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 // The SCEV baseclass this node corresponds to
54 const unsigned short SCEVType;
57 /// SubclassData - This field is initialized to zero and may be used in
58 /// subclasses to store miscelaneous information.
59 unsigned short SubclassData;
62 SCEV(const SCEV &); // DO NOT IMPLEMENT
63 void operator=(const SCEV &); // DO NOT IMPLEMENT
67 explicit SCEV(const FoldingSetNodeID &ID, unsigned SCEVTy) :
68 FastFoldingSetNode(ID), SCEVType(SCEVTy), SubclassData(0) {}
70 unsigned getSCEVType() const { return SCEVType; }
72 /// isLoopInvariant - Return true if the value of this SCEV is unchanging in
73 /// the specified loop.
74 virtual bool isLoopInvariant(const Loop *L) const = 0;
76 /// hasComputableLoopEvolution - Return true if this SCEV changes value in a
77 /// known way in the specified loop. This property being true implies that
78 /// the value is variant in the loop AND that we can emit an expression to
79 /// compute the value of the expression at any particular loop iteration.
80 virtual bool hasComputableLoopEvolution(const Loop *L) const = 0;
82 /// getType - Return the LLVM type of this SCEV expression.
84 virtual const Type *getType() const = 0;
86 /// isZero - Return true if the expression is a constant zero.
90 /// isOne - Return true if the expression is a constant one.
94 /// isAllOnesValue - Return true if the expression is a constant
97 bool isAllOnesValue() const;
99 /// hasOperand - Test whether this SCEV has Op as a direct or
100 /// indirect operand.
101 virtual bool hasOperand(const SCEV *Op) const = 0;
103 /// dominates - Return true if elements that makes up this SCEV dominates
104 /// the specified basic block.
105 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const = 0;
107 /// print - Print out the internal representation of this scalar to the
108 /// specified stream. This should really only be used for debugging
110 virtual void print(raw_ostream &OS) const = 0;
111 void print(std::ostream &OS) const;
112 void print(std::ostream *OS) const { if (OS) print(*OS); }
114 /// dump - This method is used for debugging.
119 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
124 inline std::ostream &operator<<(std::ostream &OS, const SCEV &S) {
129 /// SCEVCouldNotCompute - An object of this class is returned by queries that
130 /// could not be answered. For example, if you ask for the number of
131 /// iterations of a linked-list traversal loop, you will get one of these.
132 /// None of the standard SCEV operations are valid on this class, it is just a
134 struct SCEVCouldNotCompute : public SCEV {
135 SCEVCouldNotCompute();
137 // None of these methods are valid for this object.
138 virtual bool isLoopInvariant(const Loop *L) const;
139 virtual const Type *getType() const;
140 virtual bool hasComputableLoopEvolution(const Loop *L) const;
141 virtual void print(raw_ostream &OS) const;
142 virtual bool hasOperand(const SCEV *Op) 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 struct 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 SCEVCouldNotCompute 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 /// Max - 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(Operator *GEP);
246 /// ForgetSymbolicValue - This looks up computed SCEV values for all
247 /// instructions that depend on the given instruction and removes them from
248 /// the Scalars map if they reference SymName. This is used during PHI
250 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
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 /// isImpliedCond - Test whether the condition described by Pred, LHS,
337 /// and RHS is true whenever the given Cond value evaluates to true.
338 bool isImpliedCond(Value *Cond, ICmpInst::Predicate Pred,
339 const SCEV *LHS, const SCEV *RHS,
342 /// isImpliedCondOperands - Test whether the condition described by Pred,
343 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
344 /// and FoundRHS is true.
345 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
346 const SCEV *LHS, const SCEV *RHS,
347 const SCEV *FoundLHS, const SCEV *FoundRHS);
349 /// isImpliedCondOperandsHelper - Test whether the condition described by
350 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
351 /// FoundLHS, and FoundRHS is true.
352 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
353 const SCEV *LHS, const SCEV *RHS,
354 const SCEV *FoundLHS, const SCEV *FoundRHS);
356 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
357 /// in the header of its containing loop, we know the loop executes a
358 /// constant number of times, and the PHI node is just a recurrence
359 /// involving constants, fold it.
360 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
364 static char ID; // Pass identification, replacement for typeid
367 LLVMContext &getContext() const { return F->getContext(); }
369 /// isSCEVable - Test if values of the given type are analyzable within
370 /// the SCEV framework. This primarily includes integer types, and it
371 /// can optionally include pointer types if the ScalarEvolution class
372 /// has access to target-specific information.
373 bool isSCEVable(const Type *Ty) const;
375 /// getTypeSizeInBits - Return the size in bits of the specified type,
376 /// for which isSCEVable must return true.
377 uint64_t getTypeSizeInBits(const Type *Ty) const;
379 /// getEffectiveSCEVType - Return a type with the same bitwidth as
380 /// the given type and which represents how SCEV will treat the given
381 /// type, for which isSCEVable must return true. For pointer types,
382 /// this is the pointer-sized integer type.
383 const Type *getEffectiveSCEVType(const Type *Ty) const;
385 /// getSCEV - Return a SCEV expression handle for the full generality of the
386 /// specified expression.
387 const SCEV *getSCEV(Value *V);
389 const SCEV *getConstant(ConstantInt *V);
390 const SCEV *getConstant(const APInt& Val);
391 const SCEV *getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
392 const SCEV *getTruncateExpr(const SCEV *Op, const Type *Ty);
393 const SCEV *getZeroExtendExpr(const SCEV *Op, const Type *Ty);
394 const SCEV *getSignExtendExpr(const SCEV *Op, const Type *Ty);
395 const SCEV *getAnyExtendExpr(const SCEV *Op, const Type *Ty);
396 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops);
397 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS) {
398 SmallVector<const SCEV *, 2> Ops;
401 return getAddExpr(Ops);
403 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1,
405 SmallVector<const SCEV *, 3> Ops;
409 return getAddExpr(Ops);
411 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops);
412 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS) {
413 SmallVector<const SCEV *, 2> Ops;
416 return getMulExpr(Ops);
418 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
419 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
421 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
423 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
425 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
426 return getAddRecExpr(NewOp, L);
428 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
429 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
430 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
431 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
432 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
433 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
434 const SCEV *getUnknown(Value *V);
435 const SCEV *getCouldNotCompute();
437 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
439 const SCEV *getNegativeSCEV(const SCEV *V);
441 /// getNotSCEV - Return the SCEV object corresponding to ~V.
443 const SCEV *getNotSCEV(const SCEV *V);
445 /// getMinusSCEV - Return LHS-RHS.
447 const SCEV *getMinusSCEV(const SCEV *LHS,
450 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
451 /// of the input value to the specified type. If the type must be
452 /// extended, it is zero extended.
453 const SCEV *getTruncateOrZeroExtend(const SCEV *V, const Type *Ty);
455 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
456 /// of the input value to the specified type. If the type must be
457 /// extended, it is sign extended.
458 const SCEV *getTruncateOrSignExtend(const SCEV *V, const Type *Ty);
460 /// getNoopOrZeroExtend - 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 zero extended. The conversion must not be narrowing.
463 const SCEV *getNoopOrZeroExtend(const SCEV *V, const Type *Ty);
465 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
466 /// the input value to the specified type. If the type must be extended,
467 /// it is sign extended. The conversion must not be narrowing.
468 const SCEV *getNoopOrSignExtend(const SCEV *V, const Type *Ty);
470 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
471 /// the input value to the specified type. If the type must be extended,
472 /// it is extended with unspecified bits. The conversion must not be
474 const SCEV *getNoopOrAnyExtend(const SCEV *V, const Type *Ty);
476 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
477 /// input value to the specified type. The conversion must not be
479 const SCEV *getTruncateOrNoop(const SCEV *V, const Type *Ty);
481 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
482 /// specified signed integer value and return a SCEV for the constant.
483 const SCEV *getIntegerSCEV(int Val, const Type *Ty);
485 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
486 /// the types using zero-extension, and then perform a umax operation
488 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
491 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
492 /// the types using zero-extension, and then perform a umin operation
494 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
497 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
498 /// at the specified scope in the program. The L value specifies a loop
499 /// nest to evaluate the expression at, where null is the top-level or a
500 /// specified loop is immediately inside of the loop.
502 /// This method can be used to compute the exit value for a variable defined
503 /// in a loop by querying what the value will hold in the parent loop.
505 /// In the case that a relevant loop exit value cannot be computed, the
506 /// original value V is returned.
507 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
509 /// getSCEVAtScope - This is a convenience function which does
510 /// getSCEVAtScope(getSCEV(V), L).
511 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
513 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
514 /// a conditional between LHS and RHS. This is used to help avoid max
515 /// expressions in loop trip counts, and to eliminate casts.
516 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
517 const SCEV *LHS, const SCEV *RHS);
519 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
520 /// protected by a conditional between LHS and RHS. This is used to
521 /// to eliminate casts.
522 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
523 const SCEV *LHS, const SCEV *RHS);
525 /// getBackedgeTakenCount - If the specified loop has a predictable
526 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
527 /// object. The backedge-taken count is the number of times the loop header
528 /// will be branched to from within the loop. This is one less than the
529 /// trip count of the loop, since it doesn't count the first iteration,
530 /// when the header is branched to from outside the loop.
532 /// Note that it is not valid to call this method on a loop without a
533 /// loop-invariant backedge-taken count (see
534 /// hasLoopInvariantBackedgeTakenCount).
536 const SCEV *getBackedgeTakenCount(const Loop *L);
538 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
539 /// return the least SCEV value that is known never to be less than the
540 /// actual backedge taken count.
541 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
543 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
544 /// has an analyzable loop-invariant backedge-taken count.
545 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
547 /// forgetLoopBackedgeTakenCount - This method should be called by the
548 /// client when it has changed a loop in a way that may effect
549 /// ScalarEvolution's ability to compute a trip count, or if the loop
551 void forgetLoopBackedgeTakenCount(const Loop *L);
553 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
554 /// is guaranteed to end in (at every loop iteration). It is, at the same
555 /// time, the minimum number of times S is divisible by 2. For example,
556 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
558 uint32_t GetMinTrailingZeros(const SCEV *S);
560 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
562 ConstantRange getUnsignedRange(const SCEV *S);
564 /// getSignedRange - Determine the signed range for a particular SCEV.
566 ConstantRange getSignedRange(const SCEV *S);
568 /// isKnownNegative - Test if the given expression is known to be negative.
570 bool isKnownNegative(const SCEV *S);
572 /// isKnownPositive - Test if the given expression is known to be positive.
574 bool isKnownPositive(const SCEV *S);
576 /// isKnownNonNegative - Test if the given expression is known to be
579 bool isKnownNonNegative(const SCEV *S);
581 /// isKnownNonPositive - Test if the given expression is known to be
584 bool isKnownNonPositive(const SCEV *S);
586 /// isKnownNonZero - Test if the given expression is known to be
589 bool isKnownNonZero(const SCEV *S);
591 /// isKnownNonZero - Test if the given expression is known to satisfy
592 /// the condition described by Pred, LHS, and RHS.
594 bool isKnownPredicate(ICmpInst::Predicate Pred,
595 const SCEV *LHS, const SCEV *RHS);
597 virtual bool runOnFunction(Function &F);
598 virtual void releaseMemory();
599 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
600 void print(raw_ostream &OS, const Module* = 0) const;
601 virtual void print(std::ostream &OS, const Module* = 0) const;
602 void print(std::ostream *OS, const Module* M = 0) const {
603 if (OS) print(*OS, M);
607 FoldingSet<SCEV> UniqueSCEVs;
608 BumpPtrAllocator SCEVAllocator;