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 /// Information about the number of loop iterations for which a loop exit's
257 /// branch condition evaluates to the not-taken path. This is a temporary
258 /// pair of exact and max expressions that are eventually summarized in
259 /// ExitNotTakenInfo and BackedgeTakenInfo.
264 /*implicit*/ ExitLimit(const SCEV *E) : Exact(E), Max(E) {}
266 ExitLimit(const SCEV *E, const SCEV *M) : Exact(E), Max(M) {}
268 /// Test whether this ExitLimit contains any computed information, or
269 /// whether it's all SCEVCouldNotCompute values.
270 bool hasAnyInfo() const {
271 return !isa<SCEVCouldNotCompute>(Exact) ||
272 !isa<SCEVCouldNotCompute>(Max);
276 /// Information about the number of times a particular loop exit may be
277 /// reached before exiting the loop.
278 struct ExitNotTakenInfo {
279 AssertingVH<BasicBlock> ExitingBlock;
280 const SCEV *ExactNotTaken;
281 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
283 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
285 /// Return true if all loop exits are computable.
286 bool isCompleteList() const {
287 return NextExit.getInt() == 0;
290 void setIncomplete() { NextExit.setInt(1); }
292 /// Return a pointer to the next exit's not-taken info.
293 ExitNotTakenInfo *getNextExit() const {
294 return NextExit.getPointer();
297 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
300 /// Information about the backedge-taken count of a loop. This currently
301 /// includes an exact count and a maximum count.
303 class BackedgeTakenInfo {
304 /// A list of computable exits and their not-taken counts. Loops almost
305 /// never have more than one computable exit.
306 ExitNotTakenInfo ExitNotTaken;
308 /// An expression indicating the least maximum backedge-taken count of the
309 /// loop that is known, or a SCEVCouldNotCompute.
313 BackedgeTakenInfo() : Max(nullptr) {}
315 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
317 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
318 bool Complete, const SCEV *MaxCount);
320 /// Test whether this BackedgeTakenInfo contains any computed information,
321 /// or whether it's all SCEVCouldNotCompute values.
322 bool hasAnyInfo() const {
323 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
326 /// Return an expression indicating the exact backedge-taken count of the
327 /// loop if it is known, or SCEVCouldNotCompute otherwise. This is the
328 /// number of times the loop header can be guaranteed to execute, minus
330 const SCEV *getExact(ScalarEvolution *SE) const;
332 /// Return the number of times this loop exit may fall through to the back
333 /// edge, or SCEVCouldNotCompute. The loop is guaranteed not to exit via
334 /// this block before this number of iterations, but may exit via another
336 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
338 /// Get the max backedge taken count for the loop.
339 const SCEV *getMax(ScalarEvolution *SE) const;
341 /// Return true if any backedge taken count expressions refer to the given
343 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
345 /// Invalidate this result and free associated memory.
349 /// Cache the backedge-taken count of the loops for this function as they
351 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
353 /// This map contains entries for all of the PHI instructions that we
354 /// attempt to compute constant evolutions for. This allows us to avoid
355 /// potentially expensive recomputation of these properties. An instruction
356 /// maps to null if we are unable to compute its exit value.
357 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
359 /// This map contains entries for all the expressions that we attempt to
360 /// compute getSCEVAtScope information for, which can be expensive in
362 DenseMap<const SCEV *,
363 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
365 /// Memoized computeLoopDisposition results.
366 DenseMap<const SCEV *,
367 SmallVector<PointerIntPair<const Loop *, 2, LoopDisposition>, 2>>
370 /// Compute a LoopDisposition value.
371 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
373 /// Memoized computeBlockDisposition results.
376 SmallVector<PointerIntPair<const BasicBlock *, 2, BlockDisposition>, 2>>
379 /// Compute a BlockDisposition value.
380 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
382 /// Memoized results from getRange
383 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
385 /// Memoized results from getRange
386 DenseMap<const SCEV *, ConstantRange> SignedRanges;
388 /// Used to parameterize getRange
389 enum RangeSignHint { HINT_RANGE_UNSIGNED, HINT_RANGE_SIGNED };
391 /// Set the memoized range for the given SCEV.
392 const ConstantRange &setRange(const SCEV *S, RangeSignHint Hint,
393 const ConstantRange &CR) {
394 DenseMap<const SCEV *, ConstantRange> &Cache =
395 Hint == HINT_RANGE_UNSIGNED ? UnsignedRanges : SignedRanges;
397 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
398 Cache.insert(std::make_pair(S, CR));
400 Pair.first->second = CR;
401 return Pair.first->second;
404 /// Determine the range for a particular SCEV.
405 ConstantRange getRange(const SCEV *S, RangeSignHint Hint);
407 /// We know that there is no SCEV for the specified value. Analyze the
409 const SCEV *createSCEV(Value *V);
411 /// Provide the special handling we need to analyze PHI SCEVs.
412 const SCEV *createNodeForPHI(PHINode *PN);
414 /// Provide the special handling we need to analyze GEP SCEVs.
415 const SCEV *createNodeForGEP(GEPOperator *GEP);
417 /// Implementation code for getSCEVAtScope; called at most once for each
420 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
422 /// This looks up computed SCEV values for all instructions that depend on
423 /// the given instruction and removes them from the ValueExprMap map if they
424 /// reference SymName. This is used during PHI resolution.
425 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
427 /// Return the BackedgeTakenInfo for the given loop, lazily computing new
428 /// values if the loop hasn't been analyzed yet.
429 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
431 /// Compute the number of times the specified loop will iterate.
432 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
434 /// Compute the number of times the backedge of the specified loop will
435 /// execute if it exits via the specified block.
436 ExitLimit ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
438 /// Compute the number of times the backedge of the specified loop will
439 /// execute if its exit condition were a conditional branch of ExitCond,
441 ExitLimit ComputeExitLimitFromCond(const Loop *L,
447 /// Compute the number of times the backedge of the specified loop will
448 /// execute if its exit condition were a conditional branch of the ICmpInst
449 /// ExitCond, TBB, and FBB.
450 ExitLimit ComputeExitLimitFromICmp(const Loop *L,
456 /// Compute the number of times the backedge of the specified loop will
457 /// execute if its exit condition were a switch with a single exiting case
460 ComputeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
461 BasicBlock *ExitingBB, bool IsSubExpr);
463 /// Given an exit condition of 'icmp op load X, cst', try to see if we can
464 /// compute the backedge-taken count.
465 ExitLimit ComputeLoadConstantCompareExitLimit(LoadInst *LI,
468 ICmpInst::Predicate p);
470 /// If the loop is known to execute a constant number of times (the
471 /// condition evolves only from constants), try to evaluate a few iterations
472 /// of the loop until we get the exit condition gets a value of ExitWhen
473 /// (true or false). If we cannot evaluate the exit count of the loop,
474 /// return CouldNotCompute.
475 const SCEV *ComputeExitCountExhaustively(const Loop *L,
479 /// Return the number of times an exit condition comparing the specified
480 /// value to zero will execute. If not computable, return CouldNotCompute.
481 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
483 /// Return the number of times an exit condition checking the specified
484 /// value for nonzero will execute. If not computable, return
486 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
488 /// Return the number of times an exit condition containing the specified
489 /// less-than comparison will execute. If not computable, return
490 /// CouldNotCompute. isSigned specifies whether the less-than is signed.
491 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
492 const Loop *L, bool isSigned, bool IsSubExpr);
493 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
494 const Loop *L, bool isSigned, bool IsSubExpr);
496 /// Return a predecessor of BB (which may not be an immediate predecessor)
497 /// which has exactly one successor from which BB is reachable, or null if
498 /// no such block is found.
499 std::pair<BasicBlock *, BasicBlock *>
500 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
502 /// Test whether the condition described by Pred, LHS, and RHS is true
503 /// whenever the given FoundCondValue value evaluates to true.
504 bool isImpliedCond(ICmpInst::Predicate Pred,
505 const SCEV *LHS, const SCEV *RHS,
506 Value *FoundCondValue,
509 /// Test whether the condition described by Pred, LHS, and RHS is true
510 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
512 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
513 const SCEV *LHS, const SCEV *RHS,
514 const SCEV *FoundLHS, const SCEV *FoundRHS);
516 /// Test whether the condition described by Pred, LHS, and RHS is true
517 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
519 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
520 const SCEV *LHS, const SCEV *RHS,
521 const SCEV *FoundLHS,
522 const SCEV *FoundRHS);
524 /// Test whether the condition described by Pred, LHS, and RHS is true
525 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
526 /// true. Utility function used by isImpliedCondOperands.
527 bool isImpliedCondOperandsViaRanges(ICmpInst::Predicate Pred,
528 const SCEV *LHS, const SCEV *RHS,
529 const SCEV *FoundLHS,
530 const SCEV *FoundRHS);
532 /// Test whether the condition described by Pred, LHS, and RHS is true
533 /// whenever the condition described by Pred, FoundLHS, and FoundRHS is
536 /// This routine tries to rule out certain kinds of integer overflow, and
537 /// then tries to reason about arithmetic properties of the predicates.
538 bool isImpliedCondOperandsViaNoOverflow(ICmpInst::Predicate Pred,
539 const SCEV *LHS, const SCEV *RHS,
540 const SCEV *FoundLHS,
541 const SCEV *FoundRHS);
543 /// If we know that the specified Phi is in the header of its containing
544 /// loop, we know the loop executes a constant number of times, and the PHI
545 /// node is just a recurrence involving constants, fold it.
546 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
549 /// Test if the given expression is known to satisfy the condition described
550 /// by Pred and the known constant ranges of LHS and RHS.
552 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
553 const SCEV *LHS, const SCEV *RHS);
555 /// Drop memoized information computed for S.
556 void forgetMemoizedResults(const SCEV *S);
558 /// Return an existing SCEV for V if there is one, otherwise return nullptr.
559 const SCEV *getExistingSCEV(Value *V);
561 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
563 bool checkValidity(const SCEV *S) const;
565 /// Return true if `ExtendOpTy`({`Start`,+,`Step`}) can be proved to be
566 /// equal to {`ExtendOpTy`(`Start`),+,`ExtendOpTy`(`Step`)}. This is
567 /// equivalent to proving no signed (resp. unsigned) wrap in
568 /// {`Start`,+,`Step`} if `ExtendOpTy` is `SCEVSignExtendExpr`
569 /// (resp. `SCEVZeroExtendExpr`).
571 template<typename ExtendOpTy>
572 bool proveNoWrapByVaryingStart(const SCEV *Start, const SCEV *Step,
575 bool isMonotonicPredicateImpl(const SCEVAddRecExpr *LHS,
576 ICmpInst::Predicate Pred, bool &Increasing);
578 /// Return true if, for all loop invariant X, the predicate "LHS `Pred` X"
579 /// is monotonically increasing or decreasing. In the former case set
580 /// `Increasing` to true and in the latter case set `Increasing` to false.
582 /// A predicate is said to be monotonically increasing if may go from being
583 /// false to being true as the loop iterates, but never the other way
584 /// around. A predicate is said to be monotonically decreasing if may go
585 /// from being true to being false as the loop iterates, but never the other
587 bool isMonotonicPredicate(const SCEVAddRecExpr *LHS,
588 ICmpInst::Predicate Pred, bool &Increasing);
590 // Return SCEV no-wrap flags that can be proven based on reasoning
591 // about how poison produced from no-wrap flags on this value
592 // (e.g. a nuw add) would trigger undefined behavior on overflow.
593 SCEV::NoWrapFlags getNoWrapFlagsFromUB(const Value *V);
596 ScalarEvolution(Function &F, TargetLibraryInfo &TLI, AssumptionCache &AC,
597 DominatorTree &DT, LoopInfo &LI);
599 ScalarEvolution(ScalarEvolution &&Arg);
601 LLVMContext &getContext() const { return F.getContext(); }
603 /// Test if values of the given type are analyzable within the SCEV
604 /// framework. This primarily includes integer types, and it can optionally
605 /// include pointer types if the ScalarEvolution class has access to
606 /// target-specific information.
607 bool isSCEVable(Type *Ty) const;
609 /// Return the size in bits of the specified type, for which isSCEVable must
611 uint64_t getTypeSizeInBits(Type *Ty) const;
613 /// Return a type with the same bitwidth as the given type and which
614 /// represents how SCEV will treat the given type, for which isSCEVable must
615 /// return true. For pointer types, this is the pointer-sized integer type.
616 Type *getEffectiveSCEVType(Type *Ty) const;
618 /// Return a SCEV expression for the full generality of the specified
620 const SCEV *getSCEV(Value *V);
622 const SCEV *getConstant(ConstantInt *V);
623 const SCEV *getConstant(const APInt& Val);
624 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
625 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
626 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
627 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
628 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
629 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
630 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
631 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
632 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
633 SmallVector<const SCEV *, 2> Ops;
636 return getAddExpr(Ops, Flags);
638 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
639 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
640 SmallVector<const SCEV *, 3> Ops;
644 return getAddExpr(Ops, Flags);
646 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
647 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
648 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
649 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap)
651 SmallVector<const SCEV *, 2> Ops;
654 return getMulExpr(Ops, Flags);
656 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
657 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
658 SmallVector<const SCEV *, 3> Ops;
662 return getMulExpr(Ops, Flags);
664 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
665 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
666 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
667 const Loop *L, SCEV::NoWrapFlags Flags);
668 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
669 const Loop *L, SCEV::NoWrapFlags Flags);
670 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
671 const Loop *L, SCEV::NoWrapFlags Flags) {
672 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
673 return getAddRecExpr(NewOp, L, Flags);
675 /// \brief Returns an expression for a GEP
677 /// \p PointeeType The type used as the basis for the pointer arithmetics
678 /// \p BaseExpr The expression for the pointer operand.
679 /// \p IndexExprs The expressions for the indices.
680 /// \p InBounds Whether the GEP is in bounds.
681 const SCEV *getGEPExpr(Type *PointeeType, const SCEV *BaseExpr,
682 const SmallVectorImpl<const SCEV *> &IndexExprs,
683 bool InBounds = false);
684 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
685 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
686 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
687 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
688 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
689 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
690 const SCEV *getUnknown(Value *V);
691 const SCEV *getCouldNotCompute();
693 /// \brief Return a SCEV for the constant 0 of a specific type.
694 const SCEV *getZero(Type *Ty) { return getConstant(Ty, 0); }
696 /// \brief Return a SCEV for the constant 1 of a specific type.
697 const SCEV *getOne(Type *Ty) { return getConstant(Ty, 1); }
699 /// Return an expression for sizeof AllocTy that is type IntTy
701 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
703 /// Return an expression for offsetof on the given field with type IntTy
705 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
707 /// Return the SCEV object corresponding to -V.
709 const SCEV *getNegativeSCEV(const SCEV *V,
710 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
712 /// Return the SCEV object corresponding to ~V.
714 const SCEV *getNotSCEV(const SCEV *V);
716 /// Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
717 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
718 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
720 /// Return a SCEV corresponding to a conversion of the input value to the
721 /// specified type. If the type must be extended, it is zero extended.
722 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
724 /// Return a SCEV corresponding to a conversion of the input value to the
725 /// specified type. If the type must be extended, it is sign extended.
726 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
728 /// Return a SCEV corresponding to a conversion of the input value to the
729 /// specified type. If the type must be extended, it is zero extended. The
730 /// conversion must not be narrowing.
731 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
733 /// Return a SCEV corresponding to a conversion of the input value to the
734 /// specified type. If the type must be extended, it is sign extended. The
735 /// conversion must not be narrowing.
736 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
738 /// Return a SCEV corresponding to a conversion of the input value to the
739 /// specified type. If the type must be extended, it is extended with
740 /// unspecified bits. The conversion must not be narrowing.
741 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
743 /// Return a SCEV corresponding to a conversion of the input value to the
744 /// specified type. The conversion must not be widening.
745 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
747 /// Promote the operands to the wider of the types using zero-extension, and
748 /// then perform a umax operation with them.
749 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
752 /// Promote the operands to the wider of the types using zero-extension, and
753 /// then perform a umin operation with them.
754 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
757 /// Transitively follow the chain of pointer-type operands until reaching a
758 /// SCEV that does not have a single pointer operand. This returns a
759 /// SCEVUnknown pointer for well-formed pointer-type expressions, but corner
761 const SCEV *getPointerBase(const SCEV *V);
763 /// Return a SCEV expression for the specified value at the specified scope
764 /// in the program. The L value specifies a loop nest to evaluate the
765 /// expression at, where null is the top-level or a specified loop is
766 /// immediately inside of the loop.
768 /// This method can be used to compute the exit value for a variable defined
769 /// in a loop by querying what the value will hold in the parent loop.
771 /// In the case that a relevant loop exit value cannot be computed, the
772 /// original value V is returned.
773 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
775 /// This is a convenience function which does getSCEVAtScope(getSCEV(V), L).
776 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
778 /// Test whether entry to the loop is protected by a conditional between LHS
779 /// and RHS. This is used to help avoid max expressions in loop trip
780 /// counts, and to eliminate casts.
781 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
782 const SCEV *LHS, const SCEV *RHS);
784 /// Test whether the backedge of the loop is protected by a conditional
785 /// between LHS and RHS. This is used to to eliminate casts.
786 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
787 const SCEV *LHS, const SCEV *RHS);
789 /// \brief Returns the maximum trip count of the loop if it is a single-exit
790 /// loop and we can compute a small maximum for that loop.
792 /// Implemented in terms of the \c getSmallConstantTripCount overload with
793 /// the single exiting block passed to it. See that routine for details.
794 unsigned getSmallConstantTripCount(Loop *L);
796 /// Returns the maximum trip count of this loop as a normal unsigned
797 /// value. Returns 0 if the trip count is unknown or not constant. This
798 /// "trip count" assumes that control exits via ExitingBlock. More
799 /// precisely, it is the number of times that control may reach ExitingBlock
800 /// before taking the branch. For loops with multiple exits, it may not be
801 /// the number times that the loop header executes if the loop exits
802 /// prematurely via another branch.
803 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
805 /// \brief Returns the largest constant divisor of the trip count of the
806 /// loop if it is a single-exit loop and we can compute a small maximum for
809 /// Implemented in terms of the \c getSmallConstantTripMultiple overload with
810 /// the single exiting block passed to it. See that routine for details.
811 unsigned getSmallConstantTripMultiple(Loop *L);
813 /// Returns the largest constant divisor of the trip count of this loop as a
814 /// normal unsigned value, if possible. This means that the actual trip
815 /// count is always a multiple of the returned value (don't forget the trip
816 /// count could very well be zero as well!). As explained in the comments
817 /// for getSmallConstantTripCount, this assumes that control exits the loop
818 /// via ExitingBlock.
819 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
821 /// Get the expression for the number of loop iterations for which this loop
822 /// is guaranteed not to exit via ExitingBlock. Otherwise return
823 /// SCEVCouldNotCompute.
824 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
826 /// If the specified loop has a predictable backedge-taken count, return it,
827 /// otherwise return a SCEVCouldNotCompute object. The backedge-taken count
828 /// is the number of times the loop header will be branched to from within
829 /// the loop. This is one less than the trip count of the loop, since it
830 /// doesn't count the first iteration, when the header is branched to from
831 /// outside the loop.
833 /// Note that it is not valid to call this method on a loop without a
834 /// loop-invariant backedge-taken count (see
835 /// hasLoopInvariantBackedgeTakenCount).
837 const SCEV *getBackedgeTakenCount(const Loop *L);
839 /// Similar to getBackedgeTakenCount, except return the least SCEV value
840 /// that is known never to be less than the actual backedge taken count.
841 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
843 /// Return true if the specified loop has an analyzable loop-invariant
844 /// backedge-taken count.
845 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
847 /// This method should be called by the client when it has changed a loop in
848 /// a way that may effect ScalarEvolution's ability to compute a trip count,
849 /// or if the loop is deleted. This call is potentially expensive for large
851 void forgetLoop(const Loop *L);
853 /// This method should be called by the client when it has changed a value
854 /// in a way that may effect its value, or which may disconnect it from a
855 /// def-use chain linking it to a loop.
856 void forgetValue(Value *V);
858 /// \brief Called when the client has changed the disposition of values in
861 /// We don't have a way to invalidate per-loop dispositions. Clear and
862 /// recompute is simpler.
863 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
865 /// Determine the minimum number of zero bits that S is guaranteed to end in
866 /// (at every loop iteration). It is, at the same time, the minimum number
867 /// of times S is divisible by 2. For example, given {4,+,8} it returns 2.
868 /// If S is guaranteed to be 0, it returns the bitwidth of S.
869 uint32_t GetMinTrailingZeros(const SCEV *S);
871 /// Determine the unsigned range for a particular SCEV.
873 ConstantRange getUnsignedRange(const SCEV *S) {
874 return getRange(S, HINT_RANGE_UNSIGNED);
877 /// Determine the signed range for a particular SCEV.
879 ConstantRange getSignedRange(const SCEV *S) {
880 return getRange(S, HINT_RANGE_SIGNED);
883 /// Test if the given expression is known to be negative.
885 bool isKnownNegative(const SCEV *S);
887 /// Test if the given expression is known to be positive.
889 bool isKnownPositive(const SCEV *S);
891 /// Test if the given expression is known to be non-negative.
893 bool isKnownNonNegative(const SCEV *S);
895 /// Test if the given expression is known to be non-positive.
897 bool isKnownNonPositive(const SCEV *S);
899 /// Test if the given expression is known to be non-zero.
901 bool isKnownNonZero(const SCEV *S);
903 /// Test if the given expression is known to satisfy the condition described
904 /// by Pred, LHS, and RHS.
906 bool isKnownPredicate(ICmpInst::Predicate Pred,
907 const SCEV *LHS, const SCEV *RHS);
909 /// Return true if the result of the predicate LHS `Pred` RHS is loop
910 /// invariant with respect to L. Set InvariantPred, InvariantLHS and
911 /// InvariantLHS so that InvariantLHS `InvariantPred` InvariantRHS is the
912 /// loop invariant form of LHS `Pred` RHS.
913 bool isLoopInvariantPredicate(ICmpInst::Predicate Pred, const SCEV *LHS,
914 const SCEV *RHS, const Loop *L,
915 ICmpInst::Predicate &InvariantPred,
916 const SCEV *&InvariantLHS,
917 const SCEV *&InvariantRHS);
919 /// Simplify LHS and RHS in a comparison with predicate Pred. Return true
920 /// iff any changes were made. If the operands are provably equal or
921 /// unequal, LHS and RHS are set to the same value and Pred is set to either
922 /// ICMP_EQ or ICMP_NE.
924 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
929 /// Return the "disposition" of the given SCEV with respect to the given
931 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
933 /// Return true if the value of the given SCEV is unchanging in the
935 bool isLoopInvariant(const SCEV *S, const Loop *L);
937 /// Return true if the given SCEV changes value in a known way in the
938 /// specified loop. This property being true implies that the value is
939 /// variant in the loop AND that we can emit an expression to compute the
940 /// value of the expression at any particular loop iteration.
941 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
943 /// Return the "disposition" of the given SCEV with respect to the given
945 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
947 /// Return true if elements that makes up the given SCEV dominate the
948 /// specified basic block.
949 bool dominates(const SCEV *S, const BasicBlock *BB);
951 /// Return true if elements that makes up the given SCEV properly dominate
952 /// the specified basic block.
953 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
955 /// Test whether the given SCEV has Op as a direct or indirect operand.
956 bool hasOperand(const SCEV *S, const SCEV *Op) const;
958 /// Return the size of an element read or written by Inst.
959 const SCEV *getElementSize(Instruction *Inst);
961 /// Compute the array dimensions Sizes from the set of Terms extracted from
962 /// the memory access function of this SCEVAddRecExpr.
963 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
964 SmallVectorImpl<const SCEV *> &Sizes,
965 const SCEV *ElementSize) const;
967 void print(raw_ostream &OS) const;
970 /// Collect parametric terms occurring in step expressions.
971 void collectParametricTerms(const SCEV *Expr,
972 SmallVectorImpl<const SCEV *> &Terms);
976 /// Return in Subscripts the access functions for each dimension in Sizes.
977 void computeAccessFunctions(const SCEV *Expr,
978 SmallVectorImpl<const SCEV *> &Subscripts,
979 SmallVectorImpl<const SCEV *> &Sizes);
981 /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
982 /// subscripts and sizes of an array access.
984 /// The delinearization is a 3 step process: the first two steps compute the
985 /// sizes of each subscript and the third step computes the access functions
986 /// for the delinearized array:
988 /// 1. Find the terms in the step functions
989 /// 2. Compute the array size
990 /// 3. Compute the access function: divide the SCEV by the array size
991 /// starting with the innermost dimensions found in step 2. The Quotient
992 /// is the SCEV to be divided in the next step of the recursion. The
993 /// Remainder is the subscript of the innermost dimension. Loop over all
994 /// array dimensions computed in step 2.
996 /// To compute a uniform array size for several memory accesses to the same
997 /// object, one can collect in step 1 all the step terms for all the memory
998 /// accesses, and compute in step 2 a unique array shape. This guarantees
999 /// that the array shape will be the same across all memory accesses.
1001 /// FIXME: We could derive the result of steps 1 and 2 from a description of
1002 /// the array shape given in metadata.
1011 /// A[j+k][2i][5i] =
1013 /// The initial SCEV:
1015 /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
1017 /// 1. Find the different terms in the step functions:
1018 /// -> [2*m, 5, n*m, n*m]
1020 /// 2. Compute the array size: sort and unique them
1021 /// -> [n*m, 2*m, 5]
1022 /// find the GCD of all the terms = 1
1023 /// divide by the GCD and erase constant terms
1026 /// divide by GCD -> [n, 2]
1027 /// remove constant terms
1029 /// size of the array is A[unknown][n][m]
1031 /// 3. Compute the access function
1032 /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
1033 /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
1034 /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
1035 /// The remainder is the subscript of the innermost array dimension: [5i].
1037 /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
1038 /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
1039 /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
1040 /// The Remainder is the subscript of the next array dimension: [2i].
1042 /// The subscript of the outermost dimension is the Quotient: [j+k].
1044 /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
1045 void delinearize(const SCEV *Expr,
1046 SmallVectorImpl<const SCEV *> &Subscripts,
1047 SmallVectorImpl<const SCEV *> &Sizes,
1048 const SCEV *ElementSize);
1051 /// Compute the backedge taken count knowing the interval difference, the
1052 /// stride and presence of the equality in the comparison.
1053 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
1056 /// Verify if an linear IV with positive stride can overflow when in a
1057 /// less-than comparison, knowing the invariant term of the comparison,
1058 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1059 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
1060 bool IsSigned, bool NoWrap);
1062 /// Verify if an linear IV with negative stride can overflow when in a
1063 /// greater-than comparison, knowing the invariant term of the comparison,
1064 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
1065 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
1066 bool IsSigned, bool NoWrap);
1069 FoldingSet<SCEV> UniqueSCEVs;
1070 BumpPtrAllocator SCEVAllocator;
1072 /// The head of a linked list of all SCEVUnknown values that have been
1073 /// allocated. This is used by releaseMemory to locate them all and call
1074 /// their destructors.
1075 SCEVUnknown *FirstUnknown;
1078 /// \brief Analysis pass that exposes the \c ScalarEvolution for a function.
1079 class ScalarEvolutionAnalysis {
1083 typedef ScalarEvolution Result;
1085 /// \brief Opaque, unique identifier for this analysis pass.
1086 static void *ID() { return (void *)&PassID; }
1088 /// \brief Provide a name for the analysis for debugging and logging.
1089 static StringRef name() { return "ScalarEvolutionAnalysis"; }
1091 ScalarEvolution run(Function &F, AnalysisManager<Function> *AM);
1094 /// \brief Printer pass for the \c ScalarEvolutionAnalysis results.
1095 class ScalarEvolutionPrinterPass {
1099 explicit ScalarEvolutionPrinterPass(raw_ostream &OS) : OS(OS) {}
1100 PreservedAnalyses run(Function &F, AnalysisManager<Function> *AM);
1102 static StringRef name() { return "ScalarEvolutionPrinterPass"; }
1105 class ScalarEvolutionWrapperPass : public FunctionPass {
1106 std::unique_ptr<ScalarEvolution> SE;
1111 ScalarEvolutionWrapperPass();
1113 ScalarEvolution &getSE() { return *SE; }
1114 const ScalarEvolution &getSE() const { return *SE; }
1116 bool runOnFunction(Function &F) override;
1117 void releaseMemory() override;
1118 void getAnalysisUsage(AnalysisUsage &AU) const override;
1119 void print(raw_ostream &OS, const Module * = nullptr) const override;
1120 void verifyAnalysis() const override;