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 instructions
223 /// that we attempt to compute getSCEVAtScope information for without
224 /// using SCEV techniques, which can be expensive.
225 std::map<Instruction *, std::map<const Loop *, Constant *> > ValuesAtScopes;
227 /// createSCEV - We know that there is no SCEV for the specified value.
228 /// Analyze the expression.
229 const SCEV *createSCEV(Value *V);
231 /// createNodeForPHI - Provide the special handling we need to analyze PHI
233 const SCEV *createNodeForPHI(PHINode *PN);
235 /// createNodeForGEP - Provide the special handling we need to analyze GEP
237 const SCEV *createNodeForGEP(Operator *GEP);
239 /// ForgetSymbolicValue - This looks up computed SCEV values for all
240 /// instructions that depend on the given instruction and removes them from
241 /// the Scalars map if they reference SymName. This is used during PHI
243 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
245 /// getBECount - Subtract the end and start values and divide by the step,
246 /// rounding up, to get the number of times the backedge is executed. Return
247 /// CouldNotCompute if an intermediate computation overflows.
248 const SCEV *getBECount(const SCEV *Start,
252 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
253 /// loop, lazily computing new values if the loop hasn't been analyzed
255 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
257 /// ComputeBackedgeTakenCount - Compute the number of times the specified
258 /// loop will iterate.
259 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
261 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the
262 /// backedge of the specified loop will execute if it exits via the
264 BackedgeTakenInfo ComputeBackedgeTakenCountFromExit(const Loop *L,
265 BasicBlock *ExitingBlock);
267 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
268 /// backedge of the specified loop will execute if its exit condition
269 /// were a conditional branch of ExitCond, TBB, and FBB.
271 ComputeBackedgeTakenCountFromExitCond(const Loop *L,
276 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of
277 /// times the backedge of the specified loop will execute if its exit
278 /// condition were a conditional branch of the ICmpInst ExitCond, TBB,
281 ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
286 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition
287 /// of 'icmp op load X, cst', try to see if we can compute the
288 /// backedge-taken count.
290 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
293 ICmpInst::Predicate p);
295 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute
296 /// a constant number of times (the condition evolves only from constants),
297 /// try to evaluate a few iterations of the loop until we get the exit
298 /// condition gets a value of ExitWhen (true or false). If we cannot
299 /// evaluate the backedge-taken count of the loop, return CouldNotCompute.
300 const SCEV *ComputeBackedgeTakenCountExhaustively(const Loop *L,
304 /// HowFarToZero - Return the number of times a backedge comparing the
305 /// specified value to zero will execute. If not computable, return
307 const SCEV *HowFarToZero(const SCEV *V, const Loop *L);
309 /// HowFarToNonZero - Return the number of times a backedge checking the
310 /// specified value for nonzero will execute. If not computable, return
312 const SCEV *HowFarToNonZero(const SCEV *V, const Loop *L);
314 /// HowManyLessThans - Return the number of times a backedge containing the
315 /// specified less-than comparison will execute. If not computable, return
316 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
317 BackedgeTakenInfo HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
318 const Loop *L, bool isSigned);
320 /// getLoopPredecessor - If the given loop's header has exactly one unique
321 /// predecessor outside the loop, return it. Otherwise return null.
322 BasicBlock *getLoopPredecessor(const Loop *L);
324 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
325 /// (which may not be an immediate predecessor) which has exactly one
326 /// successor from which BB is reachable, or null if no such block is
328 BasicBlock* getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
330 /// isImpliedCond - Test whether the condition described by Pred, LHS,
331 /// and RHS is true whenever the given Cond value evaluates to true.
332 bool isImpliedCond(Value *Cond, ICmpInst::Predicate Pred,
333 const SCEV *LHS, const SCEV *RHS,
336 /// isImpliedCondOperands - Test whether the condition described by Pred,
337 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
338 /// and FoundRHS is true.
339 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
340 const SCEV *LHS, const SCEV *RHS,
341 const SCEV *FoundLHS, const SCEV *FoundRHS);
343 /// isImpliedCondOperandsHelper - Test whether the condition described by
344 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
345 /// FoundLHS, and FoundRHS is true.
346 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
347 const SCEV *LHS, const SCEV *RHS,
348 const SCEV *FoundLHS, const SCEV *FoundRHS);
350 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
351 /// in the header of its containing loop, we know the loop executes a
352 /// constant number of times, and the PHI node is just a recurrence
353 /// involving constants, fold it.
354 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
358 static char ID; // Pass identification, replacement for typeid
361 LLVMContext &getContext() const { return F->getContext(); }
363 /// isSCEVable - Test if values of the given type are analyzable within
364 /// the SCEV framework. This primarily includes integer types, and it
365 /// can optionally include pointer types if the ScalarEvolution class
366 /// has access to target-specific information.
367 bool isSCEVable(const Type *Ty) const;
369 /// getTypeSizeInBits - Return the size in bits of the specified type,
370 /// for which isSCEVable must return true.
371 uint64_t getTypeSizeInBits(const Type *Ty) const;
373 /// getEffectiveSCEVType - Return a type with the same bitwidth as
374 /// the given type and which represents how SCEV will treat the given
375 /// type, for which isSCEVable must return true. For pointer types,
376 /// this is the pointer-sized integer type.
377 const Type *getEffectiveSCEVType(const Type *Ty) const;
379 /// getSCEV - Return a SCEV expression handle for the full generality of the
380 /// specified expression.
381 const SCEV *getSCEV(Value *V);
383 const SCEV *getConstant(ConstantInt *V);
384 const SCEV *getConstant(const APInt& Val);
385 const SCEV *getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
386 const SCEV *getTruncateExpr(const SCEV *Op, const Type *Ty);
387 const SCEV *getZeroExtendExpr(const SCEV *Op, const Type *Ty);
388 const SCEV *getSignExtendExpr(const SCEV *Op, const Type *Ty);
389 const SCEV *getAnyExtendExpr(const SCEV *Op, const Type *Ty);
390 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops);
391 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS) {
392 SmallVector<const SCEV *, 2> Ops;
395 return getAddExpr(Ops);
397 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1,
399 SmallVector<const SCEV *, 3> Ops;
403 return getAddExpr(Ops);
405 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops);
406 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS) {
407 SmallVector<const SCEV *, 2> Ops;
410 return getMulExpr(Ops);
412 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
413 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
415 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
417 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
419 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
420 return getAddRecExpr(NewOp, L);
422 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
423 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
424 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
425 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
426 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
427 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
428 const SCEV *getFieldOffsetExpr(const StructType *STy, unsigned FieldNo);
429 const SCEV *getAllocSizeExpr(const Type *AllocTy);
430 const SCEV *getUnknown(Value *V);
431 const SCEV *getCouldNotCompute();
433 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
435 const SCEV *getNegativeSCEV(const SCEV *V);
437 /// getNotSCEV - Return the SCEV object corresponding to ~V.
439 const SCEV *getNotSCEV(const SCEV *V);
441 /// getMinusSCEV - Return LHS-RHS.
443 const SCEV *getMinusSCEV(const SCEV *LHS,
446 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
447 /// of the input value to the specified type. If the type must be
448 /// extended, it is zero extended.
449 const SCEV *getTruncateOrZeroExtend(const SCEV *V, const Type *Ty);
451 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
452 /// of the input value to the specified type. If the type must be
453 /// extended, it is sign extended.
454 const SCEV *getTruncateOrSignExtend(const SCEV *V, const Type *Ty);
456 /// getNoopOrZeroExtend - 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 zero extended. The conversion must not be narrowing.
459 const SCEV *getNoopOrZeroExtend(const SCEV *V, const Type *Ty);
461 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
462 /// the input value to the specified type. If the type must be extended,
463 /// it is sign extended. The conversion must not be narrowing.
464 const SCEV *getNoopOrSignExtend(const SCEV *V, const Type *Ty);
466 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
467 /// the input value to the specified type. If the type must be extended,
468 /// it is extended with unspecified bits. The conversion must not be
470 const SCEV *getNoopOrAnyExtend(const SCEV *V, const Type *Ty);
472 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
473 /// input value to the specified type. The conversion must not be
475 const SCEV *getTruncateOrNoop(const SCEV *V, const Type *Ty);
477 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
478 /// specified signed integer value and return a SCEV for the constant.
479 const SCEV *getIntegerSCEV(int Val, const Type *Ty);
481 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
482 /// the types using zero-extension, and then perform a umax operation
484 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
487 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
488 /// the types using zero-extension, and then perform a umin operation
490 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
493 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
494 /// at the specified scope in the program. The L value specifies a loop
495 /// nest to evaluate the expression at, where null is the top-level or a
496 /// specified loop is immediately inside of the loop.
498 /// This method can be used to compute the exit value for a variable defined
499 /// in a loop by querying what the value will hold in the parent loop.
501 /// In the case that a relevant loop exit value cannot be computed, the
502 /// original value V is returned.
503 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
505 /// getSCEVAtScope - This is a convenience function which does
506 /// getSCEVAtScope(getSCEV(V), L).
507 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
509 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
510 /// a conditional between LHS and RHS. This is used to help avoid max
511 /// expressions in loop trip counts, and to eliminate casts.
512 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
513 const SCEV *LHS, const SCEV *RHS);
515 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
516 /// protected by a conditional between LHS and RHS. This is used to
517 /// to eliminate casts.
518 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
519 const SCEV *LHS, const SCEV *RHS);
521 /// getBackedgeTakenCount - If the specified loop has a predictable
522 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
523 /// object. The backedge-taken count is the number of times the loop header
524 /// will be branched to from within the loop. This is one less than the
525 /// trip count of the loop, since it doesn't count the first iteration,
526 /// when the header is branched to from outside the loop.
528 /// Note that it is not valid to call this method on a loop without a
529 /// loop-invariant backedge-taken count (see
530 /// hasLoopInvariantBackedgeTakenCount).
532 const SCEV *getBackedgeTakenCount(const Loop *L);
534 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
535 /// return the least SCEV value that is known never to be less than the
536 /// actual backedge taken count.
537 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
539 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
540 /// has an analyzable loop-invariant backedge-taken count.
541 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
543 /// forgetLoopBackedgeTakenCount - This method should be called by the
544 /// client when it has changed a loop in a way that may effect
545 /// ScalarEvolution's ability to compute a trip count, or if the loop
547 void forgetLoopBackedgeTakenCount(const Loop *L);
549 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
550 /// is guaranteed to end in (at every loop iteration). It is, at the same
551 /// time, the minimum number of times S is divisible by 2. For example,
552 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
554 uint32_t GetMinTrailingZeros(const SCEV *S);
556 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
558 ConstantRange getUnsignedRange(const SCEV *S);
560 /// getSignedRange - Determine the signed range for a particular SCEV.
562 ConstantRange getSignedRange(const SCEV *S);
564 /// isKnownNegative - Test if the given expression is known to be negative.
566 bool isKnownNegative(const SCEV *S);
568 /// isKnownPositive - Test if the given expression is known to be positive.
570 bool isKnownPositive(const SCEV *S);
572 /// isKnownNonNegative - Test if the given expression is known to be
575 bool isKnownNonNegative(const SCEV *S);
577 /// isKnownNonPositive - Test if the given expression is known to be
580 bool isKnownNonPositive(const SCEV *S);
582 /// isKnownNonZero - Test if the given expression is known to be
585 bool isKnownNonZero(const SCEV *S);
587 /// isKnownNonZero - Test if the given expression is known to satisfy
588 /// the condition described by Pred, LHS, and RHS.
590 bool isKnownPredicate(ICmpInst::Predicate Pred,
591 const SCEV *LHS, const SCEV *RHS);
593 virtual bool runOnFunction(Function &F);
594 virtual void releaseMemory();
595 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
596 virtual void print(raw_ostream &OS, const Module* = 0) const;
599 FoldingSet<SCEV> UniqueSCEVs;
600 BumpPtrAllocator SCEVAllocator;