetting.
183 /// CouldNotCompute - This SCEV is used to represent unknown trip
184 /// counts and things.
185 const SCEV* CouldNotCompute;
187 /// Scalars - This is a cache of the scalars we have analyzed so far.
189 std::map<SCEVCallbackVH, const SCEV*> Scalars;
191 /// BackedgeTakenInfo - Information about the backedge-taken count
192 /// of a loop. This currently inclues an exact count and a maximum count.
194 struct BackedgeTakenInfo {
195 /// Exact - An expression indicating the exact backedge-taken count of
196 /// the loop if it is known, or a SCEVCouldNotCompute otherwise.
199 /// Exact - An expression indicating the least maximum backedge-taken
200 /// count of the loop that is known, or a SCEVCouldNotCompute.
203 /*implicit*/ BackedgeTakenInfo(const SCEV* exact) :
204 Exact(exact), Max(exact) {}
206 BackedgeTakenInfo(const SCEV* exact, const SCEV* max) :
207 Exact(exact), Max(max) {}
209 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
210 /// computed information, or whether it's all SCEVCouldNotCompute
212 bool hasAnyInfo() const {
213 return !isa<SCEVCouldNotCompute>(Exact) ||
214 !isa<SCEVCouldNotCompute>(Max);
218 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
219 /// this function as they are computed.
220 std::map<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
222 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
223 /// the PHI instructions that we attempt to compute constant evolutions for.
224 /// This allows us to avoid potentially expensive recomputation of these
225 /// properties. An instruction maps to null if we are unable to compute its
227 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
229 /// ValuesAtScopes - This map contains entries for all the instructions
230 /// that we attempt to compute getSCEVAtScope information for without
231 /// using SCEV techniques, which can be expensive.
232 std::map<Instruction *, std::map<const Loop *, Constant *> > ValuesAtScopes;
234 /// createSCEV - We know that there is no SCEV for the specified value.
235 /// Analyze the expression.
236 const SCEV* createSCEV(Value *V);
238 /// createNodeForPHI - Provide the special handling we need to analyze PHI
240 const SCEV* createNodeForPHI(PHINode *PN);
242 /// createNodeForGEP - Provide the special handling we need to analyze GEP
244 const SCEV* createNodeForGEP(User *GEP);
246 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
247 /// for the specified instruction and replaces any references to the
248 /// symbolic value SymName with the specified value. This is used during
250 void ReplaceSymbolicValueWithConcrete(Instruction *I,
254 /// getBECount - Subtract the end and start values and divide by the step,
255 /// rounding up, to get the number of times the backedge is executed. Return
256 /// CouldNotCompute if an intermediate computation overflows.
257 const SCEV* getBECount(const SCEV* Start,
261 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
262 /// loop, lazily computing new values if the loop hasn't been analyzed
264 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
266 /// ComputeBackedgeTakenCount - Compute the number of times the specified
267 /// loop will iterate.
268 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
270 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the
271 /// backedge of the specified loop will execute if it exits via the
273 BackedgeTakenInfo ComputeBackedgeTakenCountFromExit(const Loop *L,
274 BasicBlock *ExitingBlock);
276 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
277 /// backedge of the specified loop will execute if its exit condition
278 /// were a conditional branch of ExitCond, TBB, and FBB.
280 ComputeBackedgeTakenCountFromExitCond(const Loop *L,
285 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of
286 /// times the backedge of the specified loop will execute if its exit
287 /// condition were a conditional branch of the ICmpInst ExitCond, TBB,
290 ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
295 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
296 /// of 'icmp op load X, cst', try to see if we can compute the trip count.
298 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
301 ICmpInst::Predicate p);
303 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute
304 /// a constant number of times (the condition evolves only from constants),
305 /// try to evaluate a few iterations of the loop until we get the exit
306 /// condition gets a value of ExitWhen (true or false). If we cannot
307 /// evaluate the trip count of the loop, return CouldNotCompute.
308 const SCEV* ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond,
311 /// HowFarToZero - Return the number of times a backedge comparing the
312 /// specified value to zero will execute. If not computable, return
314 const SCEV* HowFarToZero(const SCEV *V, const Loop *L);
316 /// HowFarToNonZero - Return the number of times a backedge checking the
317 /// specified value for nonzero will execute. If not computable, return
319 const SCEV* HowFarToNonZero(const SCEV *V, const Loop *L);
321 /// HowManyLessThans - Return the number of times a backedge containing the
322 /// specified less-than comparison will execute. If not computable, return
323 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
324 BackedgeTakenInfo HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
325 const Loop *L, bool isSigned);
327 /// getLoopPredecessor - If the given loop's header has exactly one unique
328 /// predecessor outside the loop, return it. Otherwise return null.
329 BasicBlock *getLoopPredecessor(const Loop *L);
331 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
332 /// (which may not be an immediate predecessor) which has exactly one
333 /// successor from which BB is reachable, or null if no such block is
335 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
337 /// isNecessaryCond - Test whether the given CondValue value is a condition
338 /// which is at least as strict as the one described by Pred, LHS, and RHS.
339 bool isNecessaryCond(Value *Cond, ICmpInst::Predicate Pred,
340 const SCEV *LHS, const SCEV *RHS,
343 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
344 /// in the header of its containing loop, we know the loop executes a
345 /// constant number of times, and the PHI node is just a recurrence
346 /// involving constants, fold it.
347 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
350 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
351 /// PHI nodes in the given loop. This is used when the trip count of
352 /// the loop may have changed.
353 void forgetLoopPHIs(const Loop *L);
356 static char ID; // Pass identification, replacement for typeid
359 /// isSCEVable - Test if values of the given type are analyzable within
360 /// the SCEV framework. This primarily includes integer types, and it
361 /// can optionally include pointer types if the ScalarEvolution class
362 /// has access to target-specific information.
363 bool isSCEVable(const Type *Ty) const;
365 /// getTypeSizeInBits - Return the size in bits of the specified type,
366 /// for which isSCEVable must return true.
367 uint64_t getTypeSizeInBits(const Type *Ty) const;
369 /// getEffectiveSCEVType - Return a type with the same bitwidth as
370 /// the given type and which represents how SCEV will treat the given
371 /// type, for which isSCEVable must return true. For pointer types,
372 /// this is the pointer-sized integer type.
373 const Type *getEffectiveSCEVType(const Type *Ty) const;
375 /// getSCEV - Return a SCEV expression handle for the full generality of the
376 /// specified expression.
377 const SCEV* getSCEV(Value *V);
379 const SCEV* getConstant(ConstantInt *V);
380 const SCEV* getConstant(const APInt& Val);
381 const SCEV* getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
382 const SCEV* getTruncateExpr(const SCEV* Op, const Type *Ty);
383 const SCEV* getZeroExtendExpr(const SCEV* Op, const Type *Ty);
384 const SCEV* getSignExtendExpr(const SCEV* Op, const Type *Ty);
385 const SCEV* getAnyExtendExpr(const SCEV* Op, const Type *Ty);
386 const SCEV* getAddExpr(SmallVectorImpl<const SCEV*> &Ops);
387 const SCEV* getAddExpr(const SCEV* LHS, const SCEV* RHS) {
388 SmallVector<const SCEV*, 2> Ops;
391 return getAddExpr(Ops);
393 const SCEV* getAddExpr(const SCEV* Op0, const SCEV* Op1,
395 SmallVector<const SCEV*, 3> Ops;
399 return getAddExpr(Ops);
401 const SCEV* getMulExpr(SmallVectorImpl<const SCEV*> &Ops);
402 const SCEV* getMulExpr(const SCEV* LHS, const SCEV* RHS) {
403 SmallVector<const SCEV*, 2> Ops;
406 return getMulExpr(Ops);
408 const SCEV* getUDivExpr(const SCEV* LHS, const SCEV* RHS);
409 const SCEV* getAddRecExpr(const SCEV* Start, const SCEV* Step,
411 const SCEV* getAddRecExpr(SmallVectorImpl<const SCEV*> &Operands,
413 const SCEV* getAddRecExpr(const SmallVectorImpl<const SCEV*> &Operands,
415 SmallVector<const SCEV*, 4> NewOp(Operands.begin(), Operands.end());
416 return getAddRecExpr(NewOp, L);
418 const SCEV* getSMaxExpr(const SCEV* LHS, const SCEV* RHS);
419 const SCEV* getSMaxExpr(SmallVectorImpl<const SCEV*> &Operands);
420 const SCEV* getUMaxExpr(const SCEV* LHS, const SCEV* RHS);
421 const SCEV* getUMaxExpr(SmallVectorImpl<const SCEV*> &Operands);
422 const SCEV* getSMinExpr(const SCEV* LHS, const SCEV* RHS);
423 const SCEV* getUMinExpr(const SCEV* LHS, const SCEV* RHS);
424 const SCEV* getUnknown(Value *V);
425 const SCEV* getCouldNotCompute();
427 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
429 const SCEV* getNegativeSCEV(const SCEV* V);
431 /// getNotSCEV - Return the SCEV object corresponding to ~V.
433 const SCEV* getNotSCEV(const SCEV* V);
435 /// getMinusSCEV - Return LHS-RHS.
437 const SCEV* getMinusSCEV(const SCEV* LHS,
440 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
441 /// of the input value to the specified type. If the type must be
442 /// extended, it is zero extended.
443 const SCEV* getTruncateOrZeroExtend(const SCEV* V, const Type *Ty);
445 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
446 /// of the input value to the specified type. If the type must be
447 /// extended, it is sign extended.
448 const SCEV* getTruncateOrSignExtend(const SCEV* V, const Type *Ty);
450 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
451 /// the input value to the specified type. If the type must be extended,
452 /// it is zero extended. The conversion must not be narrowing.
453 const SCEV* getNoopOrZeroExtend(const SCEV* V, const Type *Ty);
455 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
456 /// the input value to the specified type. If the type must be extended,
457 /// it is sign extended. The conversion must not be narrowing.
458 const SCEV* getNoopOrSignExtend(const SCEV* V, const Type *Ty);
460 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
461 /// the input value to the specified type. If the type must be extended,
462 /// it is extended with unspecified bits. The conversion must not be
464 const SCEV* getNoopOrAnyExtend(const SCEV* V, const Type *Ty);
466 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
467 /// input value to the specified type. The conversion must not be
469 const SCEV* getTruncateOrNoop(const SCEV* V, const Type *Ty);
471 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
472 /// specified signed integer value and return a SCEV for the constant.
473 const SCEV* getIntegerSCEV(int Val, const Type *Ty);
475 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
476 /// the types using zero-extension, and then perform a umax operation
478 const SCEV* getUMaxFromMismatchedTypes(const SCEV* LHS,
481 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
482 /// the types using zero-extension, and then perform a umin operation
484 const SCEV* getUMinFromMismatchedTypes(const SCEV* LHS,
487 /// hasSCEV - Return true if the SCEV for this value has already been
489 bool hasSCEV(Value *V) const;
491 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
492 /// the specified value.
493 void setSCEV(Value *V, const SCEV* H);
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.
514 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
515 const SCEV *LHS, const SCEV *RHS);
517 /// getBackedgeTakenCount - If the specified loop has a predictable
518 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
519 /// object. The backedge-taken count is the number of times the loop header
520 /// will be branched to from within the loop. This is one less than the
521 /// trip count of the loop, since it doesn't count the first iteration,
522 /// when the header is branched to from outside the loop.
524 /// Note that it is not valid to call this method on a loop without a
525 /// loop-invariant backedge-taken count (see
526 /// hasLoopInvariantBackedgeTakenCount).
528 const SCEV* getBackedgeTakenCount(const Loop *L);
530 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
531 /// return the least SCEV value that is known never to be less than the
532 /// actual backedge taken count.
533 const SCEV* getMaxBackedgeTakenCount(const Loop *L);
535 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
536 /// has an analyzable loop-invariant backedge-taken count.
537 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
539 /// forgetLoopBackedgeTakenCount - This method should be called by the
540 /// client when it has changed a loop in a way that may effect
541 /// ScalarEvolution's ability to compute a trip count, or if the loop
543 void forgetLoopBackedgeTakenCount(const Loop *L);
545 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
546 /// guaranteed to end in (at every loop iteration). It is, at the same time,
547 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
548 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
549 uint32_t GetMinTrailingZeros(const SCEV* S);
551 /// GetMinLeadingZeros - Determine the minimum number of zero bits that S is
552 /// guaranteed to begin with (at every loop iteration).
553 uint32_t GetMinLeadingZeros(const SCEV* S);
555 /// GetMinSignBits - Determine the minimum number of sign bits that S is
556 /// guaranteed to begin with.
557 uint32_t GetMinSignBits(const SCEV* S);
559 virtual bool runOnFunction(Function &F);
560 virtual void releaseMemory();
561 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
562 void print(raw_ostream &OS, const Module* = 0) const;
563 virtual void print(std::ostream &OS, const Module* = 0) const;
564 void print(std::ostream *OS, const Module* M = 0) const {
565 if (OS) print(*OS, M);
570 std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
571 std::map<std::pair<const SCEV*, const Type*>,
572 SCEVTruncateExpr*> SCEVTruncates;
573 std::map<std::pair<const SCEV*, const Type*>,
574 SCEVZeroExtendExpr*> SCEVZeroExtends;
575 std::map<std::pair<unsigned, std::vector<const SCEV*> >,
576 SCEVCommutativeExpr*> SCEVCommExprs;
577 std::map<std::pair<const SCEV*, const SCEV*>,
578 SCEVUDivExpr*> SCEVUDivs;
579 std::map<std::pair<const SCEV*, const Type*>,
580 SCEVSignExtendExpr*> SCEVSignExtends;
581 std::map<std::pair<const Loop *, std::vector<const SCEV*> >,
582 SCEVAddRecExpr*> SCEVAddRecExprs;
583 std::map<Value*, SCEVUnknown*> SCEVUnknowns;