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.
241 class SCEVEqualPredicate final : public SCEVPredicate {
242 /// We assume that LHS == RHS.
247 SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEV *LHS,
250 /// Implementation of the SCEVPredicate interface
251 bool implies(const SCEVPredicate *N) const override;
252 void print(raw_ostream &OS, unsigned Depth = 0) const override;
253 bool isAlwaysTrue() const override;
254 const SCEV *getExpr() const override;
256 /// Returns the left hand side of the equality.
257 const SCEV *getLHS() const { return LHS; }
259 /// Returns the right hand side of the equality.
260 const SCEV *getRHS() const { return RHS; }
262 /// Methods for support type inquiry through isa, cast, and dyn_cast:
263 static bool classof(const SCEVPredicate *P) {
264 return P->getKind() == P_Equal;
268 /// This class represents an assumption made on an AddRec expression. Given an
269 /// affine AddRec expression {a,+,b}, we assume that it has the nssw or nusw
270 /// flags (defined below) in the first X iterations of the loop, where X is a
271 /// SCEV expression returned by getPredicatedBackedgeTakenCount).
273 /// Note that this does not imply that X is equal to the backedge taken
274 /// count. This means that if we have a nusw predicate for i32 {0,+,1} with a
275 /// predicated backedge taken count of X, we only guarantee that {0,+,1} has
276 /// nusw in the first X iterations. {0,+,1} may still wrap in the loop if we
277 /// have more than X iterations.
278 class SCEVWrapPredicate final : public SCEVPredicate {
280 /// Similar to SCEV::NoWrapFlags, but with slightly different semantics
281 /// for FlagNUSW. The increment is considered to be signed, and a + b
282 /// (where b is the increment) is considered to wrap if:
283 /// zext(a + b) != zext(a) + sext(b)
285 /// If Signed is a function that takes an n-bit tuple and maps to the
286 /// integer domain as the tuples value interpreted as twos complement,
287 /// and Unsigned a function that takes an n-bit tuple and maps to the
288 /// integer domain as as the base two value of input tuple, then a + b
289 /// has IncrementNUSW iff:
291 /// 0 <= Unsigned(a) + Signed(b) < 2^n
293 /// The IncrementNSSW flag has identical semantics with SCEV::FlagNSW.
295 /// Note that the IncrementNUSW flag is not commutative: if base + inc
296 /// has IncrementNUSW, then inc + base doesn't neccessarily have this
297 /// property. The reason for this is that this is used for sign/zero
298 /// extending affine AddRec SCEV expressions when a SCEVWrapPredicate is
299 /// assumed. A {base,+,inc} expression is already non-commutative with
300 /// regards to base and inc, since it is interpreted as:
301 /// (((base + inc) + inc) + inc) ...
302 enum IncrementWrapFlags {
303 IncrementAnyWrap = 0, // No guarantee.
304 IncrementNUSW = (1 << 0), // No unsigned with signed increment wrap.
305 IncrementNSSW = (1 << 1), // No signed with signed increment wrap
306 // (equivalent with SCEV::NSW)
307 IncrementNoWrapMask = (1 << 2) - 1
310 /// Convenient IncrementWrapFlags manipulation methods.
311 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
312 clearFlags(SCEVWrapPredicate::IncrementWrapFlags Flags,
313 SCEVWrapPredicate::IncrementWrapFlags OffFlags) {
314 assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
315 assert((OffFlags & IncrementNoWrapMask) == OffFlags &&
316 "Invalid flags value!");
317 return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & ~OffFlags);
320 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
321 maskFlags(SCEVWrapPredicate::IncrementWrapFlags Flags, int Mask) {
322 assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
323 assert((Mask & IncrementNoWrapMask) == Mask && "Invalid mask value!");
325 return (SCEVWrapPredicate::IncrementWrapFlags)(Flags & Mask);
328 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
329 setFlags(SCEVWrapPredicate::IncrementWrapFlags Flags,
330 SCEVWrapPredicate::IncrementWrapFlags OnFlags) {
331 assert((Flags & IncrementNoWrapMask) == Flags && "Invalid flags value!");
332 assert((OnFlags & IncrementNoWrapMask) == OnFlags &&
333 "Invalid flags value!");
335 return (SCEVWrapPredicate::IncrementWrapFlags)(Flags | OnFlags);
338 /// Returns the set of SCEVWrapPredicate no wrap flags implied by a
340 LLVM_NODISCARD static SCEVWrapPredicate::IncrementWrapFlags
341 getImpliedFlags(const SCEVAddRecExpr *AR, ScalarEvolution &SE);
344 const SCEVAddRecExpr *AR;
345 IncrementWrapFlags Flags;
348 explicit SCEVWrapPredicate(const FoldingSetNodeIDRef ID,
349 const SCEVAddRecExpr *AR,
350 IncrementWrapFlags Flags);
352 /// Returns the set assumed no overflow flags.
353 IncrementWrapFlags getFlags() const { return Flags; }
354 /// Implementation of the SCEVPredicate interface
355 const SCEV *getExpr() const override;
356 bool implies(const SCEVPredicate *N) const override;
357 void print(raw_ostream &OS, unsigned Depth = 0) const override;
358 bool isAlwaysTrue() const override;
360 /// Methods for support type inquiry through isa, cast, and dyn_cast:
361 static bool classof(const SCEVPredicate *P) {
362 return P->getKind() == P_Wrap;
366 /// This class represents a composition of other SCEV predicates, and is the
367 /// class that most clients will interact with. This is equivalent to a
368 /// logical "AND" of all the predicates in the union.
370 /// NB! Unlike other SCEVPredicate sub-classes this class does not live in the
371 /// ScalarEvolution::Preds folding set. This is why the \c add function is sound.
372 class SCEVUnionPredicate final : public SCEVPredicate {
374 typedef DenseMap<const SCEV *, SmallVector<const SCEVPredicate *, 4>>
377 /// Vector with references to all predicates in this union.
378 SmallVector<const SCEVPredicate *, 16> Preds;
379 /// Maps SCEVs to predicates for quick look-ups.
380 PredicateMap SCEVToPreds;
383 SCEVUnionPredicate();
385 const SmallVectorImpl<const SCEVPredicate *> &getPredicates() const {
389 /// Adds a predicate to this union.
390 void add(const SCEVPredicate *N);
392 /// Returns a reference to a vector containing all predicates which apply to
394 ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
396 /// Implementation of the SCEVPredicate interface
397 bool isAlwaysTrue() const override;
398 bool implies(const SCEVPredicate *N) const override;
399 void print(raw_ostream &OS, unsigned Depth) const override;
400 const SCEV *getExpr() const override;
402 /// We estimate the complexity of a union predicate as the size number of
403 /// predicates in the union.
404 unsigned getComplexity() const override { return Preds.size(); }
406 /// Methods for support type inquiry through isa, cast, and dyn_cast:
407 static bool classof(const SCEVPredicate *P) {
408 return P->getKind() == P_Union;
412 /// The main scalar evolution driver. Because client code (intentionally)
413 /// can't do much with the SCEV objects directly, they must ask this class
415 class ScalarEvolution {
417 /// An enum describing the relationship between a SCEV and a loop.
418 enum LoopDisposition {
419 LoopVariant, ///< The SCEV is loop-variant (unknown).
420 LoopInvariant, ///< The SCEV is loop-invariant.
421 LoopComputable ///< The SCEV varies predictably with the loop.
424 /// An enum describing the relationship between a SCEV and a basic block.
425 enum BlockDisposition {
426 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
427 DominatesBlock, ///< The SCEV dominates the block.
428 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
431 /// Convenient NoWrapFlags manipulation that hides enum casts and is
432 /// visible in the ScalarEvolution name space.
433 LLVM_NODISCARD static SCEV::NoWrapFlags maskFlags(SCEV::NoWrapFlags Flags,
435 return (SCEV::NoWrapFlags)(Flags & Mask);
437 LLVM_NODISCARD static SCEV::NoWrapFlags setFlags(SCEV::NoWrapFlags Flags,
438 SCEV::NoWrapFlags OnFlags) {
439 return (SCEV::NoWrapFlags)(Flags | OnFlags);
441 LLVM_NODISCARD static SCEV::NoWrapFlags
442 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
443 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
447 /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
448 /// Value is deleted.
449 class SCEVCallbackVH final : public CallbackVH {
451 void deleted() override;
452 void allUsesReplacedWith(Value *New) override;
455 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
458 friend class SCEVCallbackVH;
459 friend class SCEVExpander;
460 friend class SCEVUnknown;
462 /// The function we are analyzing.
466 /// Does the module have any calls to the llvm.experimental.guard intrinsic
467 /// at all? If this is false, we avoid doing work that will only help if
468 /// thare are guards present in the IR.
472 /// The target library information for the target we are targeting.
474 TargetLibraryInfo &TLI;
476 /// The tracker for @llvm.assume intrinsics in this function.
479 /// The dominator tree.
483 /// The loop information for the function we are currently analyzing.
487 /// This SCEV is used to represent unknown trip counts and things.
488 std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
490 /// The typedef for HasRecMap.
492 typedef DenseMap<const SCEV *, bool> HasRecMapType;
494 /// This is a cache to record whether a SCEV contains any scAddRecExpr.
495 HasRecMapType HasRecMap;
497 /// The typedef for ExprValueMap.
499 typedef std::pair<Value *, ConstantInt *> ValueOffsetPair;
500 typedef DenseMap<const SCEV *, SetVector<ValueOffsetPair>> ExprValueMapType;
502 /// ExprValueMap -- This map records the original values from which
503 /// the SCEV expr is generated from.
505 /// We want to represent the mapping as SCEV -> ValueOffsetPair instead
506 /// of SCEV -> Value:
507 /// Suppose we know S1 expands to V1, and
510 /// where C_a and C_b are different SCEVConstants. Then we'd like to
511 /// expand S3 as V1 - C_a + C_b instead of expanding S2 literally.
512 /// It is helpful when S2 is a complex SCEV expr.
514 /// In order to do that, we represent ExprValueMap as a mapping from
515 /// SCEV to ValueOffsetPair. We will save both S1->{V1, 0} and
516 /// S2->{V1, C_a} into the map when we create SCEV for V1. When S3
517 /// is expanded, it will first expand S2 to V1 - C_a because of
518 /// S2->{V1, C_a} in the map, then expand S3 to V1 - C_a + C_b.
520 /// Note: S->{V, Offset} in the ExprValueMap means S can be expanded
522 ExprValueMapType ExprValueMap;
524 /// The typedef for ValueExprMap.
526 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *>>
529 /// This is a cache of the values we have analyzed so far.
531 ValueExprMapType ValueExprMap;
533 /// Mark predicate values currently being processed by isImpliedCond.
534 SmallPtrSet<Value *, 6> PendingLoopPredicates;
536 /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
537 /// conditions dominating the backedge of a loop.
538 bool WalkingBEDominatingConds;
540 /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
541 /// predicate by splitting it into a set of independent predicates.
542 bool ProvingSplitPredicate;
544 /// Memoized values for the GetMinTrailingZeros
545 DenseMap<const SCEV *, uint32_t> MinTrailingZerosCache;
547 /// Private helper method for the GetMinTrailingZeros method
548 uint32_t GetMinTrailingZerosImpl(const SCEV *S);
550 /// Information about the number of loop iterations for which a loop exit's
551 /// branch condition evaluates to the not-taken path. This is a temporary
552 /// pair of exact and max expressions that are eventually summarized in
553 /// ExitNotTakenInfo and BackedgeTakenInfo.
555 const SCEV *ExactNotTaken; // The exit is not taken exactly this many times
556 const SCEV *MaxNotTaken; // The exit is not taken at most this many times
557 bool MaxOrZero; // Not taken either exactly MaxNotTaken or zero times
559 /// A set of predicate guards for this ExitLimit. The result is only valid
560 /// if all of the predicates in \c Predicates evaluate to 'true' at
562 SmallPtrSet<const SCEVPredicate *, 4> Predicates;
564 void addPredicate(const SCEVPredicate *P) {
565 assert(!isa<SCEVUnionPredicate>(P) && "Only add leaf predicates here!");
566 Predicates.insert(P);
569 /*implicit*/ ExitLimit(const SCEV *E);
572 const SCEV *E, const SCEV *M, bool MaxOrZero,
573 ArrayRef<const SmallPtrSetImpl<const SCEVPredicate *> *> PredSetList);
575 ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero,
576 const SmallPtrSetImpl<const SCEVPredicate *> &PredSet);
578 ExitLimit(const SCEV *E, const SCEV *M, bool MaxOrZero);
580 /// Test whether this ExitLimit contains any computed information, or
581 /// whether it's all SCEVCouldNotCompute values.
582 bool hasAnyInfo() const {
583 return !isa<SCEVCouldNotCompute>(ExactNotTaken) ||
584 !isa<SCEVCouldNotCompute>(MaxNotTaken);
587 /// Test whether this ExitLimit contains all information.
588 bool hasFullInfo() const {
589 return !isa<SCEVCouldNotCompute>(ExactNotTaken);
593 /// Information about the number of times a particular loop exit may be
594 /// reached before exiting the loop.
595 struct ExitNotTakenInfo {
596 PoisoningVH<BasicBlock> ExitingBlock;
597 const SCEV *ExactNotTaken;
598 std::unique_ptr<SCEVUnionPredicate> Predicate;
599 bool hasAlwaysTruePredicate() const {
600 return !Predicate || Predicate->isAlwaysTrue();
603 explicit ExitNotTakenInfo(PoisoningVH<BasicBlock> ExitingBlock,
604 const SCEV *ExactNotTaken,
605 std::unique_ptr<SCEVUnionPredicate> Predicate)
606 : ExitingBlock(ExitingBlock), ExactNotTaken(ExactNotTaken),
607 Predicate(std::move(Predicate)) {}
610 /// Information about the backedge-taken count of a loop. This currently
611 /// includes an exact count and a maximum count.
613 class BackedgeTakenInfo {
614 /// A list of computable exits and their not-taken counts. Loops almost
615 /// never have more than one computable exit.
616 SmallVector<ExitNotTakenInfo, 1> ExitNotTaken;
618 /// The pointer part of \c MaxAndComplete is an expression indicating the
619 /// least maximum backedge-taken count of the loop that is known, or a
620 /// SCEVCouldNotCompute. This expression is only valid if the predicates
621 /// associated with all loop exits are true.
623 /// The integer part of \c MaxAndComplete is a boolean indicating if \c
624 /// ExitNotTaken has an element for every exiting block in the loop.
625 PointerIntPair<const SCEV *, 1> MaxAndComplete;
627 /// True iff the backedge is taken either exactly Max or zero times.
630 /// \name Helper projection functions on \c MaxAndComplete.
632 bool isComplete() const { return MaxAndComplete.getInt(); }
633 const SCEV *getMax() const { return MaxAndComplete.getPointer(); }
637 BackedgeTakenInfo() : MaxAndComplete(nullptr, 0), MaxOrZero(false) {}
639 BackedgeTakenInfo(BackedgeTakenInfo &&) = default;
640 BackedgeTakenInfo &operator=(BackedgeTakenInfo &&) = default;
642 typedef std::pair<BasicBlock *, ExitLimit> EdgeExitInfo;
644 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
645 BackedgeTakenInfo(SmallVectorImpl<EdgeExitInfo> &&ExitCounts, bool Complete,
646 const SCEV *MaxCount, bool MaxOrZero);
648 /// Test whether this BackedgeTakenInfo contains any computed information,
649 /// or whether it's all SCEVCouldNotCompute values.
650 bool hasAnyInfo() const {
651 return !ExitNotTaken.empty() || !isa<SCEVCouldNotCompute>(getMax());
654 /// Test whether this BackedgeTakenInfo contains complete information.
655 bool hasFullInfo() const { return isComplete(); }
657 /// Return an expression indicating the exact *backedge-taken*
658 /// count of the loop if it is known or SCEVCouldNotCompute
659 /// otherwise. If execution makes it to the backedge on every
660 /// iteration (i.e. there are no abnormal exists like exception
661 /// throws and thread exits) then this is the number of times the
662 /// loop header will execute minus one.
664 /// If the SCEV predicate associated with the answer can be different
665 /// from AlwaysTrue, we must add a (non null) Predicates argument.
666 /// The SCEV predicate associated with the answer will be added to
667 /// Predicates. A run-time check needs to be emitted for the SCEV
668 /// predicate in order for the answer to be valid.
670 /// Note that we should always know if we need to pass a predicate
671 /// argument or not from the way the ExitCounts vector was computed.
672 /// If we allowed SCEV predicates to be generated when populating this
673 /// vector, this information can contain them and therefore a
674 /// SCEVPredicate argument should be added to getExact.
675 const SCEV *getExact(ScalarEvolution *SE,
676 SCEVUnionPredicate *Predicates = nullptr) const;
678 /// Return the number of times this loop exit may fall through to the back
679 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
680 /// this block before this number of iterations, but may exit via another
682 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
684 /// Get the max backedge taken count for the loop.
685 const SCEV *getMax(ScalarEvolution *SE) const;
687 /// Return true if the number of times this backedge is taken is either the
688 /// value returned by getMax or zero.
689 bool isMaxOrZero(ScalarEvolution *SE) const;
691 /// Return true if any backedge taken count expressions refer to the given
693 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
695 /// Invalidate this result and free associated memory.
699 /// Cache the backedge-taken count of the loops for this function as they
701 DenseMap<const Loop *, BackedgeTakenInfo> BackedgeTakenCounts;
703 /// Cache the predicated backedge-taken count of the loops for this
704 /// function as they are computed.
705 DenseMap<const Loop *, BackedgeTakenInfo> PredicatedBackedgeTakenCounts;
707 /// This map contains entries for all of the PHI instructions that we
708 /// attempt to compute constant evolutions for. This allows us to avoid
709 /// potentially expensive recomputation of these properties. An instruction
710 /// maps to null if we are unable to compute its exit value.
711 DenseMap<PHINode *, Constant *> ConstantEvolutionLoopExitValue;
713 /// This map contains entries for all the expressions that we attempt to
714 /// compute getSCEVAtScope information for, which can be expensive in
716 DenseMap<const SCEV *, SmallVector<std::pair<const Loop *, const SCEV *>, 2>>
719 /// Memoized computeLoopDisposition results.
720 DenseMap<const SCEV *,
721 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
724 struct LoopProperties {
725 /// Set to true if the loop contains no instruction that can have side
726 /// effects (i.e. via throwing an exception, volatile or atomic access).
727 bool HasNoAbnormalExits;
729 /// Set to true if the loop contains no instruction that can abnormally exit
730 /// the loop (i.e. via throwing an exception, by terminating the thread
731 /// cleanly or by infinite looping in a called function). Strictly
732 /// speaking, the last one is not leaving the loop, but is identical to
733 /// leaving the loop for reasoning about undefined behavior.
734 bool HasNoSideEffects;
737 /// Cache for \c getLoopProperties.
738 DenseMap<const Loop *, LoopProperties> LoopPropertiesCache;
740 /// Return a \c LoopProperties instance for \p L, creating one if necessary.
741 LoopProperties getLoopProperties(const Loop *L);
743 bool loopHasNoSideEffects(const Loop *L) {
744 return getLoopProperties(L).HasNoSideEffects;
747 bool loopHasNoAbnormalExits(const Loop *L) {
748 return getLoopProperties(L).HasNoAbnormalExits;
751 /// Compute a LoopDisposition value.
752 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
754 /// Memoized computeBlockDisposition results.
757 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
760 /// Compute a BlockDisposition value.
761 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
763 /// Memoized results from getRange
764 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
766 /// Memoized results from getRange
767 DenseMap<const SCEV *, ConstantRange> SignedRanges;
769 /// Used to parameterize getRange
770 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
772 /// Set the memoized range for the given SCEV.
773 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
775 DenseMap<const SCEV *, ConstantRange> &Cache =
776 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
778 auto Pair = Cache.try_emplace(S, std::move(CR));
780 Pair.first->second = std::move(CR);
781 return Pair.first->second;
784 /// Determine the range for a particular SCEV.
785 /// NOTE: This returns a reference to an entry in a cache. It must be
786 /// copied if its needed for longer.
787 const ConstantRange &getRangeRef(const SCEV *S, RangeSignHint Hint);
789 /// Determines the range for the affine SCEVAddRecExpr {\p Start,+,\p Stop}.
790 /// Helper for \c getRange.
791 ConstantRange getRangeForAffineAR(const SCEV *Start, const SCEV *Stop,
792 const SCEV *MaxBECount, unsigned BitWidth);
794 /// Try to compute a range for the affine SCEVAddRecExpr {\p Start,+,\p
795 /// Stop} by "factoring out" a ternary expression from the add recurrence.
796 /// Helper called by \c getRange.
797 ConstantRange getRangeViaFactoring(const SCEV *Start, const SCEV *Stop,
798 const SCEV *MaxBECount, unsigned BitWidth);
800 /// We know that there is no SCEV for the specified value. Analyze the
802 const SCEV *createSCEV(Value *V);
804 /// Provide the special handling we need to analyze PHI SCEVs.
805 const SCEV *createNodeForPHI(PHINode *PN);
807 /// Helper function called from createNodeForPHI.
808 const SCEV *createAddRecFromPHI(PHINode *PN);
810 /// A helper function for createAddRecFromPHI to handle simple cases.
811 const SCEV *createSimpleAffineAddRec(PHINode *PN, Value *BEValueV,
814 /// Helper function called from createNodeForPHI.
815 const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
817 /// Provide special handling for a select-like instruction (currently this
818 /// is either a select instruction or a phi node). \p I is the instruction
819 /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
821 const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
822 Value *TrueVal, Value *FalseVal);
824 /// Provide the special handling we need to analyze GEP SCEVs.
825 const SCEV *createNodeForGEP(GEPOperator *GEP);
827 /// Implementation code for getSCEVAtScope; called at most once for each
830 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
832 /// This looks up computed SCEV values for all instructions that depend on
833 /// the given instruction and removes them from the ValueExprMap map if they
834 /// reference SymName. This is used during PHI resolution.
835 void forgetSymbolicName(Instruction *I, const SCEV *SymName);
837 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
838 /// values if the loop hasn't been analyzed yet. The returned result is
839 /// guaranteed not to be predicated.
840 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
842 /// Similar to getBackedgeTakenInfo, but will add predicates as required
843 /// with the purpose of returning complete information.
844 const BackedgeTakenInfo &getPredicatedBackedgeTakenInfo(const Loop *L);
846 /// Compute the number of times the specified loop will iterate.
847 /// If AllowPredicates is set, we will create new SCEV predicates as
848 /// necessary in order to return an exact answer.
849 BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L,
850 bool AllowPredicates = false);
852 /// Compute the number of times the backedge of the specified loop will
853 /// execute if it exits via the specified block. If AllowPredicates is set,
854 /// this call will try to use a minimal set of SCEV predicates in order to
855 /// return an exact answer.
856 ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock,
857 bool AllowPredicates = false);
859 /// Compute the number of times the backedge of the specified loop will
860 /// execute if its exit condition were a conditional branch of ExitCond,
863 /// \p ControlsExit is true if ExitCond directly controls the exit
864 /// branch. In this case, we can assume that the loop exits only if the
865 /// condition is true and can infer that failing to meet the condition prior
866 /// to integer wraparound results in undefined behavior.
868 /// If \p AllowPredicates is set, this call will try to use a minimal set of
869 /// SCEV predicates in order to return an exact answer.
870 ExitLimit computeExitLimitFromCond(const Loop *L, Value *ExitCond,
871 BasicBlock *TBB, BasicBlock *FBB,
873 bool AllowPredicates = false);
875 // Helper functions for computeExitLimitFromCond to avoid exponential time
878 class ExitLimitCache {
879 // It may look like we need key on the whole (L, TBB, FBB, ControlsExit,
880 // AllowPredicates) tuple, but recursive calls to
881 // computeExitLimitFromCondCached from computeExitLimitFromCondImpl only
882 // vary the in \c ExitCond and \c ControlsExit parameters. We remember the
883 // initial values of the other values to assert our assumption.
884 SmallDenseMap<PointerIntPair<Value *, 1>, ExitLimit> TripCountMap;
889 bool AllowPredicates;
892 ExitLimitCache(const Loop *L, BasicBlock *TBB, BasicBlock *FBB,
893 bool AllowPredicates)
894 : L(L), TBB(TBB), FBB(FBB), AllowPredicates(AllowPredicates) {}
896 Optional<ExitLimit> find(const Loop *L, Value *ExitCond, BasicBlock *TBB,
897 BasicBlock *FBB, bool ControlsExit,
898 bool AllowPredicates);
900 void insert(const Loop *L, Value *ExitCond, BasicBlock *TBB,
901 BasicBlock *FBB, bool ControlsExit, bool AllowPredicates,
902 const ExitLimit &EL);
905 typedef ExitLimitCache ExitLimitCacheTy;
906 ExitLimit computeExitLimitFromCondCached(ExitLimitCacheTy &Cache,
907 const Loop *L, Value *ExitCond,
908 BasicBlock *TBB, BasicBlock *FBB,
910 bool AllowPredicates);
911 ExitLimit computeExitLimitFromCondImpl(ExitLimitCacheTy &Cache, const Loop *L,
912 Value *ExitCond, BasicBlock *TBB,
913 BasicBlock *FBB, bool ControlsExit,
914 bool AllowPredicates);
916 /// Compute the number of times the backedge of the specified loop will
917 /// execute if its exit condition were a conditional branch of the ICmpInst
918 /// ExitCond, TBB, and FBB. If AllowPredicates is set, this call will try
919 /// to use a minimal set of SCEV predicates in order to return an exact
921 ExitLimit computeExitLimitFromICmp(const Loop *L, ICmpInst *ExitCond,
922 BasicBlock *TBB, BasicBlock *FBB,
924 bool AllowPredicates = false);
926 /// Compute the number of times the backedge of the specified loop will
927 /// execute if its exit condition were a switch with a single exiting case
929 ExitLimit computeExitLimitFromSingleExitSwitch(const Loop *L,
931 BasicBlock *ExitingBB,
934 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
935 /// compute the backedge-taken count.
936 ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI, Constant *RHS,
938 ICmpInst::Predicate p);
940 /// Compute the exit limit of a loop that is controlled by a
941 /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
942 /// count in these cases (since SCEV has no way of expressing them), but we
943 /// can still sometimes compute an upper bound.
945 /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
947 ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS, const Loop *L,
948 ICmpInst::Predicate Pred);
950 /// If the loop is known to execute a constant number of times (the
951 /// condition evolves only from constants), try to evaluate a few iterations
952 /// of the loop until we get the exit condition gets a value of ExitWhen
953 /// (true or false). If we cannot evaluate the exit count of the loop,
954 /// return CouldNotCompute.
955 const SCEV *computeExitCountExhaustively(const Loop *L, Value *Cond,
958 /// Return the number of times an exit condition comparing the specified
959 /// value to zero will execute. If not computable, return CouldNotCompute.
960 /// If AllowPredicates is set, this call will try to use a minimal set of
961 /// SCEV predicates in order to return an exact answer.
962 ExitLimit howFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr,
963 bool AllowPredicates = false);
965 /// Return the number of times an exit condition checking the specified
966 /// value for nonzero will execute. If not computable, return
968 ExitLimit howFarToNonZero(const SCEV *V, const Loop *L);
970 /// Return the number of times an exit condition containing the specified
971 /// less-than comparison will execute. If not computable, return
974 /// \p isSigned specifies whether the less-than is signed.
976 /// \p ControlsExit is true when the LHS < RHS condition directly controls
977 /// the branch (loops exits only if condition is true). In this case, we can
978 /// use NoWrapFlags to skip overflow checks.
980 /// If \p AllowPredicates is set, this call will try to use a minimal set of
981 /// SCEV predicates in order to return an exact answer.
982 ExitLimit howManyLessThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
983 bool isSigned, bool ControlsExit,
984 bool AllowPredicates = false);
986 ExitLimit howManyGreaterThans(const SCEV *LHS, const SCEV *RHS, const Loop *L,
987 bool isSigned, bool IsSubExpr,
988 bool AllowPredicates = false);
990 /// Return a predecessor of BB (which may not be an immediate predecessor)
991 /// which has exactly one successor from which BB is reachable, or null if
992 /// no such block is found.
993 std::pair<BasicBlock *, BasicBlock *>
994 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
996 /// Test whether the condition described by Pred, LHS, and RHS is true
997 /// whenever the given FoundCondValue value evaluates to true.
998 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
999 Value *FoundCondValue, bool Inverse);
1001 /// Test whether the condition described by Pred, LHS, and RHS is true
1002 /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
1004 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS, const SCEV *RHS,
1005 ICmpInst::Predicate FoundPred, const SCEV *FoundLHS,
1006 const SCEV *FoundRHS);
1008 /// Test whether the condition described by Pred, LHS, and RHS is true
1009 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1011 bool isImpliedCondOperands(ICmpInst::Predicate Pred, const SCEV *LHS,
1012 const SCEV *RHS, const SCEV *FoundLHS,
1013 const SCEV *FoundRHS);
1015 /// Test whether the condition described by Pred, LHS, and RHS is true
1016 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1017 /// true. Here LHS is an operation that includes FoundLHS as one of its
1019 bool isImpliedViaOperations(ICmpInst::Predicate Pred,
1020 const SCEV *LHS, const SCEV *RHS,
1021 const SCEV *FoundLHS, const SCEV *FoundRHS,
1022 unsigned Depth = 0);
1024 /// Test whether the condition described by Pred, LHS, and RHS is true.
1025 /// Use only simple non-recursive types of checks, such as range analysis etc.
1026 bool isKnownViaSimpleReasoning(ICmpInst::Predicate Pred,
1027 const SCEV *LHS, const SCEV *RHS);
1029 /// Test whether the condition described by Pred, LHS, and RHS is true
1030 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1032 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred, const SCEV *LHS,
1033 const SCEV *RHS, const SCEV *FoundLHS,
1034 const SCEV *FoundRHS);
1036 /// Test whether the condition described by Pred, LHS, and RHS is true
1037 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1038 /// true. Utility function used by isImpliedCondOperands. Tries to get
1039 /// cases like "X `sgt` 0 => X - 1 `sgt` -1".
1040 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred, const SCEV *LHS,
1041 const SCEV *RHS, const SCEV *FoundLHS,
1042 const SCEV *FoundRHS);
1044 /// Return true if the condition denoted by \p LHS \p Pred \p RHS is implied
1045 /// by a call to \c @llvm.experimental.guard in \p BB.
1046 bool isImpliedViaGuard(BasicBlock *BB, ICmpInst::Predicate Pred,
1047 const SCEV *LHS, const SCEV *RHS);
1049 /// Test whether the condition described by Pred, LHS, and RHS is true
1050 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
1053 /// This routine tries to rule out certain kinds of integer overflow, and
1054 /// then tries to reason about arithmetic properties of the predicates.
1055 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
1056 const SCEV *LHS, const SCEV *RHS,
1057 const SCEV *FoundLHS,
1058 const SCEV *FoundRHS);
1060 /// If we know that the specified Phi is in the header of its containing
1061 /// loop, we know the loop executes a constant number of times, and the PHI
1062 /// node is just a recurrence involving constants, fold it.
1063 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt &BEs,
1066 /// Test if the given expression is known to satisfy the condition described
1067 /// by Pred and the known constant ranges of LHS and RHS.
1069 bool isKnownPredicateViaConstantRanges(ICmpInst::Predicate Pred,
1070 const SCEV *LHS, const SCEV *RHS);
1072 /// Try to prove the condition described by "LHS Pred RHS" by ruling out
1073 /// integer overflow.
1075 /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
1077 bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred, const SCEV *LHS,
1080 /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
1081 /// prove them individually.
1082 bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
1085 /// Try to match the Expr as "(L + R)<Flags>".
1086 bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
1087 SCEV::NoWrapFlags &Flags);
1089 /// Compute \p LHS - \p RHS and returns the result as an APInt if it is a
1090 /// constant, and None if it isn't.
1092 /// This is intended to be a cheaper version of getMinusSCEV. We can be
1093 /// frugal here since we just bail out of actually constructing and
1094 /// canonicalizing an expression in the cases where the result isn't going
1095 /// to be a constant.
1096 Optional<APInt> computeConstantDifference(const SCEV *LHS, const SCEV *RHS);
1098 /// Drop memoized information computed for S.
1099 void forgetMemoizedResults(const SCEV *S);
1101 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
1102 const SCEV *getExistingSCEV(Value *V);
1104 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
1106 bool checkValidity(const SCEV *S) const;
1108 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
1109 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
1110 /// equivalent to proving no signed (resp. unsigned) wrap in
1111 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
1112 /// (resp. `SCEVZeroExtendExpr`).
1114 template <typename ExtendOpTy>
1115 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
1118 /// Try to prove NSW or NUW on \p AR relying on ConstantRange manipulation.
1119 SCEV::NoWrapFlags proveNoWrapViaConstantRanges(const SCEVAddRecExpr *AR);
1121 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
1122 ICmpInst::Predicate Pred, bool &Increasing);
1124 /// Return SCEV no-wrap flags that can be proven based on reasoning about
1125 /// how poison produced from no-wrap flags on this value (e.g. a nuw add)
1126 /// would trigger undefined behavior on overflow.
1127 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
1129 /// Return true if the SCEV corresponding to \p I is never poison. Proving
1130 /// this is more complex than proving that just \p I is never poison, since
1131 /// SCEV commons expressions across control flow, and you can have cases
1135 /// ptr[idx0] = 100;
1136 /// if (<condition>) {
1137 /// idx1 = a +nsw b;
1138 /// ptr[idx1] = 200;
1141 /// where the SCEV expression (+ a b) is guaranteed to not be poison (and
1142 /// hence not sign-overflow) only if "<condition>" is true. Since both
1143 /// `idx0` and `idx1` will be mapped to the same SCEV expression, (+ a b),
1144 /// it is not okay to annotate (+ a b) with <nsw> in the above example.
1145 bool isSCEVExprNeverPoison(const Instruction *I);
1147 /// This is like \c isSCEVExprNeverPoison but it specifically works for
1148 /// instructions that will get mapped to SCEV add recurrences. Return true
1149 /// if \p I will never generate poison under the assumption that \p I is an
1150 /// add recurrence on the loop \p L.
1151 bool isAddRecNeverPoison(const Instruction *I, const Loop *L);
1154 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
1155 DominatorTree &DT, LoopInfo &LI);
1157 ScalarEvolution(ScalarEvolution &&Arg);
1159 LLVMContext &getContext() const { return F.getContext(); }
1161 /// Test if values of the given type are analyzable within the SCEV
1162 /// framework. This primarily includes integer types, and it can optionally
1163 /// include pointer types if the ScalarEvolution class has access to
1164 /// target-specific information.
1165 bool isSCEVable(Type *Ty) const;
1167 /// Return the size in bits of the specified type, for which isSCEVable must
1169 uint64_t getTypeSizeInBits(Type *Ty) const;
1171 /// Return a type with the same bitwidth as the given type and which
1172 /// represents how SCEV will treat the given type, for which isSCEVable must
1173 /// return true. For pointer types, this is the pointer-sized integer type.
1174 Type *getEffectiveSCEVType(Type *Ty) const;
1176 // Returns a wider type among {Ty1, Ty2}.
1177 Type *getWiderType(Type *Ty1, Type *Ty2) const;
1179 /// Return true if the SCEV is a scAddRecExpr or it contains
1180 /// scAddRecExpr. The result will be cached in HasRecMap.
1182 bool containsAddRecurrence(const SCEV *S);
1184 /// Return the Value set from which the SCEV expr is generated.
1185 SetVector<ValueOffsetPair> *getSCEVValues(const SCEV *S);
1187 /// Erase Value from ValueExprMap and ExprValueMap.
1188 void eraseValueFromMap(Value *V);
1190 /// Return a SCEV expression for the full generality of the specified
1192 const SCEV *getSCEV(Value *V);
1194 const SCEV *getConstant(ConstantInt *V);
1195 const SCEV *getConstant(const APInt &Val);
1196 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
1197 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
1198 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
1199 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty, unsigned Depth = 0);
1200 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
1201 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1202 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1203 unsigned Depth = 0);
1204 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
1205 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1206 unsigned Depth = 0) {
1207 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
1208 return getAddExpr(Ops, Flags, Depth);
1210 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
1211 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1212 unsigned Depth = 0) {
1213 SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
1214 return getAddExpr(Ops, Flags, Depth);
1216 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1217 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1218 unsigned Depth = 0);
1219 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
1220 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1221 unsigned Depth = 0) {
1222 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
1223 return getMulExpr(Ops, Flags, Depth);
1225 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
1226 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1227 unsigned Depth = 0) {
1228 SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
1229 return getMulExpr(Ops, Flags, Depth);
1231 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
1232 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
1233 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step, const Loop *L,
1234 SCEV::NoWrapFlags Flags);
1235 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1236 const Loop *L, SCEV::NoWrapFlags Flags);
1237 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
1238 const Loop *L, SCEV::NoWrapFlags Flags) {
1239 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
1240 return getAddRecExpr(NewOp, L, Flags);
1243 /// Checks if \p SymbolicPHI can be rewritten as an AddRecExpr under some
1244 /// Predicates. If successful return these <AddRecExpr, Predicates>;
1245 /// The function is intended to be called from PSCEV (the caller will decide
1246 /// whether to actually add the predicates and carry out the rewrites).
1247 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1248 createAddRecFromPHIWithCasts(const SCEVUnknown *SymbolicPHI);
1250 /// Returns an expression for a GEP
1252 /// \p GEP The GEP. The indices contained in the GEP itself are ignored,
1253 /// instead we use IndexExprs.
1254 /// \p IndexExprs The expressions for the indices.
1255 const SCEV *getGEPExpr(GEPOperator *GEP,
1256 const SmallVectorImpl<const SCEV *> &IndexExprs);
1257 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
1258 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
1259 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
1260 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
1261 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
1262 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
1263 const SCEV *getUnknown(Value *V);
1264 const SCEV *getCouldNotCompute();
1266 /// Return a SCEV for the constant 0 of a specific type.
1267 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
1269 /// Return a SCEV for the constant 1 of a specific type.
1270 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
1272 /// Return an expression for sizeof AllocTy that is type IntTy
1274 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
1276 /// Return an expression for offsetof on the given field with type IntTy
1278 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
1280 /// Return the SCEV object corresponding to -V.
1282 const SCEV *getNegativeSCEV(const SCEV *V,
1283 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
1285 /// Return the SCEV object corresponding to ~V.
1287 const SCEV *getNotSCEV(const SCEV *V);
1289 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
1290 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
1291 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap,
1292 unsigned Depth = 0);
1294 /// Return a SCEV corresponding to a conversion of the input value to the
1295 /// specified type. If the type must be extended, it is zero extended.
1296 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
1298 /// Return a SCEV corresponding to a conversion of the input value to the
1299 /// specified type. If the type must be extended, it is sign extended.
1300 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
1302 /// Return a SCEV corresponding to a conversion of the input value to the
1303 /// specified type. If the type must be extended, it is zero extended. The
1304 /// conversion must not be narrowing.
1305 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
1307 /// Return a SCEV corresponding to a conversion of the input value to the
1308 /// specified type. If the type must be extended, it is sign extended. The
1309 /// conversion must not be narrowing.
1310 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
1312 /// Return a SCEV corresponding to a conversion of the input value to the
1313 /// specified type. If the type must be extended, it is extended with
1314 /// unspecified bits. The conversion must not be narrowing.
1315 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
1317 /// Return a SCEV corresponding to a conversion of the input value to the
1318 /// specified type. The conversion must not be widening.
1319 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
1321 /// Promote the operands to the wider of the types using zero-extension, and
1322 /// then perform a umax operation with them.
1323 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
1325 /// Promote the operands to the wider of the types using zero-extension, and
1326 /// then perform a umin operation with them.
1327 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS, const SCEV *RHS);
1329 /// Transitively follow the chain of pointer-type operands until reaching a
1330 /// SCEV that does not have a single pointer operand. This returns a
1331 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
1333 const SCEV *getPointerBase(const SCEV *V);
1335 /// Return a SCEV expression for the specified value at the specified scope
1336 /// in the program. The L value specifies a loop nest to evaluate the
1337 /// expression at, where null is the top-level or a specified loop is
1338 /// immediately inside of the loop.
1340 /// This method can be used to compute the exit value for a variable defined
1341 /// in a loop by querying what the value will hold in the parent loop.
1343 /// In the case that a relevant loop exit value cannot be computed, the
1344 /// original value V is returned.
1345 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
1347 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
1348 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
1350 /// Test whether entry to the loop is protected by a conditional between LHS
1351 /// and RHS. This is used to help avoid max expressions in loop trip
1352 /// counts, and to eliminate casts.
1353 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
1354 const SCEV *LHS, const SCEV *RHS);
1356 /// Test whether the backedge of the loop is protected by a conditional
1357 /// between LHS and RHS. This is used to to eliminate casts.
1358 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
1359 const SCEV *LHS, const SCEV *RHS);
1361 /// Returns the maximum trip count of the loop if it is a single-exit
1362 /// loop and we can compute a small maximum for that loop.
1364 /// Implemented in terms of the \c getSmallConstantTripCount overload with
1365 /// the single exiting block passed to it. See that routine for details.
1366 unsigned getSmallConstantTripCount(const Loop *L);
1368 /// Returns the maximum trip count of this loop as a normal unsigned
1369 /// value. Returns 0 if the trip count is unknown or not constant. This
1370 /// "trip count" assumes that control exits via ExitingBlock. More
1371 /// precisely, it is the number of times that control may reach ExitingBlock
1372 /// before taking the branch. For loops with multiple exits, it may not be
1373 /// the number times that the loop header executes if the loop exits
1374 /// prematurely via another branch.
1375 unsigned getSmallConstantTripCount(const Loop *L, BasicBlock *ExitingBlock);
1377 /// Returns the upper bound of the loop trip count as a normal unsigned
1379 /// Returns 0 if the trip count is unknown or not constant.
1380 unsigned getSmallConstantMaxTripCount(const Loop *L);
1382 /// Returns the largest constant divisor of the trip count of the
1383 /// loop if it is a single-exit loop and we can compute a small maximum for
1386 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
1387 /// the single exiting block passed to it. See that routine for details.
1388 unsigned getSmallConstantTripMultiple(const Loop *L);
1390 /// Returns the largest constant divisor of the trip count of this loop as a
1391 /// normal unsigned value, if possible. This means that the actual trip
1392 /// count is always a multiple of the returned value (don't forget the trip
1393 /// count could very well be zero as well!). As explained in the comments
1394 /// for getSmallConstantTripCount, this assumes that control exits the loop
1395 /// via ExitingBlock.
1396 unsigned getSmallConstantTripMultiple(const Loop *L,
1397 BasicBlock *ExitingBlock);
1399 /// Get the expression for the number of loop iterations for which this loop
1400 /// is guaranteed not to exit via ExitingBlock. Otherwise return
1401 /// SCEVCouldNotCompute.
1402 const SCEV *getExitCount(const Loop *L, BasicBlock *ExitingBlock);
1404 /// If the specified loop has a predictable backedge-taken count, return it,
1405 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count is
1406 /// the number of times the loop header will be branched to from within the
1407 /// loop, assuming there are no abnormal exists like exception throws. This is
1408 /// one less than the trip count of the loop, since it doesn't count the first
1409 /// iteration, when the header is branched to from outside the loop.
1411 /// Note that it is not valid to call this method on a loop without a
1412 /// loop-invariant backedge-taken count (see
1413 /// hasLoopInvariantBackedgeTakenCount).
1415 const SCEV *getBackedgeTakenCount(const Loop *L);
1417 /// Similar to getBackedgeTakenCount, except it will add a set of
1418 /// SCEV predicates to Predicates that are required to be true in order for
1419 /// the answer to be correct. Predicates can be checked with run-time
1420 /// checks and can be used to perform loop versioning.
1421 const SCEV *getPredicatedBackedgeTakenCount(const Loop *L,
1422 SCEVUnionPredicate &Predicates);
1424 /// When successful, this returns a SCEVConstant that is greater than or equal
1425 /// to (i.e. a "conservative over-approximation") of the value returend by
1426 /// getBackedgeTakenCount. If such a value cannot be computed, it returns the
1427 /// SCEVCouldNotCompute object.
1428 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
1430 /// Return true if the backedge taken count is either the value returned by
1431 /// getMaxBackedgeTakenCount or zero.
1432 bool isBackedgeTakenCountMaxOrZero(const Loop *L);
1434 /// Return true if the specified loop has an analyzable loop-invariant
1435 /// backedge-taken count.
1436 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
1438 /// This method should be called by the client when it has changed a loop in
1439 /// a way that may effect ScalarEvolution's ability to compute a trip count,
1440 /// or if the loop is deleted. This call is potentially expensive for large
1442 void forgetLoop(const Loop *L);
1444 /// This method should be called by the client when it has changed a value
1445 /// in a way that may effect its value, or which may disconnect it from a
1446 /// def-use chain linking it to a loop.
1447 void forgetValue(Value *V);
1449 /// Called when the client has changed the disposition of values in
1452 /// We don't have a way to invalidate per-loop dispositions. Clear and
1453 /// recompute is simpler.
1454 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
1456 /// Determine the minimum number of zero bits that S is guaranteed to end in
1457 /// (at every loop iteration). It is, at the same time, the minimum number
1458 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
1459 /// If S is guaranteed to be 0, it returns the bitwidth of S.
1460 uint32_t GetMinTrailingZeros(const SCEV *S);
1462 /// Determine the unsigned range for a particular SCEV.
1463 /// NOTE: This returns a copy of the reference returned by getRangeRef.
1464 ConstantRange getUnsignedRange(const SCEV *S) {
1465 return getRangeRef(S, HINT_RANGE_UNSIGNED);
1468 /// Determine the min of the unsigned range for a particular SCEV.
1469 APInt getUnsignedRangeMin(const SCEV *S) {
1470 return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMin();
1473 /// Determine the max of the unsigned range for a particular SCEV.
1474 APInt getUnsignedRangeMax(const SCEV *S) {
1475 return getRangeRef(S, HINT_RANGE_UNSIGNED).getUnsignedMax();
1478 /// Determine the signed range for a particular SCEV.
1479 /// NOTE: This returns a copy of the reference returned by getRangeRef.
1480 ConstantRange getSignedRange(const SCEV *S) {
1481 return getRangeRef(S, HINT_RANGE_SIGNED);
1484 /// Determine the min of the signed range for a particular SCEV.
1485 APInt getSignedRangeMin(const SCEV *S) {
1486 return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMin();
1489 /// Determine the max of the signed range for a particular SCEV.
1490 APInt getSignedRangeMax(const SCEV *S) {
1491 return getRangeRef(S, HINT_RANGE_SIGNED).getSignedMax();
1494 /// Test if the given expression is known to be negative.
1496 bool isKnownNegative(const SCEV *S);
1498 /// Test if the given expression is known to be positive.
1500 bool isKnownPositive(const SCEV *S);
1502 /// Test if the given expression is known to be non-negative.
1504 bool isKnownNonNegative(const SCEV *S);
1506 /// Test if the given expression is known to be non-positive.
1508 bool isKnownNonPositive(const SCEV *S);
1510 /// Test if the given expression is known to be non-zero.
1512 bool isKnownNonZero(const SCEV *S);
1514 /// Test if the given expression is known to satisfy the condition described
1515 /// by Pred, LHS, and RHS.
1517 bool isKnownPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
1520 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
1521 /// is monotonically increasing or decreasing. In the former case set
1522 /// `Increasing` to true and in the latter case set `Increasing` to false.
1524 /// A predicate is said to be monotonically increasing if may go from being
1525 /// false to being true as the loop iterates, but never the other way
1526 /// around. A predicate is said to be monotonically decreasing if may go
1527 /// from being true to being false as the loop iterates, but never the other
1529 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS, ICmpInst::Predicate Pred,
1532 /// Return true if the result of the predicate LHS `Pred` RHS is loop
1533 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
1534 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
1535 /// loop invariant form of LHS `Pred` RHS.
1536 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
1537 const SCEV *RHS, const Loop *L,
1538 ICmpInst::Predicate &InvariantPred,
1539 const SCEV *&InvariantLHS,
1540 const SCEV *&InvariantRHS);
1542 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
1543 /// iff any changes were made. If the operands are provably equal or
1544 /// unequal, LHS and RHS are set to the same value and Pred is set to either
1545 /// ICMP_EQ or ICMP_NE.
1547 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred, const SCEV *&LHS,
1548 const SCEV *&RHS, unsigned Depth = 0);
1550 /// Return the "disposition" of the given SCEV with respect to the given
1552 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
1554 /// Return true if the value of the given SCEV is unchanging in the
1556 bool isLoopInvariant(const SCEV *S, const Loop *L);
1558 /// Determine if the SCEV can be evaluated at loop's entry. It is true if it
1559 /// doesn't depend on a SCEVUnknown of an instruction which is dominated by
1560 /// the header of loop L.
1561 bool isAvailableAtLoopEntry(const SCEV *S, const Loop *L);
1563 /// Return true if the given SCEV changes value in a known way in the
1564 /// specified loop. This property being true implies that the value is
1565 /// variant in the loop AND that we can emit an expression to compute the
1566 /// value of the expression at any particular loop iteration.
1567 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
1569 /// Return the "disposition" of the given SCEV with respect to the given
1571 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
1573 /// Return true if elements that makes up the given SCEV dominate the
1574 /// specified basic block.
1575 bool dominates(const SCEV *S, const BasicBlock *BB);
1577 /// Return true if elements that makes up the given SCEV properly dominate
1578 /// the specified basic block.
1579 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
1581 /// Test whether the given SCEV has Op as a direct or indirect operand.
1582 bool hasOperand(const SCEV *S, const SCEV *Op) const;
1584 /// Return the size of an element read or written by Inst.
1585 const SCEV *getElementSize(Instruction *Inst);
1587 /// Compute the array dimensions Sizes from the set of Terms extracted from
1588 /// the memory access function of this SCEVAddRecExpr (second step of
1589 /// delinearization).
1590 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
1591 SmallVectorImpl<const SCEV *> &Sizes,
1592 const SCEV *ElementSize);
1594 void print(raw_ostream &OS) const;
1595 void verify() const;
1596 bool invalidate(Function &F, const PreservedAnalyses &PA,
1597 FunctionAnalysisManager::Invalidator &Inv);
1599 /// Collect parametric terms occurring in step expressions (first step of
1600 /// delinearization).
1601 void collectParametricTerms(const SCEV *Expr,
1602 SmallVectorImpl<const SCEV *> &Terms);
1604 /// Return in Subscripts the access functions for each dimension in Sizes
1605 /// (third step of delinearization).
1606 void computeAccessFunctions(const SCEV *Expr,
1607 SmallVectorImpl<const SCEV *> &Subscripts,
1608 SmallVectorImpl<const SCEV *> &Sizes);
1610 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1611 /// subscripts and sizes of an array access.
1613 /// The delinearization is a 3 step process: the first two steps compute the
1614 /// sizes of each subscript and the third step computes the access functions
1615 /// for the delinearized array:
1617 /// 1. Find the terms in the step functions
1618 /// 2. Compute the array size
1619 /// 3. Compute the access function: divide the SCEV by the array size
1620 /// starting with the innermost dimensions found in step 2. The Quotient
1621 /// is the SCEV to be divided in the next step of the recursion. The
1622 /// Remainder is the subscript of the innermost dimension. Loop over all
1623 /// array dimensions computed in step 2.
1625 /// To compute a uniform array size for several memory accesses to the same
1626 /// object, one can collect in step 1 all the step terms for all the memory
1627 /// accesses, and compute in step 2 a unique array shape. This guarantees
1628 /// that the array shape will be the same across all memory accesses.
1630 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1631 /// the array shape given in metadata.
1640 /// A[j+k][2i][5i] =
1642 /// The initial SCEV:
1644 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1646 /// 1. Find the different terms in the step functions:
1647 /// -> [2*m, 5, n*m, n*m]
1649 /// 2. Compute the array size: sort and unique them
1650 /// -> [n*m, 2*m, 5]
1651 /// find the GCD of all the terms = 1
1652 /// divide by the GCD and erase constant terms
1655 /// divide by GCD -> [n, 2]
1656 /// remove constant terms
1658 /// size of the array is A[unknown][n][m]
1660 /// 3. Compute the access function
1661 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1662 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1663 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1664 /// The remainder is the subscript of the innermost array dimension: [5i].
1666 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1667 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1668 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1669 /// The Remainder is the subscript of the next array dimension: [2i].
1671 /// The subscript of the outermost dimension is the Quotient: [j+k].
1673 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1674 void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
1675 SmallVectorImpl<const SCEV *> &Sizes,
1676 const SCEV *ElementSize);
1678 /// Return the DataLayout associated with the module this SCEV instance is
1680 const DataLayout &getDataLayout() const {
1681 return F.getParent()->getDataLayout();
1684 const SCEVPredicate *getEqualPredicate(const SCEV *LHS, const SCEV *RHS);
1686 const SCEVPredicate *
1687 getWrapPredicate(const SCEVAddRecExpr *AR,
1688 SCEVWrapPredicate::IncrementWrapFlags AddedFlags);
1690 /// Re-writes the SCEV according to the Predicates in \p A.
1691 const SCEV *rewriteUsingPredicate(const SCEV *S, const Loop *L,
1692 SCEVUnionPredicate &A);
1693 /// Tries to convert the \p S expression to an AddRec expression,
1694 /// adding additional predicates to \p Preds as required.
1695 const SCEVAddRecExpr *convertSCEVToAddRecWithPredicates(
1696 const SCEV *S, const Loop *L,
1697 SmallPtrSetImpl<const SCEVPredicate *> &Preds);
1700 /// Similar to createAddRecFromPHI, but with the additional flexibility of
1701 /// suggesting runtime overflow checks in case casts are encountered.
1702 /// If successful, the analysis records that for this loop, \p SymbolicPHI,
1703 /// which is the UnknownSCEV currently representing the PHI, can be rewritten
1704 /// into an AddRec, assuming some predicates; The function then returns the
1705 /// AddRec and the predicates as a pair, and caches this pair in
1706 /// PredicatedSCEVRewrites.
1707 /// If the analysis is not successful, a mapping from the \p SymbolicPHI to
1708 /// itself (with no predicates) is recorded, and a nullptr with an empty
1709 /// predicates vector is returned as a pair.
1710 Optional<std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1711 createAddRecFromPHIWithCastsImpl(const SCEVUnknown *SymbolicPHI);
1713 /// Compute the backedge taken count knowing the interval difference, the
1714 /// stride and presence of the equality in the comparison.
1715 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1718 /// Verify if an linear IV with positive stride can overflow when in a
1719 /// less-than comparison, knowing the invariant term of the comparison,
1720 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1721 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1724 /// Verify if an linear IV with negative stride can overflow when in a
1725 /// greater-than comparison, knowing the invariant term of the comparison,
1726 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1727 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride, bool IsSigned,
1730 /// Get add expr already created or create a new one.
1731 const SCEV *getOrCreateAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1732 SCEV::NoWrapFlags Flags);
1734 /// Get mul expr already created or create a new one.
1735 const SCEV *getOrCreateMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1736 SCEV::NoWrapFlags Flags);
1739 FoldingSet<SCEV> UniqueSCEVs;
1740 FoldingSet<SCEVPredicate> UniquePreds;
1741 BumpPtrAllocator SCEVAllocator;
1743 /// Cache tentative mappings from UnknownSCEVs in a Loop, to a SCEV expression
1744 /// they can be rewritten into under certain predicates.
1745 DenseMap<std::pair<const SCEVUnknown *, const Loop *>,
1746 std::pair<const SCEV *, SmallVector<const SCEVPredicate *, 3>>>
1747 PredicatedSCEVRewrites;
1749 /// The head of a linked list of all SCEVUnknown values that have been
1750 /// allocated. This is used by releaseMemory to locate them all and call
1751 /// their destructors.
1752 SCEVUnknown *FirstUnknown;
1755 /// Analysis pass that exposes the \c ScalarEvolution for a function.
1756 class ScalarEvolutionAnalysis
1757 : public AnalysisInfoMixin<ScalarEvolutionAnalysis> {
1758 friend AnalysisInfoMixin<ScalarEvolutionAnalysis>;
1759 static AnalysisKey Key;
1762 typedef ScalarEvolution Result;
1764 ScalarEvolution run(Function &F, FunctionAnalysisManager &AM);
1767 /// Printer pass for the \c ScalarEvolutionAnalysis results.
1768 class ScalarEvolutionPrinterPass
1769 : public PassInfoMixin<ScalarEvolutionPrinterPass> {
1773 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1774 PreservedAnalyses run(Function &F, FunctionAnalysisManager &AM);
1777 class ScalarEvolutionWrapperPass : public FunctionPass {
1778 std::unique_ptr<ScalarEvolution> SE;
1783 ScalarEvolutionWrapperPass();
1785 ScalarEvolution &getSE() { return *SE; }
1786 const ScalarEvolution &getSE() const { return *SE; }
1788 bool runOnFunction(Function &F) override;
1789 void releaseMemory() override;
1790 void getAnalysisUsage(AnalysisUsage &AU) const override;
1791 void print(raw_ostream &OS, const Module * = nullptr) const override;
1792 void verifyAnalysis() const override;
1795 /// An interface layer with SCEV used to manage how we see SCEV expressions
1796 /// for values in the context of existing predicates. We can add new
1797 /// predicates, but we cannot remove them.
1799 /// This layer has multiple purposes:
1800 /// - provides a simple interface for SCEV versioning.
1801 /// - guarantees that the order of transformations applied on a SCEV
1802 /// expression for a single Value is consistent across two different
1803 /// getSCEV calls. This means that, for example, once we've obtained
1804 /// an AddRec expression for a certain value through expression
1805 /// rewriting, we will continue to get an AddRec expression for that
1807 /// - lowers the number of expression rewrites.
1808 class PredicatedScalarEvolution {
1810 PredicatedScalarEvolution(ScalarEvolution &SE, Loop &L);
1811 const SCEVUnionPredicate &getUnionPredicate() const;
1813 /// Returns the SCEV expression of V, in the context of the current SCEV
1814 /// predicate. The order of transformations applied on the expression of V
1815 /// returned by ScalarEvolution is guaranteed to be preserved, even when
1816 /// adding new predicates.
1817 const SCEV *getSCEV(Value *V);
1819 /// Get the (predicated) backedge count for the analyzed loop.
1820 const SCEV *getBackedgeTakenCount();
1822 /// Adds a new predicate.
1823 void addPredicate(const SCEVPredicate &Pred);
1825 /// Attempts to produce an AddRecExpr for V by adding additional SCEV
1826 /// predicates. If we can't transform the expression into an AddRecExpr we
1827 /// return nullptr and not add additional SCEV predicates to the current
1829 const SCEVAddRecExpr *getAsAddRec(Value *V);
1831 /// Proves that V doesn't overflow by adding SCEV predicate.
1832 void setNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1834 /// Returns true if we've proved that V doesn't wrap by means of a SCEV
1836 bool hasNoOverflow(Value *V, SCEVWrapPredicate::IncrementWrapFlags Flags);
1838 /// Returns the ScalarEvolution analysis used.
1839 ScalarEvolution *getSE() const { return &SE; }
1841 /// We need to explicitly define the copy constructor because of FlagsMap.
1842 PredicatedScalarEvolution(const PredicatedScalarEvolution &);
1844 /// Print the SCEV mappings done by the Predicated Scalar Evolution.
1845 /// The printed text is indented by \p Depth.
1846 void print(raw_ostream &OS, unsigned Depth) const;
1849 /// Increments the version number of the predicate. This needs to be called
1850 /// every time the SCEV predicate changes.
1851 void updateGeneration();
1853 /// Holds a SCEV and the version number of the SCEV predicate used to
1854 /// perform the rewrite of the expression.
1855 typedef std::pair<unsigned, const SCEV *> RewriteEntry;
1857 /// Maps a SCEV to the rewrite result of that SCEV at a certain version
1858 /// number. If this number doesn't match the current Generation, we will
1859 /// need to do a rewrite. To preserve the transformation order of previous
1860 /// rewrites, we will rewrite the previous result instead of the original
1862 DenseMap<const SCEV *, RewriteEntry> RewriteMap;
1864 /// Records what NoWrap flags we've added to a Value *.
1865 ValueMap<Value *, SCEVWrapPredicate::IncrementWrapFlags> FlagsMap;
1867 /// The ScalarEvolution analysis.
1868 ScalarEvolution &SE;
1870 /// The analyzed Loop.
1873 /// The SCEVPredicate that forms our context. We will rewrite all
1874 /// expressions assuming that this predicate true.
1875 SCEVUnionPredicate Preds;
1877 /// Marks the version of the SCEV predicate used. When rewriting a SCEV
1878 /// expression we mark it with the version of the predicate. We use this to
1879 /// figure out if the predicate has changed from the last rewrite of the
1880 /// SCEV. If so, we need to perform a new rewrite.
1881 unsigned Generation;
1883 /// The backedge taken count.
1884 const SCEV *BackedgeCount;