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/PassManager.h"
31 #include "llvm/IR/ValueHandle.h"
32 #include "llvm/Pass.h"
33 #include "llvm/Support/Allocator.h"
34 #include "llvm/Support/DataTypes.h"
39 class AssumptionCache;
44 class ScalarEvolution;
46 class TargetLibraryInfo;
58 template <> struct FoldingSetTrait<SCEV>;
59 template <> struct FoldingSetTrait<SCEVPredicate>;
61 /// This class represents an analyzed expression in the program. These are
62 /// opaque objects that the client is not allowed to do much with directly.
64 class SCEV : public FoldingSetNode {
65 friend struct FoldingSetTrait<SCEV>;
67 /// A reference to an Interned FoldingSetNodeID for this node. The
68 /// ScalarEvolution's BumpPtrAllocator holds the data.
69 FoldingSetNodeIDRef FastID;
71 // The SCEV baseclass this node corresponds to
72 const unsigned short SCEVType;
75 /// This field is initialized to zero and may be used in subclasses to store
76 /// miscellaneous information.
77 unsigned short SubclassData;
80 SCEV(const SCEV &) = delete;
81 void operator=(const SCEV &) = delete;
84 /// NoWrapFlags are bitfield indices into SubclassData.
86 /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
87 /// no-signed-wrap <NSW> properties, which are derived from the IR
88 /// operator. NSW is a misnomer that we use to mean no signed overflow or
91 /// AddRec expressions may have a no-self-wraparound <NW> property if, in
92 /// the integer domain, abs(step) * max-iteration(loop) <=
93 /// unsigned-max(bitwidth). This means that the recurrence will never reach
94 /// its start value if the step is non-zero. Computing the same value on
95 /// each iteration is not considered wrapping, and recurrences with step = 0
96 /// are trivially <NW>. <NW> is independent of the sign of step and the
97 /// value the add recurrence starts with.
99 /// Note that NUW and NSW are also valid properties of a recurrence, and
100 /// either implies NW. For convenience, NW will be set for a recurrence
101 /// whenever either NUW or NSW are set.
102 enum NoWrapFlags { FlagAnyWrap = 0, // No guarantee.
103 FlagNW = (1 << 0), // No self-wrap.
104 FlagNUW = (1 << 1), // No unsigned wrap.
105 FlagNSW = (1 << 2), // No signed wrap.
106 NoWrapMask = (1 << 3) -1 };
108 explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy) :
109 FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
111 unsigned getSCEVType() const { return SCEVType; }
113 /// Return the LLVM type of this SCEV expression.
115 Type *getType() const;
117 /// Return true if the expression is a constant zero.
121 /// Return true if the expression is a constant one.
125 /// Return true if the expression is a constant all-ones value.
127 bool isAllOnesValue() const;
129 /// Return true if the specified scev is negated, but not a constant.
130 bool isNonConstantNegative() const;
132 /// Print out the internal representation of this scalar to the specified
133 /// stream. This should really only be used for debugging purposes.
134 void print(raw_ostream &OS) const;
136 /// This method is used for debugging.
141 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
142 // temporary FoldingSetNodeID values.
143 template<> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
144 static void Profile(const SCEV &X, FoldingSetNodeID& ID) {
147 static bool Equals(const SCEV &X, const FoldingSetNodeID &ID,
148 unsigned IDHash, FoldingSetNodeID &TempID) {
149 return ID == X.FastID;
151 static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
152 return X.FastID.ComputeHash();
156 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
161 /// An object of this class is returned by queries that could not be answered.
162 /// For example, if you ask for the number of iterations of a linked-list
163 /// traversal loop, you will get one of these. None of the standard SCEV
164 /// operations are valid on this class, it is just a marker.
165 struct SCEVCouldNotCompute : public SCEV {
166 SCEVCouldNotCompute();
168 /// Methods for support type inquiry through isa, cast, and dyn_cast:
169 static bool classof(const SCEV *S);
172 /// SCEVPredicate - This class represents an assumption made using SCEV
173 /// expressions which can be checked at run-time.
174 class SCEVPredicate : public FoldingSetNode {
175 friend struct FoldingSetTrait<SCEVPredicate>;
177 /// A reference to an Interned FoldingSetNodeID for this node. The
178 /// ScalarEvolution's BumpPtrAllocator holds the data.
179 FoldingSetNodeIDRef FastID;
182 enum SCEVPredicateKind { P_Union, P_Equal };
185 SCEVPredicateKind Kind;
186 ~SCEVPredicate() = default;
187 SCEVPredicate(const SCEVPredicate&) = default;
188 SCEVPredicate &operator=(const SCEVPredicate&) = default;
191 SCEVPredicate(const FoldingSetNodeIDRef ID, SCEVPredicateKind Kind);
193 SCEVPredicateKind getKind() const { return Kind; }
195 /// \brief Returns the estimated complexity of this predicate.
196 /// This is roughly measured in the number of run-time checks required.
197 virtual unsigned getComplexity() const { return 1; }
199 /// \brief Returns true if the predicate is always true. This means that no
200 /// assumptions were made and nothing needs to be checked at run-time.
201 virtual bool isAlwaysTrue() const = 0;
203 /// \brief Returns true if this predicate implies \p N.
204 virtual bool implies(const SCEVPredicate *N) const = 0;
206 /// \brief Prints a textual representation of this predicate with an
207 /// indentation of \p Depth.
208 virtual void print(raw_ostream &OS, unsigned Depth = 0) const = 0;
210 /// \brief Returns the SCEV to which this predicate applies, or nullptr
211 /// if this is a SCEVUnionPredicate.
212 virtual const SCEV *getExpr() const = 0;
215 inline raw_ostream &operator<<(raw_ostream &OS, const SCEVPredicate &P) {
220 // Specialize FoldingSetTrait for SCEVPredicate to avoid needing to compute
221 // temporary FoldingSetNodeID values.
223 struct FoldingSetTrait<SCEVPredicate>
224 : DefaultFoldingSetTrait<SCEVPredicate> {
226 static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID) {
230 static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID,
231 unsigned IDHash, FoldingSetNodeID &TempID) {
232 return ID == X.FastID;
234 static unsigned ComputeHash(const SCEVPredicate &X,
235 FoldingSetNodeID &TempID) {
236 return X.FastID.ComputeHash();
240 /// SCEVEqualPredicate - This class represents an assumption that two SCEV
241 /// expressions are equal, and this can be checked at run-time. We assume
242 /// that the left hand side is a SCEVUnknown and the right hand side a
244 class SCEVEqualPredicate final : public SCEVPredicate {
245 /// We assume that LHS == RHS, where LHS is a SCEVUnknown and RHS a
247 const SCEVUnknown *LHS;
248 const SCEVConstant *RHS;
251 SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEVUnknown *LHS,
252 const SCEVConstant *RHS);
254 /// Implementation of the SCEVPredicate interface
255 bool implies(const SCEVPredicate *N) const override;
256 void print(raw_ostream &OS, unsigned Depth = 0) const override;
257 bool isAlwaysTrue() const override;
258 const SCEV *getExpr() const override;
260 /// \brief Returns the left hand side of the equality.
261 const SCEVUnknown *getLHS() const { return LHS; }
263 /// \brief Returns the right hand side of the equality.
264 const SCEVConstant *getRHS() const { return RHS; }
266 /// Methods for support type inquiry through isa, cast, and dyn_cast:
267 static inline bool classof(const SCEVPredicate *P) {
268 return P->getKind() == P_Equal;
272 /// SCEVUnionPredicate - This class represents a composition of other
273 /// SCEV predicates, and is the class that most clients will interact with.
274 /// This is equivalent to a logical "AND" of all the predicates in the union.
275 class SCEVUnionPredicate final : public SCEVPredicate {
277 typedef DenseMap<const SCEV *, SmallVector<const SCEVPredicate *, 4>>
280 /// Vector with references to all predicates in this union.
281 SmallVector<const SCEVPredicate *, 16> Preds;
282 /// Maps SCEVs to predicates for quick look-ups.
283 PredicateMap SCEVToPreds;
286 SCEVUnionPredicate();
288 const SmallVectorImpl<const SCEVPredicate *> &getPredicates() const {
292 /// \brief Adds a predicate to this union.
293 void add(const SCEVPredicate *N);
295 /// \brief Returns a reference to a vector containing all predicates
296 /// which apply to \p Expr.
297 ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
299 /// Implementation of the SCEVPredicate interface
300 bool isAlwaysTrue() const override;
301 bool implies(const SCEVPredicate *N) const override;
302 void print(raw_ostream &OS, unsigned Depth) const override;
303 const SCEV *getExpr() const override;
305 /// \brief We estimate the complexity of a union predicate as the size
306 /// number of predicates in the union.
307 unsigned getComplexity() const override { return Preds.size(); }
309 /// Methods for support type inquiry through isa, cast, and dyn_cast:
310 static inline bool classof(const SCEVPredicate *P) {
311 return P->getKind() == P_Union;
315 /// The main scalar evolution driver. Because client code (intentionally)
316 /// can't do much with the SCEV objects directly, they must ask this class
318 class ScalarEvolution {
320 /// An enum describing the relationship between a SCEV and a loop.
321 enum LoopDisposition {
322 LoopVariant, ///< The SCEV is loop-variant (unknown).
323 LoopInvariant, ///< The SCEV is loop-invariant.
324 LoopComputable ///< The SCEV varies predictably with the loop.
327 /// An enum describing the relationship between a SCEV and a basic block.
328 enum BlockDisposition {
329 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
330 DominatesBlock, ///< The SCEV dominates the block.
331 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
334 /// Convenient NoWrapFlags manipulation that hides enum casts and is
335 /// visible in the ScalarEvolution name space.
336 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
337 maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
338 return (SCEV::NoWrapFlags)(Flags & Mask);
340 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
341 setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
342 return (SCEV::NoWrapFlags)(Flags | OnFlags);
344 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
345 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
346 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
350 /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
351 /// Value is deleted.
352 class SCEVCallbackVH final : public CallbackVH {
354 void deleted() override;
355 void allUsesReplacedWith(Value *New) override;
357 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
360 friend class SCEVCallbackVH;
361 friend class SCEVExpander;
362 friend class SCEVUnknown;
364 /// The function we are analyzing.
368 /// The target library information for the target we are targeting.
370 TargetLibraryInfo &TLI;
372 /// The tracker for @llvm.assume intrinsics in this function.
375 /// The dominator tree.
379 /// The loop information for the function we are currently analyzing.
383 /// This SCEV is used to represent unknown trip counts and things.
384 std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
386 /// The typedef for ValueExprMap.
388 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
391 /// This is a cache of the values we have analyzed so far.
393 ValueExprMapType ValueExprMap;
395 /// Mark predicate values currently being processed by isImpliedCond.
396 DenseSet<Value*> PendingLoopPredicates;
398 /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
399 /// conditions dominating the backedge of a loop.
400 bool WalkingBEDominatingConds;
402 /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
403 /// predicate by splitting it into a set of independent predicates.
404 bool ProvingSplitPredicate;
406 /// Information about the number of loop iterations for which a loop exit's
407 /// branch condition evaluates to the not-taken path. This is a temporary
408 /// pair of exact and max expressions that are eventually summarized in
409 /// ExitNotTakenInfo and BackedgeTakenInfo.
414 /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
416 ExitLimit(const SCEV *E, const SCEV *M) : Exact(E), Max(M) {}
418 /// Test whether this ExitLimit contains any computed information, or
419 /// whether it's all SCEVCouldNotCompute values.
420 bool hasAnyInfo() const {
421 return !isa<SCEVCouldNotCompute>(Exact) ||
422 !isa<SCEVCouldNotCompute>(Max);
426 /// Information about the number of times a particular loop exit may be
427 /// reached before exiting the loop.
428 struct ExitNotTakenInfo {
429 AssertingVH<BasicBlock> ExitingBlock;
430 const SCEV *ExactNotTaken;
431 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
433 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
435 /// Return true if all loop exits are computable.
436 bool isCompleteList() const {
437 return NextExit.getInt() == 0;
440 void setIncomplete() { NextExit.setInt(1); }
442 /// Return a pointer to the next exit's not-taken info.
443 ExitNotTakenInfo *getNextExit() const {
444 return NextExit.getPointer();
447 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
450 /// Information about the backedge-taken count of a loop. This currently
451 /// includes an exact count and a maximum count.
453 class BackedgeTakenInfo {
454 /// A list of computable exits and their not-taken counts. Loops almost
455 /// never have more than one computable exit.
456 ExitNotTakenInfo ExitNotTaken;
458 /// An expression indicating the least maximum backedge-taken count of the
459 /// loop that is known, or a SCEVCouldNotCompute.
463 BackedgeTakenInfo() : Max(nullptr) {}
465 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
467 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
468 bool Complete, const SCEV *MaxCount);
470 /// Test whether this BackedgeTakenInfo contains any computed information,
471 /// or whether it's all SCEVCouldNotCompute values.
472 bool hasAnyInfo() const {
473 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
476 /// Return an expression indicating the exact backedge-taken count of the
477 /// loop if it is known, or SCEVCouldNotCompute otherwise. This is the
478 /// number of times the loop header can be guaranteed to execute, minus
480 const SCEV *getExact(ScalarEvolution *SE) const;
482 /// Return the number of times this loop exit may fall through to the back
483 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
484 /// this block before this number of iterations, but may exit via another
486 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
488 /// Get the max backedge taken count for the loop.
489 const SCEV *getMax(ScalarEvolution *SE) const;
491 /// Return true if any backedge taken count expressions refer to the given
493 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
495 /// Invalidate this result and free associated memory.
499 /// Cache the backedge-taken count of the loops for this function as they
501 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
503 /// This map contains entries for all of the PHI instructions that we
504 /// attempt to compute constant evolutions for. This allows us to avoid
505 /// potentially expensive recomputation of these properties. An instruction
506 /// maps to null if we are unable to compute its exit value.
507 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
509 /// This map contains entries for all the expressions that we attempt to
510 /// compute getSCEVAtScope information for, which can be expensive in
512 DenseMap<const SCEV *,
513 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
515 /// Memoized computeLoopDisposition results.
516 DenseMap<const SCEV *,
517 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
520 /// Compute a LoopDisposition value.
521 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
523 /// Memoized computeBlockDisposition results.
526 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
529 /// Compute a BlockDisposition value.
530 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
532 /// Memoized results from getRange
533 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
535 /// Memoized results from getRange
536 DenseMap<const SCEV *, ConstantRange> SignedRanges;
538 /// Used to parameterize getRange
539 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
541 /// Set the memoized range for the given SCEV.
542 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
543 const ConstantRange &CR) {
544 DenseMap<const SCEV *, ConstantRange> &Cache =
545 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
547 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
548 Cache.insert(std::make_pair(S, CR));
550 Pair.first->second = CR;
551 return Pair.first->second;
554 /// Determine the range for a particular SCEV.
555 ConstantRange getRange(const SCEV *S, RangeSignHint Hint);
557 /// We know that there is no SCEV for the specified value. Analyze the
559 const SCEV *createSCEV(Value *V);
561 /// Provide the special handling we need to analyze PHI SCEVs.
562 const SCEV *createNodeForPHI(PHINode *PN);
564 /// Helper function called from createNodeForPHI.
565 const SCEV *createAddRecFromPHI(PHINode *PN);
567 /// Helper function called from createNodeForPHI.
568 const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
570 /// Provide special handling for a select-like instruction (currently this
571 /// is either a select instruction or a phi node). \p I is the instruction
572 /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
574 const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
575 Value *TrueVal, Value *FalseVal);
577 /// Provide the special handling we need to analyze GEP SCEVs.
578 const SCEV *createNodeForGEP(GEPOperator *GEP);
580 /// Implementation code for getSCEVAtScope; called at most once for each
583 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
585 /// This looks up computed SCEV values for all instructions that depend on
586 /// the given instruction and removes them from the ValueExprMap map if they
587 /// reference SymName. This is used during PHI resolution.
588 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
590 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
591 /// values if the loop hasn't been analyzed yet.
592 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
594 /// Compute the number of times the specified loop will iterate.
595 BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L);
597 /// Compute the number of times the backedge of the specified loop will
598 /// execute if it exits via the specified block.
599 ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
601 /// Compute the number of times the backedge of the specified loop will
602 /// execute if its exit condition were a conditional branch of ExitCond,
604 ExitLimit computeExitLimitFromCond(const Loop *L,
610 /// Compute the number of times the backedge of the specified loop will
611 /// execute if its exit condition were a conditional branch of the ICmpInst
612 /// ExitCond, TBB, and FBB.
613 ExitLimit computeExitLimitFromICmp(const Loop *L,
619 /// Compute the number of times the backedge of the specified loop will
620 /// execute if its exit condition were a switch with a single exiting case
623 computeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
624 BasicBlock *ExitingBB, bool IsSubExpr);
626 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
627 /// compute the backedge-taken count.
628 ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI,
631 ICmpInst::Predicate p);
633 /// Compute the exit limit of a loop that is controlled by a
634 /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
635 /// count in these cases (since SCEV has no way of expressing them), but we
636 /// can still sometimes compute an upper bound.
638 /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
640 ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS,
642 ICmpInst::Predicate Pred);
644 /// If the loop is known to execute a constant number of times (the
645 /// condition evolves only from constants), try to evaluate a few iterations
646 /// of the loop until we get the exit condition gets a value of ExitWhen
647 /// (true or false). If we cannot evaluate the exit count of the loop,
648 /// return CouldNotCompute.
649 const SCEV *computeExitCountExhaustively(const Loop *L,
653 /// Return the number of times an exit condition comparing the specified
654 /// value to zero will execute. If not computable, return CouldNotCompute.
655 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
657 /// Return the number of times an exit condition checking the specified
658 /// value for nonzero will execute. If not computable, return
660 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
662 /// Return the number of times an exit condition containing the specified
663 /// less-than comparison will execute. If not computable, return
664 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
665 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
666 const Loop *L, bool isSigned, bool IsSubExpr);
667 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
668 const Loop *L, bool isSigned, bool IsSubExpr);
670 /// Return a predecessor of BB (which may not be an immediate predecessor)
671 /// which has exactly one successor from which BB is reachable, or null if
672 /// no such block is found.
673 std::pair<BasicBlock *, BasicBlock *>
674 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
676 /// Test whether the condition described by Pred, LHS, and RHS is true
677 /// whenever the given FoundCondValue value evaluates to true.
678 bool isImpliedCond(ICmpInst::Predicate Pred,
679 const SCEV *LHS, const SCEV *RHS,
680 Value *FoundCondValue,
683 /// Test whether the condition described by Pred, LHS, and RHS is true
684 /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
686 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
687 const SCEV *RHS, ICmpInst::Predicate FoundPred,
688 const SCEV *FoundLHS, const SCEV *FoundRHS);
690 /// Test whether the condition described by Pred, LHS, and RHS is true
691 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
693 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
694 const SCEV *LHS, const SCEV *RHS,
695 const SCEV *FoundLHS, const SCEV *FoundRHS);
697 /// Test whether the condition described by Pred, LHS, and RHS is true
698 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
700 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
701 const SCEV *LHS, const SCEV *RHS,
702 const SCEV *FoundLHS,
703 const SCEV *FoundRHS);
705 /// Test whether the condition described by Pred, LHS, and RHS is true
706 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
707 /// true. Utility function used by isImpliedCondOperands.
708 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
709 const SCEV *LHS, const SCEV *RHS,
710 const SCEV *FoundLHS,
711 const SCEV *FoundRHS);
713 /// Test whether the condition described by Pred, LHS, and RHS is true
714 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
717 /// This routine tries to rule out certain kinds of integer overflow, and
718 /// then tries to reason about arithmetic properties of the predicates.
719 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
720 const SCEV *LHS, const SCEV *RHS,
721 const SCEV *FoundLHS,
722 const SCEV *FoundRHS);
724 /// If we know that the specified Phi is in the header of its containing
725 /// loop, we know the loop executes a constant number of times, and the PHI
726 /// node is just a recurrence involving constants, fold it.
727 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
730 /// Test if the given expression is known to satisfy the condition described
731 /// by Pred and the known constant ranges of LHS and RHS.
733 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
734 const SCEV *LHS, const SCEV *RHS);
736 /// Try to prove the condition described by "LHS Pred RHS" by ruling out
737 /// integer overflow.
739 /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
741 bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
742 const SCEV *LHS, const SCEV *RHS);
744 /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
745 /// prove them individually.
746 bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
749 /// Try to match the Expr as "(L + R)<Flags>".
750 bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
751 SCEV::NoWrapFlags &Flags);
753 /// Return true if More == (Less + C), where C is a constant. This is
754 /// intended to be used as a cheaper substitute for full SCEV subtraction.
755 bool computeConstantDifference(const SCEV *Less, const SCEV *More,
758 /// Drop memoized information computed for S.
759 void forgetMemoizedResults(const SCEV *S);
761 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
762 const SCEV *getExistingSCEV(Value *V);
764 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
766 bool checkValidity(const SCEV *S) const;
768 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
769 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
770 /// equivalent to proving no signed (resp. unsigned) wrap in
771 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
772 /// (resp. `SCEVZeroExtendExpr`).
774 template<typename ExtendOpTy>
775 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
778 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
779 ICmpInst::Predicate Pred, bool &Increasing);
781 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
782 /// is monotonically increasing or decreasing. In the former case set
783 /// `Increasing` to true and in the latter case set `Increasing` to false.
785 /// A predicate is said to be monotonically increasing if may go from being
786 /// false to being true as the loop iterates, but never the other way
787 /// around. A predicate is said to be monotonically decreasing if may go
788 /// from being true to being false as the loop iterates, but never the other
790 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS,
791 ICmpInst::Predicate Pred, bool &Increasing);
793 // Return SCEV no-wrap flags that can be proven based on reasoning
794 // about how poison produced from no-wrap flags on this value
795 // (e.g. a nuw add) would trigger undefined behavior on overflow.
796 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
799 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
800 DominatorTree &DT, LoopInfo &LI);
802 ScalarEvolution(ScalarEvolution &&Arg);
804 LLVMContext &getContext() const { return F.getContext(); }
806 /// Test if values of the given type are analyzable within the SCEV
807 /// framework. This primarily includes integer types, and it can optionally
808 /// include pointer types if the ScalarEvolution class has access to
809 /// target-specific information.
810 bool isSCEVable(Type *Ty) const;
812 /// Return the size in bits of the specified type, for which isSCEVable must
814 uint64_t getTypeSizeInBits(Type *Ty) const;
816 /// Return a type with the same bitwidth as the given type and which
817 /// represents how SCEV will treat the given type, for which isSCEVable must
818 /// return true. For pointer types, this is the pointer-sized integer type.
819 Type *getEffectiveSCEVType(Type *Ty) const;
821 /// Return a SCEV expression for the full generality of the specified
823 const SCEV *getSCEV(Value *V);
825 const SCEV *getConstant(ConstantInt *V);
826 const SCEV *getConstant(const APInt& Val);
827 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
828 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
829 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
830 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
831 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
832 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
833 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
834 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
835 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
836 SmallVector<const SCEV *, 2> Ops;
839 return getAddExpr(Ops, Flags);
841 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
842 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
843 SmallVector<const SCEV *, 3> Ops;
847 return getAddExpr(Ops, Flags);
849 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
850 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
851 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
852 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap)
854 SmallVector<const SCEV *, 2> Ops;
857 return getMulExpr(Ops, Flags);
859 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
860 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
861 SmallVector<const SCEV *, 3> Ops;
865 return getMulExpr(Ops, Flags);
867 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
868 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
869 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
870 const Loop *L, SCEV::NoWrapFlags Flags);
871 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
872 const Loop *L, SCEV::NoWrapFlags Flags);
873 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
874 const Loop *L, SCEV::NoWrapFlags Flags) {
875 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
876 return getAddRecExpr(NewOp, L, Flags);
878 /// \brief Returns an expression for a GEP
880 /// \p PointeeType The type used as the basis for the pointer arithmetics
881 /// \p BaseExpr The expression for the pointer operand.
882 /// \p IndexExprs The expressions for the indices.
883 /// \p InBounds Whether the GEP is in bounds.
884 const SCEV *getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
885 const SmallVectorImpl<const SCEV *> &IndexExprs,
886 bool InBounds = false);
887 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
888 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
889 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
890 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
891 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
892 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
893 const SCEV *getUnknown(Value *V);
894 const SCEV *getCouldNotCompute();
896 /// \brief Return a SCEV for the constant 0 of a specific type.
897 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
899 /// \brief Return a SCEV for the constant 1 of a specific type.
900 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
902 /// Return an expression for sizeof AllocTy that is type IntTy
904 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
906 /// Return an expression for offsetof on the given field with type IntTy
908 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
910 /// Return the SCEV object corresponding to -V.
912 const SCEV *getNegativeSCEV(const SCEV *V,
913 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
915 /// Return the SCEV object corresponding to ~V.
917 const SCEV *getNotSCEV(const SCEV *V);
919 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
920 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
921 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
923 /// Return a SCEV corresponding to a conversion of the input value to the
924 /// specified type. If the type must be extended, it is zero extended.
925 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
927 /// Return a SCEV corresponding to a conversion of the input value to the
928 /// specified type. If the type must be extended, it is sign extended.
929 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
931 /// Return a SCEV corresponding to a conversion of the input value to the
932 /// specified type. If the type must be extended, it is zero extended. The
933 /// conversion must not be narrowing.
934 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
936 /// Return a SCEV corresponding to a conversion of the input value to the
937 /// specified type. If the type must be extended, it is sign extended. The
938 /// conversion must not be narrowing.
939 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
941 /// Return a SCEV corresponding to a conversion of the input value to the
942 /// specified type. If the type must be extended, it is extended with
943 /// unspecified bits. The conversion must not be narrowing.
944 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
946 /// Return a SCEV corresponding to a conversion of the input value to the
947 /// specified type. The conversion must not be widening.
948 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
950 /// Promote the operands to the wider of the types using zero-extension, and
951 /// then perform a umax operation with them.
952 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
955 /// Promote the operands to the wider of the types using zero-extension, and
956 /// then perform a umin operation with them.
957 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
960 /// Transitively follow the chain of pointer-type operands until reaching a
961 /// SCEV that does not have a single pointer operand. This returns a
962 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
964 const SCEV *getPointerBase(const SCEV *V);
966 /// Return a SCEV expression for the specified value at the specified scope
967 /// in the program. The L value specifies a loop nest to evaluate the
968 /// expression at, where null is the top-level or a specified loop is
969 /// immediately inside of the loop.
971 /// This method can be used to compute the exit value for a variable defined
972 /// in a loop by querying what the value will hold in the parent loop.
974 /// In the case that a relevant loop exit value cannot be computed, the
975 /// original value V is returned.
976 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
978 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
979 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
981 /// Test whether entry to the loop is protected by a conditional between LHS
982 /// and RHS. This is used to help avoid max expressions in loop trip
983 /// counts, and to eliminate casts.
984 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
985 const SCEV *LHS, const SCEV *RHS);
987 /// Test whether the backedge of the loop is protected by a conditional
988 /// between LHS and RHS. This is used to to eliminate casts.
989 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
990 const SCEV *LHS, const SCEV *RHS);
992 /// \brief Returns the maximum trip count of the loop if it is a single-exit
993 /// loop and we can compute a small maximum for that loop.
995 /// Implemented in terms of the \c getSmallConstantTripCount overload with
996 /// the single exiting block passed to it. See that routine for details.
997 unsigned getSmallConstantTripCount(Loop *L);
999 /// Returns the maximum trip count of this loop as a normal unsigned
1000 /// value. Returns 0 if the trip count is unknown or not constant. This
1001 /// "trip count" assumes that control exits via ExitingBlock. More
1002 /// precisely, it is the number of times that control may reach ExitingBlock
1003 /// before taking the branch. For loops with multiple exits, it may not be
1004 /// the number times that the loop header executes if the loop exits
1005 /// prematurely via another branch.
1006 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
1008 /// \brief Returns the largest constant divisor of the trip count of the
1009 /// loop if it is a single-exit loop and we can compute a small maximum for
1012 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
1013 /// the single exiting block passed to it. See that routine for details.
1014 unsigned getSmallConstantTripMultiple(Loop *L);
1016 /// Returns the largest constant divisor of the trip count of this loop as a
1017 /// normal unsigned value, if possible. This means that the actual trip
1018 /// count is always a multiple of the returned value (don't forget the trip
1019 /// count could very well be zero as well!). As explained in the comments
1020 /// for getSmallConstantTripCount, this assumes that control exits the loop
1021 /// via ExitingBlock.
1022 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
1024 /// Get the expression for the number of loop iterations for which this loop
1025 /// is guaranteed not to exit via ExitingBlock. Otherwise return
1026 /// SCEVCouldNotCompute.
1027 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
1029 /// If the specified loop has a predictable backedge-taken count, return it,
1030 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
1031 /// is the number of times the loop header will be branched to from within
1032 /// the loop. This is one less than the trip count of the loop, since it
1033 /// doesn't count the first iteration, when the header is branched to from
1034 /// outside the loop.
1036 /// Note that it is not valid to call this method on a loop without a
1037 /// loop-invariant backedge-taken count (see
1038 /// hasLoopInvariantBackedgeTakenCount).
1040 const SCEV *getBackedgeTakenCount(const Loop *L);
1042 /// Similar to getBackedgeTakenCount, except return the least SCEV value
1043 /// that is known never to be less than the actual backedge taken count.
1044 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
1046 /// Return true if the specified loop has an analyzable loop-invariant
1047 /// backedge-taken count.
1048 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
1050 /// This method should be called by the client when it has changed a loop in
1051 /// a way that may effect ScalarEvolution's ability to compute a trip count,
1052 /// or if the loop is deleted. This call is potentially expensive for large
1054 void forgetLoop(const Loop *L);
1056 /// This method should be called by the client when it has changed a value
1057 /// in a way that may effect its value, or which may disconnect it from a
1058 /// def-use chain linking it to a loop.
1059 void forgetValue(Value *V);
1061 /// \brief Called when the client has changed the disposition of values in
1064 /// We don't have a way to invalidate per-loop dispositions. Clear and
1065 /// recompute is simpler.
1066 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
1068 /// Determine the minimum number of zero bits that S is guaranteed to end in
1069 /// (at every loop iteration). It is, at the same time, the minimum number
1070 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
1071 /// If S is guaranteed to be 0, it returns the bitwidth of S.
1072 uint32_t GetMinTrailingZeros(const SCEV *S);
1074 /// Determine the unsigned range for a particular SCEV.
1076 ConstantRange getUnsignedRange(const SCEV *S) {
1077 return getRange(S, HINT_RANGE_UNSIGNED);
1080 /// Determine the signed range for a particular SCEV.
1082 ConstantRange getSignedRange(const SCEV *S) {
1083 return getRange(S, HINT_RANGE_SIGNED);
1086 /// Test if the given expression is known to be negative.
1088 bool isKnownNegative(const SCEV *S);
1090 /// Test if the given expression is known to be positive.
1092 bool isKnownPositive(const SCEV *S);
1094 /// Test if the given expression is known to be non-negative.
1096 bool isKnownNonNegative(const SCEV *S);
1098 /// Test if the given expression is known to be non-positive.
1100 bool isKnownNonPositive(const SCEV *S);
1102 /// Test if the given expression is known to be non-zero.
1104 bool isKnownNonZero(const SCEV *S);
1106 /// Test if the given expression is known to satisfy the condition described
1107 /// by Pred, LHS, and RHS.
1109 bool isKnownPredicate(ICmpInst::Predicate Pred,
1110 const SCEV *LHS, const SCEV *RHS);
1112 /// Return true if the result of the predicate LHS `Pred` RHS is loop
1113 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
1114 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
1115 /// loop invariant form of LHS `Pred` RHS.
1116 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
1117 const SCEV *RHS, const Loop *L,
1118 ICmpInst::Predicate &InvariantPred,
1119 const SCEV *&InvariantLHS,
1120 const SCEV *&InvariantRHS);
1122 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
1123 /// iff any changes were made. If the operands are provably equal or
1124 /// unequal, LHS and RHS are set to the same value and Pred is set to either
1125 /// ICMP_EQ or ICMP_NE.
1127 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
1130 unsigned Depth = 0);
1132 /// Return the "disposition" of the given SCEV with respect to the given
1134 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
1136 /// Return true if the value of the given SCEV is unchanging in the
1138 bool isLoopInvariant(const SCEV *S, const Loop *L);
1140 /// Return true if the given SCEV changes value in a known way in the
1141 /// specified loop. This property being true implies that the value is
1142 /// variant in the loop AND that we can emit an expression to compute the
1143 /// value of the expression at any particular loop iteration.
1144 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
1146 /// Return the "disposition" of the given SCEV with respect to the given
1148 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
1150 /// Return true if elements that makes up the given SCEV dominate the
1151 /// specified basic block.
1152 bool dominates(const SCEV *S, const BasicBlock *BB);
1154 /// Return true if elements that makes up the given SCEV properly dominate
1155 /// the specified basic block.
1156 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
1158 /// Test whether the given SCEV has Op as a direct or indirect operand.
1159 bool hasOperand(const SCEV *S, const SCEV *Op) const;
1161 /// Return the size of an element read or written by Inst.
1162 const SCEV *getElementSize(Instruction *Inst);
1164 /// Compute the array dimensions Sizes from the set of Terms extracted from
1165 /// the memory access function of this SCEVAddRecExpr.
1166 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
1167 SmallVectorImpl<const SCEV *> &Sizes,
1168 const SCEV *ElementSize) const;
1170 void print(raw_ostream &OS) const;
1171 void verify() const;
1173 /// Collect parametric terms occurring in step expressions.
1174 void collectParametricTerms(const SCEV *Expr,
1175 SmallVectorImpl<const SCEV *> &Terms);
1179 /// Return in Subscripts the access functions for each dimension in Sizes.
1180 void computeAccessFunctions(const SCEV *Expr,
1181 SmallVectorImpl<const SCEV *> &Subscripts,
1182 SmallVectorImpl<const SCEV *> &Sizes);
1184 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1185 /// subscripts and sizes of an array access.
1187 /// The delinearization is a 3 step process: the first two steps compute the
1188 /// sizes of each subscript and the third step computes the access functions
1189 /// for the delinearized array:
1191 /// 1. Find the terms in the step functions
1192 /// 2. Compute the array size
1193 /// 3. Compute the access function: divide the SCEV by the array size
1194 /// starting with the innermost dimensions found in step 2. The Quotient
1195 /// is the SCEV to be divided in the next step of the recursion. The
1196 /// Remainder is the subscript of the innermost dimension. Loop over all
1197 /// array dimensions computed in step 2.
1199 /// To compute a uniform array size for several memory accesses to the same
1200 /// object, one can collect in step 1 all the step terms for all the memory
1201 /// accesses, and compute in step 2 a unique array shape. This guarantees
1202 /// that the array shape will be the same across all memory accesses.
1204 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1205 /// the array shape given in metadata.
1214 /// A[j+k][2i][5i] =
1216 /// The initial SCEV:
1218 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1220 /// 1. Find the different terms in the step functions:
1221 /// -> [2*m, 5, n*m, n*m]
1223 /// 2. Compute the array size: sort and unique them
1224 /// -> [n*m, 2*m, 5]
1225 /// find the GCD of all the terms = 1
1226 /// divide by the GCD and erase constant terms
1229 /// divide by GCD -> [n, 2]
1230 /// remove constant terms
1232 /// size of the array is A[unknown][n][m]
1234 /// 3. Compute the access function
1235 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1236 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1237 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1238 /// The remainder is the subscript of the innermost array dimension: [5i].
1240 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1241 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1242 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1243 /// The Remainder is the subscript of the next array dimension: [2i].
1245 /// The subscript of the outermost dimension is the Quotient: [j+k].
1247 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1248 void delinearize(const SCEV *Expr,
1249 SmallVectorImpl<const SCEV *> &Subscripts,
1250 SmallVectorImpl<const SCEV *> &Sizes,
1251 const SCEV *ElementSize);
1253 /// Return the DataLayout associated with the module this SCEV instance is
1255 const DataLayout &getDataLayout() const {
1256 return F.getParent()->getDataLayout();
1259 const SCEVPredicate *getEqualPredicate(const SCEVUnknown *LHS,
1260 const SCEVConstant *RHS);
1262 /// Re-writes the SCEV according to the Predicates in \p Preds.
1263 const SCEV *rewriteUsingPredicate(const SCEV *Scev, SCEVUnionPredicate &A);
1266 /// Compute the backedge taken count knowing the interval difference, the
1267 /// stride and presence of the equality in the comparison.
1268 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1271 /// Verify if an linear IV with positive stride can overflow when in a
1272 /// less-than comparison, knowing the invariant term of the comparison,
1273 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1274 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
1275 bool IsSigned, bool NoWrap);
1277 /// Verify if an linear IV with negative stride can overflow when in a
1278 /// greater-than comparison, knowing the invariant term of the comparison,
1279 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1280 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
1281 bool IsSigned, bool NoWrap);
1284 FoldingSet<SCEV> UniqueSCEVs;
1285 FoldingSet<SCEVPredicate> UniquePreds;
1286 BumpPtrAllocator SCEVAllocator;
1288 /// The head of a linked list of all SCEVUnknown values that have been
1289 /// allocated. This is used by releaseMemory to locate them all and call
1290 /// their destructors.
1291 SCEVUnknown *FirstUnknown;
1294 /// \brief Analysis pass that exposes the \c ScalarEvolution for a function.
1295 class ScalarEvolutionAnalysis {
1299 typedef ScalarEvolution Result;
1301 /// \brief Opaque, unique identifier for this analysis pass.
1302 static void *ID() { return (void *)&PassID; }
1304 /// \brief Provide a name for the analysis for debugging and logging.
1305 static StringRef name() { return "ScalarEvolutionAnalysis"; }
1307 ScalarEvolution run(Function &F, AnalysisManager<Function> *AM);
1310 /// \brief Printer pass for the \c ScalarEvolutionAnalysis results.
1311 class ScalarEvolutionPrinterPass {
1315 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1316 PreservedAnalyses run(Function &F, AnalysisManager<Function> *AM);
1318 static StringRef name() { return "ScalarEvolutionPrinterPass"; }
1321 class ScalarEvolutionWrapperPass : public FunctionPass {
1322 std::unique_ptr<ScalarEvolution> SE;
1327 ScalarEvolutionWrapperPass();
1329 ScalarEvolution &getSE() { return *SE; }
1330 const ScalarEvolution &getSE() const { return *SE; }
1332 bool runOnFunction(Function &F) override;
1333 void releaseMemory() override;
1334 void getAnalysisUsage(AnalysisUsage &AU) const override;
1335 void print(raw_ostream &OS, const Module * = nullptr) const override;
1336 void verifyAnalysis() const override;