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 // categorize 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/ADT/DenseSet.h"
25 #include "llvm/ADT/FoldingSet.h"
26 #include "llvm/IR/ConstantRange.h"
27 #include "llvm/IR/Function.h"
28 #include "llvm/IR/Instructions.h"
29 #include "llvm/IR/Operator.h"
30 #include "llvm/IR/ValueHandle.h"
31 #include "llvm/Pass.h"
32 #include "llvm/Support/Allocator.h"
33 #include "llvm/Support/DataTypes.h"
38 class AssumptionTracker;
43 class ScalarEvolution;
45 class TargetLibraryInfo;
52 template<> struct FoldingSetTrait<SCEV>;
54 /// SCEV - This class represents an analyzed expression in the program. These
55 /// are opaque objects that the client is not allowed to do much with
58 class SCEV : public FoldingSetNode {
59 friend struct FoldingSetTrait<SCEV>;
61 /// FastID - A reference to an Interned FoldingSetNodeID for this node.
62 /// The ScalarEvolution's BumpPtrAllocator holds the data.
63 FoldingSetNodeIDRef FastID;
65 // The SCEV baseclass this node corresponds to
66 const unsigned short SCEVType;
69 /// SubclassData - This field is initialized to zero and may be used in
70 /// subclasses to store miscellaneous information.
71 unsigned short SubclassData;
74 SCEV(const SCEV &) LLVM_DELETED_FUNCTION;
75 void operator=(const SCEV &) LLVM_DELETED_FUNCTION;
78 /// NoWrapFlags are bitfield indices into SubclassData.
80 /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
81 /// no-signed-wrap <NSW> properties, which are derived from the IR
82 /// operator. NSW is a misnomer that we use to mean no signed overflow or
85 /// AddRec expression may have a no-self-wraparound <NW> property if the
86 /// result can never reach the start value. This property is independent of
87 /// the actual start value and step direction. Self-wraparound is defined
88 /// purely in terms of the recurrence's loop, step size, and
89 /// bitwidth. Formally, a recurrence with no self-wraparound satisfies:
90 /// abs(step) * max-iteration(loop) <= unsigned-max(bitwidth).
92 /// Note that NUW and NSW are also valid properties of a recurrence, and
93 /// either implies NW. For convenience, NW will be set for a recurrence
94 /// whenever either NUW or NSW are set.
95 enum NoWrapFlags { FlagAnyWrap = 0, // No guarantee.
96 FlagNW = (1 << 0), // No self-wrap.
97 FlagNUW = (1 << 1), // No unsigned wrap.
98 FlagNSW = (1 << 2), // No signed wrap.
99 NoWrapMask = (1 << 3) -1 };
101 explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy) :
102 FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
104 unsigned getSCEVType() const { return SCEVType; }
106 /// getType - Return the LLVM type of this SCEV expression.
108 Type *getType() const;
110 /// isZero - Return true if the expression is a constant zero.
114 /// isOne - Return true if the expression is a constant one.
118 /// isAllOnesValue - Return true if the expression is a constant
121 bool isAllOnesValue() const;
123 /// isNonConstantNegative - Return true if the specified scev is negated,
124 /// but not a constant.
125 bool isNonConstantNegative() const;
127 /// print - Print out the internal representation of this scalar to the
128 /// specified stream. This should really only be used for debugging
130 void print(raw_ostream &OS) const;
132 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
133 /// dump - This method is used for debugging.
139 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
140 // temporary FoldingSetNodeID values.
141 template<> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
142 static void Profile(const SCEV &X, FoldingSetNodeID& ID) {
145 static bool Equals(const SCEV &X, const FoldingSetNodeID &ID,
146 unsigned IDHash, FoldingSetNodeID &TempID) {
147 return ID == X.FastID;
149 static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
150 return X.FastID.ComputeHash();
154 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
159 /// SCEVCouldNotCompute - An object of this class is returned by queries that
160 /// could not be answered. For example, if you ask for the number of
161 /// iterations of a linked-list traversal loop, you will get one of these.
162 /// None of the standard SCEV operations are valid on this class, it is just a
164 struct SCEVCouldNotCompute : public SCEV {
165 SCEVCouldNotCompute();
167 /// Methods for support type inquiry through isa, cast, and dyn_cast:
168 static bool classof(const SCEV *S);
171 /// ScalarEvolution - This class is the main scalar evolution driver. Because
172 /// client code (intentionally) can't do much with the SCEV objects directly,
173 /// they must ask this class for services.
175 class ScalarEvolution : public FunctionPass {
177 /// LoopDisposition - An enum describing the relationship between a
179 enum LoopDisposition {
180 LoopVariant, ///< The SCEV is loop-variant (unknown).
181 LoopInvariant, ///< The SCEV is loop-invariant.
182 LoopComputable ///< The SCEV varies predictably with the loop.
185 /// BlockDisposition - An enum describing the relationship between a
186 /// SCEV and a basic block.
187 enum BlockDisposition {
188 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
189 DominatesBlock, ///< The SCEV dominates the block.
190 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
193 /// Convenient NoWrapFlags manipulation that hides enum casts and is
194 /// visible in the ScalarEvolution name space.
195 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
196 maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
197 return (SCEV::NoWrapFlags)(Flags & Mask);
199 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
200 setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
201 return (SCEV::NoWrapFlags)(Flags | OnFlags);
203 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
204 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
205 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
209 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
210 /// notified whenever a Value is deleted.
211 class SCEVCallbackVH : public CallbackVH {
213 void deleted() override;
214 void allUsesReplacedWith(Value *New) override;
216 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
219 friend class SCEVCallbackVH;
220 friend class SCEVExpander;
221 friend class SCEVUnknown;
223 /// F - The function we are analyzing.
227 /// The tracker for @llvm.assume intrinsics in this function.
228 AssumptionTracker *AT;
230 /// LI - The loop information for the function we are currently analyzing.
234 /// The DataLayout information for the target we are targeting.
236 const DataLayout *DL;
238 /// TLI - The target library information for the target we are targeting.
240 TargetLibraryInfo *TLI;
242 /// DT - The dominator tree.
246 /// CouldNotCompute - This SCEV is used to represent unknown trip
247 /// counts and things.
248 SCEVCouldNotCompute CouldNotCompute;
250 /// ValueExprMapType - The typedef for ValueExprMap.
252 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
255 /// ValueExprMap - This is a cache of the values we have analyzed so far.
257 ValueExprMapType ValueExprMap;
259 /// Mark predicate values currently being processed by isImpliedCond.
260 DenseSet<Value*> PendingLoopPredicates;
262 /// ExitLimit - Information about the number of loop iterations for which a
263 /// loop exit's branch condition evaluates to the not-taken path. This is a
264 /// temporary pair of exact and max expressions that are eventually
265 /// summarized in ExitNotTakenInfo and BackedgeTakenInfo.
270 /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
272 ExitLimit(const SCEV *E, const SCEV *M) : Exact(E), Max(M) {}
274 /// hasAnyInfo - Test whether this ExitLimit contains any computed
275 /// information, or whether it's all SCEVCouldNotCompute values.
276 bool hasAnyInfo() const {
277 return !isa<SCEVCouldNotCompute>(Exact) ||
278 !isa<SCEVCouldNotCompute>(Max);
282 /// ExitNotTakenInfo - Information about the number of times a particular
283 /// loop exit may be reached before exiting the loop.
284 struct ExitNotTakenInfo {
285 AssertingVH<BasicBlock> ExitingBlock;
286 const SCEV *ExactNotTaken;
287 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
289 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
291 /// isCompleteList - Return true if all loop exits are computable.
292 bool isCompleteList() const {
293 return NextExit.getInt() == 0;
296 void setIncomplete() { NextExit.setInt(1); }
298 /// getNextExit - Return a pointer to the next exit's not-taken info.
299 ExitNotTakenInfo *getNextExit() const {
300 return NextExit.getPointer();
303 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
306 /// BackedgeTakenInfo - Information about the backedge-taken count
307 /// of a loop. This currently includes an exact count and a maximum count.
309 class BackedgeTakenInfo {
310 /// ExitNotTaken - A list of computable exits and their not-taken counts.
311 /// Loops almost never have more than one computable exit.
312 ExitNotTakenInfo ExitNotTaken;
314 /// Max - An expression indicating the least maximum backedge-taken
315 /// count of the loop that is known, or a SCEVCouldNotCompute.
319 BackedgeTakenInfo() : Max(nullptr) {}
321 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
323 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
324 bool Complete, const SCEV *MaxCount);
326 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
327 /// computed information, or whether it's all SCEVCouldNotCompute
329 bool hasAnyInfo() const {
330 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
333 /// getExact - Return an expression indicating the exact backedge-taken
334 /// count of the loop if it is known, or SCEVCouldNotCompute
335 /// otherwise. This is the number of times the loop header can be
336 /// guaranteed to execute, minus one.
337 const SCEV *getExact(ScalarEvolution *SE) const;
339 /// getExact - Return the number of times this loop exit may fall through
340 /// to the back edge, or SCEVCouldNotCompute. The loop is guaranteed not
341 /// to exit via this block before this number of iterations, but may exit
342 /// via another block.
343 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
345 /// getMax - Get the max backedge taken count for the loop.
346 const SCEV *getMax(ScalarEvolution *SE) const;
348 /// Return true if any backedge taken count expressions refer to the given
350 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
352 /// clear - Invalidate this result and free associated memory.
356 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
357 /// this function as they are computed.
358 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
360 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
361 /// the PHI instructions that we attempt to compute constant evolutions for.
362 /// This allows us to avoid potentially expensive recomputation of these
363 /// properties. An instruction maps to null if we are unable to compute its
365 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
367 /// ValuesAtScopes - This map contains entries for all the expressions
368 /// that we attempt to compute getSCEVAtScope information for, which can
369 /// be expensive in extreme cases.
370 DenseMap<const SCEV *,
371 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
373 /// LoopDispositions - Memoized computeLoopDisposition results.
374 DenseMap<const SCEV *,
375 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> > LoopDispositions;
377 /// computeLoopDisposition - Compute a LoopDisposition value.
378 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
380 /// BlockDispositions - Memoized computeBlockDisposition results.
381 DenseMap<const SCEV *,
382 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> > BlockDispositions;
384 /// computeBlockDisposition - Compute a BlockDisposition value.
385 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
387 /// UnsignedRanges - Memoized results from getUnsignedRange
388 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
390 /// SignedRanges - Memoized results from getSignedRange
391 DenseMap<const SCEV *, ConstantRange> SignedRanges;
393 /// setUnsignedRange - Set the memoized unsigned range for the given SCEV.
394 const ConstantRange &setUnsignedRange(const SCEV *S,
395 const ConstantRange &CR) {
396 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
397 UnsignedRanges.insert(std::make_pair(S, CR));
399 Pair.first->second = CR;
400 return Pair.first->second;
403 /// setUnsignedRange - Set the memoized signed range for the given SCEV.
404 const ConstantRange &setSignedRange(const SCEV *S,
405 const ConstantRange &CR) {
406 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
407 SignedRanges.insert(std::make_pair(S, CR));
409 Pair.first->second = CR;
410 return Pair.first->second;
413 /// createSCEV - We know that there is no SCEV for the specified value.
414 /// Analyze the expression.
415 const SCEV *createSCEV(Value *V);
417 /// createNodeForPHI - Provide the special handling we need to analyze PHI
419 const SCEV *createNodeForPHI(PHINode *PN);
421 /// createNodeForGEP - Provide the special handling we need to analyze GEP
423 const SCEV *createNodeForGEP(GEPOperator *GEP);
425 /// computeSCEVAtScope - Implementation code for getSCEVAtScope; called
426 /// at most once for each SCEV+Loop pair.
428 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
430 /// ForgetSymbolicValue - This looks up computed SCEV values for all
431 /// instructions that depend on the given instruction and removes them from
432 /// the ValueExprMap map if they reference SymName. This is used during PHI
434 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
436 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
437 /// loop, lazily computing new values if the loop hasn't been analyzed
439 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
441 /// ComputeBackedgeTakenCount - Compute the number of times the specified
442 /// loop will iterate.
443 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
445 /// ComputeExitLimit - Compute the number of times the backedge of the
446 /// specified loop will execute if it exits via the specified block.
447 ExitLimit ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
449 /// ComputeExitLimitFromCond - Compute the number of times the backedge of
450 /// the specified loop will execute if its exit condition were a conditional
451 /// branch of ExitCond, TBB, and FBB.
452 ExitLimit ComputeExitLimitFromCond(const Loop *L,
458 /// ComputeExitLimitFromICmp - Compute the number of times the backedge of
459 /// the specified loop will execute if its exit condition were a conditional
460 /// branch of the ICmpInst ExitCond, TBB, and FBB.
461 ExitLimit ComputeExitLimitFromICmp(const Loop *L,
467 /// ComputeExitLimitFromSingleExitSwitch - Compute the number of times the
468 /// backedge of the specified loop will execute if its exit condition were a
469 /// switch with a single exiting case to ExitingBB.
471 ComputeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
472 BasicBlock *ExitingBB, bool IsSubExpr);
474 /// ComputeLoadConstantCompareExitLimit - Given an exit condition
475 /// of 'icmp op load X, cst', try to see if we can compute the
476 /// backedge-taken count.
477 ExitLimit ComputeLoadConstantCompareExitLimit(LoadInst *LI,
480 ICmpInst::Predicate p);
482 /// ComputeExitCountExhaustively - If the loop is known to execute a
483 /// constant number of times (the condition evolves only from constants),
484 /// try to evaluate a few iterations of the loop until we get the exit
485 /// condition gets a value of ExitWhen (true or false). If we cannot
486 /// evaluate the exit count of the loop, return CouldNotCompute.
487 const SCEV *ComputeExitCountExhaustively(const Loop *L,
491 /// HowFarToZero - Return the number of times an exit condition comparing
492 /// the specified value to zero will execute. If not computable, return
494 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
496 /// HowFarToNonZero - Return the number of times an exit condition checking
497 /// the specified value for nonzero will execute. If not computable, return
499 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
501 /// HowManyLessThans - Return the number of times an exit condition
502 /// containing the specified less-than comparison will execute. If not
503 /// computable, return CouldNotCompute. isSigned specifies whether the
504 /// less-than is signed.
505 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
506 const Loop *L, bool isSigned, bool IsSubExpr);
507 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
508 const Loop *L, bool isSigned, bool IsSubExpr);
510 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
511 /// (which may not be an immediate predecessor) which has exactly one
512 /// successor from which BB is reachable, or null if no such block is
514 std::pair<BasicBlock *, BasicBlock *>
515 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
517 /// isImpliedCond - Test whether the condition described by Pred, LHS, and
518 /// RHS is true whenever the given FoundCondValue value evaluates to true.
519 bool isImpliedCond(ICmpInst::Predicate Pred,
520 const SCEV *LHS, const SCEV *RHS,
521 Value *FoundCondValue,
524 /// isImpliedCondOperands - Test whether the condition described by Pred,
525 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
526 /// and FoundRHS is true.
527 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
528 const SCEV *LHS, const SCEV *RHS,
529 const SCEV *FoundLHS, const SCEV *FoundRHS);
531 /// isImpliedCondOperandsHelper - Test whether the condition described by
532 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
533 /// FoundLHS, and FoundRHS is true.
534 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
535 const SCEV *LHS, const SCEV *RHS,
536 const SCEV *FoundLHS,
537 const SCEV *FoundRHS);
539 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
540 /// in the header of its containing loop, we know the loop executes a
541 /// constant number of times, and the PHI node is just a recurrence
542 /// involving constants, fold it.
543 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
546 /// isKnownPredicateWithRanges - Test if the given expression is known to
547 /// satisfy the condition described by Pred and the known constant ranges
550 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
551 const SCEV *LHS, const SCEV *RHS);
553 /// forgetMemoizedResults - Drop memoized information computed for S.
554 void forgetMemoizedResults(const SCEV *S);
556 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
558 bool checkValidity(const SCEV *S) const;
561 static char ID; // Pass identification, replacement for typeid
564 LLVMContext &getContext() const { return F->getContext(); }
566 /// isSCEVable - Test if values of the given type are analyzable within
567 /// the SCEV framework. This primarily includes integer types, and it
568 /// can optionally include pointer types if the ScalarEvolution class
569 /// has access to target-specific information.
570 bool isSCEVable(Type *Ty) const;
572 /// getTypeSizeInBits - Return the size in bits of the specified type,
573 /// for which isSCEVable must return true.
574 uint64_t getTypeSizeInBits(Type *Ty) const;
576 /// getEffectiveSCEVType - Return a type with the same bitwidth as
577 /// the given type and which represents how SCEV will treat the given
578 /// type, for which isSCEVable must return true. For pointer types,
579 /// this is the pointer-sized integer type.
580 Type *getEffectiveSCEVType(Type *Ty) const;
582 /// getSCEV - Return a SCEV expression for the full generality of the
583 /// specified expression.
584 const SCEV *getSCEV(Value *V);
586 const SCEV *getConstant(ConstantInt *V);
587 const SCEV *getConstant(const APInt& Val);
588 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
589 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
590 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
591 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
592 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
593 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
594 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
595 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
596 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
597 SmallVector<const SCEV *, 2> Ops;
600 return getAddExpr(Ops, Flags);
602 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
603 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
604 SmallVector<const SCEV *, 3> Ops;
608 return getAddExpr(Ops, Flags);
610 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
611 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
612 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
613 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap)
615 SmallVector<const SCEV *, 2> Ops;
618 return getMulExpr(Ops, Flags);
620 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
621 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
622 SmallVector<const SCEV *, 3> Ops;
626 return getMulExpr(Ops, Flags);
628 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
629 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
630 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
631 const Loop *L, SCEV::NoWrapFlags Flags);
632 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
633 const Loop *L, SCEV::NoWrapFlags Flags);
634 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
635 const Loop *L, SCEV::NoWrapFlags Flags) {
636 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
637 return getAddRecExpr(NewOp, L, Flags);
639 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
640 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
641 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
642 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
643 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
644 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
645 const SCEV *getUnknown(Value *V);
646 const SCEV *getCouldNotCompute();
648 /// getSizeOfExpr - Return an expression for sizeof AllocTy that is type
651 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
653 /// getOffsetOfExpr - Return an expression for offsetof on the given field
656 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
658 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
660 const SCEV *getNegativeSCEV(const SCEV *V);
662 /// getNotSCEV - Return the SCEV object corresponding to ~V.
664 const SCEV *getNotSCEV(const SCEV *V);
666 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
667 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
668 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
670 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
671 /// of the input value to the specified type. If the type must be
672 /// extended, it is zero extended.
673 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
675 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
676 /// of the input value to the specified type. If the type must be
677 /// extended, it is sign extended.
678 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
680 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
681 /// the input value to the specified type. If the type must be extended,
682 /// it is zero extended. The conversion must not be narrowing.
683 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
685 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
686 /// the input value to the specified type. If the type must be extended,
687 /// it is sign extended. The conversion must not be narrowing.
688 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
690 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
691 /// the input value to the specified type. If the type must be extended,
692 /// it is extended with unspecified bits. The conversion must not be
694 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
696 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
697 /// input value to the specified type. The conversion must not be
699 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
701 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
702 /// the types using zero-extension, and then perform a umax operation
704 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
707 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
708 /// the types using zero-extension, and then perform a umin operation
710 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
713 /// getPointerBase - Transitively follow the chain of pointer-type operands
714 /// until reaching a SCEV that does not have a single pointer operand. This
715 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
716 /// but corner cases do exist.
717 const SCEV *getPointerBase(const SCEV *V);
719 /// getSCEVAtScope - Return a SCEV expression for the specified value
720 /// at the specified scope in the program. The L value specifies a loop
721 /// nest to evaluate the expression at, where null is the top-level or a
722 /// specified loop is immediately inside of the loop.
724 /// This method can be used to compute the exit value for a variable defined
725 /// in a loop by querying what the value will hold in the parent loop.
727 /// In the case that a relevant loop exit value cannot be computed, the
728 /// original value V is returned.
729 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
731 /// getSCEVAtScope - This is a convenience function which does
732 /// getSCEVAtScope(getSCEV(V), L).
733 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
735 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
736 /// by a conditional between LHS and RHS. This is used to help avoid max
737 /// expressions in loop trip counts, and to eliminate casts.
738 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
739 const SCEV *LHS, const SCEV *RHS);
741 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
742 /// protected by a conditional between LHS and RHS. This is used to
743 /// to eliminate casts.
744 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
745 const SCEV *LHS, const SCEV *RHS);
747 /// \brief Returns the maximum trip count of the loop if it is a single-exit
748 /// loop and we can compute a small maximum for that loop.
750 /// Implemented in terms of the \c getSmallConstantTripCount overload with
751 /// the single exiting block passed to it. See that routine for details.
752 unsigned getSmallConstantTripCount(Loop *L);
754 /// getSmallConstantTripCount - Returns the maximum trip count of this loop
755 /// as a normal unsigned value. Returns 0 if the trip count is unknown or
756 /// not constant. This "trip count" assumes that control exits via
757 /// ExitingBlock. More precisely, it is the number of times that control may
758 /// reach ExitingBlock before taking the branch. For loops with multiple
759 /// exits, it may not be the number times that the loop header executes if
760 /// the loop exits prematurely via another branch.
761 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
763 /// \brief Returns the largest constant divisor of the trip count of the
764 /// loop if it is a single-exit loop and we can compute a small maximum for
767 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
768 /// the single exiting block passed to it. See that routine for details.
769 unsigned getSmallConstantTripMultiple(Loop *L);
771 /// getSmallConstantTripMultiple - Returns the largest constant divisor of
772 /// the trip count of this loop as a normal unsigned value, if
773 /// possible. This means that the actual trip count is always a multiple of
774 /// the returned value (don't forget the trip count could very well be zero
775 /// as well!). As explained in the comments for getSmallConstantTripCount,
776 /// this assumes that control exits the loop via ExitingBlock.
777 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
779 // getExitCount - Get the expression for the number of loop iterations for
780 // which this loop is guaranteed not to exit via ExitingBlock. Otherwise
781 // return SCEVCouldNotCompute.
782 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
784 /// getBackedgeTakenCount - If the specified loop has a predictable
785 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
786 /// object. The backedge-taken count is the number of times the loop header
787 /// will be branched to from within the loop. This is one less than the
788 /// trip count of the loop, since it doesn't count the first iteration,
789 /// when the header is branched to from outside the loop.
791 /// Note that it is not valid to call this method on a loop without a
792 /// loop-invariant backedge-taken count (see
793 /// hasLoopInvariantBackedgeTakenCount).
795 const SCEV *getBackedgeTakenCount(const Loop *L);
797 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
798 /// return the least SCEV value that is known never to be less than the
799 /// actual backedge taken count.
800 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
802 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
803 /// has an analyzable loop-invariant backedge-taken count.
804 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
806 /// forgetLoop - This method should be called by the client when it has
807 /// changed a loop in a way that may effect ScalarEvolution's ability to
808 /// compute a trip count, or if the loop is deleted. This call is
809 /// potentially expensive for large loop bodies.
810 void forgetLoop(const Loop *L);
812 /// forgetValue - This method should be called by the client when it has
813 /// changed a value in a way that may effect its value, or which may
814 /// disconnect it from a def-use chain linking it to a loop.
815 void forgetValue(Value *V);
817 /// \brief Called when the client has changed the disposition of values in
820 /// We don't have a way to invalidate per-loop dispositions. Clear and
821 /// recompute is simpler.
822 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
824 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
825 /// is guaranteed to end in (at every loop iteration). It is, at the same
826 /// time, the minimum number of times S is divisible by 2. For example,
827 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
829 uint32_t GetMinTrailingZeros(const SCEV *S);
831 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
833 ConstantRange getUnsignedRange(const SCEV *S);
835 /// getSignedRange - Determine the signed range for a particular SCEV.
837 ConstantRange getSignedRange(const SCEV *S);
839 /// isKnownNegative - Test if the given expression is known to be negative.
841 bool isKnownNegative(const SCEV *S);
843 /// isKnownPositive - Test if the given expression is known to be positive.
845 bool isKnownPositive(const SCEV *S);
847 /// isKnownNonNegative - Test if the given expression is known to be
850 bool isKnownNonNegative(const SCEV *S);
852 /// isKnownNonPositive - Test if the given expression is known to be
855 bool isKnownNonPositive(const SCEV *S);
857 /// isKnownNonZero - Test if the given expression is known to be
860 bool isKnownNonZero(const SCEV *S);
862 /// isKnownPredicate - Test if the given expression is known to satisfy
863 /// the condition described by Pred, LHS, and RHS.
865 bool isKnownPredicate(ICmpInst::Predicate Pred,
866 const SCEV *LHS, const SCEV *RHS);
868 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
869 /// predicate Pred. Return true iff any changes were made. If the
870 /// operands are provably equal or unequal, LHS and RHS are set to
871 /// the same value and Pred is set to either ICMP_EQ or ICMP_NE.
873 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
878 /// getLoopDisposition - Return the "disposition" of the given SCEV with
879 /// respect to the given loop.
880 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
882 /// isLoopInvariant - Return true if the value of the given SCEV is
883 /// unchanging in the specified loop.
884 bool isLoopInvariant(const SCEV *S, const Loop *L);
886 /// hasComputableLoopEvolution - Return true if the given SCEV changes value
887 /// in a known way in the specified loop. This property being true implies
888 /// that the value is variant in the loop AND that we can emit an expression
889 /// to compute the value of the expression at any particular loop iteration.
890 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
892 /// getLoopDisposition - Return the "disposition" of the given SCEV with
893 /// respect to the given block.
894 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
896 /// dominates - Return true if elements that makes up the given SCEV
897 /// dominate the specified basic block.
898 bool dominates(const SCEV *S, const BasicBlock *BB);
900 /// properlyDominates - Return true if elements that makes up the given SCEV
901 /// properly dominate the specified basic block.
902 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
904 /// hasOperand - Test whether the given SCEV has Op as a direct or
905 /// indirect operand.
906 bool hasOperand(const SCEV *S, const SCEV *Op) const;
908 /// Return the size of an element read or written by Inst.
909 const SCEV *getElementSize(Instruction *Inst);
911 /// Compute the array dimensions Sizes from the set of Terms extracted from
912 /// the memory access function of this SCEVAddRecExpr.
913 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
914 SmallVectorImpl<const SCEV *> &Sizes,
915 const SCEV *ElementSize) const;
917 bool runOnFunction(Function &F) override;
918 void releaseMemory() override;
919 void getAnalysisUsage(AnalysisUsage &AU) const override;
920 void print(raw_ostream &OS, const Module* = nullptr) const override;
921 void verifyAnalysis() const override;
924 /// Compute the backedge taken count knowing the interval difference, the
925 /// stride and presence of the equality in the comparison.
926 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
929 /// Verify if an linear IV with positive stride can overflow when in a
930 /// less-than comparison, knowing the invariant term of the comparison,
931 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
932 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
933 bool IsSigned, bool NoWrap);
935 /// Verify if an linear IV with negative stride can overflow when in a
936 /// greater-than comparison, knowing the invariant term of the comparison,
937 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
938 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
939 bool IsSigned, bool NoWrap);
942 FoldingSet<SCEV> UniqueSCEVs;
943 BumpPtrAllocator SCEVAllocator;
945 /// FirstUnknown - The head of a linked list of all SCEVUnknown
946 /// values that have been allocated. This is used by releaseMemory
947 /// to locate them all and call their destructors.
948 SCEVUnknown *FirstUnknown;