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 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
132 /// This method is used for debugging.
138 // Specialize FoldingSetTrait for SCEV to avoid needing to compute
139 // temporary FoldingSetNodeID values.
140 template<> struct FoldingSetTrait<SCEV> : DefaultFoldingSetTrait<SCEV> {
141 static void Profile(const SCEV &X, FoldingSetNodeID& ID) {
144 static bool Equals(const SCEV &X, const FoldingSetNodeID &ID,
145 unsigned IDHash, FoldingSetNodeID &TempID) {
146 return ID == X.FastID;
148 static unsigned ComputeHash(const SCEV &X, FoldingSetNodeID &TempID) {
149 return X.FastID.ComputeHash();
153 inline raw_ostream &operator<<(raw_ostream &OS, const SCEV &S) {
158 /// An object of this class is returned by queries that could not be answered.
159 /// For example, if you ask for the number of iterations of a linked-list
160 /// traversal loop, you will get one of these. None of the standard SCEV
161 /// operations are valid on this class, it is just a marker.
162 struct SCEVCouldNotCompute : public SCEV {
163 SCEVCouldNotCompute();
165 /// Methods for support type inquiry through isa, cast, and dyn_cast:
166 static bool classof(const SCEV *S);
169 /// The main scalar evolution driver. Because client code (intentionally)
170 /// can't do much with the SCEV objects directly, they must ask this class
172 class ScalarEvolution {
174 /// An enum describing the relationship between a SCEV and a loop.
175 enum LoopDisposition {
176 LoopVariant, ///< The SCEV is loop-variant (unknown).
177 LoopInvariant, ///< The SCEV is loop-invariant.
178 LoopComputable ///< The SCEV varies predictably with the loop.
181 /// An enum describing the relationship between a SCEV and a basic block.
182 enum BlockDisposition {
183 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
184 DominatesBlock, ///< The SCEV dominates the block.
185 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
188 /// Convenient NoWrapFlags manipulation that hides enum casts and is
189 /// visible in the ScalarEvolution name space.
190 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
191 maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
192 return (SCEV::NoWrapFlags)(Flags & Mask);
194 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
195 setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
196 return (SCEV::NoWrapFlags)(Flags | OnFlags);
198 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
199 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
200 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
204 /// A CallbackVH to arrange for ScalarEvolution to be notified whenever a
205 /// Value is deleted.
206 class SCEVCallbackVH final : public CallbackVH {
208 void deleted() override;
209 void allUsesReplacedWith(Value *New) override;
211 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
214 friend class SCEVCallbackVH;
215 friend class SCEVExpander;
216 friend class SCEVUnknown;
218 /// The function we are analyzing.
222 /// The target library information for the target we are targeting.
224 TargetLibraryInfo &TLI;
226 /// The tracker for @llvm.assume intrinsics in this function.
229 /// The dominator tree.
233 /// The loop information for the function we are currently analyzing.
237 /// This SCEV is used to represent unknown trip counts and things.
238 std::unique_ptr<SCEVCouldNotCompute> CouldNotCompute;
240 /// The typedef for ValueExprMap.
242 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
245 /// This is a cache of the values we have analyzed so far.
247 ValueExprMapType ValueExprMap;
249 /// Mark predicate values currently being processed by isImpliedCond.
250 DenseSet<Value*> PendingLoopPredicates;
252 /// Set to true by isLoopBackedgeGuardedByCond when we're walking the set of
253 /// conditions dominating the backedge of a loop.
254 bool WalkingBEDominatingConds;
256 /// Set to true by isKnownPredicateViaSplitting when we're trying to prove a
257 /// predicate by splitting it into a set of independent predicates.
258 bool ProvingSplitPredicate;
260 /// Information about the number of loop iterations for which a loop exit's
261 /// branch condition evaluates to the not-taken path. This is a temporary
262 /// pair of exact and max expressions that are eventually summarized in
263 /// ExitNotTakenInfo and BackedgeTakenInfo.
268 /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
270 ExitLimit(const SCEV *E, const SCEV *M) : Exact(E), Max(M) {}
272 /// Test whether this ExitLimit contains any computed information, or
273 /// whether it's all SCEVCouldNotCompute values.
274 bool hasAnyInfo() const {
275 return !isa<SCEVCouldNotCompute>(Exact) ||
276 !isa<SCEVCouldNotCompute>(Max);
280 /// Information about the number of times a particular loop exit may be
281 /// reached before exiting the loop.
282 struct ExitNotTakenInfo {
283 AssertingVH<BasicBlock> ExitingBlock;
284 const SCEV *ExactNotTaken;
285 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
287 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
289 /// Return true if all loop exits are computable.
290 bool isCompleteList() const {
291 return NextExit.getInt() == 0;
294 void setIncomplete() { NextExit.setInt(1); }
296 /// Return a pointer to the next exit's not-taken info.
297 ExitNotTakenInfo *getNextExit() const {
298 return NextExit.getPointer();
301 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
304 /// Information about the backedge-taken count of a loop. This currently
305 /// includes an exact count and a maximum count.
307 class BackedgeTakenInfo {
308 /// A list of computable exits and their not-taken counts. Loops almost
309 /// never have more than one computable exit.
310 ExitNotTakenInfo ExitNotTaken;
312 /// An expression indicating the least maximum backedge-taken count of the
313 /// loop that is known, or a SCEVCouldNotCompute.
317 BackedgeTakenInfo() : Max(nullptr) {}
319 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
321 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
322 bool Complete, const SCEV *MaxCount);
324 /// Test whether this BackedgeTakenInfo contains any computed information,
325 /// or whether it's all SCEVCouldNotCompute values.
326 bool hasAnyInfo() const {
327 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
330 /// Return an expression indicating the exact backedge-taken count of the
331 /// loop if it is known, or SCEVCouldNotCompute otherwise. This is the
332 /// number of times the loop header can be guaranteed to execute, minus
334 const SCEV *getExact(ScalarEvolution *SE) const;
336 /// Return the number of times this loop exit may fall through to the back
337 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
338 /// this block before this number of iterations, but may exit via another
340 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
342 /// Get the max backedge taken count for the loop.
343 const SCEV *getMax(ScalarEvolution *SE) const;
345 /// Return true if any backedge taken count expressions refer to the given
347 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
349 /// Invalidate this result and free associated memory.
353 /// Cache the backedge-taken count of the loops for this function as they
355 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
357 /// This map contains entries for all of the PHI instructions that we
358 /// attempt to compute constant evolutions for. This allows us to avoid
359 /// potentially expensive recomputation of these properties. An instruction
360 /// maps to null if we are unable to compute its exit value.
361 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
363 /// This map contains entries for all the expressions that we attempt to
364 /// compute getSCEVAtScope information for, which can be expensive in
366 DenseMap<const SCEV *,
367 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
369 /// Memoized computeLoopDisposition results.
370 DenseMap<const SCEV *,
371 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
374 /// Compute a LoopDisposition value.
375 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
377 /// Memoized computeBlockDisposition results.
380 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
383 /// Compute a BlockDisposition value.
384 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
386 /// Memoized results from getRange
387 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
389 /// Memoized results from getRange
390 DenseMap<const SCEV *, ConstantRange> SignedRanges;
392 /// Used to parameterize getRange
393 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
395 /// Set the memoized range for the given SCEV.
396 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
397 const ConstantRange &CR) {
398 DenseMap<const SCEV *, ConstantRange> &Cache =
399 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
401 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
402 Cache.insert(std::make_pair(S, CR));
404 Pair.first->second = CR;
405 return Pair.first->second;
408 /// Determine the range for a particular SCEV.
409 ConstantRange getRange(const SCEV *S, RangeSignHint Hint);
411 /// We know that there is no SCEV for the specified value. Analyze the
413 const SCEV *createSCEV(Value *V);
415 /// Provide the special handling we need to analyze PHI SCEVs.
416 const SCEV *createNodeForPHI(PHINode *PN);
418 /// Helper function called from createNodeForPHI.
419 const SCEV *createAddRecFromPHI(PHINode *PN);
421 /// Helper function called from createNodeForPHI.
422 const SCEV *createNodeFromSelectLikePHI(PHINode *PN);
424 /// Provide special handling for a select-like instruction (currently this
425 /// is either a select instruction or a phi node). \p I is the instruction
426 /// being processed, and it is assumed equivalent to "Cond ? TrueVal :
428 const SCEV *createNodeForSelectOrPHI(Instruction *I, Value *Cond,
429 Value *TrueVal, Value *FalseVal);
431 /// Provide the special handling we need to analyze GEP SCEVs.
432 const SCEV *createNodeForGEP(GEPOperator *GEP);
434 /// Implementation code for getSCEVAtScope; called at most once for each
437 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
439 /// This looks up computed SCEV values for all instructions that depend on
440 /// the given instruction and removes them from the ValueExprMap map if they
441 /// reference SymName. This is used during PHI resolution.
442 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
444 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
445 /// values if the loop hasn't been analyzed yet.
446 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
448 /// Compute the number of times the specified loop will iterate.
449 BackedgeTakenInfo computeBackedgeTakenCount(const Loop *L);
451 /// Compute the number of times the backedge of the specified loop will
452 /// execute if it exits via the specified block.
453 ExitLimit computeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
455 /// Compute the number of times the backedge of the specified loop will
456 /// execute if its exit condition were a conditional branch of ExitCond,
458 ExitLimit computeExitLimitFromCond(const Loop *L,
464 /// Compute the number of times the backedge of the specified loop will
465 /// execute if its exit condition were a conditional branch of the ICmpInst
466 /// ExitCond, TBB, and FBB.
467 ExitLimit computeExitLimitFromICmp(const Loop *L,
473 /// Compute the number of times the backedge of the specified loop will
474 /// execute if its exit condition were a switch with a single exiting case
477 computeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
478 BasicBlock *ExitingBB, bool IsSubExpr);
480 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
481 /// compute the backedge-taken count.
482 ExitLimit computeLoadConstantCompareExitLimit(LoadInst *LI,
485 ICmpInst::Predicate p);
487 /// If the loop is known to execute a constant number of times (the
488 /// condition evolves only from constants), try to evaluate a few iterations
489 /// of the loop until we get the exit condition gets a value of ExitWhen
490 /// (true or false). If we cannot evaluate the exit count of the loop,
491 /// return CouldNotCompute.
492 const SCEV *computeExitCountExhaustively(const Loop *L,
496 /// Return the number of times an exit condition comparing the specified
497 /// value to zero will execute. If not computable, return CouldNotCompute.
498 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
500 /// Return the number of times an exit condition checking the specified
501 /// value for nonzero will execute. If not computable, return
503 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
505 /// Return the number of times an exit condition containing the specified
506 /// less-than comparison will execute. If not computable, return
507 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
508 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
509 const Loop *L, bool isSigned, bool IsSubExpr);
510 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
511 const Loop *L, bool isSigned, bool IsSubExpr);
513 /// Return a predecessor of BB (which may not be an immediate predecessor)
514 /// which has exactly one successor from which BB is reachable, or null if
515 /// no such block is found.
516 std::pair<BasicBlock *, BasicBlock *>
517 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
519 /// Test whether the condition described by Pred, LHS, and RHS is true
520 /// whenever the given FoundCondValue value evaluates to true.
521 bool isImpliedCond(ICmpInst::Predicate Pred,
522 const SCEV *LHS, const SCEV *RHS,
523 Value *FoundCondValue,
526 /// Test whether the condition described by Pred, LHS, and RHS is true
527 /// whenever the condition described by FoundPred, FoundLHS, FoundRHS is
529 bool isImpliedCond(ICmpInst::Predicate Pred, const SCEV *LHS,
530 const SCEV *RHS, ICmpInst::Predicate FoundPred,
531 const SCEV *FoundLHS, const SCEV *FoundRHS);
533 /// Test whether the condition described by Pred, LHS, and RHS is true
534 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
536 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
537 const SCEV *LHS, const SCEV *RHS,
538 const SCEV *FoundLHS, const SCEV *FoundRHS);
540 /// Test whether the condition described by Pred, LHS, and RHS is true
541 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
543 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
544 const SCEV *LHS, const SCEV *RHS,
545 const SCEV *FoundLHS,
546 const SCEV *FoundRHS);
548 /// Test whether the condition described by Pred, LHS, and RHS is true
549 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
550 /// true. Utility function used by isImpliedCondOperands.
551 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
552 const SCEV *LHS, const SCEV *RHS,
553 const SCEV *FoundLHS,
554 const SCEV *FoundRHS);
556 /// Test whether the condition described by Pred, LHS, and RHS is true
557 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
560 /// This routine tries to rule out certain kinds of integer overflow, and
561 /// then tries to reason about arithmetic properties of the predicates.
562 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
563 const SCEV *LHS, const SCEV *RHS,
564 const SCEV *FoundLHS,
565 const SCEV *FoundRHS);
567 /// If we know that the specified Phi is in the header of its containing
568 /// loop, we know the loop executes a constant number of times, and the PHI
569 /// node is just a recurrence involving constants, fold it.
570 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
573 /// Test if the given expression is known to satisfy the condition described
574 /// by Pred and the known constant ranges of LHS and RHS.
576 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
577 const SCEV *LHS, const SCEV *RHS);
579 /// Try to split Pred LHS RHS into logical conjunctions (and's) and try to
580 /// prove them individually.
581 bool isKnownPredicateViaSplitting(ICmpInst::Predicate Pred, const SCEV *LHS,
584 /// Try to match the Expr as "(L + R)<Flags>".
585 bool splitBinaryAdd(const SCEV *Expr, const SCEV *&L, const SCEV *&R,
586 SCEV::NoWrapFlags &Flags);
588 /// Return true if More == (Less + C), where C is a constant. This is
589 /// intended to be used as a cheaper substitute for full SCEV subtraction.
590 bool computeConstantDifference(const SCEV *Less, const SCEV *More,
593 /// Drop memoized information computed for S.
594 void forgetMemoizedResults(const SCEV *S);
596 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
597 const SCEV *getExistingSCEV(Value *V);
599 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
601 bool checkValidity(const SCEV *S) const;
603 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
604 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
605 /// equivalent to proving no signed (resp. unsigned) wrap in
606 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
607 /// (resp. `SCEVZeroExtendExpr`).
609 template<typename ExtendOpTy>
610 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
613 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
614 ICmpInst::Predicate Pred, bool &Increasing);
616 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
617 /// is monotonically increasing or decreasing. In the former case set
618 /// `Increasing` to true and in the latter case set `Increasing` to false.
620 /// A predicate is said to be monotonically increasing if may go from being
621 /// false to being true as the loop iterates, but never the other way
622 /// around. A predicate is said to be monotonically decreasing if may go
623 /// from being true to being false as the loop iterates, but never the other
625 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS,
626 ICmpInst::Predicate Pred, bool &Increasing);
628 // Return SCEV no-wrap flags that can be proven based on reasoning
629 // about how poison produced from no-wrap flags on this value
630 // (e.g. a nuw add) would trigger undefined behavior on overflow.
631 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
634 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
635 DominatorTree &DT, LoopInfo &LI);
637 ScalarEvolution(ScalarEvolution &&Arg);
639 LLVMContext &getContext() const { return F.getContext(); }
641 /// Test if values of the given type are analyzable within the SCEV
642 /// framework. This primarily includes integer types, and it can optionally
643 /// include pointer types if the ScalarEvolution class has access to
644 /// target-specific information.
645 bool isSCEVable(Type *Ty) const;
647 /// Return the size in bits of the specified type, for which isSCEVable must
649 uint64_t getTypeSizeInBits(Type *Ty) const;
651 /// Return a type with the same bitwidth as the given type and which
652 /// represents how SCEV will treat the given type, for which isSCEVable must
653 /// return true. For pointer types, this is the pointer-sized integer type.
654 Type *getEffectiveSCEVType(Type *Ty) const;
656 /// Return a SCEV expression for the full generality of the specified
658 const SCEV *getSCEV(Value *V);
660 const SCEV *getConstant(ConstantInt *V);
661 const SCEV *getConstant(const APInt& Val);
662 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
663 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
664 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
665 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
666 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
667 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
668 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
669 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
670 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
671 SmallVector<const SCEV *, 2> Ops;
674 return getAddExpr(Ops, Flags);
676 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
677 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
678 SmallVector<const SCEV *, 3> Ops;
682 return getAddExpr(Ops, Flags);
684 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
685 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
686 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
687 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap)
689 SmallVector<const SCEV *, 2> Ops;
692 return getMulExpr(Ops, Flags);
694 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
695 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
696 SmallVector<const SCEV *, 3> Ops;
700 return getMulExpr(Ops, Flags);
702 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
703 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
704 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
705 const Loop *L, SCEV::NoWrapFlags Flags);
706 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
707 const Loop *L, SCEV::NoWrapFlags Flags);
708 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
709 const Loop *L, SCEV::NoWrapFlags Flags) {
710 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
711 return getAddRecExpr(NewOp, L, Flags);
713 /// \brief Returns an expression for a GEP
715 /// \p PointeeType The type used as the basis for the pointer arithmetics
716 /// \p BaseExpr The expression for the pointer operand.
717 /// \p IndexExprs The expressions for the indices.
718 /// \p InBounds Whether the GEP is in bounds.
719 const SCEV *getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
720 const SmallVectorImpl<const SCEV *> &IndexExprs,
721 bool InBounds = false);
722 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
723 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
724 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
725 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
726 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
727 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
728 const SCEV *getUnknown(Value *V);
729 const SCEV *getCouldNotCompute();
731 /// \brief Return a SCEV for the constant 0 of a specific type.
732 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
734 /// \brief Return a SCEV for the constant 1 of a specific type.
735 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
737 /// Return an expression for sizeof AllocTy that is type IntTy
739 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
741 /// Return an expression for offsetof on the given field with type IntTy
743 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
745 /// Return the SCEV object corresponding to -V.
747 const SCEV *getNegativeSCEV(const SCEV *V,
748 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
750 /// Return the SCEV object corresponding to ~V.
752 const SCEV *getNotSCEV(const SCEV *V);
754 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
755 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
756 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
758 /// Return a SCEV corresponding to a conversion of the input value to the
759 /// specified type. If the type must be extended, it is zero extended.
760 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
762 /// Return a SCEV corresponding to a conversion of the input value to the
763 /// specified type. If the type must be extended, it is sign extended.
764 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
766 /// Return a SCEV corresponding to a conversion of the input value to the
767 /// specified type. If the type must be extended, it is zero extended. The
768 /// conversion must not be narrowing.
769 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
771 /// Return a SCEV corresponding to a conversion of the input value to the
772 /// specified type. If the type must be extended, it is sign extended. The
773 /// conversion must not be narrowing.
774 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
776 /// Return a SCEV corresponding to a conversion of the input value to the
777 /// specified type. If the type must be extended, it is extended with
778 /// unspecified bits. The conversion must not be narrowing.
779 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
781 /// Return a SCEV corresponding to a conversion of the input value to the
782 /// specified type. The conversion must not be widening.
783 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
785 /// Promote the operands to the wider of the types using zero-extension, and
786 /// then perform a umax operation with them.
787 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
790 /// Promote the operands to the wider of the types using zero-extension, and
791 /// then perform a umin operation with them.
792 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
795 /// Transitively follow the chain of pointer-type operands until reaching a
796 /// SCEV that does not have a single pointer operand. This returns a
797 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
799 const SCEV *getPointerBase(const SCEV *V);
801 /// Return a SCEV expression for the specified value at the specified scope
802 /// in the program. The L value specifies a loop nest to evaluate the
803 /// expression at, where null is the top-level or a specified loop is
804 /// immediately inside of the loop.
806 /// This method can be used to compute the exit value for a variable defined
807 /// in a loop by querying what the value will hold in the parent loop.
809 /// In the case that a relevant loop exit value cannot be computed, the
810 /// original value V is returned.
811 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
813 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
814 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
816 /// Test whether entry to the loop is protected by a conditional between LHS
817 /// and RHS. This is used to help avoid max expressions in loop trip
818 /// counts, and to eliminate casts.
819 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
820 const SCEV *LHS, const SCEV *RHS);
822 /// Test whether the backedge of the loop is protected by a conditional
823 /// between LHS and RHS. This is used to to eliminate casts.
824 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
825 const SCEV *LHS, const SCEV *RHS);
827 /// \brief Returns the maximum trip count of the loop if it is a single-exit
828 /// loop and we can compute a small maximum for that loop.
830 /// Implemented in terms of the \c getSmallConstantTripCount overload with
831 /// the single exiting block passed to it. See that routine for details.
832 unsigned getSmallConstantTripCount(Loop *L);
834 /// Returns the maximum trip count of this loop as a normal unsigned
835 /// value. Returns 0 if the trip count is unknown or not constant. This
836 /// "trip count" assumes that control exits via ExitingBlock. More
837 /// precisely, it is the number of times that control may reach ExitingBlock
838 /// before taking the branch. For loops with multiple exits, it may not be
839 /// the number times that the loop header executes if the loop exits
840 /// prematurely via another branch.
841 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
843 /// \brief Returns the largest constant divisor of the trip count of the
844 /// loop if it is a single-exit loop and we can compute a small maximum for
847 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
848 /// the single exiting block passed to it. See that routine for details.
849 unsigned getSmallConstantTripMultiple(Loop *L);
851 /// Returns the largest constant divisor of the trip count of this loop as a
852 /// normal unsigned value, if possible. This means that the actual trip
853 /// count is always a multiple of the returned value (don't forget the trip
854 /// count could very well be zero as well!). As explained in the comments
855 /// for getSmallConstantTripCount, this assumes that control exits the loop
856 /// via ExitingBlock.
857 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
859 /// Get the expression for the number of loop iterations for which this loop
860 /// is guaranteed not to exit via ExitingBlock. Otherwise return
861 /// SCEVCouldNotCompute.
862 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
864 /// If the specified loop has a predictable backedge-taken count, return it,
865 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
866 /// is the number of times the loop header will be branched to from within
867 /// the loop. This is one less than the trip count of the loop, since it
868 /// doesn't count the first iteration, when the header is branched to from
869 /// outside the loop.
871 /// Note that it is not valid to call this method on a loop without a
872 /// loop-invariant backedge-taken count (see
873 /// hasLoopInvariantBackedgeTakenCount).
875 const SCEV *getBackedgeTakenCount(const Loop *L);
877 /// Similar to getBackedgeTakenCount, except return the least SCEV value
878 /// that is known never to be less than the actual backedge taken count.
879 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
881 /// Return true if the specified loop has an analyzable loop-invariant
882 /// backedge-taken count.
883 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
885 /// This method should be called by the client when it has changed a loop in
886 /// a way that may effect ScalarEvolution's ability to compute a trip count,
887 /// or if the loop is deleted. This call is potentially expensive for large
889 void forgetLoop(const Loop *L);
891 /// This method should be called by the client when it has changed a value
892 /// in a way that may effect its value, or which may disconnect it from a
893 /// def-use chain linking it to a loop.
894 void forgetValue(Value *V);
896 /// \brief Called when the client has changed the disposition of values in
899 /// We don't have a way to invalidate per-loop dispositions. Clear and
900 /// recompute is simpler.
901 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
903 /// Determine the minimum number of zero bits that S is guaranteed to end in
904 /// (at every loop iteration). It is, at the same time, the minimum number
905 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
906 /// If S is guaranteed to be 0, it returns the bitwidth of S.
907 uint32_t GetMinTrailingZeros(const SCEV *S);
909 /// Determine the unsigned range for a particular SCEV.
911 ConstantRange getUnsignedRange(const SCEV *S) {
912 return getRange(S, HINT_RANGE_UNSIGNED);
915 /// Determine the signed range for a particular SCEV.
917 ConstantRange getSignedRange(const SCEV *S) {
918 return getRange(S, HINT_RANGE_SIGNED);
921 /// Test if the given expression is known to be negative.
923 bool isKnownNegative(const SCEV *S);
925 /// Test if the given expression is known to be positive.
927 bool isKnownPositive(const SCEV *S);
929 /// Test if the given expression is known to be non-negative.
931 bool isKnownNonNegative(const SCEV *S);
933 /// Test if the given expression is known to be non-positive.
935 bool isKnownNonPositive(const SCEV *S);
937 /// Test if the given expression is known to be non-zero.
939 bool isKnownNonZero(const SCEV *S);
941 /// Test if the given expression is known to satisfy the condition described
942 /// by Pred, LHS, and RHS.
944 bool isKnownPredicate(ICmpInst::Predicate Pred,
945 const SCEV *LHS, const SCEV *RHS);
947 /// Return true if the result of the predicate LHS `Pred` RHS is loop
948 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
949 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
950 /// loop invariant form of LHS `Pred` RHS.
951 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
952 const SCEV *RHS, const Loop *L,
953 ICmpInst::Predicate &InvariantPred,
954 const SCEV *&InvariantLHS,
955 const SCEV *&InvariantRHS);
957 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
958 /// iff any changes were made. If the operands are provably equal or
959 /// unequal, LHS and RHS are set to the same value and Pred is set to either
960 /// ICMP_EQ or ICMP_NE.
962 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
967 /// Return the "disposition" of the given SCEV with respect to the given
969 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
971 /// Return true if the value of the given SCEV is unchanging in the
973 bool isLoopInvariant(const SCEV *S, const Loop *L);
975 /// Return true if the given SCEV changes value in a known way in the
976 /// specified loop. This property being true implies that the value is
977 /// variant in the loop AND that we can emit an expression to compute the
978 /// value of the expression at any particular loop iteration.
979 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
981 /// Return the "disposition" of the given SCEV with respect to the given
983 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
985 /// Return true if elements that makes up the given SCEV dominate the
986 /// specified basic block.
987 bool dominates(const SCEV *S, const BasicBlock *BB);
989 /// Return true if elements that makes up the given SCEV properly dominate
990 /// the specified basic block.
991 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
993 /// Test whether the given SCEV has Op as a direct or indirect operand.
994 bool hasOperand(const SCEV *S, const SCEV *Op) const;
996 /// Return the size of an element read or written by Inst.
997 const SCEV *getElementSize(Instruction *Inst);
999 /// Compute the array dimensions Sizes from the set of Terms extracted from
1000 /// the memory access function of this SCEVAddRecExpr.
1001 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
1002 SmallVectorImpl<const SCEV *> &Sizes,
1003 const SCEV *ElementSize) const;
1005 void print(raw_ostream &OS) const;
1006 void verify() const;
1008 /// Collect parametric terms occurring in step expressions.
1009 void collectParametricTerms(const SCEV *Expr,
1010 SmallVectorImpl<const SCEV *> &Terms);
1014 /// Return in Subscripts the access functions for each dimension in Sizes.
1015 void computeAccessFunctions(const SCEV *Expr,
1016 SmallVectorImpl<const SCEV *> &Subscripts,
1017 SmallVectorImpl<const SCEV *> &Sizes);
1019 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
1020 /// subscripts and sizes of an array access.
1022 /// The delinearization is a 3 step process: the first two steps compute the
1023 /// sizes of each subscript and the third step computes the access functions
1024 /// for the delinearized array:
1026 /// 1. Find the terms in the step functions
1027 /// 2. Compute the array size
1028 /// 3. Compute the access function: divide the SCEV by the array size
1029 /// starting with the innermost dimensions found in step 2. The Quotient
1030 /// is the SCEV to be divided in the next step of the recursion. The
1031 /// Remainder is the subscript of the innermost dimension. Loop over all
1032 /// array dimensions computed in step 2.
1034 /// To compute a uniform array size for several memory accesses to the same
1035 /// object, one can collect in step 1 all the step terms for all the memory
1036 /// accesses, and compute in step 2 a unique array shape. This guarantees
1037 /// that the array shape will be the same across all memory accesses.
1039 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1040 /// the array shape given in metadata.
1049 /// A[j+k][2i][5i] =
1051 /// The initial SCEV:
1053 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1055 /// 1. Find the different terms in the step functions:
1056 /// -> [2*m, 5, n*m, n*m]
1058 /// 2. Compute the array size: sort and unique them
1059 /// -> [n*m, 2*m, 5]
1060 /// find the GCD of all the terms = 1
1061 /// divide by the GCD and erase constant terms
1064 /// divide by GCD -> [n, 2]
1065 /// remove constant terms
1067 /// size of the array is A[unknown][n][m]
1069 /// 3. Compute the access function
1070 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1071 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1072 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1073 /// The remainder is the subscript of the innermost array dimension: [5i].
1075 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1076 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1077 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1078 /// The Remainder is the subscript of the next array dimension: [2i].
1080 /// The subscript of the outermost dimension is the Quotient: [j+k].
1082 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1083 void delinearize(const SCEV *Expr,
1084 SmallVectorImpl<const SCEV *> &Subscripts,
1085 SmallVectorImpl<const SCEV *> &Sizes,
1086 const SCEV *ElementSize);
1089 /// Compute the backedge taken count knowing the interval difference, the
1090 /// stride and presence of the equality in the comparison.
1091 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1094 /// Verify if an linear IV with positive stride can overflow when in a
1095 /// less-than comparison, knowing the invariant term of the comparison,
1096 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1097 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
1098 bool IsSigned, bool NoWrap);
1100 /// Verify if an linear IV with negative stride can overflow when in a
1101 /// greater-than comparison, knowing the invariant term of the comparison,
1102 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1103 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
1104 bool IsSigned, bool NoWrap);
1107 FoldingSet<SCEV> UniqueSCEVs;
1108 BumpPtrAllocator SCEVAllocator;
1110 /// The head of a linked list of all SCEVUnknown values that have been
1111 /// allocated. This is used by releaseMemory to locate them all and call
1112 /// their destructors.
1113 SCEVUnknown *FirstUnknown;
1116 /// \brief Analysis pass that exposes the \c ScalarEvolution for a function.
1117 class ScalarEvolutionAnalysis {
1121 typedef ScalarEvolution Result;
1123 /// \brief Opaque, unique identifier for this analysis pass.
1124 static void *ID() { return (void *)&PassID; }
1126 /// \brief Provide a name for the analysis for debugging and logging.
1127 static StringRef name() { return "ScalarEvolutionAnalysis"; }
1129 ScalarEvolution run(Function &F, AnalysisManager<Function> *AM);
1132 /// \brief Printer pass for the \c ScalarEvolutionAnalysis results.
1133 class ScalarEvolutionPrinterPass {
1137 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1138 PreservedAnalyses run(Function &F, AnalysisManager<Function> *AM);
1140 static StringRef name() { return "ScalarEvolutionPrinterPass"; }
1143 class ScalarEvolutionWrapperPass : public FunctionPass {
1144 std::unique_ptr<ScalarEvolution> SE;
1149 ScalarEvolutionWrapperPass();
1151 ScalarEvolution &getSE() { return *SE; }
1152 const ScalarEvolution &getSE() const { return *SE; }
1154 bool runOnFunction(Function &F) override;
1155 void releaseMemory() override;
1156 void getAnalysisUsage(AnalysisUsage &AU) const override;
1157 void print(raw_ostream &OS, const Module * = nullptr) const override;
1158 void verifyAnalysis() const override;