1 //===- llvm/Analysis/ScalarEvolution.h - Scalar Evolution -------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // The ScalarEvolution class is an LLVM pass which can be used to analyze and
11 // categorize scalar expressions in loops. It specializes in recognizing
12 // general induction variables, representing them with the abstract and opaque
13 // SCEV class. Given this analysis, trip counts of loops and other important
14 // properties can be obtained.
16 // This analysis is primarily useful for induction variable substitution and
17 // strength reduction.
19 //===----------------------------------------------------------------------===//
21 #ifndef LLVM_ANALYSIS_SCALAREVOLUTION_H
22 #define LLVM_ANALYSIS_SCALAREVOLUTION_H
24 #include "llvm/ADT/DenseSet.h"
25 #include "llvm/ADT/FoldingSet.h"
26 #include "llvm/IR/ConstantRange.h"
27 #include "llvm/IR/Function.h"
28 #include "llvm/IR/Instructions.h"
29 #include "llvm/IR/Operator.h"
30 #include "llvm/IR/PassManager.h"
31 #include "llvm/IR/ValueHandle.h"
32 #include "llvm/Pass.h"
33 #include "llvm/Support/Allocator.h"
34 #include "llvm/Support/DataTypes.h"
39 class AssumptionCache;
44 class ScalarEvolution;
46 class TargetLibraryInfo;
54 template<> struct FoldingSetTrait<SCEV>;
56 /// This class represents an analyzed expression in the program. These are
57 /// opaque objects that the client is not allowed to do much with directly.
59 class SCEV : public FoldingSetNode {
60 friend struct FoldingSetTrait<SCEV>;
62 /// A reference to an Interned FoldingSetNodeID for this node. The
63 /// ScalarEvolution's BumpPtrAllocator holds the data.
64 FoldingSetNodeIDRef FastID;
66 // The SCEV baseclass this node corresponds to
67 const unsigned short SCEVType;
70 /// This field is initialized to zero and may be used in subclasses to store
71 /// miscellaneous information.
72 unsigned short SubclassData;
75 SCEV(const SCEV &) = delete;
76 void operator=(const SCEV &) = delete;
79 /// NoWrapFlags are bitfield indices into SubclassData.
81 /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
82 /// no-signed-wrap <NSW> properties, which are derived from the IR
83 /// operator. NSW is a misnomer that we use to mean no signed overflow or
86 /// AddRec expressions may have a no-self-wraparound <NW> property if, in
87 /// the integer domain, abs(step) * max-iteration(loop) <=
88 /// unsigned-max(bitwidth). This means that the recurrence will never reach
89 /// its start value if the step is non-zero. Computing the same value on
90 /// each iteration is not considered wrapping, and recurrences with step = 0
91 /// are trivially <NW>. <NW> is independent of the sign of step and the
92 /// value the add recurrence starts with.
94 /// Note that NUW and NSW are also valid properties of a recurrence, and
95 /// either implies NW. For convenience, NW will be set for a recurrence
96 /// whenever either NUW or NSW are set.
97 enum NoWrapFlags { FlagAnyWrap = 0, // No guarantee.
98 FlagNW = (1 << 0), // No self-wrap.
99 FlagNUW = (1 << 1), // No unsigned wrap.
100 FlagNSW = (1 << 2), // No signed wrap.
101 NoWrapMask = (1 << 3) -1 };
103 explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy) :
104 FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
106 unsigned getSCEVType() const { return SCEVType; }
108 /// Return the LLVM type of this SCEV expression.
110 Type *getType() const;
112 /// Return true if the expression is a constant zero.
116 /// Return true if the expression is a constant one.
120 /// Return true if the expression is a constant all-ones value.
122 bool isAllOnesValue() const;
124 /// Return true if the specified scev is negated, but not a constant.
125 bool isNonConstantNegative() const;
127 /// Print out the internal representation of this scalar to the specified
128 /// stream. This should really only be used for debugging purposes.
129 void print(raw_ostream &OS) const;
131 /// This method is used for debugging.
136 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
137 // temporary FoldingSetNodeID values.
138 template<> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
139 static void Profile(const SCEV &X, FoldingSetNodeID& ID) {
142 static bool Equals(const SCEV &X, const FoldingSetNodeID &ID,
143 unsigned IDHash, FoldingSetNodeID &TempID) {
144 return ID == X.FastID;
146 static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
147 return X.FastID.ComputeHash();
151 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
156 /// An object of this class is returned by queries that could not be answered.
157 /// For example, if you ask for the number of iterations of a linked-list
158 /// traversal loop, you will get one of these. None of the standard SCEV
159 /// operations are valid on this class, it is just a marker.
160 struct SCEVCouldNotCompute : public SCEV {
161 SCEVCouldNotCompute();
163 /// Methods for support type inquiry through isa, cast, and dyn_cast:
164 static bool classof(const SCEV *S);
167 /// The main scalar evolution driver. Because client code (intentionally)
168 /// can't do much with the SCEV objects directly, they must ask this class
170 class ScalarEvolution {
172 /// An enum describing the relationship between a SCEV and a loop.
173 enum LoopDisposition {
174 LoopVariant, ///< The SCEV is loop-variant (unknown).
175 LoopInvariant, ///< The SCEV is loop-invariant.
176 LoopComputable ///< The SCEV varies predictably with the loop.
179 /// An enum describing the relationship between a SCEV and a basic block.
180 enum BlockDisposition {
181 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
182 DominatesBlock, ///< The SCEV dominates the block.
183 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
186 /// Convenient NoWrapFlags manipulation that hides enum casts and is
187 /// visible in the ScalarEvolution name space.
188 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
189 maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
190 return (SCEV::NoWrapFlags)(Flags & Mask);
192 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
193 setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
194 return (SCEV::NoWrapFlags)(Flags | OnFlags);
196 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
197 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
198 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
202 /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
203 /// Value is deleted.
204 class SCEVCallbackVH final : public CallbackVH {
206 void deleted() override;
207 void allUsesReplacedWith(Value *New) override;
209 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
212 friend class SCEVCallbackVH;
213 friend class SCEVExpander;
214 friend class SCEVUnknown;
216 /// The function we are analyzing.
220 /// The target library information for the target we are targeting.
222 TargetLibraryInfo &TLI;
224 /// The tracker for @llvm.assume intrinsics in this function.
227 /// The dominator tree.
231 /// The loop information for the function we are currently analyzing.
235 /// This SCEV is used to represent unknown trip counts and things.
236 std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
238 /// The typedef for ValueExprMap.
240 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
243 /// This is a cache of the values we have analyzed so far.
245 ValueExprMapType ValueExprMap;
247 /// Mark predicate values currently being processed by isImpliedCond.
248 DenseSet<Value*> PendingLoopPredicates;
250 /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
251 /// conditions dominating the backedge of a loop.
252 bool WalkingBEDominatingConds;
254 /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
255 /// predicate by splitting it into a set of independent predicates.
256 bool ProvingSplitPredicate;
258 /// Information about the number of loop iterations for which a loop exit's
259 /// branch condition evaluates to the not-taken path. This is a temporary
260 /// pair of exact and max expressions that are eventually summarized in
261 /// ExitNotTakenInfo and BackedgeTakenInfo.
266 /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
268 ExitLimit(const SCEV *E, const SCEV *M) : Exact(E), Max(M) {}
270 /// Test whether this ExitLimit contains any computed information, or
271 /// whether it's all SCEVCouldNotCompute values.
272 bool hasAnyInfo() const {
273 return !isa<SCEVCouldNotCompute>(Exact) ||
274 !isa<SCEVCouldNotCompute>(Max);
278 /// Information about the number of times a particular loop exit may be
279 /// reached before exiting the loop.
280 struct ExitNotTakenInfo {
281 AssertingVH<BasicBlock> ExitingBlock;
282 const SCEV *ExactNotTaken;
283 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
285 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
287 /// Return true if all loop exits are computable.
288 bool isCompleteList() const {
289 return NextExit.getInt() == 0;
292 void setIncomplete() { NextExit.setInt(1); }
294 /// Return a pointer to the next exit's not-taken info.
295 ExitNotTakenInfo *getNextExit() const {
296 return NextExit.getPointer();
299 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
302 /// Information about the backedge-taken count of a loop. This currently
303 /// includes an exact count and a maximum count.
305 class BackedgeTakenInfo {
306 /// A list of computable exits and their not-taken counts. Loops almost
307 /// never have more than one computable exit.
308 ExitNotTakenInfo ExitNotTaken;
310 /// An expression indicating the least maximum backedge-taken count of the
311 /// loop that is known, or a SCEVCouldNotCompute.
315 BackedgeTakenInfo() : Max(nullptr) {}
317 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
319 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
320 bool Complete, const SCEV *MaxCount);
322 /// Test whether this BackedgeTakenInfo contains any computed information,
323 /// or whether it's all SCEVCouldNotCompute values.
324 bool hasAnyInfo() const {
325 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
328 /// Return an expression indicating the exact backedge-taken count of the
329 /// loop if it is known, or SCEVCouldNotCompute otherwise. This is the
330 /// number of times the loop header can be guaranteed to execute, minus
332 const SCEV *getExact(ScalarEvolution *SE) const;
334 /// Return the number of times this loop exit may fall through to the back
335 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
336 /// this block before this number of iterations, but may exit via another
338 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
340 /// Get the max backedge taken count for the loop.
341 const SCEV *getMax(ScalarEvolution *SE) const;
343 /// Return true if any backedge taken count expressions refer to the given
345 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
347 /// Invalidate this result and free associated memory.
351 /// Cache the backedge-taken count of the loops for this function as they
353 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
355 /// This map contains entries for all of the PHI instructions that we
356 /// attempt to compute constant evolutions for. This allows us to avoid
357 /// potentially expensive recomputation of these properties. An instruction
358 /// maps to null if we are unable to compute its exit value.
359 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
361 /// This map contains entries for all the expressions that we attempt to
362 /// compute getSCEVAtScope information for, which can be expensive in
364 DenseMap<const SCEV *,
365 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
367 /// Memoized computeLoopDisposition results.
368 DenseMap<const SCEV *,
369 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
372 /// Compute a LoopDisposition value.
373 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
375 /// Memoized computeBlockDisposition results.
378 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
381 /// Compute a BlockDisposition value.
382 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
384 /// Memoized results from getRange
385 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
387 /// Memoized results from getRange
388 DenseMap<const SCEV *, ConstantRange> SignedRanges;
390 /// Used to parameterize getRange
391 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
393 /// Set the memoized range for the given SCEV.
394 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
395 const ConstantRange &CR) {
396 DenseMap<const SCEV *, ConstantRange> &Cache =
397 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
399 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
400 Cache.insert(std::make_pair(S, CR));
402 Pair.first->second = CR;
403 return Pair.first->second;
406 /// Determine the range for a particular SCEV.
407 ConstantRange getRange(const SCEV *S, RangeSignHint Hint);
409 /// We know that there is no SCEV for the specified value. Analyze the
411 const SCEV *createSCEV(Value *V);
413 /// Provide the special handling we need to analyze PHI SCEVs.
414 const SCEV *createNodeForPHI(PHINode *PN);
416 /// Helper function called from createNodeForPHI.
417 const SCEV *createAddRecFromPHI(PHINode *PN);
419 /// Helper function called from createNodeForPHI.
420 const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
422 /// Provide special handling for a select-like instruction (currently this
423 /// is either a select instruction or a phi node). \p I is the instruction
424 /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
426 const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
427 Value *TrueVal, Value *FalseVal);
429 /// Provide the special handling we need to analyze GEP SCEVs.
430 const SCEV *createNodeForGEP(GEPOperator *GEP);
432 /// Implementation code for getSCEVAtScope; called at most once for each
435 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
437 /// This looks up computed SCEV values for all instructions that depend on
438 /// the given instruction and removes them from the ValueExprMap map if they
439 /// reference SymName. This is used during PHI resolution.
440 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
442 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
443 /// values if the loop hasn't been analyzed yet.
444 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
446 /// Compute the number of times the specified loop will iterate.
447 BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L);
449 /// Compute the number of times the backedge of the specified loop will
450 /// execute if it exits via the specified block.
451 ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
453 /// Compute the number of times the backedge of the specified loop will
454 /// execute if its exit condition were a conditional branch of ExitCond,
456 ExitLimit computeExitLimitFromCond(const Loop *L,
462 /// Compute the number of times the backedge of the specified loop will
463 /// execute if its exit condition were a conditional branch of the ICmpInst
464 /// ExitCond, TBB, and FBB.
465 ExitLimit computeExitLimitFromICmp(const Loop *L,
471 /// Compute the number of times the backedge of the specified loop will
472 /// execute if its exit condition were a switch with a single exiting case
475 computeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
476 BasicBlock *ExitingBB, bool IsSubExpr);
478 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
479 /// compute the backedge-taken count.
480 ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI,
483 ICmpInst::Predicate p);
485 /// If the loop is known to execute a constant number of times (the
486 /// condition evolves only from constants), try to evaluate a few iterations
487 /// of the loop until we get the exit condition gets a value of ExitWhen
488 /// (true or false). If we cannot evaluate the exit count of the loop,
489 /// return CouldNotCompute.
490 const SCEV *computeExitCountExhaustively(const Loop *L,
494 /// Return the number of times an exit condition comparing the specified
495 /// value to zero will execute. If not computable, return CouldNotCompute.
496 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
498 /// Return the number of times an exit condition checking the specified
499 /// value for nonzero will execute. If not computable, return
501 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
503 /// Return the number of times an exit condition containing the specified
504 /// less-than comparison will execute. If not computable, return
505 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
506 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
507 const Loop *L, bool isSigned, bool IsSubExpr);
508 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
509 const Loop *L, bool isSigned, bool IsSubExpr);
511 /// Return a predecessor of BB (which may not be an immediate predecessor)
512 /// which has exactly one successor from which BB is reachable, or null if
513 /// no such block is found.
514 std::pair<BasicBlock *, BasicBlock *>
515 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
517 /// Test whether the condition described by Pred, LHS, and RHS is true
518 /// whenever the given FoundCondValue value evaluates to true.
519 bool isImpliedCond(ICmpInst::Predicate Pred,
520 const SCEV *LHS, const SCEV *RHS,
521 Value *FoundCondValue,
524 /// Test whether the condition described by Pred, LHS, and RHS is true
525 /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
527 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
528 const SCEV *RHS, ICmpInst::Predicate FoundPred,
529 const SCEV *FoundLHS, const SCEV *FoundRHS);
531 /// Test whether the condition described by Pred, LHS, and RHS is true
532 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
534 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
535 const SCEV *LHS, const SCEV *RHS,
536 const SCEV *FoundLHS, const SCEV *FoundRHS);
538 /// Test whether the condition described by Pred, LHS, and RHS is true
539 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
541 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
542 const SCEV *LHS, const SCEV *RHS,
543 const SCEV *FoundLHS,
544 const SCEV *FoundRHS);
546 /// Test whether the condition described by Pred, LHS, and RHS is true
547 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
548 /// true. Utility function used by isImpliedCondOperands.
549 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
550 const SCEV *LHS, const SCEV *RHS,
551 const SCEV *FoundLHS,
552 const SCEV *FoundRHS);
554 /// Test whether the condition described by Pred, LHS, and RHS is true
555 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
558 /// This routine tries to rule out certain kinds of integer overflow, and
559 /// then tries to reason about arithmetic properties of the predicates.
560 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
561 const SCEV *LHS, const SCEV *RHS,
562 const SCEV *FoundLHS,
563 const SCEV *FoundRHS);
565 /// If we know that the specified Phi is in the header of its containing
566 /// loop, we know the loop executes a constant number of times, and the PHI
567 /// node is just a recurrence involving constants, fold it.
568 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
571 /// Test if the given expression is known to satisfy the condition described
572 /// by Pred and the known constant ranges of LHS and RHS.
574 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
575 const SCEV *LHS, const SCEV *RHS);
577 /// Try to prove the condition described by "LHS Pred RHS" by ruling out
578 /// integer overflow.
580 /// For instance, this will return true for "A s< (A + C)<nsw>" if C is
582 bool isKnownPredicateViaNoOverflow(ICmpInst::Predicate Pred,
583 const SCEV *LHS, const SCEV *RHS);
585 /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
586 /// prove them individually.
587 bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
590 /// Try to match the Expr as "(L + R)<Flags>".
591 bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
592 SCEV::NoWrapFlags &Flags);
594 /// Return true if More == (Less + C), where C is a constant. This is
595 /// intended to be used as a cheaper substitute for full SCEV subtraction.
596 bool computeConstantDifference(const SCEV *Less, const SCEV *More,
599 /// Drop memoized information computed for S.
600 void forgetMemoizedResults(const SCEV *S);
602 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
603 const SCEV *getExistingSCEV(Value *V);
605 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
607 bool checkValidity(const SCEV *S) const;
609 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
610 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
611 /// equivalent to proving no signed (resp. unsigned) wrap in
612 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
613 /// (resp. `SCEVZeroExtendExpr`).
615 template<typename ExtendOpTy>
616 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
619 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
620 ICmpInst::Predicate Pred, bool &Increasing);
622 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
623 /// is monotonically increasing or decreasing. In the former case set
624 /// `Increasing` to true and in the latter case set `Increasing` to false.
626 /// A predicate is said to be monotonically increasing if may go from being
627 /// false to being true as the loop iterates, but never the other way
628 /// around. A predicate is said to be monotonically decreasing if may go
629 /// from being true to being false as the loop iterates, but never the other
631 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS,
632 ICmpInst::Predicate Pred, bool &Increasing);
634 // Return SCEV no-wrap flags that can be proven based on reasoning
635 // about how poison produced from no-wrap flags on this value
636 // (e.g. a nuw add) would trigger undefined behavior on overflow.
637 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
640 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
641 DominatorTree &DT, LoopInfo &LI);
643 ScalarEvolution(ScalarEvolution &&Arg);
645 LLVMContext &getContext() const { return F.getContext(); }
647 /// Test if values of the given type are analyzable within the SCEV
648 /// framework. This primarily includes integer types, and it can optionally
649 /// include pointer types if the ScalarEvolution class has access to
650 /// target-specific information.
651 bool isSCEVable(Type *Ty) const;
653 /// Return the size in bits of the specified type, for which isSCEVable must
655 uint64_t getTypeSizeInBits(Type *Ty) const;
657 /// Return a type with the same bitwidth as the given type and which
658 /// represents how SCEV will treat the given type, for which isSCEVable must
659 /// return true. For pointer types, this is the pointer-sized integer type.
660 Type *getEffectiveSCEVType(Type *Ty) const;
662 /// Return a SCEV expression for the full generality of the specified
664 const SCEV *getSCEV(Value *V);
666 const SCEV *getConstant(ConstantInt *V);
667 const SCEV *getConstant(const APInt& Val);
668 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
669 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
670 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
671 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
672 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
673 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
674 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
675 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
676 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
677 SmallVector<const SCEV *, 2> Ops;
680 return getAddExpr(Ops, Flags);
682 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
683 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
684 SmallVector<const SCEV *, 3> Ops;
688 return getAddExpr(Ops, Flags);
690 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
691 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
692 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
693 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap)
695 SmallVector<const SCEV *, 2> Ops;
698 return getMulExpr(Ops, Flags);
700 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
701 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
702 SmallVector<const SCEV *, 3> Ops;
706 return getMulExpr(Ops, Flags);
708 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
709 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
710 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
711 const Loop *L, SCEV::NoWrapFlags Flags);
712 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
713 const Loop *L, SCEV::NoWrapFlags Flags);
714 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
715 const Loop *L, SCEV::NoWrapFlags Flags) {
716 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
717 return getAddRecExpr(NewOp, L, Flags);
719 /// \brief Returns an expression for a GEP
721 /// \p PointeeType The type used as the basis for the pointer arithmetics
722 /// \p BaseExpr The expression for the pointer operand.
723 /// \p IndexExprs The expressions for the indices.
724 /// \p InBounds Whether the GEP is in bounds.
725 const SCEV *getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
726 const SmallVectorImpl<const SCEV *> &IndexExprs,
727 bool InBounds = false);
728 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
729 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
730 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
731 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
732 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
733 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
734 const SCEV *getUnknown(Value *V);
735 const SCEV *getCouldNotCompute();
737 /// \brief Return a SCEV for the constant 0 of a specific type.
738 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
740 /// \brief Return a SCEV for the constant 1 of a specific type.
741 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
743 /// Return an expression for sizeof AllocTy that is type IntTy
745 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
747 /// Return an expression for offsetof on the given field with type IntTy
749 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
751 /// Return the SCEV object corresponding to -V.
753 const SCEV *getNegativeSCEV(const SCEV *V,
754 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
756 /// Return the SCEV object corresponding to ~V.
758 const SCEV *getNotSCEV(const SCEV *V);
760 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
761 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
762 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
764 /// Return a SCEV corresponding to a conversion of the input value to the
765 /// specified type. If the type must be extended, it is zero extended.
766 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
768 /// Return a SCEV corresponding to a conversion of the input value to the
769 /// specified type. If the type must be extended, it is sign extended.
770 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
772 /// Return a SCEV corresponding to a conversion of the input value to the
773 /// specified type. If the type must be extended, it is zero extended. The
774 /// conversion must not be narrowing.
775 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
777 /// Return a SCEV corresponding to a conversion of the input value to the
778 /// specified type. If the type must be extended, it is sign extended. The
779 /// conversion must not be narrowing.
780 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
782 /// Return a SCEV corresponding to a conversion of the input value to the
783 /// specified type. If the type must be extended, it is extended with
784 /// unspecified bits. The conversion must not be narrowing.
785 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
787 /// Return a SCEV corresponding to a conversion of the input value to the
788 /// specified type. The conversion must not be widening.
789 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
791 /// Promote the operands to the wider of the types using zero-extension, and
792 /// then perform a umax operation with them.
793 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
796 /// Promote the operands to the wider of the types using zero-extension, and
797 /// then perform a umin operation with them.
798 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
801 /// Transitively follow the chain of pointer-type operands until reaching a
802 /// SCEV that does not have a single pointer operand. This returns a
803 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
805 const SCEV *getPointerBase(const SCEV *V);
807 /// Return a SCEV expression for the specified value at the specified scope
808 /// in the program. The L value specifies a loop nest to evaluate the
809 /// expression at, where null is the top-level or a specified loop is
810 /// immediately inside of the loop.
812 /// This method can be used to compute the exit value for a variable defined
813 /// in a loop by querying what the value will hold in the parent loop.
815 /// In the case that a relevant loop exit value cannot be computed, the
816 /// original value V is returned.
817 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
819 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
820 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
822 /// Test whether entry to the loop is protected by a conditional between LHS
823 /// and RHS. This is used to help avoid max expressions in loop trip
824 /// counts, and to eliminate casts.
825 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
826 const SCEV *LHS, const SCEV *RHS);
828 /// Test whether the backedge of the loop is protected by a conditional
829 /// between LHS and RHS. This is used to to eliminate casts.
830 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
831 const SCEV *LHS, const SCEV *RHS);
833 /// \brief Returns the maximum trip count of the loop if it is a single-exit
834 /// loop and we can compute a small maximum for that loop.
836 /// Implemented in terms of the \c getSmallConstantTripCount overload with
837 /// the single exiting block passed to it. See that routine for details.
838 unsigned getSmallConstantTripCount(Loop *L);
840 /// Returns the maximum trip count of this loop as a normal unsigned
841 /// value. Returns 0 if the trip count is unknown or not constant. This
842 /// "trip count" assumes that control exits via ExitingBlock. More
843 /// precisely, it is the number of times that control may reach ExitingBlock
844 /// before taking the branch. For loops with multiple exits, it may not be
845 /// the number times that the loop header executes if the loop exits
846 /// prematurely via another branch.
847 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
849 /// \brief Returns the largest constant divisor of the trip count of the
850 /// loop if it is a single-exit loop and we can compute a small maximum for
853 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
854 /// the single exiting block passed to it. See that routine for details.
855 unsigned getSmallConstantTripMultiple(Loop *L);
857 /// Returns the largest constant divisor of the trip count of this loop as a
858 /// normal unsigned value, if possible. This means that the actual trip
859 /// count is always a multiple of the returned value (don't forget the trip
860 /// count could very well be zero as well!). As explained in the comments
861 /// for getSmallConstantTripCount, this assumes that control exits the loop
862 /// via ExitingBlock.
863 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
865 /// Get the expression for the number of loop iterations for which this loop
866 /// is guaranteed not to exit via ExitingBlock. Otherwise return
867 /// SCEVCouldNotCompute.
868 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
870 /// If the specified loop has a predictable backedge-taken count, return it,
871 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
872 /// is the number of times the loop header will be branched to from within
873 /// the loop. This is one less than the trip count of the loop, since it
874 /// doesn't count the first iteration, when the header is branched to from
875 /// outside the loop.
877 /// Note that it is not valid to call this method on a loop without a
878 /// loop-invariant backedge-taken count (see
879 /// hasLoopInvariantBackedgeTakenCount).
881 const SCEV *getBackedgeTakenCount(const Loop *L);
883 /// Similar to getBackedgeTakenCount, except return the least SCEV value
884 /// that is known never to be less than the actual backedge taken count.
885 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
887 /// Return true if the specified loop has an analyzable loop-invariant
888 /// backedge-taken count.
889 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
891 /// This method should be called by the client when it has changed a loop in
892 /// a way that may effect ScalarEvolution's ability to compute a trip count,
893 /// or if the loop is deleted. This call is potentially expensive for large
895 void forgetLoop(const Loop *L);
897 /// This method should be called by the client when it has changed a value
898 /// in a way that may effect its value, or which may disconnect it from a
899 /// def-use chain linking it to a loop.
900 void forgetValue(Value *V);
902 /// \brief Called when the client has changed the disposition of values in
905 /// We don't have a way to invalidate per-loop dispositions. Clear and
906 /// recompute is simpler.
907 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
909 /// Determine the minimum number of zero bits that S is guaranteed to end in
910 /// (at every loop iteration). It is, at the same time, the minimum number
911 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
912 /// If S is guaranteed to be 0, it returns the bitwidth of S.
913 uint32_t GetMinTrailingZeros(const SCEV *S);
915 /// Determine the unsigned range for a particular SCEV.
917 ConstantRange getUnsignedRange(const SCEV *S) {
918 return getRange(S, HINT_RANGE_UNSIGNED);
921 /// Determine the signed range for a particular SCEV.
923 ConstantRange getSignedRange(const SCEV *S) {
924 return getRange(S, HINT_RANGE_SIGNED);
927 /// Test if the given expression is known to be negative.
929 bool isKnownNegative(const SCEV *S);
931 /// Test if the given expression is known to be positive.
933 bool isKnownPositive(const SCEV *S);
935 /// Test if the given expression is known to be non-negative.
937 bool isKnownNonNegative(const SCEV *S);
939 /// Test if the given expression is known to be non-positive.
941 bool isKnownNonPositive(const SCEV *S);
943 /// Test if the given expression is known to be non-zero.
945 bool isKnownNonZero(const SCEV *S);
947 /// Test if the given expression is known to satisfy the condition described
948 /// by Pred, LHS, and RHS.
950 bool isKnownPredicate(ICmpInst::Predicate Pred,
951 const SCEV *LHS, const SCEV *RHS);
953 /// Return true if the result of the predicate LHS `Pred` RHS is loop
954 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
955 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
956 /// loop invariant form of LHS `Pred` RHS.
957 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
958 const SCEV *RHS, const Loop *L,
959 ICmpInst::Predicate &InvariantPred,
960 const SCEV *&InvariantLHS,
961 const SCEV *&InvariantRHS);
963 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
964 /// iff any changes were made. If the operands are provably equal or
965 /// unequal, LHS and RHS are set to the same value and Pred is set to either
966 /// ICMP_EQ or ICMP_NE.
968 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
973 /// Return the "disposition" of the given SCEV with respect to the given
975 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
977 /// Return true if the value of the given SCEV is unchanging in the
979 bool isLoopInvariant(const SCEV *S, const Loop *L);
981 /// Return true if the given SCEV changes value in a known way in the
982 /// specified loop. This property being true implies that the value is
983 /// variant in the loop AND that we can emit an expression to compute the
984 /// value of the expression at any particular loop iteration.
985 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
987 /// Return the "disposition" of the given SCEV with respect to the given
989 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
991 /// Return true if elements that makes up the given SCEV dominate the
992 /// specified basic block.
993 bool dominates(const SCEV *S, const BasicBlock *BB);
995 /// Return true if elements that makes up the given SCEV properly dominate
996 /// the specified basic block.
997 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
999 /// Test whether the given SCEV has Op as a direct or indirect operand.
1000 bool hasOperand(const SCEV *S, const SCEV *Op) const;
1002 /// Return the size of an element read or written by Inst.
1003 const SCEV *getElementSize(Instruction *Inst);
1005 /// Compute the array dimensions Sizes from the set of Terms extracted from
1006 /// the memory access function of this SCEVAddRecExpr.
1007 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
1008 SmallVectorImpl<const SCEV *> &Sizes,
1009 const SCEV *ElementSize) const;
1011 void print(raw_ostream &OS) const;
1012 void verify() const;
1014 /// Collect parametric terms occurring in step expressions.
1015 void collectParametricTerms(const SCEV *Expr,
1016 SmallVectorImpl<const SCEV *> &Terms);
1020 /// Return in Subscripts the access functions for each dimension in Sizes.
1021 void computeAccessFunctions(const SCEV *Expr,
1022 SmallVectorImpl<const SCEV *> &Subscripts,
1023 SmallVectorImpl<const SCEV *> &Sizes);
1025 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1026 /// subscripts and sizes of an array access.
1028 /// The delinearization is a 3 step process: the first two steps compute the
1029 /// sizes of each subscript and the third step computes the access functions
1030 /// for the delinearized array:
1032 /// 1. Find the terms in the step functions
1033 /// 2. Compute the array size
1034 /// 3. Compute the access function: divide the SCEV by the array size
1035 /// starting with the innermost dimensions found in step 2. The Quotient
1036 /// is the SCEV to be divided in the next step of the recursion. The
1037 /// Remainder is the subscript of the innermost dimension. Loop over all
1038 /// array dimensions computed in step 2.
1040 /// To compute a uniform array size for several memory accesses to the same
1041 /// object, one can collect in step 1 all the step terms for all the memory
1042 /// accesses, and compute in step 2 a unique array shape. This guarantees
1043 /// that the array shape will be the same across all memory accesses.
1045 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1046 /// the array shape given in metadata.
1055 /// A[j+k][2i][5i] =
1057 /// The initial SCEV:
1059 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1061 /// 1. Find the different terms in the step functions:
1062 /// -> [2*m, 5, n*m, n*m]
1064 /// 2. Compute the array size: sort and unique them
1065 /// -> [n*m, 2*m, 5]
1066 /// find the GCD of all the terms = 1
1067 /// divide by the GCD and erase constant terms
1070 /// divide by GCD -> [n, 2]
1071 /// remove constant terms
1073 /// size of the array is A[unknown][n][m]
1075 /// 3. Compute the access function
1076 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1077 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1078 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1079 /// The remainder is the subscript of the innermost array dimension: [5i].
1081 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1082 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1083 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1084 /// The Remainder is the subscript of the next array dimension: [2i].
1086 /// The subscript of the outermost dimension is the Quotient: [j+k].
1088 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1089 void delinearize(const SCEV *Expr,
1090 SmallVectorImpl<const SCEV *> &Subscripts,
1091 SmallVectorImpl<const SCEV *> &Sizes,
1092 const SCEV *ElementSize);
1095 /// Compute the backedge taken count knowing the interval difference, the
1096 /// stride and presence of the equality in the comparison.
1097 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1100 /// Verify if an linear IV with positive stride can overflow when in a
1101 /// less-than comparison, knowing the invariant term of the comparison,
1102 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1103 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
1104 bool IsSigned, bool NoWrap);
1106 /// Verify if an linear IV with negative stride can overflow when in a
1107 /// greater-than comparison, knowing the invariant term of the comparison,
1108 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1109 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
1110 bool IsSigned, bool NoWrap);
1113 FoldingSet<SCEV> UniqueSCEVs;
1114 BumpPtrAllocator SCEVAllocator;
1116 /// The head of a linked list of all SCEVUnknown values that have been
1117 /// allocated. This is used by releaseMemory to locate them all and call
1118 /// their destructors.
1119 SCEVUnknown *FirstUnknown;
1122 /// \brief Analysis pass that exposes the \c ScalarEvolution for a function.
1123 class ScalarEvolutionAnalysis {
1127 typedef ScalarEvolution Result;
1129 /// \brief Opaque, unique identifier for this analysis pass.
1130 static void *ID() { return (void *)&PassID; }
1132 /// \brief Provide a name for the analysis for debugging and logging.
1133 static StringRef name() { return "ScalarEvolutionAnalysis"; }
1135 ScalarEvolution run(Function &F, AnalysisManager<Function> *AM);
1138 /// \brief Printer pass for the \c ScalarEvolutionAnalysis results.
1139 class ScalarEvolutionPrinterPass {
1143 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1144 PreservedAnalyses run(Function &F, AnalysisManager<Function> *AM);
1146 static StringRef name() { return "ScalarEvolutionPrinterPass"; }
1149 class ScalarEvolutionWrapperPass : public FunctionPass {
1150 std::unique_ptr<ScalarEvolution> SE;
1155 ScalarEvolutionWrapperPass();
1157 ScalarEvolution &getSE() { return *SE; }
1158 const ScalarEvolution &getSE() const { return *SE; }
1160 bool runOnFunction(Function &F) override;
1161 void releaseMemory() override;
1162 void getAnalysisUsage(AnalysisUsage &AU) const override;
1163 void print(raw_ostream &OS, const Module * = nullptr) const override;
1164 void verifyAnalysis() const override;