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/Analysis/LoopInfo.h"
27 #include "llvm/IR/ConstantRange.h"
28 #include "llvm/IR/Function.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/Pass.h"
34 #include "llvm/Support/Allocator.h"
35 #include "llvm/Support/DataTypes.h"
40 class AssumptionCache;
45 class ScalarEvolution;
47 class TargetLibraryInfo;
57 template <> struct FoldingSetTrait<SCEV>;
58 template <> struct FoldingSetTrait<SCEVPredicate>;
60 /// This class represents an analyzed expression in the program. These are
61 /// opaque objects that the client is not allowed to do much with directly.
63 class SCEV : public FoldingSetNode {
64 friend struct FoldingSetTrait<SCEV>;
66 /// A reference to an Interned FoldingSetNodeID for this node. The
67 /// ScalarEvolution's BumpPtrAllocator holds the data.
68 FoldingSetNodeIDRef FastID;
70 // The SCEV baseclass this node corresponds to
71 const unsigned short SCEVType;
74 /// This field is initialized to zero and may be used in subclasses to store
75 /// miscellaneous information.
76 unsigned short SubclassData;
79 SCEV(const SCEV &) = delete;
80 void operator=(const SCEV &) = delete;
83 /// NoWrapFlags are bitfield indices into SubclassData.
85 /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
86 /// no-signed-wrap <NSW> properties, which are derived from the IR
87 /// operator. NSW is a misnomer that we use to mean no signed overflow or
90 /// AddRec expressions may have a no-self-wraparound <NW> property if, in
91 /// the integer domain, abs(step) * max-iteration(loop) <=
92 /// unsigned-max(bitwidth). This means that the recurrence will never reach
93 /// its start value if the step is non-zero. Computing the same value on
94 /// each iteration is not considered wrapping, and recurrences with step = 0
95 /// are trivially <NW>. <NW> is independent of the sign of step and the
96 /// value the add recurrence starts with.
98 /// Note that NUW and NSW are also valid properties of a recurrence, and
99 /// either implies NW. For convenience, NW will be set for a recurrence
100 /// whenever either NUW or NSW are set.
101 enum NoWrapFlags { FlagAnyWrap = 0, // No guarantee.
102 FlagNW = (1 << 0), // No self-wrap.
103 FlagNUW = (1 << 1), // No unsigned wrap.
104 FlagNSW = (1 << 2), // No signed wrap.
105 NoWrapMask = (1 << 3) -1 };
107 explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy) :
108 FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
110 unsigned getSCEVType() const { return SCEVType; }
112 /// Return the LLVM type of this SCEV expression.
114 Type *getType() const;
116 /// Return true if the expression is a constant zero.
120 /// Return true if the expression is a constant one.
124 /// Return true if the expression is a constant all-ones value.
126 bool isAllOnesValue() const;
128 /// Return true if the specified scev is negated, but not a constant.
129 bool isNonConstantNegative() const;
131 /// Print out the internal representation of this scalar to the specified
132 /// stream. This should really only be used for debugging purposes.
133 void print(raw_ostream &OS) const;
135 /// This method is used for debugging.
140 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
141 // temporary FoldingSetNodeID values.
142 template<> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
143 static void Profile(const SCEV &X, FoldingSetNodeID& ID) {
146 static bool Equals(const SCEV &X, const FoldingSetNodeID &ID,
147 unsigned IDHash, FoldingSetNodeID &TempID) {
148 return ID == X.FastID;
150 static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
151 return X.FastID.ComputeHash();
155 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
160 /// An object of this class is returned by queries that could not be answered.
161 /// For example, if you ask for the number of iterations of a linked-list
162 /// traversal loop, you will get one of these. None of the standard SCEV
163 /// operations are valid on this class, it is just a marker.
164 struct SCEVCouldNotCompute : public SCEV {
165 SCEVCouldNotCompute();
167 /// Methods for support type inquiry through isa, cast, and dyn_cast:
168 static bool classof(const SCEV *S);
171 /// SCEVPredicate - This class represents an assumption made using SCEV
172 /// expressions which can be checked at run-time.
173 class SCEVPredicate : public FoldingSetNode {
174 friend struct FoldingSetTrait<SCEVPredicate>;
176 /// A reference to an Interned FoldingSetNodeID for this node. The
177 /// ScalarEvolution's BumpPtrAllocator holds the data.
178 FoldingSetNodeIDRef FastID;
181 enum SCEVPredicateKind { P_Union, P_Equal };
184 SCEVPredicateKind Kind;
185 ~SCEVPredicate() = default;
186 SCEVPredicate(const SCEVPredicate&) = default;
187 SCEVPredicate &operator=(const SCEVPredicate&) = default;
190 SCEVPredicate(const FoldingSetNodeIDRef ID, SCEVPredicateKind Kind);
192 SCEVPredicateKind getKind() const { return Kind; }
194 /// \brief Returns the estimated complexity of this predicate.
195 /// This is roughly measured in the number of run-time checks required.
196 virtual unsigned getComplexity() const { return 1; }
198 /// \brief Returns true if the predicate is always true. This means that no
199 /// assumptions were made and nothing needs to be checked at run-time.
200 virtual bool isAlwaysTrue() const = 0;
202 /// \brief Returns true if this predicate implies \p N.
203 virtual bool implies(const SCEVPredicate *N) const = 0;
205 /// \brief Prints a textual representation of this predicate with an
206 /// indentation of \p Depth.
207 virtual void print(raw_ostream &OS, unsigned Depth = 0) const = 0;
209 /// \brief Returns the SCEV to which this predicate applies, or nullptr
210 /// if this is a SCEVUnionPredicate.
211 virtual const SCEV *getExpr() const = 0;
214 inline raw_ostream &operator<<(raw_ostream &OS, const SCEVPredicate &P) {
219 // Specialize FoldingSetTrait for SCEVPredicate to avoid needing to compute
220 // temporary FoldingSetNodeID values.
222 struct FoldingSetTrait<SCEVPredicate>
223 : 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 /// SCEVEqualPredicate - This class represents an assumption that two SCEV
240 /// expressions are equal, and this can be checked at run-time. We assume
241 /// that the left hand side is a SCEVUnknown and the right hand side a
243 class SCEVEqualPredicate final : public SCEVPredicate {
244 /// We assume that LHS == RHS, where LHS is a SCEVUnknown and RHS a
246 const SCEVUnknown *LHS;
247 const SCEVConstant *RHS;
250 SCEVEqualPredicate(const FoldingSetNodeIDRef ID, const SCEVUnknown *LHS,
251 const SCEVConstant *RHS);
253 /// Implementation of the SCEVPredicate interface
254 bool implies(const SCEVPredicate *N) const override;
255 void print(raw_ostream &OS, unsigned Depth = 0) const override;
256 bool isAlwaysTrue() const override;
257 const SCEV *getExpr() const override;
259 /// \brief Returns the left hand side of the equality.
260 const SCEVUnknown *getLHS() const { return LHS; }
262 /// \brief Returns the right hand side of the equality.
263 const SCEVConstant *getRHS() const { return RHS; }
265 /// Methods for support type inquiry through isa, cast, and dyn_cast:
266 static inline bool classof(const SCEVPredicate *P) {
267 return P->getKind() == P_Equal;
271 /// SCEVUnionPredicate - This class represents a composition of other
272 /// SCEV predicates, and is the class that most clients will interact with.
273 /// This is equivalent to a logical "AND" of all the predicates in the union.
274 class SCEVUnionPredicate final : public SCEVPredicate {
276 typedef DenseMap<const SCEV *, SmallVector<const SCEVPredicate *, 4>>
279 /// Vector with references to all predicates in this union.
280 SmallVector<const SCEVPredicate *, 16> Preds;
281 /// Maps SCEVs to predicates for quick look-ups.
282 PredicateMap SCEVToPreds;
285 SCEVUnionPredicate();
287 const SmallVectorImpl<const SCEVPredicate *> &getPredicates() const {
291 /// \brief Adds a predicate to this union.
292 void add(const SCEVPredicate *N);
294 /// \brief Returns a reference to a vector containing all predicates
295 /// which apply to \p Expr.
296 ArrayRef<const SCEVPredicate *> getPredicatesForExpr(const SCEV *Expr);
298 /// Implementation of the SCEVPredicate interface
299 bool isAlwaysTrue() const override;
300 bool implies(const SCEVPredicate *N) const override;
301 void print(raw_ostream &OS, unsigned Depth) const override;
302 const SCEV *getExpr() const override;
304 /// \brief We estimate the complexity of a union predicate as the size
305 /// number of predicates in the union.
306 unsigned getComplexity() const override { return Preds.size(); }
308 /// Methods for support type inquiry through isa, cast, and dyn_cast:
309 static inline bool classof(const SCEVPredicate *P) {
310 return P->getKind() == P_Union;
314 /// The main scalar evolution driver. Because client code (intentionally)
315 /// can't do much with the SCEV objects directly, they must ask this class
317 class ScalarEvolution {
319 /// An enum describing the relationship between a SCEV and a loop.
320 enum LoopDisposition {
321 LoopVariant, ///< The SCEV is loop-variant (unknown).
322 LoopInvariant, ///< The SCEV is loop-invariant.
323 LoopComputable ///< The SCEV varies predictably with the loop.
326 /// An enum describing the relationship between a SCEV and a basic block.
327 enum BlockDisposition {
328 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
329 DominatesBlock, ///< The SCEV dominates the block.
330 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
333 /// Convenient NoWrapFlags manipulation that hides enum casts and is
334 /// visible in the ScalarEvolution name space.
335 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
336 maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
337 return (SCEV::NoWrapFlags)(Flags & Mask);
339 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
340 setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
341 return (SCEV::NoWrapFlags)(Flags | OnFlags);
343 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
344 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
345 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
349 /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
350 /// Value is deleted.
351 class SCEVCallbackVH final : public CallbackVH {
353 void deleted() override;
354 void allUsesReplacedWith(Value *New) override;
356 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
359 friend class SCEVCallbackVH;
360 friend class SCEVExpander;
361 friend class SCEVUnknown;
363 /// The function we are analyzing.
367 /// The target library information for the target we are targeting.
369 TargetLibraryInfo &TLI;
371 /// The tracker for @llvm.assume intrinsics in this function.
374 /// The dominator tree.
378 /// The loop information for the function we are currently analyzing.
382 /// This SCEV is used to represent unknown trip counts and things.
383 std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
385 /// The typedef for ValueExprMap.
387 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
390 /// This is a cache of the values we have analyzed so far.
392 ValueExprMapType ValueExprMap;
394 /// Mark predicate values currently being processed by isImpliedCond.
395 DenseSet<Value*> PendingLoopPredicates;
397 /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
398 /// conditions dominating the backedge of a loop.
399 bool WalkingBEDominatingConds;
401 /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
402 /// predicate by splitting it into a set of independent predicates.
403 bool ProvingSplitPredicate;
405 /// Information about the number of loop iterations for which a loop exit's
406 /// branch condition evaluates to the not-taken path. This is a temporary
407 /// pair of exact and max expressions that are eventually summarized in
408 /// ExitNotTakenInfo and BackedgeTakenInfo.
413 /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
415 ExitLimit(const SCEV *E, const SCEV *M) : Exact(E), Max(M) {}
417 /// Test whether this ExitLimit contains any computed information, or
418 /// whether it's all SCEVCouldNotCompute values.
419 bool hasAnyInfo() const {
420 return !isa<SCEVCouldNotCompute>(Exact) ||
421 !isa<SCEVCouldNotCompute>(Max);
425 /// Information about the number of times a particular loop exit may be
426 /// reached before exiting the loop.
427 struct ExitNotTakenInfo {
428 AssertingVH<BasicBlock> ExitingBlock;
429 const SCEV *ExactNotTaken;
430 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
432 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
434 /// Return true if all loop exits are computable.
435 bool isCompleteList() const {
436 return NextExit.getInt() == 0;
439 void setIncomplete() { NextExit.setInt(1); }
441 /// Return a pointer to the next exit's not-taken info.
442 ExitNotTakenInfo *getNextExit() const {
443 return NextExit.getPointer();
446 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
449 /// Information about the backedge-taken count of a loop. This currently
450 /// includes an exact count and a maximum count.
452 class BackedgeTakenInfo {
453 /// A list of computable exits and their not-taken counts. Loops almost
454 /// never have more than one computable exit.
455 ExitNotTakenInfo ExitNotTaken;
457 /// An expression indicating the least maximum backedge-taken count of the
458 /// loop that is known, or a SCEVCouldNotCompute.
462 BackedgeTakenInfo() : Max(nullptr) {}
464 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
466 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
467 bool Complete, const SCEV *MaxCount);
469 /// Test whether this BackedgeTakenInfo contains any computed information,
470 /// or whether it's all SCEVCouldNotCompute values.
471 bool hasAnyInfo() const {
472 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
475 /// Return an expression indicating the exact backedge-taken count of the
476 /// loop if it is known, or SCEVCouldNotCompute otherwise. This is the
477 /// number of times the loop header can be guaranteed to execute, minus
479 const SCEV *getExact(ScalarEvolution *SE) const;
481 /// Return the number of times this loop exit may fall through to the back
482 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
483 /// this block before this number of iterations, but may exit via another
485 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
487 /// Get the max backedge taken count for the loop.
488 const SCEV *getMax(ScalarEvolution *SE) const;
490 /// Return true if any backedge taken count expressions refer to the given
492 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
494 /// Invalidate this result and free associated memory.
498 /// Cache the backedge-taken count of the loops for this function as they
500 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
502 /// This map contains entries for all of the PHI instructions that we
503 /// attempt to compute constant evolutions for. This allows us to avoid
504 /// potentially expensive recomputation of these properties. An instruction
505 /// maps to null if we are unable to compute its exit value.
506 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
508 /// This map contains entries for all the expressions that we attempt to
509 /// compute getSCEVAtScope information for, which can be expensive in
511 DenseMap<const SCEV *,
512 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
514 /// Memoized computeLoopDisposition results.
515 DenseMap<const SCEV *,
516 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
519 /// Compute a LoopDisposition value.
520 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
522 /// Memoized computeBlockDisposition results.
525 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
528 /// Compute a BlockDisposition value.
529 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
531 /// Memoized results from getRange
532 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
534 /// Memoized results from getRange
535 DenseMap<const SCEV *, ConstantRange> SignedRanges;
537 /// Used to parameterize getRange
538 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
540 /// Set the memoized range for the given SCEV.
541 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
542 const ConstantRange &CR) {
543 DenseMap<const SCEV *, ConstantRange> &Cache =
544 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
546 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
547 Cache.insert(std::make_pair(S, CR));
549 Pair.first->second = CR;
550 return Pair.first->second;
553 /// Determine the range for a particular SCEV.
554 ConstantRange getRange(const SCEV *S, RangeSignHint Hint);
556 /// We know that there is no SCEV for the specified value. Analyze the
558 const SCEV *createSCEV(Value *V);
560 /// Provide the special handling we need to analyze PHI SCEVs.
561 const SCEV *createNodeForPHI(PHINode *PN);
563 /// Helper function called from createNodeForPHI.
564 const SCEV *createAddRecFromPHI(PHINode *PN);
566 /// Helper function called from createNodeForPHI.
567 const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
569 /// Provide special handling for a select-like instruction (currently this
570 /// is either a select instruction or a phi node). \p I is the instruction
571 /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
573 const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
574 Value *TrueVal, Value *FalseVal);
576 /// Provide the special handling we need to analyze GEP SCEVs.
577 const SCEV *createNodeForGEP(GEPOperator *GEP);
579 /// Implementation code for getSCEVAtScope; called at most once for each
582 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
584 /// This looks up computed SCEV values for all instructions that depend on
585 /// the given instruction and removes them from the ValueExprMap map if they
586 /// reference SymName. This is used during PHI resolution.
587 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
589 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
590 /// values if the loop hasn't been analyzed yet.
591 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
593 /// Compute the number of times the specified loop will iterate.
594 BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L);
596 /// Compute the number of times the backedge of the specified loop will
597 /// execute if it exits via the specified block.
598 ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
600 /// Compute the number of times the backedge of the specified loop will
601 /// execute if its exit condition were a conditional branch of ExitCond,
603 ExitLimit computeExitLimitFromCond(const Loop *L,
609 /// Compute the number of times the backedge of the specified loop will
610 /// execute if its exit condition were a conditional branch of the ICmpInst
611 /// ExitCond, TBB, and FBB.
612 ExitLimit computeExitLimitFromICmp(const Loop *L,
618 /// Compute the number of times the backedge of the specified loop will
619 /// execute if its exit condition were a switch with a single exiting case
622 computeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
623 BasicBlock *ExitingBB, bool IsSubExpr);
625 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
626 /// compute the backedge-taken count.
627 ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI,
630 ICmpInst::Predicate p);
632 /// Compute the exit limit of a loop that is controlled by a
633 /// "(IV >> 1) != 0" type comparison. We cannot compute the exact trip
634 /// count in these cases (since SCEV has no way of expressing them), but we
635 /// can still sometimes compute an upper bound.
637 /// Return an ExitLimit for a loop whose backedge is guarded by `LHS Pred
639 ExitLimit computeShiftCompareExitLimit(Value *LHS, Value *RHS,
641 ICmpInst::Predicate Pred);
643 /// If the loop is known to execute a constant number of times (the
644 /// condition evolves only from constants), try to evaluate a few iterations
645 /// of the loop until we get the exit condition gets a value of ExitWhen
646 /// (true or false). If we cannot evaluate the exit count of the loop,
647 /// return CouldNotCompute.
648 const SCEV *computeExitCountExhaustively(const Loop *L,
652 /// Return the number of times an exit condition comparing the specified
653 /// value to zero will execute. If not computable, return CouldNotCompute.
654 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
656 /// Return the number of times an exit condition checking the specified
657 /// value for nonzero will execute. If not computable, return
659 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
661 /// Return the number of times an exit condition containing the specified
662 /// less-than comparison will execute. If not computable, return
663 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
664 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
665 const Loop *L, bool isSigned, bool IsSubExpr);
666 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
667 const Loop *L, bool isSigned, bool IsSubExpr);
669 /// Return a predecessor of BB (which may not be an immediate predecessor)
670 /// which has exactly one successor from which BB is reachable, or null if
671 /// no such block is found.
672 std::pair<BasicBlock *, BasicBlock *>
673 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
675 /// Test whether the condition described by Pred, LHS, and RHS is true
676 /// whenever the given FoundCondValue value evaluates to true.
677 bool isImpliedCond(ICmpInst::Predicate Pred,
678 const SCEV *LHS, const SCEV *RHS,
679 Value *FoundCondValue,
682 /// Test whether the condition described by Pred, LHS, and RHS is true
683 /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
685 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
686 const SCEV *RHS, ICmpInst::Predicate FoundPred,
687 const SCEV *FoundLHS, const SCEV *FoundRHS);
689 /// Test whether the condition described by Pred, LHS, and RHS is true
690 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
692 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
693 const SCEV *LHS, const SCEV *RHS,
694 const SCEV *FoundLHS, const SCEV *FoundRHS);
696 /// Test whether the condition described by Pred, LHS, and RHS is true
697 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
699 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
700 const SCEV *LHS, const SCEV *RHS,
701 const SCEV *FoundLHS,
702 const SCEV *FoundRHS);
704 /// Test whether the condition described by Pred, LHS, and RHS is true
705 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
706 /// true. Utility function used by isImpliedCondOperands.
707 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
708 const SCEV *LHS, const SCEV *RHS,
709 const SCEV *FoundLHS,
710 const SCEV *FoundRHS);
712 /// Test whether the condition described by Pred, LHS, and RHS is true
713 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
716 /// This routine tries to rule out certain kinds of integer overflow, and
717 /// then tries to reason about arithmetic properties of the predicates.
718 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
719 const SCEV *LHS, const SCEV *RHS,
720 const SCEV *FoundLHS,
721 const SCEV *FoundRHS);
723 /// If we know that the specified Phi is in the header of its containing
724 /// loop, we know the loop executes a constant number of times, and the PHI
725 /// node is just a recurrence involving constants, fold it.
726 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
729 /// Test if the given expression is known to satisfy the condition described
730 /// by Pred and the known constant ranges of LHS and RHS.
732 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
733 const SCEV *LHS, const SCEV *RHS);
735 /// Try to prove the condition described by "LHS Pred RHS" by ruling out
736 /// integer overflow.
738 /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
740 bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
741 const SCEV *LHS, const SCEV *RHS);
743 /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
744 /// prove them individually.
745 bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
748 /// Try to match the Expr as "(L + R)<Flags>".
749 bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
750 SCEV::NoWrapFlags &Flags);
752 /// Return true if More == (Less + C), where C is a constant. This is
753 /// intended to be used as a cheaper substitute for full SCEV subtraction.
754 bool computeConstantDifference(const SCEV *Less, const SCEV *More,
757 /// Drop memoized information computed for S.
758 void forgetMemoizedResults(const SCEV *S);
760 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
761 const SCEV *getExistingSCEV(Value *V);
763 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
765 bool checkValidity(const SCEV *S) const;
767 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
768 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
769 /// equivalent to proving no signed (resp. unsigned) wrap in
770 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
771 /// (resp. `SCEVZeroExtendExpr`).
773 template<typename ExtendOpTy>
774 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
777 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
778 ICmpInst::Predicate Pred, bool &Increasing);
780 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
781 /// is monotonically increasing or decreasing. In the former case set
782 /// `Increasing` to true and in the latter case set `Increasing` to false.
784 /// A predicate is said to be monotonically increasing if may go from being
785 /// false to being true as the loop iterates, but never the other way
786 /// around. A predicate is said to be monotonically decreasing if may go
787 /// from being true to being false as the loop iterates, but never the other
789 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS,
790 ICmpInst::Predicate Pred, bool &Increasing);
792 // Return SCEV no-wrap flags that can be proven based on reasoning
793 // about how poison produced from no-wrap flags on this value
794 // (e.g. a nuw add) would trigger undefined behavior on overflow.
795 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
798 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
799 DominatorTree &DT, LoopInfo &LI);
801 ScalarEvolution(ScalarEvolution &&Arg);
803 LLVMContext &getContext() const { return F.getContext(); }
805 /// Test if values of the given type are analyzable within the SCEV
806 /// framework. This primarily includes integer types, and it can optionally
807 /// include pointer types if the ScalarEvolution class has access to
808 /// target-specific information.
809 bool isSCEVable(Type *Ty) const;
811 /// Return the size in bits of the specified type, for which isSCEVable must
813 uint64_t getTypeSizeInBits(Type *Ty) const;
815 /// Return a type with the same bitwidth as the given type and which
816 /// represents how SCEV will treat the given type, for which isSCEVable must
817 /// return true. For pointer types, this is the pointer-sized integer type.
818 Type *getEffectiveSCEVType(Type *Ty) const;
820 /// Return a SCEV expression for the full generality of the specified
822 const SCEV *getSCEV(Value *V);
824 const SCEV *getConstant(ConstantInt *V);
825 const SCEV *getConstant(const APInt& Val);
826 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
827 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
828 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
829 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
830 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
831 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
832 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
833 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
834 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
835 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
836 return getAddExpr(Ops, Flags);
838 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
839 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
840 SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
841 return getAddExpr(Ops, Flags);
843 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
844 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
845 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
846 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
847 SmallVector<const SCEV *, 2> Ops = {LHS, RHS};
848 return getMulExpr(Ops, Flags);
850 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
851 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
852 SmallVector<const SCEV *, 3> Ops = {Op0, Op1, Op2};
853 return getMulExpr(Ops, Flags);
855 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
856 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
857 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
858 const Loop *L, SCEV::NoWrapFlags Flags);
859 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
860 const Loop *L, SCEV::NoWrapFlags Flags);
861 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
862 const Loop *L, SCEV::NoWrapFlags Flags) {
863 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
864 return getAddRecExpr(NewOp, L, Flags);
866 /// \brief Returns an expression for a GEP
868 /// \p PointeeType The type used as the basis for the pointer arithmetics
869 /// \p BaseExpr The expression for the pointer operand.
870 /// \p IndexExprs The expressions for the indices.
871 /// \p InBounds Whether the GEP is in bounds.
872 const SCEV *getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
873 const SmallVectorImpl<const SCEV *> &IndexExprs,
874 bool InBounds = false);
875 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
876 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
877 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
878 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
879 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
880 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
881 const SCEV *getUnknown(Value *V);
882 const SCEV *getCouldNotCompute();
884 /// \brief Return a SCEV for the constant 0 of a specific type.
885 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
887 /// \brief Return a SCEV for the constant 1 of a specific type.
888 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
890 /// Return an expression for sizeof AllocTy that is type IntTy
892 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
894 /// Return an expression for offsetof on the given field with type IntTy
896 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
898 /// Return the SCEV object corresponding to -V.
900 const SCEV *getNegativeSCEV(const SCEV *V,
901 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
903 /// Return the SCEV object corresponding to ~V.
905 const SCEV *getNotSCEV(const SCEV *V);
907 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
908 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
909 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
911 /// Return a SCEV corresponding to a conversion of the input value to the
912 /// specified type. If the type must be extended, it is zero extended.
913 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
915 /// Return a SCEV corresponding to a conversion of the input value to the
916 /// specified type. If the type must be extended, it is sign extended.
917 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
919 /// Return a SCEV corresponding to a conversion of the input value to the
920 /// specified type. If the type must be extended, it is zero extended. The
921 /// conversion must not be narrowing.
922 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
924 /// Return a SCEV corresponding to a conversion of the input value to the
925 /// specified type. If the type must be extended, it is sign extended. The
926 /// conversion must not be narrowing.
927 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
929 /// Return a SCEV corresponding to a conversion of the input value to the
930 /// specified type. If the type must be extended, it is extended with
931 /// unspecified bits. The conversion must not be narrowing.
932 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
934 /// Return a SCEV corresponding to a conversion of the input value to the
935 /// specified type. The conversion must not be widening.
936 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
938 /// Promote the operands to the wider of the types using zero-extension, and
939 /// then perform a umax operation with them.
940 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
943 /// Promote the operands to the wider of the types using zero-extension, and
944 /// then perform a umin operation with them.
945 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
948 /// Transitively follow the chain of pointer-type operands until reaching a
949 /// SCEV that does not have a single pointer operand. This returns a
950 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
952 const SCEV *getPointerBase(const SCEV *V);
954 /// Return a SCEV expression for the specified value at the specified scope
955 /// in the program. The L value specifies a loop nest to evaluate the
956 /// expression at, where null is the top-level or a specified loop is
957 /// immediately inside of the loop.
959 /// This method can be used to compute the exit value for a variable defined
960 /// in a loop by querying what the value will hold in the parent loop.
962 /// In the case that a relevant loop exit value cannot be computed, the
963 /// original value V is returned.
964 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
966 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
967 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
969 /// Test whether entry to the loop is protected by a conditional between LHS
970 /// and RHS. This is used to help avoid max expressions in loop trip
971 /// counts, and to eliminate casts.
972 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
973 const SCEV *LHS, const SCEV *RHS);
975 /// Test whether the backedge of the loop is protected by a conditional
976 /// between LHS and RHS. This is used to to eliminate casts.
977 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
978 const SCEV *LHS, const SCEV *RHS);
980 /// \brief Returns the maximum trip count of the loop if it is a single-exit
981 /// loop and we can compute a small maximum for that loop.
983 /// Implemented in terms of the \c getSmallConstantTripCount overload with
984 /// the single exiting block passed to it. See that routine for details.
985 unsigned getSmallConstantTripCount(Loop *L);
987 /// Returns the maximum trip count of this loop as a normal unsigned
988 /// value. Returns 0 if the trip count is unknown or not constant. This
989 /// "trip count" assumes that control exits via ExitingBlock. More
990 /// precisely, it is the number of times that control may reach ExitingBlock
991 /// before taking the branch. For loops with multiple exits, it may not be
992 /// the number times that the loop header executes if the loop exits
993 /// prematurely via another branch.
994 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
996 /// \brief Returns the largest constant divisor of the trip count of the
997 /// loop if it is a single-exit loop and we can compute a small maximum for
1000 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
1001 /// the single exiting block passed to it. See that routine for details.
1002 unsigned getSmallConstantTripMultiple(Loop *L);
1004 /// Returns the largest constant divisor of the trip count of this loop as a
1005 /// normal unsigned value, if possible. This means that the actual trip
1006 /// count is always a multiple of the returned value (don't forget the trip
1007 /// count could very well be zero as well!). As explained in the comments
1008 /// for getSmallConstantTripCount, this assumes that control exits the loop
1009 /// via ExitingBlock.
1010 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
1012 /// Get the expression for the number of loop iterations for which this loop
1013 /// is guaranteed not to exit via ExitingBlock. Otherwise return
1014 /// SCEVCouldNotCompute.
1015 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
1017 /// If the specified loop has a predictable backedge-taken count, return it,
1018 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
1019 /// is the number of times the loop header will be branched to from within
1020 /// the loop. This is one less than the trip count of the loop, since it
1021 /// doesn't count the first iteration, when the header is branched to from
1022 /// outside the loop.
1024 /// Note that it is not valid to call this method on a loop without a
1025 /// loop-invariant backedge-taken count (see
1026 /// hasLoopInvariantBackedgeTakenCount).
1028 const SCEV *getBackedgeTakenCount(const Loop *L);
1030 /// Similar to getBackedgeTakenCount, except return the least SCEV value
1031 /// that is known never to be less than the actual backedge taken count.
1032 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
1034 /// Return true if the specified loop has an analyzable loop-invariant
1035 /// backedge-taken count.
1036 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
1038 /// This method should be called by the client when it has changed a loop in
1039 /// a way that may effect ScalarEvolution's ability to compute a trip count,
1040 /// or if the loop is deleted. This call is potentially expensive for large
1042 void forgetLoop(const Loop *L);
1044 /// This method should be called by the client when it has changed a value
1045 /// in a way that may effect its value, or which may disconnect it from a
1046 /// def-use chain linking it to a loop.
1047 void forgetValue(Value *V);
1049 /// \brief Called when the client has changed the disposition of values in
1052 /// We don't have a way to invalidate per-loop dispositions. Clear and
1053 /// recompute is simpler.
1054 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
1056 /// Determine the minimum number of zero bits that S is guaranteed to end in
1057 /// (at every loop iteration). It is, at the same time, the minimum number
1058 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
1059 /// If S is guaranteed to be 0, it returns the bitwidth of S.
1060 uint32_t GetMinTrailingZeros(const SCEV *S);
1062 /// Determine the unsigned range for a particular SCEV.
1064 ConstantRange getUnsignedRange(const SCEV *S) {
1065 return getRange(S, HINT_RANGE_UNSIGNED);
1068 /// Determine the signed range for a particular SCEV.
1070 ConstantRange getSignedRange(const SCEV *S) {
1071 return getRange(S, HINT_RANGE_SIGNED);
1074 /// Test if the given expression is known to be negative.
1076 bool isKnownNegative(const SCEV *S);
1078 /// Test if the given expression is known to be positive.
1080 bool isKnownPositive(const SCEV *S);
1082 /// Test if the given expression is known to be non-negative.
1084 bool isKnownNonNegative(const SCEV *S);
1086 /// Test if the given expression is known to be non-positive.
1088 bool isKnownNonPositive(const SCEV *S);
1090 /// Test if the given expression is known to be non-zero.
1092 bool isKnownNonZero(const SCEV *S);
1094 /// Test if the given expression is known to satisfy the condition described
1095 /// by Pred, LHS, and RHS.
1097 bool isKnownPredicate(ICmpInst::Predicate Pred,
1098 const SCEV *LHS, const SCEV *RHS);
1100 /// Return true if the result of the predicate LHS `Pred` RHS is loop
1101 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
1102 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
1103 /// loop invariant form of LHS `Pred` RHS.
1104 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
1105 const SCEV *RHS, const Loop *L,
1106 ICmpInst::Predicate &InvariantPred,
1107 const SCEV *&InvariantLHS,
1108 const SCEV *&InvariantRHS);
1110 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
1111 /// iff any changes were made. If the operands are provably equal or
1112 /// unequal, LHS and RHS are set to the same value and Pred is set to either
1113 /// ICMP_EQ or ICMP_NE.
1115 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
1118 unsigned Depth = 0);
1120 /// Return the "disposition" of the given SCEV with respect to the given
1122 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
1124 /// Return true if the value of the given SCEV is unchanging in the
1126 bool isLoopInvariant(const SCEV *S, const Loop *L);
1128 /// Return true if the given SCEV changes value in a known way in the
1129 /// specified loop. This property being true implies that the value is
1130 /// variant in the loop AND that we can emit an expression to compute the
1131 /// value of the expression at any particular loop iteration.
1132 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
1134 /// Return the "disposition" of the given SCEV with respect to the given
1136 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
1138 /// Return true if elements that makes up the given SCEV dominate the
1139 /// specified basic block.
1140 bool dominates(const SCEV *S, const BasicBlock *BB);
1142 /// Return true if elements that makes up the given SCEV properly dominate
1143 /// the specified basic block.
1144 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
1146 /// Test whether the given SCEV has Op as a direct or indirect operand.
1147 bool hasOperand(const SCEV *S, const SCEV *Op) const;
1149 /// Return the size of an element read or written by Inst.
1150 const SCEV *getElementSize(Instruction *Inst);
1152 /// Compute the array dimensions Sizes from the set of Terms extracted from
1153 /// the memory access function of this SCEVAddRecExpr.
1154 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
1155 SmallVectorImpl<const SCEV *> &Sizes,
1156 const SCEV *ElementSize) const;
1158 void print(raw_ostream &OS) const;
1159 void verify() const;
1161 /// Collect parametric terms occurring in step expressions.
1162 void collectParametricTerms(const SCEV *Expr,
1163 SmallVectorImpl<const SCEV *> &Terms);
1167 /// Return in Subscripts the access functions for each dimension in Sizes.
1168 void computeAccessFunctions(const SCEV *Expr,
1169 SmallVectorImpl<const SCEV *> &Subscripts,
1170 SmallVectorImpl<const SCEV *> &Sizes);
1172 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1173 /// subscripts and sizes of an array access.
1175 /// The delinearization is a 3 step process: the first two steps compute the
1176 /// sizes of each subscript and the third step computes the access functions
1177 /// for the delinearized array:
1179 /// 1. Find the terms in the step functions
1180 /// 2. Compute the array size
1181 /// 3. Compute the access function: divide the SCEV by the array size
1182 /// starting with the innermost dimensions found in step 2. The Quotient
1183 /// is the SCEV to be divided in the next step of the recursion. The
1184 /// Remainder is the subscript of the innermost dimension. Loop over all
1185 /// array dimensions computed in step 2.
1187 /// To compute a uniform array size for several memory accesses to the same
1188 /// object, one can collect in step 1 all the step terms for all the memory
1189 /// accesses, and compute in step 2 a unique array shape. This guarantees
1190 /// that the array shape will be the same across all memory accesses.
1192 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1193 /// the array shape given in metadata.
1202 /// A[j+k][2i][5i] =
1204 /// The initial SCEV:
1206 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1208 /// 1. Find the different terms in the step functions:
1209 /// -> [2*m, 5, n*m, n*m]
1211 /// 2. Compute the array size: sort and unique them
1212 /// -> [n*m, 2*m, 5]
1213 /// find the GCD of all the terms = 1
1214 /// divide by the GCD and erase constant terms
1217 /// divide by GCD -> [n, 2]
1218 /// remove constant terms
1220 /// size of the array is A[unknown][n][m]
1222 /// 3. Compute the access function
1223 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1224 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1225 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1226 /// The remainder is the subscript of the innermost array dimension: [5i].
1228 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1229 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1230 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1231 /// The Remainder is the subscript of the next array dimension: [2i].
1233 /// The subscript of the outermost dimension is the Quotient: [j+k].
1235 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1236 void delinearize(const SCEV *Expr,
1237 SmallVectorImpl<const SCEV *> &Subscripts,
1238 SmallVectorImpl<const SCEV *> &Sizes,
1239 const SCEV *ElementSize);
1241 /// Return the DataLayout associated with the module this SCEV instance is
1243 const DataLayout &getDataLayout() const {
1244 return F.getParent()->getDataLayout();
1247 const SCEVPredicate *getEqualPredicate(const SCEVUnknown *LHS,
1248 const SCEVConstant *RHS);
1250 /// Re-writes the SCEV according to the Predicates in \p Preds.
1251 const SCEV *rewriteUsingPredicate(const SCEV *Scev, SCEVUnionPredicate &A);
1254 /// Compute the backedge taken count knowing the interval difference, the
1255 /// stride and presence of the equality in the comparison.
1256 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1259 /// Verify if an linear IV with positive stride can overflow when in a
1260 /// less-than comparison, knowing the invariant term of the comparison,
1261 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1262 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
1263 bool IsSigned, bool NoWrap);
1265 /// Verify if an linear IV with negative stride can overflow when in a
1266 /// greater-than comparison, knowing the invariant term of the comparison,
1267 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1268 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
1269 bool IsSigned, bool NoWrap);
1272 FoldingSet<SCEV> UniqueSCEVs;
1273 FoldingSet<SCEVPredicate> UniquePreds;
1274 BumpPtrAllocator SCEVAllocator;
1276 /// The head of a linked list of all SCEVUnknown values that have been
1277 /// allocated. This is used by releaseMemory to locate them all and call
1278 /// their destructors.
1279 SCEVUnknown *FirstUnknown;
1282 /// \brief Analysis pass that exposes the \c ScalarEvolution for a function.
1283 class ScalarEvolutionAnalysis {
1287 typedef ScalarEvolution Result;
1289 /// \brief Opaque, unique identifier for this analysis pass.
1290 static void *ID() { return (void *)&PassID; }
1292 /// \brief Provide a name for the analysis for debugging and logging.
1293 static StringRef name() { return "ScalarEvolutionAnalysis"; }
1295 ScalarEvolution run(Function &F, AnalysisManager<Function> *AM);
1298 /// \brief Printer pass for the \c ScalarEvolutionAnalysis results.
1299 class ScalarEvolutionPrinterPass {
1303 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1304 PreservedAnalyses run(Function &F, AnalysisManager<Function> *AM);
1306 static StringRef name() { return "ScalarEvolutionPrinterPass"; }
1309 class ScalarEvolutionWrapperPass : public FunctionPass {
1310 std::unique_ptr<ScalarEvolution> SE;
1315 ScalarEvolutionWrapperPass();
1317 ScalarEvolution &getSE() { return *SE; }
1318 const ScalarEvolution &getSE() const { return *SE; }
1320 bool runOnFunction(Function &F) override;
1321 void releaseMemory() override;
1322 void getAnalysisUsage(AnalysisUsage &AU) const override;
1323 void print(raw_ostream &OS, const Module * = nullptr) const override;
1324 void verifyAnalysis() const override;
1327 /// An interface layer with SCEV used to manage how we see SCEV expressions
1328 /// for values in the context of existing predicates. We can add new
1329 /// predicates, but we cannot remove them.
1331 /// This layer has multiple purposes:
1332 /// - provides a simple interface for SCEV versioning.
1333 /// - guarantees that the order of transformations applied on a SCEV
1334 /// expression for a single Value is consistent across two different
1335 /// getSCEV calls. This means that, for example, once we've obtained
1336 /// an AddRec expression for a certain value through expression
1337 /// rewriting, we will continue to get an AddRec expression for that
1339 /// - lowers the number of expression rewrites.
1340 class PredicatedScalarEvolution {
1342 PredicatedScalarEvolution(ScalarEvolution &SE);
1343 const SCEVUnionPredicate &getUnionPredicate() const;
1344 /// \brief Returns the SCEV expression of V, in the context of the current
1346 /// The order of transformations applied on the expression of V returned
1347 /// by ScalarEvolution is guaranteed to be preserved, even when adding new
1349 const SCEV *getSCEV(Value *V);
1350 /// \brief Adds a new predicate.
1351 void addPredicate(const SCEVPredicate &Pred);
1352 /// \brief Returns the ScalarEvolution analysis used.
1353 ScalarEvolution *getSE() const { return &SE; }
1356 /// \brief Increments the version number of the predicate.
1357 /// This needs to be called every time the SCEV predicate changes.
1358 void updateGeneration();
1359 /// Holds a SCEV and the version number of the SCEV predicate used to
1360 /// perform the rewrite of the expression.
1361 typedef std::pair<unsigned, const SCEV *> RewriteEntry;
1362 /// Maps a SCEV to the rewrite result of that SCEV at a certain version
1363 /// number. If this number doesn't match the current Generation, we will
1364 /// need to do a rewrite. To preserve the transformation order of previous
1365 /// rewrites, we will rewrite the previous result instead of the original
1367 DenseMap<const SCEV *, RewriteEntry> RewriteMap;
1368 /// The ScalarEvolution analysis.
1369 ScalarEvolution &SE;
1370 /// The SCEVPredicate that forms our context. We will rewrite all
1371 /// expressions assuming that this predicate true.
1372 SCEVUnionPredicate Preds;
1373 /// Marks the version of the SCEV predicate used. When rewriting a SCEV
1374 /// expression we mark it with the version of the predicate. We use this to
1375 /// figure out if the predicate has changed from the last rewrite of the
1376 /// SCEV. If so, we need to perform a new rewrite.
1377 unsigned Generation;