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/Function.h"
27 #include "llvm/Support/DataTypes.h"
28 #include "llvm/Support/ValueHandle.h"
29 #include "llvm/Support/Allocator.h"
30 #include "llvm/Support/ConstantRange.h"
31 #include "llvm/ADT/FoldingSet.h"
32 #include "llvm/ADT/DenseMap.h"
42 class ScalarEvolution;
49 /// SCEV - This class represents an analyzed expression in the program. These
50 /// are opaque objects that the client is not allowed to do much with
53 class SCEV : public FastFoldingSetNode {
54 // The SCEV baseclass this node corresponds to
55 const unsigned short SCEVType;
58 /// SubclassData - This field is initialized to zero and may be used in
59 /// subclasses to store miscelaneous information.
60 unsigned short SubclassData;
63 SCEV(const SCEV &); // DO NOT IMPLEMENT
64 void operator=(const SCEV &); // DO NOT IMPLEMENT
68 explicit SCEV(const FoldingSetNodeID &ID, unsigned SCEVTy) :
69 FastFoldingSetNode(ID), SCEVType(SCEVTy), SubclassData(0) {}
71 unsigned getSCEVType() const { return SCEVType; }
73 /// isLoopInvariant - Return true if the value of this SCEV is unchanging in
74 /// the specified loop.
75 virtual bool isLoopInvariant(const Loop *L) const = 0;
77 /// hasComputableLoopEvolution - Return true if this SCEV changes value in a
78 /// known way in the specified loop. This property being true implies that
79 /// the value is variant in the loop AND that we can emit an expression to
80 /// compute the value of the expression at any particular loop iteration.
81 virtual bool hasComputableLoopEvolution(const Loop *L) const = 0;
83 /// getType - Return the LLVM type of this SCEV expression.
85 virtual const Type *getType() const = 0;
87 /// isZero - Return true if the expression is a constant zero.
91 /// isOne - Return true if the expression is a constant one.
95 /// isAllOnesValue - Return true if the expression is a constant
98 bool isAllOnesValue() const;
100 /// hasOperand - Test whether this SCEV has Op as a direct or
101 /// indirect operand.
102 virtual bool hasOperand(const SCEV *Op) const = 0;
104 /// dominates - Return true if elements that makes up this SCEV dominates
105 /// the specified basic block.
106 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const = 0;
108 /// print - Print out the internal representation of this scalar to the
109 /// specified stream. This should really only be used for debugging
111 virtual void print(raw_ostream &OS) const = 0;
112 void print(std::ostream &OS) const;
113 void print(std::ostream *OS) const { if (OS) print(*OS); }
115 /// dump - This method is used for debugging.
120 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
125 inline std::ostream &operator<<(std::ostream &OS, const SCEV &S) {
130 /// SCEVCouldNotCompute - An object of this class is returned by queries that
131 /// could not be answered. For example, if you ask for the number of
132 /// iterations of a linked-list traversal loop, you will get one of these.
133 /// None of the standard SCEV operations are valid on this class, it is just a
135 struct SCEVCouldNotCompute : public SCEV {
136 SCEVCouldNotCompute();
138 // None of these methods are valid for this object.
139 virtual bool isLoopInvariant(const Loop *L) const;
140 virtual const Type *getType() const;
141 virtual bool hasComputableLoopEvolution(const Loop *L) const;
142 virtual void print(raw_ostream &OS) const;
143 virtual bool hasOperand(const SCEV *Op) const;
145 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const {
149 /// Methods for support type inquiry through isa, cast, and dyn_cast:
150 static inline bool classof(const SCEVCouldNotCompute *S) { return true; }
151 static bool classof(const SCEV *S);
154 /// ScalarEvolution - This class is the main scalar evolution driver. Because
155 /// client code (intentionally) can't do much with the SCEV objects directly,
156 /// they must ask this class for services.
158 class ScalarEvolution : public FunctionPass {
159 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
160 /// notified whenever a Value is deleted.
161 class SCEVCallbackVH : public CallbackVH {
163 virtual void deleted();
164 virtual void allUsesReplacedWith(Value *New);
166 SCEVCallbackVH(Value *V, ScalarEvolution *SE = 0);
169 friend class SCEVCallbackVH;
170 friend struct SCEVExpander;
172 /// F - The function we are analyzing.
176 /// LI - The loop information for the function we are currently analyzing.
180 /// TD - The target data information for the target we are targetting.
184 /// CouldNotCompute - This SCEV is used to represent unknown trip
185 /// counts and things.
186 SCEVCouldNotCompute CouldNotCompute;
188 /// Scalars - This is a cache of the scalars we have analyzed so far.
190 std::map<SCEVCallbackVH, const SCEV *> Scalars;
192 /// BackedgeTakenInfo - Information about the backedge-taken count
193 /// of a loop. This currently inclues an exact count and a maximum count.
195 struct BackedgeTakenInfo {
196 /// Exact - An expression indicating the exact backedge-taken count of
197 /// the loop if it is known, or a SCEVCouldNotCompute otherwise.
200 /// Max - An expression indicating the least maximum backedge-taken
201 /// count of the loop that is known, or a SCEVCouldNotCompute.
204 /*implicit*/ BackedgeTakenInfo(const SCEV *exact) :
205 Exact(exact), Max(exact) {}
207 BackedgeTakenInfo(const SCEV *exact, const SCEV *max) :
208 Exact(exact), Max(max) {}
210 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
211 /// computed information, or whether it's all SCEVCouldNotCompute
213 bool hasAnyInfo() const {
214 return !isa<SCEVCouldNotCompute>(Exact) ||
215 !isa<SCEVCouldNotCompute>(Max);
219 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
220 /// this function as they are computed.
221 std::map<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
223 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
224 /// the PHI instructions that we attempt to compute constant evolutions for.
225 /// This allows us to avoid potentially expensive recomputation of these
226 /// properties. An instruction maps to null if we are unable to compute its
228 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
230 /// ValuesAtScopes - This map contains entries for all the instructions
231 /// that we attempt to compute getSCEVAtScope information for without
232 /// using SCEV techniques, which can be expensive.
233 std::map<Instruction *, std::map<const Loop *, Constant *> > ValuesAtScopes;
235 /// createSCEV - We know that there is no SCEV for the specified value.
236 /// Analyze the expression.
237 const SCEV *createSCEV(Value *V);
239 /// createNodeForPHI - Provide the special handling we need to analyze PHI
241 const SCEV *createNodeForPHI(PHINode *PN);
243 /// createNodeForGEP - Provide the special handling we need to analyze GEP
245 const SCEV *createNodeForGEP(Operator *GEP);
247 /// ForgetSymbolicValue - This looks up computed SCEV values for all
248 /// instructions that depend on the given instruction and removes them from
249 /// the Scalars map if they reference SymName. This is used during PHI
251 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
253 /// getBECount - Subtract the end and start values and divide by the step,
254 /// rounding up, to get the number of times the backedge is executed. Return
255 /// CouldNotCompute if an intermediate computation overflows.
256 const SCEV *getBECount(const SCEV *Start,
260 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
261 /// loop, lazily computing new values if the loop hasn't been analyzed
263 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
265 /// ComputeBackedgeTakenCount - Compute the number of times the specified
266 /// loop will iterate.
267 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
269 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the
270 /// backedge of the specified loop will execute if it exits via the
272 BackedgeTakenInfo ComputeBackedgeTakenCountFromExit(const Loop *L,
273 BasicBlock *ExitingBlock);
275 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
276 /// backedge of the specified loop will execute if its exit condition
277 /// were a conditional branch of ExitCond, TBB, and FBB.
279 ComputeBackedgeTakenCountFromExitCond(const Loop *L,
284 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of
285 /// times the backedge of the specified loop will execute if its exit
286 /// condition were a conditional branch of the ICmpInst ExitCond, TBB,
289 ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
294 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
295 /// of 'icmp op load X, cst', try to see if we can compute the
296 /// backedge-taken count.
298 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
301 ICmpInst::Predicate p);
303 /// ComputeBackedgeTakenCountExhaustively - If the loop 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 backedge-taken count of the loop, return CouldNotCompute.
308 const SCEV *ComputeBackedgeTakenCountExhaustively(const Loop *L,
312 /// HowFarToZero - Return the number of times a backedge comparing the
313 /// specified value to zero will execute. If not computable, return
315 const SCEV *HowFarToZero(const SCEV *V, const Loop *L);
317 /// HowFarToNonZero - Return the number of times a backedge checking the
318 /// specified value for nonzero will execute. If not computable, return
320 const SCEV *HowFarToNonZero(const SCEV *V, const Loop *L);
322 /// HowManyLessThans - Return the number of times a backedge containing the
323 /// specified less-than comparison will execute. If not computable, return
324 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
325 BackedgeTakenInfo HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
326 const Loop *L, bool isSigned);
328 /// getLoopPredecessor - If the given loop's header has exactly one unique
329 /// predecessor outside the loop, return it. Otherwise return null.
330 BasicBlock *getLoopPredecessor(const Loop *L);
332 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
333 /// (which may not be an immediate predecessor) which has exactly one
334 /// successor from which BB is reachable, or null if no such block is
336 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
338 /// isImpliedCond - Test whether the condition described by Pred, LHS,
339 /// and RHS is true whenever the given Cond value evaluates to true.
340 bool isImpliedCond(Value *Cond, ICmpInst::Predicate Pred,
341 const SCEV *LHS, const SCEV *RHS,
344 /// isImpliedCondOperands - Test whether the condition described by Pred,
345 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
346 /// and FoundRHS is true.
347 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
348 const SCEV *LHS, const SCEV *RHS,
349 const SCEV *FoundLHS, const SCEV *FoundRHS);
351 /// isImpliedCondOperandsHelper - Test whether the condition described by
352 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
353 /// FoundLHS, and FoundRHS is true.
354 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
355 const SCEV *LHS, const SCEV *RHS,
356 const SCEV *FoundLHS, const SCEV *FoundRHS);
358 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
359 /// in the header of its containing loop, we know the loop executes a
360 /// constant number of times, and the PHI node is just a recurrence
361 /// involving constants, fold it.
362 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
366 static char ID; // Pass identification, replacement for typeid
369 LLVMContext &getContext() const { return F->getContext(); }
371 /// isSCEVable - Test if values of the given type are analyzable within
372 /// the SCEV framework. This primarily includes integer types, and it
373 /// can optionally include pointer types if the ScalarEvolution class
374 /// has access to target-specific information.
375 bool isSCEVable(const Type *Ty) const;
377 /// getTypeSizeInBits - Return the size in bits of the specified type,
378 /// for which isSCEVable must return true.
379 uint64_t getTypeSizeInBits(const Type *Ty) const;
381 /// getEffectiveSCEVType - Return a type with the same bitwidth as
382 /// the given type and which represents how SCEV will treat the given
383 /// type, for which isSCEVable must return true. For pointer types,
384 /// this is the pointer-sized integer type.
385 const Type *getEffectiveSCEVType(const Type *Ty) const;
387 /// getSCEV - Return a SCEV expression handle for the full generality of the
388 /// specified expression.
389 const SCEV *getSCEV(Value *V);
391 const SCEV *getConstant(ConstantInt *V);
392 const SCEV *getConstant(const APInt& Val);
393 const SCEV *getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
394 const SCEV *getTruncateExpr(const SCEV *Op, const Type *Ty);
395 const SCEV *getZeroExtendExpr(const SCEV *Op, const Type *Ty);
396 const SCEV *getSignExtendExpr(const SCEV *Op, const Type *Ty);
397 const SCEV *getAnyExtendExpr(const SCEV *Op, const Type *Ty);
398 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops);
399 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS) {
400 SmallVector<const SCEV *, 2> Ops;
403 return getAddExpr(Ops);
405 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1,
407 SmallVector<const SCEV *, 3> Ops;
411 return getAddExpr(Ops);
413 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops);
414 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS) {
415 SmallVector<const SCEV *, 2> Ops;
418 return getMulExpr(Ops);
420 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
421 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
423 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
425 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
427 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
428 return getAddRecExpr(NewOp, L);
430 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
431 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
432 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
433 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
434 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
435 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
436 const SCEV *getUnknown(Value *V);
437 const SCEV *getCouldNotCompute();
439 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
441 const SCEV *getNegativeSCEV(const SCEV *V);
443 /// getNotSCEV - Return the SCEV object corresponding to ~V.
445 const SCEV *getNotSCEV(const SCEV *V);
447 /// getMinusSCEV - Return LHS-RHS.
449 const SCEV *getMinusSCEV(const SCEV *LHS,
452 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
453 /// of the input value to the specified type. If the type must be
454 /// extended, it is zero extended.
455 const SCEV *getTruncateOrZeroExtend(const SCEV *V, const Type *Ty);
457 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
458 /// of the input value to the specified type. If the type must be
459 /// extended, it is sign extended.
460 const SCEV *getTruncateOrSignExtend(const SCEV *V, const Type *Ty);
462 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
463 /// the input value to the specified type. If the type must be extended,
464 /// it is zero extended. The conversion must not be narrowing.
465 const SCEV *getNoopOrZeroExtend(const SCEV *V, const Type *Ty);
467 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
468 /// the input value to the specified type. If the type must be extended,
469 /// it is sign extended. The conversion must not be narrowing.
470 const SCEV *getNoopOrSignExtend(const SCEV *V, const Type *Ty);
472 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
473 /// the input value to the specified type. If the type must be extended,
474 /// it is extended with unspecified bits. The conversion must not be
476 const SCEV *getNoopOrAnyExtend(const SCEV *V, const Type *Ty);
478 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
479 /// input value to the specified type. The conversion must not be
481 const SCEV *getTruncateOrNoop(const SCEV *V, const Type *Ty);
483 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
484 /// specified signed integer value and return a SCEV for the constant.
485 const SCEV *getIntegerSCEV(int Val, const Type *Ty);
487 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
488 /// the types using zero-extension, and then perform a umax operation
490 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
493 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
494 /// the types using zero-extension, and then perform a umin operation
496 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
499 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
500 /// at the specified scope in the program. The L value specifies a loop
501 /// nest to evaluate the expression at, where null is the top-level or a
502 /// specified loop is immediately inside of the loop.
504 /// This method can be used to compute the exit value for a variable defined
505 /// in a loop by querying what the value will hold in the parent loop.
507 /// In the case that a relevant loop exit value cannot be computed, the
508 /// original value V is returned.
509 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
511 /// getSCEVAtScope - This is a convenience function which does
512 /// getSCEVAtScope(getSCEV(V), L).
513 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
515 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
516 /// a conditional between LHS and RHS. This is used to help avoid max
517 /// expressions in loop trip counts, and to eliminate casts.
518 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
519 const SCEV *LHS, const SCEV *RHS);
521 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
522 /// protected by a conditional between LHS and RHS. This is used to
523 /// to eliminate casts.
524 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
525 const SCEV *LHS, const SCEV *RHS);
527 /// getBackedgeTakenCount - If the specified loop has a predictable
528 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
529 /// object. The backedge-taken count is the number of times the loop header
530 /// will be branched to from within the loop. This is one less than the
531 /// trip count of the loop, since it doesn't count the first iteration,
532 /// when the header is branched to from outside the loop.
534 /// Note that it is not valid to call this method on a loop without a
535 /// loop-invariant backedge-taken count (see
536 /// hasLoopInvariantBackedgeTakenCount).
538 const SCEV *getBackedgeTakenCount(const Loop *L);
540 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
541 /// return the least SCEV value that is known never to be less than the
542 /// actual backedge taken count.
543 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
545 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
546 /// has an analyzable loop-invariant backedge-taken count.
547 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
549 /// forgetLoopBackedgeTakenCount - This method should be called by the
550 /// client when it has changed a loop in a way that may effect
551 /// ScalarEvolution's ability to compute a trip count, or if the loop
553 void forgetLoopBackedgeTakenCount(const Loop *L);
555 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
556 /// is guaranteed to end in (at every loop iteration). It is, at the same
557 /// time, the minimum number of times S is divisible by 2. For example,
558 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
560 uint32_t GetMinTrailingZeros(const SCEV *S);
562 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
564 ConstantRange getUnsignedRange(const SCEV *S);
566 /// getSignedRange - Determine the signed range for a particular SCEV.
568 ConstantRange getSignedRange(const SCEV *S);
570 /// isKnownNegative - Test if the given expression is known to be negative.
572 bool isKnownNegative(const SCEV *S);
574 /// isKnownPositive - Test if the given expression is known to be positive.
576 bool isKnownPositive(const SCEV *S);
578 /// isKnownNonNegative - Test if the given expression is known to be
581 bool isKnownNonNegative(const SCEV *S);
583 /// isKnownNonPositive - Test if the given expression is known to be
586 bool isKnownNonPositive(const SCEV *S);
588 /// isKnownNonZero - Test if the given expression is known to be
591 bool isKnownNonZero(const SCEV *S);
593 /// isKnownNonZero - Test if the given expression is known to satisfy
594 /// the condition described by Pred, LHS, and RHS.
596 bool isKnownPredicate(ICmpInst::Predicate Pred,
597 const SCEV *LHS, const SCEV *RHS);
599 virtual bool runOnFunction(Function &F);
600 virtual void releaseMemory();
601 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
602 void print(raw_ostream &OS, const Module* = 0) const;
603 virtual void print(std::ostream &OS, const Module* = 0) const;
604 void print(std::ostream *OS, const Module* M = 0) const {
605 if (OS) print(*OS, M);
609 FoldingSet<SCEV> UniqueSCEVs;
610 BumpPtrAllocator SCEVAllocator;