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"
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;
112 /// dump - This method is used for debugging.
117 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
122 /// SCEVCouldNotCompute - An object of this class is returned by queries that
123 /// could not be answered. For example, if you ask for the number of
124 /// iterations of a linked-list traversal loop, you will get one of these.
125 /// None of the standard SCEV operations are valid on this class, it is just a
127 struct SCEVCouldNotCompute : public SCEV {
128 SCEVCouldNotCompute();
130 // None of these methods are valid for this object.
131 virtual bool isLoopInvariant(const Loop *L) const;
132 virtual const Type *getType() const;
133 virtual bool hasComputableLoopEvolution(const Loop *L) const;
134 virtual void print(raw_ostream &OS) const;
135 virtual bool hasOperand(const SCEV *Op) const;
137 virtual bool dominates(BasicBlock *BB, DominatorTree *DT) const {
141 /// Methods for support type inquiry through isa, cast, and dyn_cast:
142 static inline bool classof(const SCEVCouldNotCompute *S) { return true; }
143 static bool classof(const SCEV *S);
146 /// ScalarEvolution - This class is the main scalar evolution driver. Because
147 /// client code (intentionally) can't do much with the SCEV objects directly,
148 /// they must ask this class for services.
150 class ScalarEvolution : public FunctionPass {
151 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
152 /// notified whenever a Value is deleted.
153 class SCEVCallbackVH : public CallbackVH {
155 virtual void deleted();
156 virtual void allUsesReplacedWith(Value *New);
158 SCEVCallbackVH(Value *V, ScalarEvolution *SE = 0);
161 friend class SCEVCallbackVH;
162 friend struct SCEVExpander;
164 /// F - The function we are analyzing.
168 /// LI - The loop information for the function we are currently analyzing.
172 /// TD - The target data information for the target we are targetting.
176 /// CouldNotCompute - This SCEV is used to represent unknown trip
177 /// counts and things.
178 SCEVCouldNotCompute CouldNotCompute;
180 /// Scalars - This is a cache of the scalars we have analyzed so far.
182 std::map<SCEVCallbackVH, const SCEV *> Scalars;
184 /// BackedgeTakenInfo - Information about the backedge-taken count
185 /// of a loop. This currently inclues an exact count and a maximum count.
187 struct BackedgeTakenInfo {
188 /// Exact - An expression indicating the exact backedge-taken count of
189 /// the loop if it is known, or a SCEVCouldNotCompute otherwise.
192 /// Max - An expression indicating the least maximum backedge-taken
193 /// count of the loop that is known, or a SCEVCouldNotCompute.
196 /*implicit*/ BackedgeTakenInfo(const SCEV *exact) :
197 Exact(exact), Max(exact) {}
199 BackedgeTakenInfo(const SCEV *exact, const SCEV *max) :
200 Exact(exact), Max(max) {}
202 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
203 /// computed information, or whether it's all SCEVCouldNotCompute
205 bool hasAnyInfo() const {
206 return !isa<SCEVCouldNotCompute>(Exact) ||
207 !isa<SCEVCouldNotCompute>(Max);
211 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
212 /// this function as they are computed.
213 std::map<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
215 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
216 /// the PHI instructions that we attempt to compute constant evolutions for.
217 /// This allows us to avoid potentially expensive recomputation of these
218 /// properties. An instruction maps to null if we are unable to compute its
220 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
222 /// ValuesAtScopes - This map contains entries for all the expressions
223 /// that we attempt to compute getSCEVAtScope information for, which can
224 /// be expensive in extreme cases.
225 std::map<const SCEV *,
226 std::map<const Loop *, const SCEV *> > ValuesAtScopes;
228 /// createSCEV - We know that there is no SCEV for the specified value.
229 /// Analyze the expression.
230 const SCEV *createSCEV(Value *V);
232 /// createNodeForPHI - Provide the special handling we need to analyze PHI
234 const SCEV *createNodeForPHI(PHINode *PN);
236 /// createNodeForGEP - Provide the special handling we need to analyze GEP
238 const SCEV *createNodeForGEP(Operator *GEP);
240 /// computeSCEVAtScope - Implementation code for getSCEVAtScope; called
241 /// at most once for each SCEV+Loop pair.
243 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
245 /// ForgetSymbolicValue - This looks up computed SCEV values for all
246 /// instructions that depend on the given instruction and removes them from
247 /// the Scalars map if they reference SymName. This is used during PHI
249 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
251 /// getBECount - Subtract the end and start values and divide by the step,
252 /// rounding up, to get the number of times the backedge is executed. Return
253 /// CouldNotCompute if an intermediate computation overflows.
254 const SCEV *getBECount(const SCEV *Start,
258 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
259 /// loop, lazily computing new values if the loop hasn't been analyzed
261 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
263 /// ComputeBackedgeTakenCount - Compute the number of times the specified
264 /// loop will iterate.
265 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
267 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the
268 /// backedge of the specified loop will execute if it exits via the
270 BackedgeTakenInfo ComputeBackedgeTakenCountFromExit(const Loop *L,
271 BasicBlock *ExitingBlock);
273 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
274 /// backedge of the specified loop will execute if its exit condition
275 /// were a conditional branch of ExitCond, TBB, and FBB.
277 ComputeBackedgeTakenCountFromExitCond(const Loop *L,
282 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of
283 /// times the backedge of the specified loop will execute if its exit
284 /// condition were a conditional branch of the ICmpInst ExitCond, TBB,
287 ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
292 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
293 /// of 'icmp op load X, cst', try to see if we can compute the
294 /// backedge-taken count.
296 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
299 ICmpInst::Predicate p);
301 /// ComputeBackedgeTakenCountExhaustively - If the loop 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 backedge-taken 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 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 *getFieldOffsetExpr(const StructType *STy, unsigned FieldNo);
435 const SCEV *getAllocSizeExpr(const Type *AllocTy);
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 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 virtual void print(raw_ostream &OS, const Module* = 0) const;
605 FoldingSet<SCEV> UniqueSCEVs;
606 BumpPtrAllocator SCEVAllocator;