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/ADT/SetVector.h"
27 #include "llvm/Analysis/LoopInfo.h"
28 #include "llvm/IR/ConstantRange.h"
29 #include "llvm/IR/Instructions.h"
30 #include "llvm/IR/Operator.h"
31 #include "llvm/IR/PassManager.h"
32 #include "llvm/IR/ValueHandle.h"
33 #include "llvm/IR/ValueMap.h"
34 #include "llvm/Pass.h"
35 #include "llvm/Support/Allocator.h"
36 #include "llvm/Support/DataTypes.h"
40 class AssumptionCache;
45 class ScalarEvolution;
47 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.
103 FlagAnyWrap = 0, // No guarantee.
104 FlagNW = (1 << 0), // No self-wrap.
105 FlagNUW = (1 << 1), // No unsigned wrap.
106 FlagNSW = (1 << 2), // No signed wrap.
107 NoWrapMask = (1 << 3) - 1
110 explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy)
111 : FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
113 unsigned getSCEVType() const { return SCEVType; }
115 /// Return the LLVM type of this SCEV expression.
117 Type *getType() const;
119 /// Return true if the expression is a constant zero.
123 /// Return true if the expression is a constant one.
127 /// Return true if the expression is a constant all-ones value.
129 bool isAllOnesValue() const;
131 /// Return true if the specified scev is negated, but not a constant.
132 bool isNonConstantNegative() const;
134 /// Print out the internal representation of this scalar to the specified
135 /// stream. This should really only be used for debugging purposes.
136 void print(raw_ostream &OS) const;
138 /// This method is used for debugging.
143 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
144 // temporary FoldingSetNodeID values.
145 template <> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
146 static void Profile(const SCEV &X, FoldingSetNodeID &ID) { ID = X.FastID; }
147 static bool Equals(const SCEV &X, const FoldingSetNodeID &ID, unsigned IDHash,
148 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 /// This class represents an assumption made using SCEV expressions which can
173 /// 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, P_Wrap };
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 /// Returns the estimated complexity of this predicate. This is roughly
196 /// measured in the number of run-time checks required.
197 virtual unsigned getComplexity() const { return 1; }
199 /// 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 /// Returns true if this predicate implies \p N.
204 virtual bool implies(const SCEVPredicate *N) const = 0;
206 /// Prints a textual representation of this predicate with an indentation of
208 virtual void print(raw_ostream &OS, unsigned Depth = 0) const = 0;
210 /// Returns the SCEV to which this predicate applies, or nullptr if this is
211 /// 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> : DefaultFoldingSetTrait<SCEVPredicate> {
225 static void Profile(const SCEVPredicate &X, FoldingSetNodeID &ID) {
229 static bool Equals(const SCEVPredicate &X, const FoldingSetNodeID &ID,
230 unsigned IDHash, FoldingSetNodeID &TempID) {
231 return ID == X.FastID;
233 static unsigned ComputeHash(const SCEVPredicate &X,
234 FoldingSetNodeID &TempID) {
235 return X.FastID.ComputeHash();
239 /// This class represents an assumption that two SCEV expressions are equal,
240 /// and this can be checked at run-time. We assume that the left hand side is
241 /// a SCEVUnknown and the right hand side a constant.
242 class SCEVEqualPredicate final : public SCEVPredicate {
243 /// We assume that LHS == RHS, where LHS is a SCEVUnknown and RHS a
245 const SCEVUnknown *LHS;
246 const SCEVConstant *RHS;
249 SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEVUnknown *LHS,
250 const SCEVConstant *RHS);
252 /// Implementation of the SCEVPredicate interface
253 bool implies(const SCEVPredicate *N) const override;
254 void print(raw_ostream &OS, unsigned Depth = 0) const override;
255 bool isAlwaysTrue() const override;
256 const SCEV *getExpr() const override;
258 /// Returns the left hand side of the equality.
259 const SCEVUnknown *getLHS() const { return LHS; }
261 /// Returns the right hand side of the equality.
262 const SCEVConstant *getRHS() const { return RHS; }
264 /// Methods for support type inquiry through isa, cast, and dyn_cast:
265 static inline bool classof(const SCEVPredicate *P) {
266 return P->getKind() == P_Equal;
270 /// This class represents an assumption made on an AddRec expression. Given an
271 /// affine AddRec expression {a,+,b}, we assume that it has the nssw or nusw
272 /// flags (defined below) in the first X iterations of the loop, where X is a
273 /// SCEV expression returned by getPredicatedBackedgeTakenCount).
275 /// Note that this does not imply that X is equal to the backedge taken
276 /// count. This means that if we have a nusw predicate for i32 {0,+,1} with a
277 /// predicated backedge taken count of X, we only guarantee that {0,+,1} has
278 /// nusw in the first X iterations. {0,+,1} may still wrap in the loop if we
279 /// have more than X iterations.
280 class SCEVWrapPredicate final : public SCEVPredicate {
282 /// Similar to SCEV::NoWrapFlags, but with slightly different semantics
283 /// for FlagNUSW. The increment is considered to be signed, and a + b
284 /// (where b is the increment) is considered to wrap if:
285 /// zext(a + b) != zext(a) + sext(b)
287 /// If Signed is a function that takes an n-bit tuple and maps to the
288 /// integer domain as the tuples value interpreted as twos complement,
289 /// and Unsigned a function that takes an n-bit tuple and maps to the
290 /// integer domain as as the base two value of input tuple, then a + b
291 /// has IncrementNUSW iff:
293 /// 0 <= Unsigned(a) + Signed(b) < 2^n
295 /// The IncrementNSSW flag has identical semantics with SCEV::FlagNSW.
297 /// Note that the IncrementNUSW flag is not commutative: if base + inc
298 /// has IncrementNUSW, then inc + base doesn't neccessarily have this
299 /// property. The reason for this is that this is used for sign/zero
300 /// extending affine AddRec SCEV expressions when a SCEVWrapPredicate is
301 /// assumed. A {base,+,inc} expression is already non-commutative with
302 /// regards to base and inc, since it is interpreted as:
303 /// (((base + inc) + inc) + inc) ...
304 enum IncrementWrapFlags {
305 IncrementAnyWrap = 0, // No guarantee.
306 IncrementNUSW = (1 << 0), // No unsigned with signed increment wrap.
307 IncrementNSSW = (1 << 1), // No signed with signed increment wrap
308 // (equivalent with SCEV::NSW)
309 IncrementNoWrapMask = (1 << 2) - 1
312 /// Convenient IncrementWrapFlags manipulation methods.
313 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
314 clearFlags(SCEVWrapPredicate::IncrementWrapFlags Flags,
315 SCEVWrapPredicate::IncrementWrapFlags OffFlags) {
316 assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
317 assert((OffFlags & IncrementNoWrapMask) == OffFlags &&
318 "Invalid flags value!");
319 return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & ~OffFlags);
322 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
323 maskFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, int Mask) {
324 assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
325 assert((Mask & IncrementNoWrapMask) == Mask && "Invalid mask value!");
327 return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & Mask);
330 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
331 setFlags(SCEVWrapPredicate::IncrementWrapFlags Flags,
332 SCEVWrapPredicate::IncrementWrapFlags OnFlags) {
333 assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
334 assert((OnFlags & IncrementNoWrapMask) == OnFlags &&
335 "Invalid flags value!");
337 return (SCEVWrapPredicate::IncrementWrapFlags)(Flags | OnFlags);
340 /// Returns the set of SCEVWrapPredicate no wrap flags implied by a
342 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
343 getImpliedFlags(const SCEVAddRecExpr *AR, ScalarEvolution &SE);
346 const SCEVAddRecExpr *AR;
347 IncrementWrapFlags Flags;
350 explicit SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
351 const SCEVAddRecExpr *AR,
352 IncrementWrapFlags Flags);
354 /// Returns the set assumed no overflow flags.
355 IncrementWrapFlags getFlags() const { return Flags; }
356 /// Implementation of the SCEVPredicate interface
357 const SCEV *getExpr() const override;
358 bool implies(const SCEVPredicate *N) const override;
359 void print(raw_ostream &OS, unsigned Depth = 0) const override;
360 bool isAlwaysTrue() const override;
362 /// Methods for support type inquiry through isa, cast, and dyn_cast:
363 static inline bool classof(const SCEVPredicate *P) {
364 return P->getKind() == P_Wrap;
368 /// This class represents a composition of other SCEV predicates, and is the
369 /// class that most clients will interact with. This is equivalent to a
370 /// logical "AND" of all the predicates in the union.
372 /// NB! Unlike other SCEVPredicate sub-classes this class does not live in the
373 /// ScalarEvolution::Preds folding set. This is why the \c add function is sound.
374 class SCEVUnionPredicate final : public SCEVPredicate {
376 typedef DenseMap<const SCEV *, SmallVector<const SCEVPredicate *, 4>>
379 /// Vector with references to all predicates in this union.
380 SmallVector<const SCEVPredicate *, 16> Preds;
381 /// Maps SCEVs to predicates for quick look-ups.
382 PredicateMap SCEVToPreds;
385 SCEVUnionPredicate();
387 const SmallVectorImpl<const SCEVPredicate *> &getPredicates() const {
391 /// Adds a predicate to this union.
392 void add(const SCEVPredicate *N);
394 /// Returns a reference to a vector containing all predicates which apply to
396 ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
398 /// Implementation of the SCEVPredicate interface
399 bool isAlwaysTrue() const override;
400 bool implies(const SCEVPredicate *N) const override;
401 void print(raw_ostream &OS, unsigned Depth) const override;
402 const SCEV *getExpr() const override;
404 /// We estimate the complexity of a union predicate as the size number of
405 /// predicates in the union.
406 unsigned getComplexity() const override { return Preds.size(); }
408 /// Methods for support type inquiry through isa, cast, and dyn_cast:
409 static inline bool classof(const SCEVPredicate *P) {
410 return P->getKind() == P_Union;
414 /// The main scalar evolution driver. Because client code (intentionally)
415 /// can't do much with the SCEV objects directly, they must ask this class
417 class ScalarEvolution {
419 /// An enum describing the relationship between a SCEV and a loop.
420 enum LoopDisposition {
421 LoopVariant, ///< The SCEV is loop-variant (unknown).
422 LoopInvariant, ///< The SCEV is loop-invariant.
423 LoopComputable ///< The SCEV varies predictably with the loop.
426 /// An enum describing the relationship between a SCEV and a basic block.
427 enum BlockDisposition {
428 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
429 DominatesBlock, ///< The SCEV dominates the block.
430 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
433 /// Convenient NoWrapFlags manipulation that hides enum casts and is
434 /// visible in the ScalarEvolution name space.
435 LLVM_NODISCARD static SCEV::NoWrapFlags maskFlags(SCEV::NoWrapFlags Flags,
437 return (SCEV::NoWrapFlags)(Flags & Mask);
439 LLVM_NODISCARD static SCEV::NoWrapFlags setFlags(SCEV::NoWrapFlags Flags,
440 SCEV::NoWrapFlags OnFlags) {
441 return (SCEV::NoWrapFlags)(Flags | OnFlags);
443 LLVM_NODISCARD static SCEV::NoWrapFlags
444 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
445 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
449 /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
450 /// Value is deleted.
451 class SCEVCallbackVH final : public CallbackVH {
453 void deleted() override;
454 void allUsesReplacedWith(Value *New) override;
457 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
460 friend class SCEVCallbackVH;
461 friend class SCEVExpander;
462 friend class SCEVUnknown;
464 /// The function we are analyzing.
468 /// Does the module have any calls to the llvm.experimental.guard intrinsic
469 /// at all? If this is false, we avoid doing work that will only help if
470 /// thare are guards present in the IR.
474 /// The target library information for the target we are targeting.
476 TargetLibraryInfo &TLI;
478 /// The tracker for @llvm.assume intrinsics in this function.
481 /// The dominator tree.
485 /// The loop information for the function we are currently analyzing.
489 /// This SCEV is used to represent unknown trip counts and things.
490 std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
492 /// The typedef for HasRecMap.
494 typedef DenseMap<const SCEV *, bool> HasRecMapType;
496 /// This is a cache to record whether a SCEV contains any scAddRecExpr.
497 HasRecMapType HasRecMap;
499 /// The typedef for ExprValueMap.
501 typedef std::pair<Value *, ConstantInt *> ValueOffsetPair;
502 typedef DenseMap<const SCEV *, SetVector<ValueOffsetPair>> ExprValueMapType;
504 /// ExprValueMap -- This map records the original values from which
505 /// the SCEV expr is generated from.
507 /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
508 /// of SCEV -> Value:
509 /// Suppose we know S1 expands to V1, and
512 /// where C_a and C_b are different SCEVConstants. Then we'd like to
513 /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
514 /// It is helpful when S2 is a complex SCEV expr.
516 /// In order to do that, we represent ExprValueMap as a mapping from
517 /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
518 /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
519 /// is expanded, it will first expand S2 to V1 - C_a because of
520 /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
522 /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
524 ExprValueMapType ExprValueMap;
526 /// The typedef for ValueExprMap.
528 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *>>
531 /// This is a cache of the values we have analyzed so far.
533 ValueExprMapType ValueExprMap;
535 /// Mark predicate values currently being processed by isImpliedCond.
536 SmallPtrSet<Value *, 6> PendingLoopPredicates;
538 /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
539 /// conditions dominating the backedge of a loop.
540 bool WalkingBEDominatingConds;
542 /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
543 /// predicate by splitting it into a set of independent predicates.
544 bool ProvingSplitPredicate;
546 /// Memoized values for the GetMinTrailingZeros
547 DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
549 /// Private helper method for the GetMinTrailingZeros method
550 uint32_t GetMinTrailingZerosImpl(const SCEV *S);
552 /// Information about the number of loop iterations for which a loop exit's
553 /// branch condition evaluates to the not-taken path. This is a temporary
554 /// pair of exact and max expressions that are eventually summarized in
555 /// ExitNotTakenInfo and BackedgeTakenInfo.
557 const SCEV *ExactNotTaken; // The exit is not taken exactly this many times
558 const SCEV *MaxNotTaken; // The exit is not taken at most this many times
559 bool MaxOrZero; // Not taken either exactly MaxNotTaken or zero times
561 /// A set of predicate guards for this ExitLimit. The result is only valid
562 /// if all of the predicates in \c Predicates evaluate to 'true' at
564 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
566 void addPredicate(const SCEVPredicate *P) {
567 assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
568 Predicates.insert(P);
571 /*implicit*/ ExitLimit(const SCEV *E);
574 const SCEV *E, const SCEV *M, bool MaxOrZero,
575 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList);
577 ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero,
578 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet);
580 ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero);
582 /// Test whether this ExitLimit contains any computed information, or
583 /// whether it's all SCEVCouldNotCompute values.
584 bool hasAnyInfo() const {
585 return !isa<SCEVCouldNotCompute>(ExactNotTaken) ||
586 !isa<SCEVCouldNotCompute>(MaxNotTaken);
589 /// Test whether this ExitLimit contains all information.
590 bool hasFullInfo() const {
591 return !isa<SCEVCouldNotCompute>(ExactNotTaken);
595 /// Information about the number of times a particular loop exit may be
596 /// reached before exiting the loop.
597 struct ExitNotTakenInfo {
598 PoisoningVH<BasicBlock> ExitingBlock;
599 const SCEV *ExactNotTaken;
600 std::unique_ptr<SCEVUnionPredicate> Predicate;
601 bool hasAlwaysTruePredicate() const {
602 return !Predicate || Predicate->isAlwaysTrue();
605 explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
606 const SCEV *ExactNotTaken,
607 std::unique_ptr<SCEVUnionPredicate> Predicate)
608 : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
609 Predicate(std::move(Predicate)) {}
612 /// Information about the backedge-taken count of a loop. This currently
613 /// includes an exact count and a maximum count.
615 class BackedgeTakenInfo {
616 /// A list of computable exits and their not-taken counts. Loops almost
617 /// never have more than one computable exit.
618 SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
620 /// The pointer part of \c MaxAndComplete is an expression indicating the
621 /// least maximum backedge-taken count of the loop that is known, or a
622 /// SCEVCouldNotCompute. This expression is only valid if the predicates
623 /// associated with all loop exits are true.
625 /// The integer part of \c MaxAndComplete is a boolean indicating if \c
626 /// ExitNotTaken has an element for every exiting block in the loop.
627 PointerIntPair<const SCEV *, 1> MaxAndComplete;
629 /// True iff the backedge is taken either exactly Max or zero times.
632 /// \name Helper projection functions on \c MaxAndComplete.
634 bool isComplete() const { return MaxAndComplete.getInt(); }
635 const SCEV *getMax() const { return MaxAndComplete.getPointer(); }
639 BackedgeTakenInfo() : MaxAndComplete(nullptr, 0), MaxOrZero(false) {}
641 BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
642 BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
644 typedef std::pair<BasicBlock *, ExitLimit> EdgeExitInfo;
646 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
647 BackedgeTakenInfo(SmallVectorImpl<EdgeExitInfo> &&ExitCounts, bool Complete,
648 const SCEV *MaxCount, bool MaxOrZero);
650 /// Test whether this BackedgeTakenInfo contains any computed information,
651 /// or whether it's all SCEVCouldNotCompute values.
652 bool hasAnyInfo() const {
653 return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax());
656 /// Test whether this BackedgeTakenInfo contains complete information.
657 bool hasFullInfo() const { return isComplete(); }
659 /// Return an expression indicating the exact *backedge-taken*
660 /// count of the loop if it is known or SCEVCouldNotCompute
661 /// otherwise. If execution makes it to the backedge on every
662 /// iteration (i.e. there are no abnormal exists like exception
663 /// throws and thread exits) then this is the number of times the
664 /// loop header will execute minus one.
666 /// If the SCEV predicate associated with the answer can be different
667 /// from AlwaysTrue, we must add a (non null) Predicates argument.
668 /// The SCEV predicate associated with the answer will be added to
669 /// Predicates. A run-time check needs to be emitted for the SCEV
670 /// predicate in order for the answer to be valid.
672 /// Note that we should always know if we need to pass a predicate
673 /// argument or not from the way the ExitCounts vector was computed.
674 /// If we allowed SCEV predicates to be generated when populating this
675 /// vector, this information can contain them and therefore a
676 /// SCEVPredicate argument should be added to getExact.
677 const SCEV *getExact(ScalarEvolution *SE,
678 SCEVUnionPredicate *Predicates = nullptr) const;
680 /// Return the number of times this loop exit may fall through to the back
681 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
682 /// this block before this number of iterations, but may exit via another
684 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
686 /// Get the max backedge taken count for the loop.
687 const SCEV *getMax(ScalarEvolution *SE) const;
689 /// Return true if the number of times this backedge is taken is either the
690 /// value returned by getMax or zero.
691 bool isMaxOrZero(ScalarEvolution *SE) const;
693 /// Return true if any backedge taken count expressions refer to the given
695 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
697 /// Invalidate this result and free associated memory.
701 /// Cache the backedge-taken count of the loops for this function as they
703 DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
705 /// Cache the predicated backedge-taken count of the loops for this
706 /// function as they are computed.
707 DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
709 /// This map contains entries for all of the PHI instructions that we
710 /// attempt to compute constant evolutions for. This allows us to avoid
711 /// potentially expensive recomputation of these properties. An instruction
712 /// maps to null if we are unable to compute its exit value.
713 DenseMap<PHINode *, Constant *> ConstantEvolutionLoopExitValue;
715 /// This map contains entries for all the expressions that we attempt to
716 /// compute getSCEVAtScope information for, which can be expensive in
718 DenseMap<const SCEV *, SmallVector<std::pair<const Loop *, const SCEV *>, 2>>
721 /// Memoized computeLoopDisposition results.
722 DenseMap<const SCEV *,
723 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
726 struct LoopProperties {
727 /// Set to true if the loop contains no instruction that can have side
728 /// effects (i.e. via throwing an exception, volatile or atomic access).
729 bool HasNoAbnormalExits;
731 /// Set to true if the loop contains no instruction that can abnormally exit
732 /// the loop (i.e. via throwing an exception, by terminating the thread
733 /// cleanly or by infinite looping in a called function). Strictly
734 /// speaking, the last one is not leaving the loop, but is identical to
735 /// leaving the loop for reasoning about undefined behavior.
736 bool HasNoSideEffects;
739 /// Cache for \c getLoopProperties.
740 DenseMap<const Loop *, LoopProperties> LoopPropertiesCache;
742 /// Return a \c LoopProperties instance for \p L, creating one if necessary.
743 LoopProperties getLoopProperties(const Loop *L);
745 bool loopHasNoSideEffects(const Loop *L) {
746 return getLoopProperties(L).HasNoSideEffects;
749 bool loopHasNoAbnormalExits(const Loop *L) {
750 return getLoopProperties(L).HasNoAbnormalExits;
753 /// Compute a LoopDisposition value.
754 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
756 /// Memoized computeBlockDisposition results.
759 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
762 /// Compute a BlockDisposition value.
763 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
765 /// Memoized results from getRange
766 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
768 /// Memoized results from getRange
769 DenseMap<const SCEV *, ConstantRange> SignedRanges;
771 /// Used to parameterize getRange
772 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
774 /// Set the memoized range for the given SCEV.
775 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
777 DenseMap<const SCEV *, ConstantRange> &Cache =
778 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
780 auto Pair = Cache.try_emplace(S, std::move(CR));
782 Pair.first->second = std::move(CR);
783 return Pair.first->second;
786 /// Determine the range for a particular SCEV.
787 /// NOTE: This returns a reference to an entry in a cache. It must be
788 /// copied if its needed for longer.
789 const ConstantRange &getRangeRef(const SCEV *S, RangeSignHint Hint);
791 /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
792 /// Helper for \c getRange.
793 ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
794 const SCEV *MaxBECount, unsigned BitWidth);
796 /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
797 /// Stop} by "factoring out" a ternary expression from the add recurrence.
798 /// Helper called by \c getRange.
799 ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
800 const SCEV *MaxBECount, unsigned BitWidth);
802 /// We know that there is no SCEV for the specified value. Analyze the
804 const SCEV *createSCEV(Value *V);
806 /// Provide the special handling we need to analyze PHI SCEVs.
807 const SCEV *createNodeForPHI(PHINode *PN);
809 /// Helper function called from createNodeForPHI.
810 const SCEV *createAddRecFromPHI(PHINode *PN);
812 /// A helper function for createAddRecFromPHI to handle simple cases.
813 const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV,
816 /// Helper function called from createNodeForPHI.
817 const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
819 /// Provide special handling for a select-like instruction (currently this
820 /// is either a select instruction or a phi node). \p I is the instruction
821 /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
823 const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
824 Value *TrueVal, Value *FalseVal);
826 /// Provide the special handling we need to analyze GEP SCEVs.
827 const SCEV *createNodeForGEP(GEPOperator *GEP);
829 /// Implementation code for getSCEVAtScope; called at most once for each
832 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
834 /// This looks up computed SCEV values for all instructions that depend on
835 /// the given instruction and removes them from the ValueExprMap map if they
836 /// reference SymName. This is used during PHI resolution.
837 void forgetSymbolicName(Instruction *I, const SCEV *SymName);
839 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
840 /// values if the loop hasn't been analyzed yet. The returned result is
841 /// guaranteed not to be predicated.
842 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
844 /// Similar to getBackedgeTakenInfo, but will add predicates as required
845 /// with the purpose of returning complete information.
846 const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
848 /// Compute the number of times the specified loop will iterate.
849 /// If AllowPredicates is set, we will create new SCEV predicates as
850 /// necessary in order to return an exact answer.
851 BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
852 bool AllowPredicates = false);
854 /// Compute the number of times the backedge of the specified loop will
855 /// execute if it exits via the specified block. If AllowPredicates is set,
856 /// this call will try to use a minimal set of SCEV predicates in order to
857 /// return an exact answer.
858 ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
859 bool AllowPredicates = false);
861 /// Compute the number of times the backedge of the specified loop will
862 /// execute if its exit condition were a conditional branch of ExitCond,
865 /// \p ControlsExit is true if ExitCond directly controls the exit
866 /// branch. In this case, we can assume that the loop exits only if the
867 /// condition is true and can infer that failing to meet the condition prior
868 /// to integer wraparound results in undefined behavior.
870 /// If \p AllowPredicates is set, this call will try to use a minimal set of
871 /// SCEV predicates in order to return an exact answer.
872 ExitLimit computeExitLimitFromCond(const Loop *L, Value *ExitCond,
873 BasicBlock *TBB, BasicBlock *FBB,
875 bool AllowPredicates = false);
877 // Helper functions for computeExitLimitFromCond to avoid exponential time
880 class ExitLimitCache {
881 // It may look like we need key on the whole (L, TBB, FBB, ControlsExit,
882 // AllowPredicates) tuple, but recursive calls to
883 // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only
884 // vary the in \c ExitCond and \c ControlsExit parameters. We remember the
885 // initial values of the other values to assert our assumption.
886 SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap;
891 bool AllowPredicates;
894 ExitLimitCache(const Loop *L, BasicBlock *TBB, BasicBlock *FBB,
895 bool AllowPredicates)
896 : L(L), TBB(TBB), FBB(FBB), AllowPredicates(AllowPredicates) {}
898 Optional<ExitLimit> find(const Loop *L, Value *ExitCond, BasicBlock *TBB,
899 BasicBlock *FBB, bool ControlsExit,
900 bool AllowPredicates);
902 void insert(const Loop *L, Value *ExitCond, BasicBlock *TBB,
903 BasicBlock *FBB, bool ControlsExit, bool AllowPredicates,
904 const ExitLimit &EL);
907 typedef ExitLimitCache ExitLimitCacheTy;
908 ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
909 const Loop *L, Value *ExitCond,
910 BasicBlock *TBB, BasicBlock *FBB,
912 bool AllowPredicates);
913 ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
914 Value *ExitCond, BasicBlock *TBB,
915 BasicBlock *FBB, bool ControlsExit,
916 bool AllowPredicates);
918 /// Compute the number of times the backedge of the specified loop will
919 /// execute if its exit condition were a conditional branch of the ICmpInst
920 /// ExitCond, TBB, and FBB. If AllowPredicates is set, this call will try
921 /// to use a minimal set of SCEV predicates in order to return an exact
923 ExitLimit computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond,
924 BasicBlock *TBB, BasicBlock *FBB,
926 bool AllowPredicates = false);
928 /// Compute the number of times the backedge of the specified loop will
929 /// execute if its exit condition were a switch with a single exiting case
931 ExitLimit computeExitLimitFromSingleExitSwitch(const Loop *L,
933 BasicBlock *ExitingBB,
936 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
937 /// compute the backedge-taken count.
938 ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI, Constant *RHS,
940 ICmpInst::Predicate p);
942 /// Compute the exit limit of a loop that is controlled by a
943 /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
944 /// count in these cases (since SCEV has no way of expressing them), but we
945 /// can still sometimes compute an upper bound.
947 /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
949 ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS, const Loop *L,
950 ICmpInst::Predicate Pred);
952 /// If the loop is known to execute a constant number of times (the
953 /// condition evolves only from constants), try to evaluate a few iterations
954 /// of the loop until we get the exit condition gets a value of ExitWhen
955 /// (true or false). If we cannot evaluate the exit count of the loop,
956 /// return CouldNotCompute.
957 const SCEV *computeExitCountExhaustively(const Loop *L, Value *Cond,
960 /// Return the number of times an exit condition comparing the specified
961 /// value to zero will execute. If not computable, return CouldNotCompute.
962 /// If AllowPredicates is set, this call will try to use a minimal set of
963 /// SCEV predicates in order to return an exact answer.
964 ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
965 bool AllowPredicates = false);
967 /// Return the number of times an exit condition checking the specified
968 /// value for nonzero will execute. If not computable, return
970 ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
972 /// Return the number of times an exit condition containing the specified
973 /// less-than comparison will execute. If not computable, return
976 /// \p isSigned specifies whether the less-than is signed.
978 /// \p ControlsExit is true when the LHS < RHS condition directly controls
979 /// the branch (loops exits only if condition is true). In this case, we can
980 /// use NoWrapFlags to skip overflow checks.
982 /// If \p AllowPredicates is set, this call will try to use a minimal set of
983 /// SCEV predicates in order to return an exact answer.
984 ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
985 bool isSigned, bool ControlsExit,
986 bool AllowPredicates = false);
988 ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
989 bool isSigned, bool IsSubExpr,
990 bool AllowPredicates = false);
992 /// Return a predecessor of BB (which may not be an immediate predecessor)
993 /// which has exactly one successor from which BB is reachable, or null if
994 /// no such block is found.
995 std::pair<BasicBlock *, BasicBlock *>
996 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
998 /// Test whether the condition described by Pred, LHS, and RHS is true
999 /// whenever the given FoundCondValue value evaluates to true.
1000 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1001 Value *FoundCondValue, bool Inverse);
1003 /// Test whether the condition described by Pred, LHS, and RHS is true
1004 /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
1006 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1007 ICmpInst::Predicate FoundPred, const SCEV *FoundLHS,
1008 const SCEV *FoundRHS);
1010 /// Test whether the condition described by Pred, LHS, and RHS is true
1011 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1013 bool isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS,
1014 const SCEV *RHS, const SCEV *FoundLHS,
1015 const SCEV *FoundRHS);
1017 /// Test whether the condition described by Pred, LHS, and RHS is true
1018 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1019 /// true. Here LHS is an operation that includes FoundLHS as one of its
1021 bool isImpliedViaOperations(ICmpInst::Predicate Pred,
1022 const SCEV *LHS, const SCEV *RHS,
1023 const SCEV *FoundLHS, const SCEV *FoundRHS,
1024 unsigned Depth = 0);
1026 /// Test whether the condition described by Pred, LHS, and RHS is true.
1027 /// Use only simple non-recursive types of checks, such as range analysis etc.
1028 bool isKnownViaSimpleReasoning(ICmpInst::Predicate Pred,
1029 const SCEV *LHS, const SCEV *RHS);
1031 /// Test whether the condition described by Pred, LHS, and RHS is true
1032 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1034 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS,
1035 const SCEV *RHS, const SCEV *FoundLHS,
1036 const SCEV *FoundRHS);
1038 /// Test whether the condition described by Pred, LHS, and RHS is true
1039 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1040 /// true. Utility function used by isImpliedCondOperands. Tries to get
1041 /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
1042 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS,
1043 const SCEV *RHS, const SCEV *FoundLHS,
1044 const SCEV *FoundRHS);
1046 /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
1047 /// by a call to \c @llvm.experimental.guard in \p BB.
1048 bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
1049 const SCEV *LHS, const SCEV *RHS);
1051 /// Test whether the condition described by Pred, LHS, and RHS is true
1052 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1055 /// This routine tries to rule out certain kinds of integer overflow, and
1056 /// then tries to reason about arithmetic properties of the predicates.
1057 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
1058 const SCEV *LHS, const SCEV *RHS,
1059 const SCEV *FoundLHS,
1060 const SCEV *FoundRHS);
1062 /// If we know that the specified Phi is in the header of its containing
1063 /// loop, we know the loop executes a constant number of times, and the PHI
1064 /// node is just a recurrence involving constants, fold it.
1065 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt &BEs,
1068 /// Test if the given expression is known to satisfy the condition described
1069 /// by Pred and the known constant ranges of LHS and RHS.
1071 bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
1072 const SCEV *LHS, const SCEV *RHS);
1074 /// Try to prove the condition described by "LHS Pred RHS" by ruling out
1075 /// integer overflow.
1077 /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
1079 bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS,
1082 /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
1083 /// prove them individually.
1084 bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
1087 /// Try to match the Expr as "(L + R)<Flags>".
1088 bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
1089 SCEV::NoWrapFlags &Flags);
1091 /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a
1092 /// constant, and None if it isn't.
1094 /// This is intended to be a cheaper version of getMinusSCEV. We can be
1095 /// frugal here since we just bail out of actually constructing and
1096 /// canonicalizing an expression in the cases where the result isn't going
1097 /// to be a constant.
1098 Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS);
1100 /// Drop memoized information computed for S.
1101 void forgetMemoizedResults(const SCEV *S);
1103 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
1104 const SCEV *getExistingSCEV(Value *V);
1106 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
1108 bool checkValidity(const SCEV *S) const;
1110 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
1111 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
1112 /// equivalent to proving no signed (resp. unsigned) wrap in
1113 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
1114 /// (resp. `SCEVZeroExtendExpr`).
1116 template <typename ExtendOpTy>
1117 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
1120 /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
1121 SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
1123 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
1124 ICmpInst::Predicate Pred, bool &Increasing);
1126 /// Return SCEV no-wrap flags that can be proven based on reasoning about
1127 /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
1128 /// would trigger undefined behavior on overflow.
1129 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
1131 /// Return true if the SCEV corresponding to \p I is never poison. Proving
1132 /// this is more complex than proving that just \p I is never poison, since
1133 /// SCEV commons expressions across control flow, and you can have cases
1137 /// ptr[idx0] = 100;
1138 /// if (<condition>) {
1139 /// idx1 = a +nsw b;
1140 /// ptr[idx1] = 200;
1143 /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
1144 /// hence not sign-overflow) only if "<condition>" is true. Since both
1145 /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
1146 /// it is not okay to annotate (+ a b) with <nsw> in the above example.
1147 bool isSCEVExprNeverPoison(const Instruction *I);
1149 /// This is like \c isSCEVExprNeverPoison but it specifically works for
1150 /// instructions that will get mapped to SCEV add recurrences. Return true
1151 /// if \p I will never generate poison under the assumption that \p I is an
1152 /// add recurrence on the loop \p L.
1153 bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
1156 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
1157 DominatorTree &DT, LoopInfo &LI);
1159 ScalarEvolution(ScalarEvolution &&Arg);
1161 LLVMContext &getContext() const { return F.getContext(); }
1163 /// Test if values of the given type are analyzable within the SCEV
1164 /// framework. This primarily includes integer types, and it can optionally
1165 /// include pointer types if the ScalarEvolution class has access to
1166 /// target-specific information.
1167 bool isSCEVable(Type *Ty) const;
1169 /// Return the size in bits of the specified type, for which isSCEVable must
1171 uint64_t getTypeSizeInBits(Type *Ty) const;
1173 /// Return a type with the same bitwidth as the given type and which
1174 /// represents how SCEV will treat the given type, for which isSCEVable must
1175 /// return true. For pointer types, this is the pointer-sized integer type.
1176 Type *getEffectiveSCEVType(Type *Ty) const;
1178 // Returns a wider type among {Ty1, Ty2}.
1179 Type *getWiderType(Type *Ty1, Type *Ty2) const;
1181 /// Return true if the SCEV is a scAddRecExpr or it contains
1182 /// scAddRecExpr. The result will be cached in HasRecMap.
1184 bool containsAddRecurrence(const SCEV *S);
1186 /// Return the Value set from which the SCEV expr is generated.
1187 SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
1189 /// Erase Value from ValueExprMap and ExprValueMap.
1190 void eraseValueFromMap(Value *V);
1192 /// Return a SCEV expression for the full generality of the specified
1194 const SCEV *getSCEV(Value *V);
1196 const SCEV *getConstant(ConstantInt *V);
1197 const SCEV *getConstant(const APInt &Val);
1198 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
1199 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
1201 typedef SmallDenseMap<std::pair<const SCEV *, Type *>, const SCEV *, 8>
1203 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
1204 const SCEV *getZeroExtendExprCached(const SCEV *Op, Type *Ty,
1205 ExtendCacheTy &Cache);
1206 const SCEV *getZeroExtendExprImpl(const SCEV *Op, Type *Ty,
1207 ExtendCacheTy &Cache);
1209 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
1210 const SCEV *getSignExtendExprCached(const SCEV *Op, Type *Ty,
1211 ExtendCacheTy &Cache);
1212 const SCEV *getSignExtendExprImpl(const SCEV *Op, Type *Ty,
1213 ExtendCacheTy &Cache);
1214 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
1215 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1216 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1217 unsigned Depth = 0);
1218 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
1219 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1220 unsigned Depth = 0) {
1221 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
1222 return getAddExpr(Ops, Flags, Depth);
1224 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
1225 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1226 unsigned Depth = 0) {
1227 SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
1228 return getAddExpr(Ops, Flags, Depth);
1230 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1231 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1232 unsigned Depth = 0);
1233 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
1234 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1235 unsigned Depth = 0) {
1236 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
1237 return getMulExpr(Ops, Flags, Depth);
1239 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
1240 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1241 unsigned Depth = 0) {
1242 SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
1243 return getMulExpr(Ops, Flags, Depth);
1245 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
1246 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
1247 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step, const Loop *L,
1248 SCEV::NoWrapFlags Flags);
1249 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1250 const Loop *L, SCEV::NoWrapFlags Flags);
1251 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
1252 const Loop *L, SCEV::NoWrapFlags Flags) {
1253 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
1254 return getAddRecExpr(NewOp, L, Flags);
1256 /// Returns an expression for a GEP
1258 /// \p GEP The GEP. The indices contained in the GEP itself are ignored,
1259 /// instead we use IndexExprs.
1260 /// \p IndexExprs The expressions for the indices.
1261 const SCEV *getGEPExpr(GEPOperator *GEP,
1262 const SmallVectorImpl<const SCEV *> &IndexExprs);
1263 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
1264 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
1265 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
1266 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
1267 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
1268 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
1269 const SCEV *getUnknown(Value *V);
1270 const SCEV *getCouldNotCompute();
1272 /// Return a SCEV for the constant 0 of a specific type.
1273 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
1275 /// Return a SCEV for the constant 1 of a specific type.
1276 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
1278 /// Return an expression for sizeof AllocTy that is type IntTy
1280 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
1282 /// Return an expression for offsetof on the given field with type IntTy
1284 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
1286 /// Return the SCEV object corresponding to -V.
1288 const SCEV *getNegativeSCEV(const SCEV *V,
1289 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
1291 /// Return the SCEV object corresponding to ~V.
1293 const SCEV *getNotSCEV(const SCEV *V);
1295 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
1296 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
1297 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1298 unsigned Depth = 0);
1300 /// Return a SCEV corresponding to a conversion of the input value to the
1301 /// specified type. If the type must be extended, it is zero extended.
1302 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
1304 /// Return a SCEV corresponding to a conversion of the input value to the
1305 /// specified type. If the type must be extended, it is sign extended.
1306 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
1308 /// Return a SCEV corresponding to a conversion of the input value to the
1309 /// specified type. If the type must be extended, it is zero extended. The
1310 /// conversion must not be narrowing.
1311 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
1313 /// Return a SCEV corresponding to a conversion of the input value to the
1314 /// specified type. If the type must be extended, it is sign extended. The
1315 /// conversion must not be narrowing.
1316 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
1318 /// Return a SCEV corresponding to a conversion of the input value to the
1319 /// specified type. If the type must be extended, it is extended with
1320 /// unspecified bits. The conversion must not be narrowing.
1321 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
1323 /// Return a SCEV corresponding to a conversion of the input value to the
1324 /// specified type. The conversion must not be widening.
1325 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
1327 /// Promote the operands to the wider of the types using zero-extension, and
1328 /// then perform a umax operation with them.
1329 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
1331 /// Promote the operands to the wider of the types using zero-extension, and
1332 /// then perform a umin operation with them.
1333 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
1335 /// Transitively follow the chain of pointer-type operands until reaching a
1336 /// SCEV that does not have a single pointer operand. This returns a
1337 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
1339 const SCEV *getPointerBase(const SCEV *V);
1341 /// Return a SCEV expression for the specified value at the specified scope
1342 /// in the program. The L value specifies a loop nest to evaluate the
1343 /// expression at, where null is the top-level or a specified loop is
1344 /// immediately inside of the loop.
1346 /// This method can be used to compute the exit value for a variable defined
1347 /// in a loop by querying what the value will hold in the parent loop.
1349 /// In the case that a relevant loop exit value cannot be computed, the
1350 /// original value V is returned.
1351 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
1353 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
1354 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
1356 /// Test whether entry to the loop is protected by a conditional between LHS
1357 /// and RHS. This is used to help avoid max expressions in loop trip
1358 /// counts, and to eliminate casts.
1359 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
1360 const SCEV *LHS, const SCEV *RHS);
1362 /// Test whether the backedge of the loop is protected by a conditional
1363 /// between LHS and RHS. This is used to to eliminate casts.
1364 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
1365 const SCEV *LHS, const SCEV *RHS);
1367 /// Returns the maximum trip count of the loop if it is a single-exit
1368 /// loop and we can compute a small maximum for that loop.
1370 /// Implemented in terms of the \c getSmallConstantTripCount overload with
1371 /// the single exiting block passed to it. See that routine for details.
1372 unsigned getSmallConstantTripCount(const Loop *L);
1374 /// Returns the maximum trip count of this loop as a normal unsigned
1375 /// value. Returns 0 if the trip count is unknown or not constant. This
1376 /// "trip count" assumes that control exits via ExitingBlock. More
1377 /// precisely, it is the number of times that control may reach ExitingBlock
1378 /// before taking the branch. For loops with multiple exits, it may not be
1379 /// the number times that the loop header executes if the loop exits
1380 /// prematurely via another branch.
1381 unsigned getSmallConstantTripCount(const Loop *L, BasicBlock *ExitingBlock);
1383 /// Returns the upper bound of the loop trip count as a normal unsigned
1385 /// Returns 0 if the trip count is unknown or not constant.
1386 unsigned getSmallConstantMaxTripCount(const Loop *L);
1388 /// Returns the largest constant divisor of the trip count of the
1389 /// loop if it is a single-exit loop and we can compute a small maximum for
1392 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
1393 /// the single exiting block passed to it. See that routine for details.
1394 unsigned getSmallConstantTripMultiple(const Loop *L);
1396 /// Returns the largest constant divisor of the trip count of this loop as a
1397 /// normal unsigned value, if possible. This means that the actual trip
1398 /// count is always a multiple of the returned value (don't forget the trip
1399 /// count could very well be zero as well!). As explained in the comments
1400 /// for getSmallConstantTripCount, this assumes that control exits the loop
1401 /// via ExitingBlock.
1402 unsigned getSmallConstantTripMultiple(const Loop *L,
1403 BasicBlock *ExitingBlock);
1405 /// Get the expression for the number of loop iterations for which this loop
1406 /// is guaranteed not to exit via ExitingBlock. Otherwise return
1407 /// SCEVCouldNotCompute.
1408 const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
1410 /// If the specified loop has a predictable backedge-taken count, return it,
1411 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
1412 /// the number of times the loop header will be branched to from within the
1413 /// loop, assuming there are no abnormal exists like exception throws. This is
1414 /// one less than the trip count of the loop, since it doesn't count the first
1415 /// iteration, when the header is branched to from outside the loop.
1417 /// Note that it is not valid to call this method on a loop without a
1418 /// loop-invariant backedge-taken count (see
1419 /// hasLoopInvariantBackedgeTakenCount).
1421 const SCEV *getBackedgeTakenCount(const Loop *L);
1423 /// Similar to getBackedgeTakenCount, except it will add a set of
1424 /// SCEV predicates to Predicates that are required to be true in order for
1425 /// the answer to be correct. Predicates can be checked with run-time
1426 /// checks and can be used to perform loop versioning.
1427 const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
1428 SCEVUnionPredicate &Predicates);
1430 /// When successful, this returns a SCEVConstant that is greater than or equal
1431 /// to (i.e. a "conservative over-approximation") of the value returend by
1432 /// getBackedgeTakenCount. If such a value cannot be computed, it returns the
1433 /// SCEVCouldNotCompute object.
1434 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
1436 /// Return true if the backedge taken count is either the value returned by
1437 /// getMaxBackedgeTakenCount or zero.
1438 bool isBackedgeTakenCountMaxOrZero(const Loop *L);
1440 /// Return true if the specified loop has an analyzable loop-invariant
1441 /// backedge-taken count.
1442 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
1444 /// This method should be called by the client when it has changed a loop in
1445 /// a way that may effect ScalarEvolution's ability to compute a trip count,
1446 /// or if the loop is deleted. This call is potentially expensive for large
1448 void forgetLoop(const Loop *L);
1450 /// This method should be called by the client when it has changed a value
1451 /// in a way that may effect its value, or which may disconnect it from a
1452 /// def-use chain linking it to a loop.
1453 void forgetValue(Value *V);
1455 /// Called when the client has changed the disposition of values in
1458 /// We don't have a way to invalidate per-loop dispositions. Clear and
1459 /// recompute is simpler.
1460 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
1462 /// Determine the minimum number of zero bits that S is guaranteed to end in
1463 /// (at every loop iteration). It is, at the same time, the minimum number
1464 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
1465 /// If S is guaranteed to be 0, it returns the bitwidth of S.
1466 uint32_t GetMinTrailingZeros(const SCEV *S);
1468 /// Determine the unsigned range for a particular SCEV.
1469 /// NOTE: This returns a copy of the reference returned by getRangeRef.
1470 ConstantRange getUnsignedRange(const SCEV *S) {
1471 return getRangeRef(S, HINT_RANGE_UNSIGNED);
1474 /// Determine the min of the unsigned range for a particular SCEV.
1475 APInt getUnsignedRangeMin(const SCEV *S) {
1476 return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
1479 /// Determine the max of the unsigned range for a particular SCEV.
1480 APInt getUnsignedRangeMax(const SCEV *S) {
1481 return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
1484 /// Determine the signed range for a particular SCEV.
1485 /// NOTE: This returns a copy of the reference returned by getRangeRef.
1486 ConstantRange getSignedRange(const SCEV *S) {
1487 return getRangeRef(S, HINT_RANGE_SIGNED);
1490 /// Determine the min of the signed range for a particular SCEV.
1491 APInt getSignedRangeMin(const SCEV *S) {
1492 return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
1495 /// Determine the max of the signed range for a particular SCEV.
1496 APInt getSignedRangeMax(const SCEV *S) {
1497 return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
1500 /// Test if the given expression is known to be negative.
1502 bool isKnownNegative(const SCEV *S);
1504 /// Test if the given expression is known to be positive.
1506 bool isKnownPositive(const SCEV *S);
1508 /// Test if the given expression is known to be non-negative.
1510 bool isKnownNonNegative(const SCEV *S);
1512 /// Test if the given expression is known to be non-positive.
1514 bool isKnownNonPositive(const SCEV *S);
1516 /// Test if the given expression is known to be non-zero.
1518 bool isKnownNonZero(const SCEV *S);
1520 /// Test if the given expression is known to satisfy the condition described
1521 /// by Pred, LHS, and RHS.
1523 bool isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
1526 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
1527 /// is monotonically increasing or decreasing. In the former case set
1528 /// `Increasing` to true and in the latter case set `Increasing` to false.
1530 /// A predicate is said to be monotonically increasing if may go from being
1531 /// false to being true as the loop iterates, but never the other way
1532 /// around. A predicate is said to be monotonically decreasing if may go
1533 /// from being true to being false as the loop iterates, but never the other
1535 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred,
1538 /// Return true if the result of the predicate LHS `Pred` RHS is loop
1539 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
1540 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
1541 /// loop invariant form of LHS `Pred` RHS.
1542 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
1543 const SCEV *RHS, const Loop *L,
1544 ICmpInst::Predicate &InvariantPred,
1545 const SCEV *&InvariantLHS,
1546 const SCEV *&InvariantRHS);
1548 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
1549 /// iff any changes were made. If the operands are provably equal or
1550 /// unequal, LHS and RHS are set to the same value and Pred is set to either
1551 /// ICMP_EQ or ICMP_NE.
1553 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS,
1554 const SCEV *&RHS, unsigned Depth = 0);
1556 /// Return the "disposition" of the given SCEV with respect to the given
1558 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
1560 /// Return true if the value of the given SCEV is unchanging in the
1562 bool isLoopInvariant(const SCEV *S, const Loop *L);
1564 /// Determine if the SCEV can be evaluated at loop's entry. It is true if it
1565 /// doesn't depend on a SCEVUnknown of an instruction which is dominated by
1566 /// the header of loop L.
1567 bool isAvailableAtLoopEntry(const SCEV *S, const Loop *L);
1569 /// Return true if the given SCEV changes value in a known way in the
1570 /// specified loop. This property being true implies that the value is
1571 /// variant in the loop AND that we can emit an expression to compute the
1572 /// value of the expression at any particular loop iteration.
1573 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
1575 /// Return the "disposition" of the given SCEV with respect to the given
1577 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
1579 /// Return true if elements that makes up the given SCEV dominate the
1580 /// specified basic block.
1581 bool dominates(const SCEV *S, const BasicBlock *BB);
1583 /// Return true if elements that makes up the given SCEV properly dominate
1584 /// the specified basic block.
1585 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
1587 /// Test whether the given SCEV has Op as a direct or indirect operand.
1588 bool hasOperand(const SCEV *S, const SCEV *Op) const;
1590 /// Return the size of an element read or written by Inst.
1591 const SCEV *getElementSize(Instruction *Inst);
1593 /// Compute the array dimensions Sizes from the set of Terms extracted from
1594 /// the memory access function of this SCEVAddRecExpr (second step of
1595 /// delinearization).
1596 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
1597 SmallVectorImpl<const SCEV *> &Sizes,
1598 const SCEV *ElementSize);
1600 void print(raw_ostream &OS) const;
1601 void verify() const;
1602 bool invalidate(Function &F, const PreservedAnalyses &PA,
1603 FunctionAnalysisManager::Invalidator &Inv);
1605 /// Collect parametric terms occurring in step expressions (first step of
1606 /// delinearization).
1607 void collectParametricTerms(const SCEV *Expr,
1608 SmallVectorImpl<const SCEV *> &Terms);
1610 /// Return in Subscripts the access functions for each dimension in Sizes
1611 /// (third step of delinearization).
1612 void computeAccessFunctions(const SCEV *Expr,
1613 SmallVectorImpl<const SCEV *> &Subscripts,
1614 SmallVectorImpl<const SCEV *> &Sizes);
1616 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1617 /// subscripts and sizes of an array access.
1619 /// The delinearization is a 3 step process: the first two steps compute the
1620 /// sizes of each subscript and the third step computes the access functions
1621 /// for the delinearized array:
1623 /// 1. Find the terms in the step functions
1624 /// 2. Compute the array size
1625 /// 3. Compute the access function: divide the SCEV by the array size
1626 /// starting with the innermost dimensions found in step 2. The Quotient
1627 /// is the SCEV to be divided in the next step of the recursion. The
1628 /// Remainder is the subscript of the innermost dimension. Loop over all
1629 /// array dimensions computed in step 2.
1631 /// To compute a uniform array size for several memory accesses to the same
1632 /// object, one can collect in step 1 all the step terms for all the memory
1633 /// accesses, and compute in step 2 a unique array shape. This guarantees
1634 /// that the array shape will be the same across all memory accesses.
1636 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1637 /// the array shape given in metadata.
1646 /// A[j+k][2i][5i] =
1648 /// The initial SCEV:
1650 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1652 /// 1. Find the different terms in the step functions:
1653 /// -> [2*m, 5, n*m, n*m]
1655 /// 2. Compute the array size: sort and unique them
1656 /// -> [n*m, 2*m, 5]
1657 /// find the GCD of all the terms = 1
1658 /// divide by the GCD and erase constant terms
1661 /// divide by GCD -> [n, 2]
1662 /// remove constant terms
1664 /// size of the array is A[unknown][n][m]
1666 /// 3. Compute the access function
1667 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1668 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1669 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1670 /// The remainder is the subscript of the innermost array dimension: [5i].
1672 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1673 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1674 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1675 /// The Remainder is the subscript of the next array dimension: [2i].
1677 /// The subscript of the outermost dimension is the Quotient: [j+k].
1679 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1680 void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
1681 SmallVectorImpl<const SCEV *> &Sizes,
1682 const SCEV *ElementSize);
1684 /// Return the DataLayout associated with the module this SCEV instance is
1686 const DataLayout &getDataLayout() const {
1687 return F.getParent()->getDataLayout();
1690 const SCEVPredicate *getEqualPredicate(const SCEVUnknown *LHS,
1691 const SCEVConstant *RHS);
1693 const SCEVPredicate *
1694 getWrapPredicate(const SCEVAddRecExpr *AR,
1695 SCEVWrapPredicate::IncrementWrapFlags AddedFlags);
1697 /// Re-writes the SCEV according to the Predicates in \p A.
1698 const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
1699 SCEVUnionPredicate &A);
1700 /// Tries to convert the \p S expression to an AddRec expression,
1701 /// adding additional predicates to \p Preds as required.
1702 const SCEVAddRecExpr *convertSCEVToAddRecWithPredicates(
1703 const SCEV *S, const Loop *L,
1704 SmallPtrSetImpl<const SCEVPredicate *> &Preds);
1707 /// Compute the backedge taken count knowing the interval difference, the
1708 /// stride and presence of the equality in the comparison.
1709 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1712 /// Verify if an linear IV with positive stride can overflow when in a
1713 /// less-than comparison, knowing the invariant term of the comparison,
1714 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1715 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1718 /// Verify if an linear IV with negative stride can overflow when in a
1719 /// greater-than comparison, knowing the invariant term of the comparison,
1720 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1721 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1724 /// Get add expr already created or create a new one.
1725 const SCEV *getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1726 SCEV::NoWrapFlags Flags);
1728 /// Get mul expr already created or create a new one.
1729 const SCEV *getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1730 SCEV::NoWrapFlags Flags);
1733 FoldingSet<SCEV> UniqueSCEVs;
1734 FoldingSet<SCEVPredicate> UniquePreds;
1735 BumpPtrAllocator SCEVAllocator;
1737 /// The head of a linked list of all SCEVUnknown values that have been
1738 /// allocated. This is used by releaseMemory to locate them all and call
1739 /// their destructors.
1740 SCEVUnknown *FirstUnknown;
1743 /// Analysis pass that exposes the \c ScalarEvolution for a function.
1744 class ScalarEvolutionAnalysis
1745 : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
1746 friend AnalysisInfoMixin<ScalarEvolutionAnalysis>;
1747 static AnalysisKey Key;
1750 typedef ScalarEvolution Result;
1752 ScalarEvolution run(Function &F, FunctionAnalysisManager &AM);
1755 /// Printer pass for the \c ScalarEvolutionAnalysis results.
1756 class ScalarEvolutionPrinterPass
1757 : public PassInfoMixin<ScalarEvolutionPrinterPass> {
1761 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1762 PreservedAnalyses run(Function &F, FunctionAnalysisManager &AM);
1765 class ScalarEvolutionWrapperPass : public FunctionPass {
1766 std::unique_ptr<ScalarEvolution> SE;
1771 ScalarEvolutionWrapperPass();
1773 ScalarEvolution &getSE() { return *SE; }
1774 const ScalarEvolution &getSE() const { return *SE; }
1776 bool runOnFunction(Function &F) override;
1777 void releaseMemory() override;
1778 void getAnalysisUsage(AnalysisUsage &AU) const override;
1779 void print(raw_ostream &OS, const Module * = nullptr) const override;
1780 void verifyAnalysis() const override;
1783 /// An interface layer with SCEV used to manage how we see SCEV expressions
1784 /// for values in the context of existing predicates. We can add new
1785 /// predicates, but we cannot remove them.
1787 /// This layer has multiple purposes:
1788 /// - provides a simple interface for SCEV versioning.
1789 /// - guarantees that the order of transformations applied on a SCEV
1790 /// expression for a single Value is consistent across two different
1791 /// getSCEV calls. This means that, for example, once we've obtained
1792 /// an AddRec expression for a certain value through expression
1793 /// rewriting, we will continue to get an AddRec expression for that
1795 /// - lowers the number of expression rewrites.
1796 class PredicatedScalarEvolution {
1798 PredicatedScalarEvolution(ScalarEvolution &SE, Loop &L);
1799 const SCEVUnionPredicate &getUnionPredicate() const;
1801 /// Returns the SCEV expression of V, in the context of the current SCEV
1802 /// predicate. The order of transformations applied on the expression of V
1803 /// returned by ScalarEvolution is guaranteed to be preserved, even when
1804 /// adding new predicates.
1805 const SCEV *getSCEV(Value *V);
1807 /// Get the (predicated) backedge count for the analyzed loop.
1808 const SCEV *getBackedgeTakenCount();
1810 /// Adds a new predicate.
1811 void addPredicate(const SCEVPredicate &Pred);
1813 /// Attempts to produce an AddRecExpr for V by adding additional SCEV
1814 /// predicates. If we can't transform the expression into an AddRecExpr we
1815 /// return nullptr and not add additional SCEV predicates to the current
1817 const SCEVAddRecExpr *getAsAddRec(Value *V);
1819 /// Proves that V doesn't overflow by adding SCEV predicate.
1820 void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1822 /// Returns true if we've proved that V doesn't wrap by means of a SCEV
1824 bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1826 /// Returns the ScalarEvolution analysis used.
1827 ScalarEvolution *getSE() const { return &SE; }
1829 /// We need to explicitly define the copy constructor because of FlagsMap.
1830 PredicatedScalarEvolution(const PredicatedScalarEvolution &);
1832 /// Print the SCEV mappings done by the Predicated Scalar Evolution.
1833 /// The printed text is indented by \p Depth.
1834 void print(raw_ostream &OS, unsigned Depth) const;
1837 /// Increments the version number of the predicate. This needs to be called
1838 /// every time the SCEV predicate changes.
1839 void updateGeneration();
1841 /// Holds a SCEV and the version number of the SCEV predicate used to
1842 /// perform the rewrite of the expression.
1843 typedef std::pair<unsigned, const SCEV *> RewriteEntry;
1845 /// Maps a SCEV to the rewrite result of that SCEV at a certain version
1846 /// number. If this number doesn't match the current Generation, we will
1847 /// need to do a rewrite. To preserve the transformation order of previous
1848 /// rewrites, we will rewrite the previous result instead of the original
1850 DenseMap<const SCEV *, RewriteEntry> RewriteMap;
1852 /// Records what NoWrap flags we've added to a Value *.
1853 ValueMap<Value *, SCEVWrapPredicate::IncrementWrapFlags> FlagsMap;
1855 /// The ScalarEvolution analysis.
1856 ScalarEvolution &SE;
1858 /// The analyzed Loop.
1861 /// The SCEVPredicate that forms our context. We will rewrite all
1862 /// expressions assuming that this predicate true.
1863 SCEVUnionPredicate Preds;
1865 /// Marks the version of the SCEV predicate used. When rewriting a SCEV
1866 /// expression we mark it with the version of the predicate. We use this to
1867 /// figure out if the predicate has changed from the last rewrite of the
1868 /// SCEV. If so, we need to perform a new rewrite.
1869 unsigned Generation;
1871 /// The backedge taken count.
1872 const SCEV *BackedgeCount;