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,
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
295 /// backedge-taken count.
297 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI,
300 ICmpInst::Predicate p);
302 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute
303 /// a constant number of times (the condition evolves only from constants),
304 /// try to evaluate a few iterations of the loop until we get the exit
305 /// condition gets a value of ExitWhen (true or false). If we cannot
306 /// evaluate the backedge-taken count of the loop, return CouldNotCompute.
307 const SCEV *ComputeBackedgeTakenCountExhaustively(const Loop *L,
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 /// isImpliedCond - Test whether the condition described by Pred, LHS,
338 /// and RHS is true whenever the given Cond value evaluates to true.
339 bool isImpliedCond(Value *Cond, ICmpInst::Predicate Pred,
340 const SCEV *LHS, const SCEV *RHS,
343 /// isImpliedCondOperands - Test whether the condition described by Pred,
344 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
345 /// and FoundRHS is true.
346 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
347 const SCEV *LHS, const SCEV *RHS,
348 const SCEV *FoundLHS, const SCEV *FoundRHS);
350 /// isImpliedCondOperandsHelper - Test whether the condition described by
351 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
352 /// FoundLHS, and FoundRHS is true.
353 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
354 const SCEV *LHS, const SCEV *RHS,
355 const SCEV *FoundLHS, const SCEV *FoundRHS);
357 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
358 /// in the header of its containing loop, we know the loop executes a
359 /// constant number of times, and the PHI node is just a recurrence
360 /// involving constants, fold it.
361 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
365 static char ID; // Pass identification, replacement for typeid
368 LLVMContext &getContext() const { return F->getContext(); }
370 /// isSCEVable - Test if values of the given type are analyzable within
371 /// the SCEV framework. This primarily includes integer types, and it
372 /// can optionally include pointer types if the ScalarEvolution class
373 /// has access to target-specific information.
374 bool isSCEVable(const Type *Ty) const;
376 /// getTypeSizeInBits - Return the size in bits of the specified type,
377 /// for which isSCEVable must return true.
378 uint64_t getTypeSizeInBits(const Type *Ty) const;
380 /// getEffectiveSCEVType - Return a type with the same bitwidth as
381 /// the given type and which represents how SCEV will treat the given
382 /// type, for which isSCEVable must return true. For pointer types,
383 /// this is the pointer-sized integer type.
384 const Type *getEffectiveSCEVType(const Type *Ty) const;
386 /// getSCEV - Return a SCEV expression for the full generality of the
387 /// specified expression.
388 const SCEV *getSCEV(Value *V);
390 const SCEV *getConstant(ConstantInt *V);
391 const SCEV *getConstant(const APInt& Val);
392 const SCEV *getConstant(const Type *Ty, uint64_t V, bool isSigned = false);
393 const SCEV *getTruncateExpr(const SCEV *Op, const Type *Ty);
394 const SCEV *getZeroExtendExpr(const SCEV *Op, const Type *Ty);
395 const SCEV *getSignExtendExpr(const SCEV *Op, const Type *Ty);
396 const SCEV *getAnyExtendExpr(const SCEV *Op, const Type *Ty);
397 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops);
398 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS) {
399 SmallVector<const SCEV *, 2> Ops;
402 return getAddExpr(Ops);
404 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1,
406 SmallVector<const SCEV *, 3> Ops;
410 return getAddExpr(Ops);
412 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops);
413 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS) {
414 SmallVector<const SCEV *, 2> Ops;
417 return getMulExpr(Ops);
419 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
420 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
422 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
424 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
426 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
427 return getAddRecExpr(NewOp, L);
429 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
430 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
431 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
432 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
433 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
434 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
435 const SCEV *getFieldOffsetExpr(const StructType *STy, unsigned FieldNo);
436 const SCEV *getAllocSizeExpr(const Type *AllocTy);
437 const SCEV *getUnknown(Value *V);
438 const SCEV *getCouldNotCompute();
440 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
442 const SCEV *getNegativeSCEV(const SCEV *V);
444 /// getNotSCEV - Return the SCEV object corresponding to ~V.
446 const SCEV *getNotSCEV(const SCEV *V);
448 /// getMinusSCEV - Return LHS-RHS.
450 const SCEV *getMinusSCEV(const SCEV *LHS,
453 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
454 /// of the input value to the specified type. If the type must be
455 /// extended, it is zero extended.
456 const SCEV *getTruncateOrZeroExtend(const SCEV *V, const Type *Ty);
458 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
459 /// of the input value to the specified type. If the type must be
460 /// extended, it is sign extended.
461 const SCEV *getTruncateOrSignExtend(const SCEV *V, const Type *Ty);
463 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
464 /// the input value to the specified type. If the type must be extended,
465 /// it is zero extended. The conversion must not be narrowing.
466 const SCEV *getNoopOrZeroExtend(const SCEV *V, const Type *Ty);
468 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
469 /// the input value to the specified type. If the type must be extended,
470 /// it is sign extended. The conversion must not be narrowing.
471 const SCEV *getNoopOrSignExtend(const SCEV *V, const Type *Ty);
473 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
474 /// the input value to the specified type. If the type must be extended,
475 /// it is extended with unspecified bits. The conversion must not be
477 const SCEV *getNoopOrAnyExtend(const SCEV *V, const Type *Ty);
479 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
480 /// input value to the specified type. The conversion must not be
482 const SCEV *getTruncateOrNoop(const SCEV *V, const Type *Ty);
484 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
485 /// specified signed integer value and return a SCEV for the constant.
486 const SCEV *getIntegerSCEV(int Val, const Type *Ty);
488 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
489 /// the types using zero-extension, and then perform a umax operation
491 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
494 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
495 /// the types using zero-extension, and then perform a umin operation
497 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
500 /// getSCEVAtScope - Return a SCEV expression for the specified value
501 /// at the specified scope in the program. The L value specifies a loop
502 /// nest to evaluate the expression at, where null is the top-level or a
503 /// specified loop is immediately inside of the loop.
505 /// This method can be used to compute the exit value for a variable defined
506 /// in a loop by querying what the value will hold in the parent loop.
508 /// In the case that a relevant loop exit value cannot be computed, the
509 /// original value V is returned.
510 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
512 /// getSCEVAtScope - This is a convenience function which does
513 /// getSCEVAtScope(getSCEV(V), L).
514 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
516 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
517 /// a conditional between LHS and RHS. This is used to help avoid max
518 /// expressions in loop trip counts, and to eliminate casts.
519 bool isLoopGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
520 const SCEV *LHS, const SCEV *RHS);
522 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
523 /// protected by a conditional between LHS and RHS. This is used to
524 /// to eliminate casts.
525 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
526 const SCEV *LHS, const SCEV *RHS);
528 /// getBackedgeTakenCount - If the specified loop has a predictable
529 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
530 /// object. The backedge-taken count is the number of times the loop header
531 /// will be branched to from within the loop. This is one less than the
532 /// trip count of the loop, since it doesn't count the first iteration,
533 /// when the header is branched to from outside the loop.
535 /// Note that it is not valid to call this method on a loop without a
536 /// loop-invariant backedge-taken count (see
537 /// hasLoopInvariantBackedgeTakenCount).
539 const SCEV *getBackedgeTakenCount(const Loop *L);
541 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
542 /// return the least SCEV value that is known never to be less than the
543 /// actual backedge taken count.
544 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
546 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
547 /// has an analyzable loop-invariant backedge-taken count.
548 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
550 /// forgetLoopBackedgeTakenCount - This method should be called by the
551 /// client when it has changed a loop in a way that may effect
552 /// ScalarEvolution's ability to compute a trip count, or if the loop
554 void forgetLoopBackedgeTakenCount(const Loop *L);
556 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
557 /// is guaranteed to end in (at every loop iteration). It is, at the same
558 /// time, the minimum number of times S is divisible by 2. For example,
559 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
561 uint32_t GetMinTrailingZeros(const SCEV *S);
563 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
565 ConstantRange getUnsignedRange(const SCEV *S);
567 /// getSignedRange - Determine the signed range for a particular SCEV.
569 ConstantRange getSignedRange(const SCEV *S);
571 /// isKnownNegative - Test if the given expression is known to be negative.
573 bool isKnownNegative(const SCEV *S);
575 /// isKnownPositive - Test if the given expression is known to be positive.
577 bool isKnownPositive(const SCEV *S);
579 /// isKnownNonNegative - Test if the given expression is known to be
582 bool isKnownNonNegative(const SCEV *S);
584 /// isKnownNonPositive - Test if the given expression is known to be
587 bool isKnownNonPositive(const SCEV *S);
589 /// isKnownNonZero - Test if the given expression is known to be
592 bool isKnownNonZero(const SCEV *S);
594 /// isKnownNonZero - Test if the given expression is known to satisfy
595 /// the condition described by Pred, LHS, and RHS.
597 bool isKnownPredicate(ICmpInst::Predicate Pred,
598 const SCEV *LHS, const SCEV *RHS);
600 virtual bool runOnFunction(Function &F);
601 virtual void releaseMemory();
602 virtual void getAnalysisUsage(AnalysisUsage &AU) const;
603 virtual void print(raw_ostream &OS, const Module* = 0) const;
606 FoldingSet<SCEV> UniqueSCEVs;
607 BumpPtrAllocator SCEVAllocator;