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/ValueHandle.h"
31 #include "llvm/Pass.h"
32 #include "llvm/Support/Allocator.h"
33 #include "llvm/Support/DataTypes.h"
42 class ScalarEvolution;
44 class TargetLibraryInfo;
51 template<> struct FoldingSetTrait<SCEV>;
53 /// SCEV - This class represents an analyzed expression in the program. These
54 /// are opaque objects that the client is not allowed to do much with
57 class SCEV : public FoldingSetNode {
58 friend struct FoldingSetTrait<SCEV>;
60 /// FastID - A reference to an Interned FoldingSetNodeID for this node.
61 /// The ScalarEvolution's BumpPtrAllocator holds the data.
62 FoldingSetNodeIDRef FastID;
64 // The SCEV baseclass this node corresponds to
65 const unsigned short SCEVType;
68 /// SubclassData - This field is initialized to zero and may be used in
69 /// subclasses to store miscellaneous information.
70 unsigned short SubclassData;
73 SCEV(const SCEV &) LLVM_DELETED_FUNCTION;
74 void operator=(const SCEV &) LLVM_DELETED_FUNCTION;
77 /// NoWrapFlags are bitfield indices into SubclassData.
79 /// Add and Mul expressions may have no-unsigned-wrap <NUW> or
80 /// no-signed-wrap <NSW> properties, which are derived from the IR
81 /// operator. NSW is a misnomer that we use to mean no signed overflow or
84 /// AddRec expression may have a no-self-wraparound <NW> property if the
85 /// result can never reach the start value. This property is independent of
86 /// the actual start value and step direction. Self-wraparound is defined
87 /// purely in terms of the recurrence's loop, step size, and
88 /// bitwidth. Formally, a recurrence with no self-wraparound satisfies:
89 /// abs(step) * max-iteration(loop) <= unsigned-max(bitwidth).
91 /// Note that NUW and NSW are also valid properties of a recurrence, and
92 /// either implies NW. For convenience, NW will be set for a recurrence
93 /// whenever either NUW or NSW are set.
94 enum NoWrapFlags { FlagAnyWrap = 0, // No guarantee.
95 FlagNW = (1 << 0), // No self-wrap.
96 FlagNUW = (1 << 1), // No unsigned wrap.
97 FlagNSW = (1 << 2), // No signed wrap.
98 NoWrapMask = (1 << 3) -1 };
100 explicit SCEV(const FoldingSetNodeIDRef ID, unsigned SCEVTy) :
101 FastID(ID), SCEVType(SCEVTy), SubclassData(0) {}
103 unsigned getSCEVType() const { return SCEVType; }
105 /// getType - Return the LLVM type of this SCEV expression.
107 Type *getType() const;
109 /// isZero - Return true if the expression is a constant zero.
113 /// isOne - Return true if the expression is a constant one.
117 /// isAllOnesValue - Return true if the expression is a constant
120 bool isAllOnesValue() const;
122 /// isNonConstantNegative - Return true if the specified scev is negated,
123 /// but not a constant.
124 bool isNonConstantNegative() const;
126 /// print - Print out the internal representation of this scalar to the
127 /// specified stream. This should really only be used for debugging
129 void print(raw_ostream &OS) const;
131 /// dump - 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 /// SCEVCouldNotCompute - An object of this class is returned by queries that
157 /// could not be answered. For example, if you ask for the number of
158 /// iterations of a linked-list traversal loop, you will get one of these.
159 /// None of the standard SCEV operations are valid on this class, it is just a
161 struct SCEVCouldNotCompute : public SCEV {
162 SCEVCouldNotCompute();
164 /// Methods for support type inquiry through isa, cast, and dyn_cast:
165 static bool classof(const SCEV *S);
168 /// ScalarEvolution - This class is the main scalar evolution driver. Because
169 /// client code (intentionally) can't do much with the SCEV objects directly,
170 /// they must ask this class for services.
172 class ScalarEvolution : public FunctionPass {
174 /// LoopDisposition - An enum describing the relationship between a
176 enum LoopDisposition {
177 LoopVariant, ///< The SCEV is loop-variant (unknown).
178 LoopInvariant, ///< The SCEV is loop-invariant.
179 LoopComputable ///< The SCEV varies predictably with the loop.
182 /// BlockDisposition - An enum describing the relationship between a
183 /// SCEV and a basic block.
184 enum BlockDisposition {
185 DoesNotDominateBlock, ///< The SCEV does not dominate the block.
186 DominatesBlock, ///< The SCEV dominates the block.
187 ProperlyDominatesBlock ///< The SCEV properly dominates the block.
190 /// Convenient NoWrapFlags manipulation that hides enum casts and is
191 /// visible in the ScalarEvolution name space.
192 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
193 maskFlags(SCEV::NoWrapFlags Flags, int Mask) {
194 return (SCEV::NoWrapFlags)(Flags & Mask);
196 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
197 setFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OnFlags) {
198 return (SCEV::NoWrapFlags)(Flags | OnFlags);
200 static SCEV::NoWrapFlags LLVM_ATTRIBUTE_UNUSED_RESULT
201 clearFlags(SCEV::NoWrapFlags Flags, SCEV::NoWrapFlags OffFlags) {
202 return (SCEV::NoWrapFlags)(Flags & ~OffFlags);
206 /// SCEVCallbackVH - A CallbackVH to arrange for ScalarEvolution to be
207 /// notified whenever a Value is deleted.
208 class SCEVCallbackVH : public CallbackVH {
210 void deleted() override;
211 void allUsesReplacedWith(Value *New) override;
213 SCEVCallbackVH(Value *V, ScalarEvolution *SE = nullptr);
216 friend class SCEVCallbackVH;
217 friend class SCEVExpander;
218 friend class SCEVUnknown;
220 /// F - The function we are analyzing.
224 /// LI - The loop information for the function we are currently analyzing.
228 /// The DataLayout information for the target we are targeting.
230 const DataLayout *DL;
232 /// TLI - The target library information for the target we are targeting.
234 TargetLibraryInfo *TLI;
236 /// DT - The dominator tree.
240 /// CouldNotCompute - This SCEV is used to represent unknown trip
241 /// counts and things.
242 SCEVCouldNotCompute CouldNotCompute;
244 /// ValueExprMapType - The typedef for ValueExprMap.
246 typedef DenseMap<SCEVCallbackVH, const SCEV *, DenseMapInfo<Value *> >
249 /// ValueExprMap - This is a cache of the values we have analyzed so far.
251 ValueExprMapType ValueExprMap;
253 /// Mark predicate values currently being processed by isImpliedCond.
254 DenseSet<Value*> PendingLoopPredicates;
256 /// ExitLimit - Information about the number of loop iterations for which a
257 /// loop exit's branch condition evaluates to the not-taken path. This is a
258 /// temporary pair of exact and max expressions that are eventually
259 /// summarized in ExitNotTakenInfo and BackedgeTakenInfo.
261 /// If MustExit is true, then the exit must be taken when the BECount
262 /// reaches Exact (and before surpassing Max). If MustExit is false, then
263 /// BECount may exceed Exact or Max if the loop exits via another branch. In
264 /// either case, the loop may exit early via another branch.
266 /// MustExit is true for most cases. However, an exit guarded by an
267 /// (in)equality on a nonunit stride may be skipped.
273 /*implicit*/ ExitLimit(const SCEV *E)
274 : Exact(E), Max(E), MustExit(true) {}
276 ExitLimit(const SCEV *E, const SCEV *M, bool MustExit)
277 : Exact(E), Max(M), MustExit(MustExit) {}
279 /// hasAnyInfo - Test whether this ExitLimit contains any computed
280 /// information, or whether it's all SCEVCouldNotCompute values.
281 bool hasAnyInfo() const {
282 return !isa<SCEVCouldNotCompute>(Exact) ||
283 !isa<SCEVCouldNotCompute>(Max);
287 /// ExitNotTakenInfo - Information about the number of times a particular
288 /// loop exit may be reached before exiting the loop.
289 struct ExitNotTakenInfo {
290 AssertingVH<BasicBlock> ExitingBlock;
291 const SCEV *ExactNotTaken;
292 PointerIntPair<ExitNotTakenInfo*, 1> NextExit;
294 ExitNotTakenInfo() : ExitingBlock(nullptr), ExactNotTaken(nullptr) {}
296 /// isCompleteList - Return true if all loop exits are computable.
297 bool isCompleteList() const {
298 return NextExit.getInt() == 0;
301 void setIncomplete() { NextExit.setInt(1); }
303 /// getNextExit - Return a pointer to the next exit's not-taken info.
304 ExitNotTakenInfo *getNextExit() const {
305 return NextExit.getPointer();
308 void setNextExit(ExitNotTakenInfo *ENT) { NextExit.setPointer(ENT); }
311 /// BackedgeTakenInfo - Information about the backedge-taken count
312 /// of a loop. This currently includes an exact count and a maximum count.
314 class BackedgeTakenInfo {
315 /// ExitNotTaken - A list of computable exits and their not-taken counts.
316 /// Loops almost never have more than one computable exit.
317 ExitNotTakenInfo ExitNotTaken;
319 /// Max - An expression indicating the least maximum backedge-taken
320 /// count of the loop that is known, or a SCEVCouldNotCompute.
324 BackedgeTakenInfo() : Max(nullptr) {}
326 /// Initialize BackedgeTakenInfo from a list of exact exit counts.
328 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
329 bool Complete, const SCEV *MaxCount);
331 /// hasAnyInfo - Test whether this BackedgeTakenInfo contains any
332 /// computed information, or whether it's all SCEVCouldNotCompute
334 bool hasAnyInfo() const {
335 return ExitNotTaken.ExitingBlock || !isa<SCEVCouldNotCompute>(Max);
338 /// getExact - Return an expression indicating the exact backedge-taken
339 /// count of the loop if it is known, or SCEVCouldNotCompute
340 /// otherwise. This is the number of times the loop header can be
341 /// guaranteed to execute, minus one.
342 const SCEV *getExact(ScalarEvolution *SE) const;
344 /// getExact - Return the number of times this loop exit may fall through
345 /// to the back edge, or SCEVCouldNotCompute. The loop is guaranteed not
346 /// to exit via this block before this number of iterations, but may exit
347 /// via another block.
348 const SCEV *getExact(BasicBlock *ExitingBlock, ScalarEvolution *SE) const;
350 /// getMax - Get the max backedge taken count for the loop.
351 const SCEV *getMax(ScalarEvolution *SE) const;
353 /// Return true if any backedge taken count expressions refer to the given
355 bool hasOperand(const SCEV *S, ScalarEvolution *SE) const;
357 /// clear - Invalidate this result and free associated memory.
361 /// BackedgeTakenCounts - Cache the backedge-taken count of the loops for
362 /// this function as they are computed.
363 DenseMap<const Loop*, BackedgeTakenInfo> BackedgeTakenCounts;
365 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
366 /// the PHI instructions that we attempt to compute constant evolutions for.
367 /// This allows us to avoid potentially expensive recomputation of these
368 /// properties. An instruction maps to null if we are unable to compute its
370 DenseMap<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
372 /// ValuesAtScopes - This map contains entries for all the expressions
373 /// that we attempt to compute getSCEVAtScope information for, which can
374 /// be expensive in extreme cases.
375 DenseMap<const SCEV *,
376 SmallVector<std::pair<const Loop *, const SCEV *>, 2> > ValuesAtScopes;
378 /// LoopDispositions - Memoized computeLoopDisposition results.
379 DenseMap<const SCEV *,
380 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> > LoopDispositions;
382 /// computeLoopDisposition - Compute a LoopDisposition value.
383 LoopDisposition computeLoopDisposition(const SCEV *S, const Loop *L);
385 /// BlockDispositions - Memoized computeBlockDisposition results.
386 DenseMap<const SCEV *,
387 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> > BlockDispositions;
389 /// computeBlockDisposition - Compute a BlockDisposition value.
390 BlockDisposition computeBlockDisposition(const SCEV *S, const BasicBlock *BB);
392 /// UnsignedRanges - Memoized results from getUnsignedRange
393 DenseMap<const SCEV *, ConstantRange> UnsignedRanges;
395 /// SignedRanges - Memoized results from getSignedRange
396 DenseMap<const SCEV *, ConstantRange> SignedRanges;
398 /// setUnsignedRange - Set the memoized unsigned range for the given SCEV.
399 const ConstantRange &setUnsignedRange(const SCEV *S,
400 const ConstantRange &CR) {
401 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
402 UnsignedRanges.insert(std::make_pair(S, CR));
404 Pair.first->second = CR;
405 return Pair.first->second;
408 /// setUnsignedRange - Set the memoized signed range for the given SCEV.
409 const ConstantRange &setSignedRange(const SCEV *S,
410 const ConstantRange &CR) {
411 std::pair<DenseMap<const SCEV *, ConstantRange>::iterator, bool> Pair =
412 SignedRanges.insert(std::make_pair(S, CR));
414 Pair.first->second = CR;
415 return Pair.first->second;
418 /// createSCEV - We know that there is no SCEV for the specified value.
419 /// Analyze the expression.
420 const SCEV *createSCEV(Value *V);
422 /// createNodeForPHI - Provide the special handling we need to analyze PHI
424 const SCEV *createNodeForPHI(PHINode *PN);
426 /// createNodeForGEP - Provide the special handling we need to analyze GEP
428 const SCEV *createNodeForGEP(GEPOperator *GEP);
430 /// computeSCEVAtScope - Implementation code for getSCEVAtScope; called
431 /// at most once for each SCEV+Loop pair.
433 const SCEV *computeSCEVAtScope(const SCEV *S, const Loop *L);
435 /// ForgetSymbolicValue - This looks up computed SCEV values for all
436 /// instructions that depend on the given instruction and removes them from
437 /// the ValueExprMap map if they reference SymName. This is used during PHI
439 void ForgetSymbolicName(Instruction *I, const SCEV *SymName);
441 /// getBackedgeTakenInfo - Return the BackedgeTakenInfo for the given
442 /// loop, lazily computing new values if the loop hasn't been analyzed
444 const BackedgeTakenInfo &getBackedgeTakenInfo(const Loop *L);
446 /// ComputeBackedgeTakenCount - Compute the number of times the specified
447 /// loop will iterate.
448 BackedgeTakenInfo ComputeBackedgeTakenCount(const Loop *L);
450 /// ComputeExitLimit - Compute the number of times the backedge of the
451 /// specified loop will execute if it exits via the specified block.
452 ExitLimit ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock);
454 /// ComputeExitLimitFromCond - Compute the number of times the backedge of
455 /// the specified loop will execute if its exit condition were a conditional
456 /// branch of ExitCond, TBB, and FBB.
457 ExitLimit ComputeExitLimitFromCond(const Loop *L,
463 /// ComputeExitLimitFromICmp - Compute the number of times the backedge of
464 /// the specified loop will execute if its exit condition were a conditional
465 /// branch of the ICmpInst ExitCond, TBB, and FBB.
466 ExitLimit ComputeExitLimitFromICmp(const Loop *L,
472 /// ComputeExitLimitFromSingleExitSwitch - Compute the number of times the
473 /// backedge of the specified loop will execute if its exit condition were a
474 /// switch with a single exiting case to ExitingBB.
476 ComputeExitLimitFromSingleExitSwitch(const Loop *L, SwitchInst *Switch,
477 BasicBlock *ExitingBB, bool IsSubExpr);
479 /// ComputeLoadConstantCompareExitLimit - Given an exit condition
480 /// of 'icmp op load X, cst', try to see if we can compute the
481 /// backedge-taken count.
482 ExitLimit ComputeLoadConstantCompareExitLimit(LoadInst *LI,
485 ICmpInst::Predicate p);
487 /// ComputeExitCountExhaustively - If the loop is known to execute a
488 /// constant number of times (the condition evolves only from constants),
489 /// try to evaluate a few iterations of the loop until we get the exit
490 /// condition gets a value of ExitWhen (true or false). If we cannot
491 /// evaluate the exit count of the loop, return CouldNotCompute.
492 const SCEV *ComputeExitCountExhaustively(const Loop *L,
496 /// HowFarToZero - Return the number of times an exit condition comparing
497 /// the specified value to zero will execute. If not computable, return
499 ExitLimit HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr);
501 /// HowFarToNonZero - Return the number of times an exit condition checking
502 /// the specified value for nonzero will execute. If not computable, return
504 ExitLimit HowFarToNonZero(const SCEV *V, const Loop *L);
506 /// HowManyLessThans - Return the number of times an exit condition
507 /// containing the specified less-than comparison will execute. If not
508 /// computable, return CouldNotCompute. isSigned specifies whether the
509 /// less-than is signed.
510 ExitLimit HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
511 const Loop *L, bool isSigned, bool IsSubExpr);
512 ExitLimit HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
513 const Loop *L, bool isSigned, bool IsSubExpr);
515 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
516 /// (which may not be an immediate predecessor) which has exactly one
517 /// successor from which BB is reachable, or null if no such block is
519 std::pair<BasicBlock *, BasicBlock *>
520 getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB);
522 /// isImpliedCond - Test whether the condition described by Pred, LHS, and
523 /// RHS is true whenever the given FoundCondValue value evaluates to true.
524 bool isImpliedCond(ICmpInst::Predicate Pred,
525 const SCEV *LHS, const SCEV *RHS,
526 Value *FoundCondValue,
529 /// isImpliedCondOperands - Test whether the condition described by Pred,
530 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
531 /// and FoundRHS is true.
532 bool isImpliedCondOperands(ICmpInst::Predicate Pred,
533 const SCEV *LHS, const SCEV *RHS,
534 const SCEV *FoundLHS, const SCEV *FoundRHS);
536 /// isImpliedCondOperandsHelper - Test whether the condition described by
537 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
538 /// FoundLHS, and FoundRHS is true.
539 bool isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
540 const SCEV *LHS, const SCEV *RHS,
541 const SCEV *FoundLHS,
542 const SCEV *FoundRHS);
544 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
545 /// in the header of its containing loop, we know the loop executes a
546 /// constant number of times, and the PHI node is just a recurrence
547 /// involving constants, fold it.
548 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs,
551 /// isKnownPredicateWithRanges - Test if the given expression is known to
552 /// satisfy the condition described by Pred and the known constant ranges
555 bool isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
556 const SCEV *LHS, const SCEV *RHS);
558 /// forgetMemoizedResults - Drop memoized information computed for S.
559 void forgetMemoizedResults(const SCEV *S);
561 /// Return false iff given SCEV contains a SCEVUnknown with NULL value-
563 bool checkValidity(const SCEV *S) const;
566 static char ID; // Pass identification, replacement for typeid
569 LLVMContext &getContext() const { return F->getContext(); }
571 /// isSCEVable - Test if values of the given type are analyzable within
572 /// the SCEV framework. This primarily includes integer types, and it
573 /// can optionally include pointer types if the ScalarEvolution class
574 /// has access to target-specific information.
575 bool isSCEVable(Type *Ty) const;
577 /// getTypeSizeInBits - Return the size in bits of the specified type,
578 /// for which isSCEVable must return true.
579 uint64_t getTypeSizeInBits(Type *Ty) const;
581 /// getEffectiveSCEVType - Return a type with the same bitwidth as
582 /// the given type and which represents how SCEV will treat the given
583 /// type, for which isSCEVable must return true. For pointer types,
584 /// this is the pointer-sized integer type.
585 Type *getEffectiveSCEVType(Type *Ty) const;
587 /// getSCEV - Return a SCEV expression for the full generality of the
588 /// specified expression.
589 const SCEV *getSCEV(Value *V);
591 const SCEV *getConstant(ConstantInt *V);
592 const SCEV *getConstant(const APInt& Val);
593 const SCEV *getConstant(Type *Ty, uint64_t V, bool isSigned = false);
594 const SCEV *getTruncateExpr(const SCEV *Op, Type *Ty);
595 const SCEV *getZeroExtendExpr(const SCEV *Op, Type *Ty);
596 const SCEV *getSignExtendExpr(const SCEV *Op, Type *Ty);
597 const SCEV *getAnyExtendExpr(const SCEV *Op, Type *Ty);
598 const SCEV *getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
599 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
600 const SCEV *getAddExpr(const SCEV *LHS, const SCEV *RHS,
601 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
602 SmallVector<const SCEV *, 2> Ops;
605 return getAddExpr(Ops, Flags);
607 const SCEV *getAddExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
608 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
609 SmallVector<const SCEV *, 3> Ops;
613 return getAddExpr(Ops, Flags);
615 const SCEV *getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
616 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
617 const SCEV *getMulExpr(const SCEV *LHS, const SCEV *RHS,
618 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap)
620 SmallVector<const SCEV *, 2> Ops;
623 return getMulExpr(Ops, Flags);
625 const SCEV *getMulExpr(const SCEV *Op0, const SCEV *Op1, const SCEV *Op2,
626 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap) {
627 SmallVector<const SCEV *, 3> Ops;
631 return getMulExpr(Ops, Flags);
633 const SCEV *getUDivExpr(const SCEV *LHS, const SCEV *RHS);
634 const SCEV *getUDivExactExpr(const SCEV *LHS, const SCEV *RHS);
635 const SCEV *getAddRecExpr(const SCEV *Start, const SCEV *Step,
636 const Loop *L, SCEV::NoWrapFlags Flags);
637 const SCEV *getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
638 const Loop *L, SCEV::NoWrapFlags Flags);
639 const SCEV *getAddRecExpr(const SmallVectorImpl<const SCEV *> &Operands,
640 const Loop *L, SCEV::NoWrapFlags Flags) {
641 SmallVector<const SCEV *, 4> NewOp(Operands.begin(), Operands.end());
642 return getAddRecExpr(NewOp, L, Flags);
644 const SCEV *getSMaxExpr(const SCEV *LHS, const SCEV *RHS);
645 const SCEV *getSMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
646 const SCEV *getUMaxExpr(const SCEV *LHS, const SCEV *RHS);
647 const SCEV *getUMaxExpr(SmallVectorImpl<const SCEV *> &Operands);
648 const SCEV *getSMinExpr(const SCEV *LHS, const SCEV *RHS);
649 const SCEV *getUMinExpr(const SCEV *LHS, const SCEV *RHS);
650 const SCEV *getUnknown(Value *V);
651 const SCEV *getCouldNotCompute();
653 /// getSizeOfExpr - Return an expression for sizeof AllocTy that is type
656 const SCEV *getSizeOfExpr(Type *IntTy, Type *AllocTy);
658 /// getOffsetOfExpr - Return an expression for offsetof on the given field
661 const SCEV *getOffsetOfExpr(Type *IntTy, StructType *STy, unsigned FieldNo);
663 /// getNegativeSCEV - Return the SCEV object corresponding to -V.
665 const SCEV *getNegativeSCEV(const SCEV *V);
667 /// getNotSCEV - Return the SCEV object corresponding to ~V.
669 const SCEV *getNotSCEV(const SCEV *V);
671 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
672 const SCEV *getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
673 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap);
675 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion
676 /// of the input value to the specified type. If the type must be
677 /// extended, it is zero extended.
678 const SCEV *getTruncateOrZeroExtend(const SCEV *V, Type *Ty);
680 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion
681 /// of the input value to the specified type. If the type must be
682 /// extended, it is sign extended.
683 const SCEV *getTruncateOrSignExtend(const SCEV *V, Type *Ty);
685 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of
686 /// the input value to the specified type. If the type must be extended,
687 /// it is zero extended. The conversion must not be narrowing.
688 const SCEV *getNoopOrZeroExtend(const SCEV *V, Type *Ty);
690 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of
691 /// the input value to the specified type. If the type must be extended,
692 /// it is sign extended. The conversion must not be narrowing.
693 const SCEV *getNoopOrSignExtend(const SCEV *V, Type *Ty);
695 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
696 /// the input value to the specified type. If the type must be extended,
697 /// it is extended with unspecified bits. The conversion must not be
699 const SCEV *getNoopOrAnyExtend(const SCEV *V, Type *Ty);
701 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
702 /// input value to the specified type. The conversion must not be
704 const SCEV *getTruncateOrNoop(const SCEV *V, Type *Ty);
706 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
707 /// the types using zero-extension, and then perform a umax operation
709 const SCEV *getUMaxFromMismatchedTypes(const SCEV *LHS,
712 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
713 /// the types using zero-extension, and then perform a umin operation
715 const SCEV *getUMinFromMismatchedTypes(const SCEV *LHS,
718 /// getPointerBase - Transitively follow the chain of pointer-type operands
719 /// until reaching a SCEV that does not have a single pointer operand. This
720 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
721 /// but corner cases do exist.
722 const SCEV *getPointerBase(const SCEV *V);
724 /// getSCEVAtScope - Return a SCEV expression for the specified value
725 /// at the specified scope in the program. The L value specifies a loop
726 /// nest to evaluate the expression at, where null is the top-level or a
727 /// specified loop is immediately inside of the loop.
729 /// This method can be used to compute the exit value for a variable defined
730 /// in a loop by querying what the value will hold in the parent loop.
732 /// In the case that a relevant loop exit value cannot be computed, the
733 /// original value V is returned.
734 const SCEV *getSCEVAtScope(const SCEV *S, const Loop *L);
736 /// getSCEVAtScope - This is a convenience function which does
737 /// getSCEVAtScope(getSCEV(V), L).
738 const SCEV *getSCEVAtScope(Value *V, const Loop *L);
740 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
741 /// by a conditional between LHS and RHS. This is used to help avoid max
742 /// expressions in loop trip counts, and to eliminate casts.
743 bool isLoopEntryGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
744 const SCEV *LHS, const SCEV *RHS);
746 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
747 /// protected by a conditional between LHS and RHS. This is used to
748 /// to eliminate casts.
749 bool isLoopBackedgeGuardedByCond(const Loop *L, ICmpInst::Predicate Pred,
750 const SCEV *LHS, const SCEV *RHS);
752 /// getSmallConstantTripCount - Returns the maximum trip count of this loop
753 /// as a normal unsigned value. Returns 0 if the trip count is unknown or
754 /// not constant. This "trip count" assumes that control exits via
755 /// ExitingBlock. More precisely, it is the number of times that control may
756 /// reach ExitingBlock before taking the branch. For loops with multiple
757 /// exits, it may not be the number times that the loop header executes if
758 /// the loop exits prematurely via another branch.
759 unsigned getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock);
761 /// getSmallConstantTripMultiple - Returns the largest constant divisor of
762 /// the trip count of this loop as a normal unsigned value, if
763 /// possible. This means that the actual trip count is always a multiple of
764 /// the returned value (don't forget the trip count could very well be zero
765 /// as well!). As explained in the comments for getSmallConstantTripCount,
766 /// this assumes that control exits the loop via ExitingBlock.
767 unsigned getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock);
769 // getExitCount - Get the expression for the number of loop iterations for
770 // which this loop is guaranteed not to exit via ExitingBlock. Otherwise
771 // return SCEVCouldNotCompute.
772 const SCEV *getExitCount(Loop *L, BasicBlock *ExitingBlock);
774 /// getBackedgeTakenCount - If the specified loop has a predictable
775 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
776 /// object. The backedge-taken count is the number of times the loop header
777 /// will be branched to from within the loop. This is one less than the
778 /// trip count of the loop, since it doesn't count the first iteration,
779 /// when the header is branched to from outside the loop.
781 /// Note that it is not valid to call this method on a loop without a
782 /// loop-invariant backedge-taken count (see
783 /// hasLoopInvariantBackedgeTakenCount).
785 const SCEV *getBackedgeTakenCount(const Loop *L);
787 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
788 /// return the least SCEV value that is known never to be less than the
789 /// actual backedge taken count.
790 const SCEV *getMaxBackedgeTakenCount(const Loop *L);
792 /// hasLoopInvariantBackedgeTakenCount - Return true if the specified loop
793 /// has an analyzable loop-invariant backedge-taken count.
794 bool hasLoopInvariantBackedgeTakenCount(const Loop *L);
796 /// forgetLoop - This method should be called by the client when it has
797 /// changed a loop in a way that may effect ScalarEvolution's ability to
798 /// compute a trip count, or if the loop is deleted. This call is
799 /// potentially expensive for large loop bodies.
800 void forgetLoop(const Loop *L);
802 /// forgetValue - This method should be called by the client when it has
803 /// changed a value in a way that may effect its value, or which may
804 /// disconnect it from a def-use chain linking it to a loop.
805 void forgetValue(Value *V);
807 /// \brief Called when the client has changed the disposition of values in
810 /// We don't have a way to invalidate per-loop dispositions. Clear and
811 /// recompute is simpler.
812 void forgetLoopDispositions(const Loop *L) { LoopDispositions.clear(); }
814 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S
815 /// is guaranteed to end in (at every loop iteration). It is, at the same
816 /// time, the minimum number of times S is divisible by 2. For example,
817 /// given {4,+,8} it returns 2. If S is guaranteed to be 0, it returns the
819 uint32_t GetMinTrailingZeros(const SCEV *S);
821 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
823 ConstantRange getUnsignedRange(const SCEV *S);
825 /// getSignedRange - Determine the signed range for a particular SCEV.
827 ConstantRange getSignedRange(const SCEV *S);
829 /// isKnownNegative - Test if the given expression is known to be negative.
831 bool isKnownNegative(const SCEV *S);
833 /// isKnownPositive - Test if the given expression is known to be positive.
835 bool isKnownPositive(const SCEV *S);
837 /// isKnownNonNegative - Test if the given expression is known to be
840 bool isKnownNonNegative(const SCEV *S);
842 /// isKnownNonPositive - Test if the given expression is known to be
845 bool isKnownNonPositive(const SCEV *S);
847 /// isKnownNonZero - Test if the given expression is known to be
850 bool isKnownNonZero(const SCEV *S);
852 /// isKnownPredicate - Test if the given expression is known to satisfy
853 /// the condition described by Pred, LHS, and RHS.
855 bool isKnownPredicate(ICmpInst::Predicate Pred,
856 const SCEV *LHS, const SCEV *RHS);
858 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
859 /// predicate Pred. Return true iff any changes were made. If the
860 /// operands are provably equal or unequal, LHS and RHS are set to
861 /// the same value and Pred is set to either ICMP_EQ or ICMP_NE.
863 bool SimplifyICmpOperands(ICmpInst::Predicate &Pred,
868 /// getLoopDisposition - Return the "disposition" of the given SCEV with
869 /// respect to the given loop.
870 LoopDisposition getLoopDisposition(const SCEV *S, const Loop *L);
872 /// isLoopInvariant - Return true if the value of the given SCEV is
873 /// unchanging in the specified loop.
874 bool isLoopInvariant(const SCEV *S, const Loop *L);
876 /// hasComputableLoopEvolution - Return true if the given SCEV changes value
877 /// in a known way in the specified loop. This property being true implies
878 /// that the value is variant in the loop AND that we can emit an expression
879 /// to compute the value of the expression at any particular loop iteration.
880 bool hasComputableLoopEvolution(const SCEV *S, const Loop *L);
882 /// getLoopDisposition - Return the "disposition" of the given SCEV with
883 /// respect to the given block.
884 BlockDisposition getBlockDisposition(const SCEV *S, const BasicBlock *BB);
886 /// dominates - Return true if elements that makes up the given SCEV
887 /// dominate the specified basic block.
888 bool dominates(const SCEV *S, const BasicBlock *BB);
890 /// properlyDominates - Return true if elements that makes up the given SCEV
891 /// properly dominate the specified basic block.
892 bool properlyDominates(const SCEV *S, const BasicBlock *BB);
894 /// hasOperand - Test whether the given SCEV has Op as a direct or
895 /// indirect operand.
896 bool hasOperand(const SCEV *S, const SCEV *Op) const;
898 /// Return the size of an element read or written by Inst.
899 const SCEV *getElementSize(Instruction *Inst);
901 /// Compute the array dimensions Sizes from the set of Terms extracted from
902 /// the memory access function of this SCEVAddRecExpr.
903 void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
904 SmallVectorImpl<const SCEV *> &Sizes,
905 const SCEV *ElementSize) const;
907 bool runOnFunction(Function &F) override;
908 void releaseMemory() override;
909 void getAnalysisUsage(AnalysisUsage &AU) const override;
910 void print(raw_ostream &OS, const Module* = nullptr) const override;
911 void verifyAnalysis() const override;
914 /// Compute the backedge taken count knowing the interval difference, the
915 /// stride and presence of the equality in the comparison.
916 const SCEV *computeBECount(const SCEV *Delta, const SCEV *Stride,
919 /// Verify if an linear IV with positive stride can overflow when in a
920 /// less-than comparison, knowing the invariant term of the comparison,
921 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
922 bool doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
923 bool IsSigned, bool NoWrap);
925 /// Verify if an linear IV with negative stride can overflow when in a
926 /// greater-than comparison, knowing the invariant term of the comparison,
927 /// the stride and the knowledge of NSW/NUW flags on the recurrence.
928 bool doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
929 bool IsSigned, bool NoWrap);
932 FoldingSet<SCEV> UniqueSCEVs;
933 BumpPtrAllocator SCEVAllocator;
935 /// FirstUnknown - The head of a linked list of all SCEVUnknown
936 /// values that have been allocated. This is used by releaseMemory
937 /// to locate them all and call their destructors.
938 SCEVUnknown *FirstUnknown;