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1 //===-- llvm/Analysis/DependenceAnalysis.h -------------------- -*- C++ -*-===//
2 //
3 //                     The LLVM Compiler Infrastructure
4 //
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
7 //
8 //===----------------------------------------------------------------------===//
9 //
10 // DependenceAnalysis is an LLVM pass that analyses dependences between memory
11 // accesses. Currently, it is an implementation of the approach described in
12 //
13 //            Practical Dependence Testing
14 //            Goff, Kennedy, Tseng
15 //            PLDI 1991
16 //
17 // There's a single entry point that analyzes the dependence between a pair
18 // of memory references in a function, returning either NULL, for no dependence,
19 // or a more-or-less detailed description of the dependence between them.
20 //
21 // This pass exists to support the DependenceGraph pass. There are two separate
22 // passes because there's a useful separation of concerns. A dependence exists
23 // if two conditions are met:
24 //
25 //    1) Two instructions reference the same memory location, and
26 //    2) There is a flow of control leading from one instruction to the other.
27 //
28 // DependenceAnalysis attacks the first condition; DependenceGraph will attack
29 // the second (it's not yet ready).
30 //
31 // Please note that this is work in progress and the interface is subject to
32 // change.
33 //
34 // Plausible changes:
35 //    Return a set of more precise dependences instead of just one dependence
36 //    summarizing all.
37 //
38 //===----------------------------------------------------------------------===//
39 
40 #ifndef LLVM_ANALYSIS_DEPENDENCEANALYSIS_H
41 #define LLVM_ANALYSIS_DEPENDENCEANALYSIS_H
42 
43 #include "llvm/ADT/SmallBitVector.h"
44 #include "llvm/Analysis/AliasAnalysis.h"
45 #include "llvm/IR/Instructions.h"
46 #include "llvm/Pass.h"
47 
48 namespace llvm {
49 template <typename T> class ArrayRef;
50   class Loop;
51   class LoopInfo;
52   class ScalarEvolution;
53   class SCEV;
54   class SCEVConstant;
55   class raw_ostream;
56 
57   /// Dependence - This class represents a dependence between two memory
58   /// memory references in a function. It contains minimal information and
59   /// is used in the very common situation where the compiler is unable to
60   /// determine anything beyond the existence of a dependence; that is, it
61   /// represents a confused dependence (see also FullDependence). In most
62   /// cases (for output, flow, and anti dependences), the dependence implies
63   /// an ordering, where the source must precede the destination; in contrast,
64   /// input dependences are unordered.
65   ///
66   /// When a dependence graph is built, each Dependence will be a member of
67   /// the set of predecessor edges for its destination instruction and a set
68   /// if successor edges for its source instruction. These sets are represented
69   /// as singly-linked lists, with the "next" fields stored in the dependence
70   /// itelf.
71   class Dependence {
72   protected:
73     Dependence(const Dependence &) = default;
74 
75     // FIXME: When we move to MSVC 2015 as the base compiler for Visual Studio
76     // support, uncomment this line to allow a defaulted move constructor for
77     // Dependence. Currently, FullDependence relies on the copy constructor, but
78     // that is acceptable given the triviality of the class.
79     // Dependence(Dependence &&) = default;
80 
81   public:
Dependence(Instruction * Source,Instruction * Destination)82     Dependence(Instruction *Source,
83                Instruction *Destination) :
84       Src(Source),
85       Dst(Destination),
86       NextPredecessor(nullptr),
87       NextSuccessor(nullptr) {}
~Dependence()88     virtual ~Dependence() {}
89 
90     /// Dependence::DVEntry - Each level in the distance/direction vector
91     /// has a direction (or perhaps a union of several directions), and
92     /// perhaps a distance.
93     struct DVEntry {
94       enum { NONE = 0,
95              LT = 1,
96              EQ = 2,
97              LE = 3,
98              GT = 4,
99              NE = 5,
100              GE = 6,
101              ALL = 7 };
102       unsigned char Direction : 3; // Init to ALL, then refine.
103       bool Scalar    : 1; // Init to true.
104       bool PeelFirst : 1; // Peeling the first iteration will break dependence.
105       bool PeelLast  : 1; // Peeling the last iteration will break the dependence.
106       bool Splitable : 1; // Splitting the loop will break dependence.
107       const SCEV *Distance; // NULL implies no distance available.
DVEntryDVEntry108       DVEntry() : Direction(ALL), Scalar(true), PeelFirst(false),
109                   PeelLast(false), Splitable(false), Distance(nullptr) { }
110     };
111 
112     /// getSrc - Returns the source instruction for this dependence.
113     ///
getSrc()114     Instruction *getSrc() const { return Src; }
115 
116     /// getDst - Returns the destination instruction for this dependence.
117     ///
getDst()118     Instruction *getDst() const { return Dst; }
119 
120     /// isInput - Returns true if this is an input dependence.
121     ///
122     bool isInput() const;
123 
124     /// isOutput - Returns true if this is an output dependence.
125     ///
126     bool isOutput() const;
127 
128     /// isFlow - Returns true if this is a flow (aka true) dependence.
129     ///
130     bool isFlow() const;
131 
132     /// isAnti - Returns true if this is an anti dependence.
133     ///
134     bool isAnti() const;
135 
136     /// isOrdered - Returns true if dependence is Output, Flow, or Anti
137     ///
isOrdered()138     bool isOrdered() const { return isOutput() || isFlow() || isAnti(); }
139 
140     /// isUnordered - Returns true if dependence is Input
141     ///
isUnordered()142     bool isUnordered() const { return isInput(); }
143 
144     /// isLoopIndependent - Returns true if this is a loop-independent
145     /// dependence.
isLoopIndependent()146     virtual bool isLoopIndependent() const { return true; }
147 
148     /// isConfused - Returns true if this dependence is confused
149     /// (the compiler understands nothing and makes worst-case
150     /// assumptions).
isConfused()151     virtual bool isConfused() const { return true; }
152 
153     /// isConsistent - Returns true if this dependence is consistent
154     /// (occurs every time the source and destination are executed).
isConsistent()155     virtual bool isConsistent() const { return false; }
156 
157     /// getLevels - Returns the number of common loops surrounding the
158     /// source and destination of the dependence.
getLevels()159     virtual unsigned getLevels() const { return 0; }
160 
161     /// getDirection - Returns the direction associated with a particular
162     /// level.
getDirection(unsigned Level)163     virtual unsigned getDirection(unsigned Level) const { return DVEntry::ALL; }
164 
165     /// getDistance - Returns the distance (or NULL) associated with a
166     /// particular level.
getDistance(unsigned Level)167     virtual const SCEV *getDistance(unsigned Level) const { return nullptr; }
168 
169     /// isPeelFirst - Returns true if peeling the first iteration from
170     /// this loop will break this dependence.
isPeelFirst(unsigned Level)171     virtual bool isPeelFirst(unsigned Level) const { return false; }
172 
173     /// isPeelLast - Returns true if peeling the last iteration from
174     /// this loop will break this dependence.
isPeelLast(unsigned Level)175     virtual bool isPeelLast(unsigned Level) const { return false; }
176 
177     /// isSplitable - Returns true if splitting this loop will break
178     /// the dependence.
isSplitable(unsigned Level)179     virtual bool isSplitable(unsigned Level) const { return false; }
180 
181     /// isScalar - Returns true if a particular level is scalar; that is,
182     /// if no subscript in the source or destination mention the induction
183     /// variable associated with the loop at this level.
184     virtual bool isScalar(unsigned Level) const;
185 
186     /// getNextPredecessor - Returns the value of the NextPredecessor
187     /// field.
getNextPredecessor()188     const Dependence *getNextPredecessor() const { return NextPredecessor; }
189 
190     /// getNextSuccessor - Returns the value of the NextSuccessor
191     /// field.
getNextSuccessor()192     const Dependence *getNextSuccessor() const { return NextSuccessor; }
193 
194     /// setNextPredecessor - Sets the value of the NextPredecessor
195     /// field.
setNextPredecessor(const Dependence * pred)196     void setNextPredecessor(const Dependence *pred) { NextPredecessor = pred; }
197 
198     /// setNextSuccessor - Sets the value of the NextSuccessor
199     /// field.
setNextSuccessor(const Dependence * succ)200     void setNextSuccessor(const Dependence *succ) { NextSuccessor = succ; }
201 
202     /// dump - For debugging purposes, dumps a dependence to OS.
203     ///
204     void dump(raw_ostream &OS) const;
205 
206   private:
207     Instruction *Src, *Dst;
208     const Dependence *NextPredecessor, *NextSuccessor;
209     friend class DependenceInfo;
210   };
211 
212   /// FullDependence - This class represents a dependence between two memory
213   /// references in a function. It contains detailed information about the
214   /// dependence (direction vectors, etc.) and is used when the compiler is
215   /// able to accurately analyze the interaction of the references; that is,
216   /// it is not a confused dependence (see Dependence). In most cases
217   /// (for output, flow, and anti dependences), the dependence implies an
218   /// ordering, where the source must precede the destination; in contrast,
219   /// input dependences are unordered.
220   class FullDependence final : public Dependence {
221   public:
222     FullDependence(Instruction *Src, Instruction *Dst, bool LoopIndependent,
223                    unsigned Levels);
224 
FullDependence(FullDependence && RHS)225     FullDependence(FullDependence &&RHS)
226         : Dependence(std::move(RHS)), Levels(RHS.Levels),
227           LoopIndependent(RHS.LoopIndependent), Consistent(RHS.Consistent),
228           DV(std::move(RHS.DV)) {}
229 
230     /// isLoopIndependent - Returns true if this is a loop-independent
231     /// dependence.
isLoopIndependent()232     bool isLoopIndependent() const override { return LoopIndependent; }
233 
234     /// isConfused - Returns true if this dependence is confused
235     /// (the compiler understands nothing and makes worst-case
236     /// assumptions).
isConfused()237     bool isConfused() const override { return false; }
238 
239     /// isConsistent - Returns true if this dependence is consistent
240     /// (occurs every time the source and destination are executed).
isConsistent()241     bool isConsistent() const override { return Consistent; }
242 
243     /// getLevels - Returns the number of common loops surrounding the
244     /// source and destination of the dependence.
getLevels()245     unsigned getLevels() const override { return Levels; }
246 
247     /// getDirection - Returns the direction associated with a particular
248     /// level.
249     unsigned getDirection(unsigned Level) const override;
250 
251     /// getDistance - Returns the distance (or NULL) associated with a
252     /// particular level.
253     const SCEV *getDistance(unsigned Level) const override;
254 
255     /// isPeelFirst - Returns true if peeling the first iteration from
256     /// this loop will break this dependence.
257     bool isPeelFirst(unsigned Level) const override;
258 
259     /// isPeelLast - Returns true if peeling the last iteration from
260     /// this loop will break this dependence.
261     bool isPeelLast(unsigned Level) const override;
262 
263     /// isSplitable - Returns true if splitting the loop will break
264     /// the dependence.
265     bool isSplitable(unsigned Level) const override;
266 
267     /// isScalar - Returns true if a particular level is scalar; that is,
268     /// if no subscript in the source or destination mention the induction
269     /// variable associated with the loop at this level.
270     bool isScalar(unsigned Level) const override;
271 
272   private:
273     unsigned short Levels;
274     bool LoopIndependent;
275     bool Consistent; // Init to true, then refine.
276     std::unique_ptr<DVEntry[]> DV;
277     friend class DependenceInfo;
278   };
279 
280   /// DependenceInfo - This class is the main dependence-analysis driver.
281   ///
282   class DependenceInfo {
283   public:
DependenceInfo(Function * F,AliasAnalysis * AA,ScalarEvolution * SE,LoopInfo * LI)284     DependenceInfo(Function *F, AliasAnalysis *AA, ScalarEvolution *SE,
285                    LoopInfo *LI)
286         : AA(AA), SE(SE), LI(LI), F(F) {}
287 
288     /// depends - Tests for a dependence between the Src and Dst instructions.
289     /// Returns NULL if no dependence; otherwise, returns a Dependence (or a
290     /// FullDependence) with as much information as can be gleaned.
291     /// The flag PossiblyLoopIndependent should be set by the caller
292     /// if it appears that control flow can reach from Src to Dst
293     /// without traversing a loop back edge.
294     std::unique_ptr<Dependence> depends(Instruction *Src,
295                                         Instruction *Dst,
296                                         bool PossiblyLoopIndependent);
297 
298     /// getSplitIteration - Give a dependence that's splittable at some
299     /// particular level, return the iteration that should be used to split
300     /// the loop.
301     ///
302     /// Generally, the dependence analyzer will be used to build
303     /// a dependence graph for a function (basically a map from instructions
304     /// to dependences). Looking for cycles in the graph shows us loops
305     /// that cannot be trivially vectorized/parallelized.
306     ///
307     /// We can try to improve the situation by examining all the dependences
308     /// that make up the cycle, looking for ones we can break.
309     /// Sometimes, peeling the first or last iteration of a loop will break
310     /// dependences, and there are flags for those possibilities.
311     /// Sometimes, splitting a loop at some other iteration will do the trick,
312     /// and we've got a flag for that case. Rather than waste the space to
313     /// record the exact iteration (since we rarely know), we provide
314     /// a method that calculates the iteration. It's a drag that it must work
315     /// from scratch, but wonderful in that it's possible.
316     ///
317     /// Here's an example:
318     ///
319     ///    for (i = 0; i < 10; i++)
320     ///        A[i] = ...
321     ///        ... = A[11 - i]
322     ///
323     /// There's a loop-carried flow dependence from the store to the load,
324     /// found by the weak-crossing SIV test. The dependence will have a flag,
325     /// indicating that the dependence can be broken by splitting the loop.
326     /// Calling getSplitIteration will return 5.
327     /// Splitting the loop breaks the dependence, like so:
328     ///
329     ///    for (i = 0; i <= 5; i++)
330     ///        A[i] = ...
331     ///        ... = A[11 - i]
332     ///    for (i = 6; i < 10; i++)
333     ///        A[i] = ...
334     ///        ... = A[11 - i]
335     ///
336     /// breaks the dependence and allows us to vectorize/parallelize
337     /// both loops.
338     const SCEV *getSplitIteration(const Dependence &Dep, unsigned Level);
339 
getFunction()340     Function *getFunction() const { return F; }
341 
342   private:
343     AliasAnalysis *AA;
344     ScalarEvolution *SE;
345     LoopInfo *LI;
346     Function *F;
347 
348     /// Subscript - This private struct represents a pair of subscripts from
349     /// a pair of potentially multi-dimensional array references. We use a
350     /// vector of them to guide subscript partitioning.
351     struct Subscript {
352       const SCEV *Src;
353       const SCEV *Dst;
354       enum ClassificationKind { ZIV, SIV, RDIV, MIV, NonLinear } Classification;
355       SmallBitVector Loops;
356       SmallBitVector GroupLoops;
357       SmallBitVector Group;
358     };
359 
360     struct CoefficientInfo {
361       const SCEV *Coeff;
362       const SCEV *PosPart;
363       const SCEV *NegPart;
364       const SCEV *Iterations;
365     };
366 
367     struct BoundInfo {
368       const SCEV *Iterations;
369       const SCEV *Upper[8];
370       const SCEV *Lower[8];
371       unsigned char Direction;
372       unsigned char DirSet;
373     };
374 
375     /// Constraint - This private class represents a constraint, as defined
376     /// in the paper
377     ///
378     ///           Practical Dependence Testing
379     ///           Goff, Kennedy, Tseng
380     ///           PLDI 1991
381     ///
382     /// There are 5 kinds of constraint, in a hierarchy.
383     ///   1) Any - indicates no constraint, any dependence is possible.
384     ///   2) Line - A line ax + by = c, where a, b, and c are parameters,
385     ///             representing the dependence equation.
386     ///   3) Distance - The value d of the dependence distance;
387     ///   4) Point - A point <x, y> representing the dependence from
388     ///              iteration x to iteration y.
389     ///   5) Empty - No dependence is possible.
390     class Constraint {
391     private:
392       enum ConstraintKind { Empty, Point, Distance, Line, Any } Kind;
393       ScalarEvolution *SE;
394       const SCEV *A;
395       const SCEV *B;
396       const SCEV *C;
397       const Loop *AssociatedLoop;
398 
399     public:
400       /// isEmpty - Return true if the constraint is of kind Empty.
isEmpty()401       bool isEmpty() const { return Kind == Empty; }
402 
403       /// isPoint - Return true if the constraint is of kind Point.
isPoint()404       bool isPoint() const { return Kind == Point; }
405 
406       /// isDistance - Return true if the constraint is of kind Distance.
isDistance()407       bool isDistance() const { return Kind == Distance; }
408 
409       /// isLine - Return true if the constraint is of kind Line.
410       /// Since Distance's can also be represented as Lines, we also return
411       /// true if the constraint is of kind Distance.
isLine()412       bool isLine() const { return Kind == Line || Kind == Distance; }
413 
414       /// isAny - Return true if the constraint is of kind Any;
isAny()415       bool isAny() const { return Kind == Any; }
416 
417       /// getX - If constraint is a point <X, Y>, returns X.
418       /// Otherwise assert.
419       const SCEV *getX() const;
420 
421       /// getY - If constraint is a point <X, Y>, returns Y.
422       /// Otherwise assert.
423       const SCEV *getY() const;
424 
425       /// getA - If constraint is a line AX + BY = C, returns A.
426       /// Otherwise assert.
427       const SCEV *getA() const;
428 
429       /// getB - If constraint is a line AX + BY = C, returns B.
430       /// Otherwise assert.
431       const SCEV *getB() const;
432 
433       /// getC - If constraint is a line AX + BY = C, returns C.
434       /// Otherwise assert.
435       const SCEV *getC() const;
436 
437       /// getD - If constraint is a distance, returns D.
438       /// Otherwise assert.
439       const SCEV *getD() const;
440 
441       /// getAssociatedLoop - Returns the loop associated with this constraint.
442       const Loop *getAssociatedLoop() const;
443 
444       /// setPoint - Change a constraint to Point.
445       void setPoint(const SCEV *X, const SCEV *Y, const Loop *CurrentLoop);
446 
447       /// setLine - Change a constraint to Line.
448       void setLine(const SCEV *A, const SCEV *B,
449                    const SCEV *C, const Loop *CurrentLoop);
450 
451       /// setDistance - Change a constraint to Distance.
452       void setDistance(const SCEV *D, const Loop *CurrentLoop);
453 
454       /// setEmpty - Change a constraint to Empty.
455       void setEmpty();
456 
457       /// setAny - Change a constraint to Any.
458       void setAny(ScalarEvolution *SE);
459 
460       /// dump - For debugging purposes. Dumps the constraint
461       /// out to OS.
462       void dump(raw_ostream &OS) const;
463     };
464 
465     /// establishNestingLevels - Examines the loop nesting of the Src and Dst
466     /// instructions and establishes their shared loops. Sets the variables
467     /// CommonLevels, SrcLevels, and MaxLevels.
468     /// The source and destination instructions needn't be contained in the same
469     /// loop. The routine establishNestingLevels finds the level of most deeply
470     /// nested loop that contains them both, CommonLevels. An instruction that's
471     /// not contained in a loop is at level = 0. MaxLevels is equal to the level
472     /// of the source plus the level of the destination, minus CommonLevels.
473     /// This lets us allocate vectors MaxLevels in length, with room for every
474     /// distinct loop referenced in both the source and destination subscripts.
475     /// The variable SrcLevels is the nesting depth of the source instruction.
476     /// It's used to help calculate distinct loops referenced by the destination.
477     /// Here's the map from loops to levels:
478     ///            0 - unused
479     ///            1 - outermost common loop
480     ///          ... - other common loops
481     /// CommonLevels - innermost common loop
482     ///          ... - loops containing Src but not Dst
483     ///    SrcLevels - innermost loop containing Src but not Dst
484     ///          ... - loops containing Dst but not Src
485     ///    MaxLevels - innermost loop containing Dst but not Src
486     /// Consider the follow code fragment:
487     ///    for (a = ...) {
488     ///      for (b = ...) {
489     ///        for (c = ...) {
490     ///          for (d = ...) {
491     ///            A[] = ...;
492     ///          }
493     ///        }
494     ///        for (e = ...) {
495     ///          for (f = ...) {
496     ///            for (g = ...) {
497     ///              ... = A[];
498     ///            }
499     ///          }
500     ///        }
501     ///      }
502     ///    }
503     /// If we're looking at the possibility of a dependence between the store
504     /// to A (the Src) and the load from A (the Dst), we'll note that they
505     /// have 2 loops in common, so CommonLevels will equal 2 and the direction
506     /// vector for Result will have 2 entries. SrcLevels = 4 and MaxLevels = 7.
507     /// A map from loop names to level indices would look like
508     ///     a - 1
509     ///     b - 2 = CommonLevels
510     ///     c - 3
511     ///     d - 4 = SrcLevels
512     ///     e - 5
513     ///     f - 6
514     ///     g - 7 = MaxLevels
515     void establishNestingLevels(const Instruction *Src,
516                                 const Instruction *Dst);
517 
518     unsigned CommonLevels, SrcLevels, MaxLevels;
519 
520     /// mapSrcLoop - Given one of the loops containing the source, return
521     /// its level index in our numbering scheme.
522     unsigned mapSrcLoop(const Loop *SrcLoop) const;
523 
524     /// mapDstLoop - Given one of the loops containing the destination,
525     /// return its level index in our numbering scheme.
526     unsigned mapDstLoop(const Loop *DstLoop) const;
527 
528     /// isLoopInvariant - Returns true if Expression is loop invariant
529     /// in LoopNest.
530     bool isLoopInvariant(const SCEV *Expression, const Loop *LoopNest) const;
531 
532     /// Makes sure all subscript pairs share the same integer type by
533     /// sign-extending as necessary.
534     /// Sign-extending a subscript is safe because getelementptr assumes the
535     /// array subscripts are signed.
536     void unifySubscriptType(ArrayRef<Subscript *> Pairs);
537 
538     /// removeMatchingExtensions - Examines a subscript pair.
539     /// If the source and destination are identically sign (or zero)
540     /// extended, it strips off the extension in an effort to
541     /// simplify the actual analysis.
542     void removeMatchingExtensions(Subscript *Pair);
543 
544     /// collectCommonLoops - Finds the set of loops from the LoopNest that
545     /// have a level <= CommonLevels and are referred to by the SCEV Expression.
546     void collectCommonLoops(const SCEV *Expression,
547                             const Loop *LoopNest,
548                             SmallBitVector &Loops) const;
549 
550     /// checkSrcSubscript - Examines the SCEV Src, returning true iff it's
551     /// linear. Collect the set of loops mentioned by Src.
552     bool checkSrcSubscript(const SCEV *Src,
553                            const Loop *LoopNest,
554                            SmallBitVector &Loops);
555 
556     /// checkDstSubscript - Examines the SCEV Dst, returning true iff it's
557     /// linear. Collect the set of loops mentioned by Dst.
558     bool checkDstSubscript(const SCEV *Dst,
559                            const Loop *LoopNest,
560                            SmallBitVector &Loops);
561 
562     /// isKnownPredicate - Compare X and Y using the predicate Pred.
563     /// Basically a wrapper for SCEV::isKnownPredicate,
564     /// but tries harder, especially in the presence of sign and zero
565     /// extensions and symbolics.
566     bool isKnownPredicate(ICmpInst::Predicate Pred,
567                           const SCEV *X,
568                           const SCEV *Y) const;
569 
570     /// collectUpperBound - All subscripts are the same type (on my machine,
571     /// an i64). The loop bound may be a smaller type. collectUpperBound
572     /// find the bound, if available, and zero extends it to the Type T.
573     /// (I zero extend since the bound should always be >= 0.)
574     /// If no upper bound is available, return NULL.
575     const SCEV *collectUpperBound(const Loop *l, Type *T) const;
576 
577     /// collectConstantUpperBound - Calls collectUpperBound(), then
578     /// attempts to cast it to SCEVConstant. If the cast fails,
579     /// returns NULL.
580     const SCEVConstant *collectConstantUpperBound(const Loop *l, Type *T) const;
581 
582     /// classifyPair - Examines the subscript pair (the Src and Dst SCEVs)
583     /// and classifies it as either ZIV, SIV, RDIV, MIV, or Nonlinear.
584     /// Collects the associated loops in a set.
585     Subscript::ClassificationKind classifyPair(const SCEV *Src,
586                                            const Loop *SrcLoopNest,
587                                            const SCEV *Dst,
588                                            const Loop *DstLoopNest,
589                                            SmallBitVector &Loops);
590 
591     /// testZIV - Tests the ZIV subscript pair (Src and Dst) for dependence.
592     /// Returns true if any possible dependence is disproved.
593     /// If there might be a dependence, returns false.
594     /// If the dependence isn't proven to exist,
595     /// marks the Result as inconsistent.
596     bool testZIV(const SCEV *Src,
597                  const SCEV *Dst,
598                  FullDependence &Result) const;
599 
600     /// testSIV - Tests the SIV subscript pair (Src and Dst) for dependence.
601     /// Things of the form [c1 + a1*i] and [c2 + a2*j], where
602     /// i and j are induction variables, c1 and c2 are loop invariant,
603     /// and a1 and a2 are constant.
604     /// Returns true if any possible dependence is disproved.
605     /// If there might be a dependence, returns false.
606     /// Sets appropriate direction vector entry and, when possible,
607     /// the distance vector entry.
608     /// If the dependence isn't proven to exist,
609     /// marks the Result as inconsistent.
610     bool testSIV(const SCEV *Src,
611                  const SCEV *Dst,
612                  unsigned &Level,
613                  FullDependence &Result,
614                  Constraint &NewConstraint,
615                  const SCEV *&SplitIter) const;
616 
617     /// testRDIV - Tests the RDIV subscript pair (Src and Dst) for dependence.
618     /// Things of the form [c1 + a1*i] and [c2 + a2*j]
619     /// where i and j are induction variables, c1 and c2 are loop invariant,
620     /// and a1 and a2 are constant.
621     /// With minor algebra, this test can also be used for things like
622     /// [c1 + a1*i + a2*j][c2].
623     /// Returns true if any possible dependence is disproved.
624     /// If there might be a dependence, returns false.
625     /// Marks the Result as inconsistent.
626     bool testRDIV(const SCEV *Src,
627                   const SCEV *Dst,
628                   FullDependence &Result) const;
629 
630     /// testMIV - Tests the MIV subscript pair (Src and Dst) for dependence.
631     /// Returns true if dependence disproved.
632     /// Can sometimes refine direction vectors.
633     bool testMIV(const SCEV *Src,
634                  const SCEV *Dst,
635                  const SmallBitVector &Loops,
636                  FullDependence &Result) const;
637 
638     /// strongSIVtest - Tests the strong SIV subscript pair (Src and Dst)
639     /// for dependence.
640     /// Things of the form [c1 + a*i] and [c2 + a*i],
641     /// where i is an induction variable, c1 and c2 are loop invariant,
642     /// and a is a constant
643     /// Returns true if any possible dependence is disproved.
644     /// If there might be a dependence, returns false.
645     /// Sets appropriate direction and distance.
646     bool strongSIVtest(const SCEV *Coeff,
647                        const SCEV *SrcConst,
648                        const SCEV *DstConst,
649                        const Loop *CurrentLoop,
650                        unsigned Level,
651                        FullDependence &Result,
652                        Constraint &NewConstraint) const;
653 
654     /// weakCrossingSIVtest - Tests the weak-crossing SIV subscript pair
655     /// (Src and Dst) for dependence.
656     /// Things of the form [c1 + a*i] and [c2 - a*i],
657     /// where i is an induction variable, c1 and c2 are loop invariant,
658     /// and a is a constant.
659     /// Returns true if any possible dependence is disproved.
660     /// If there might be a dependence, returns false.
661     /// Sets appropriate direction entry.
662     /// Set consistent to false.
663     /// Marks the dependence as splitable.
664     bool weakCrossingSIVtest(const SCEV *SrcCoeff,
665                              const SCEV *SrcConst,
666                              const SCEV *DstConst,
667                              const Loop *CurrentLoop,
668                              unsigned Level,
669                              FullDependence &Result,
670                              Constraint &NewConstraint,
671                              const SCEV *&SplitIter) const;
672 
673     /// ExactSIVtest - Tests the SIV subscript pair
674     /// (Src and Dst) for dependence.
675     /// Things of the form [c1 + a1*i] and [c2 + a2*i],
676     /// where i is an induction variable, c1 and c2 are loop invariant,
677     /// and a1 and a2 are constant.
678     /// Returns true if any possible dependence is disproved.
679     /// If there might be a dependence, returns false.
680     /// Sets appropriate direction entry.
681     /// Set consistent to false.
682     bool exactSIVtest(const SCEV *SrcCoeff,
683                       const SCEV *DstCoeff,
684                       const SCEV *SrcConst,
685                       const SCEV *DstConst,
686                       const Loop *CurrentLoop,
687                       unsigned Level,
688                       FullDependence &Result,
689                       Constraint &NewConstraint) const;
690 
691     /// weakZeroSrcSIVtest - Tests the weak-zero SIV subscript pair
692     /// (Src and Dst) for dependence.
693     /// Things of the form [c1] and [c2 + a*i],
694     /// where i is an induction variable, c1 and c2 are loop invariant,
695     /// and a is a constant. See also weakZeroDstSIVtest.
696     /// Returns true if any possible dependence is disproved.
697     /// If there might be a dependence, returns false.
698     /// Sets appropriate direction entry.
699     /// Set consistent to false.
700     /// If loop peeling will break the dependence, mark appropriately.
701     bool weakZeroSrcSIVtest(const SCEV *DstCoeff,
702                             const SCEV *SrcConst,
703                             const SCEV *DstConst,
704                             const Loop *CurrentLoop,
705                             unsigned Level,
706                             FullDependence &Result,
707                             Constraint &NewConstraint) const;
708 
709     /// weakZeroDstSIVtest - Tests the weak-zero SIV subscript pair
710     /// (Src and Dst) for dependence.
711     /// Things of the form [c1 + a*i] and [c2],
712     /// where i is an induction variable, c1 and c2 are loop invariant,
713     /// and a is a constant. See also weakZeroSrcSIVtest.
714     /// Returns true if any possible dependence is disproved.
715     /// If there might be a dependence, returns false.
716     /// Sets appropriate direction entry.
717     /// Set consistent to false.
718     /// If loop peeling will break the dependence, mark appropriately.
719     bool weakZeroDstSIVtest(const SCEV *SrcCoeff,
720                             const SCEV *SrcConst,
721                             const SCEV *DstConst,
722                             const Loop *CurrentLoop,
723                             unsigned Level,
724                             FullDependence &Result,
725                             Constraint &NewConstraint) const;
726 
727     /// exactRDIVtest - Tests the RDIV subscript pair for dependence.
728     /// Things of the form [c1 + a*i] and [c2 + b*j],
729     /// where i and j are induction variable, c1 and c2 are loop invariant,
730     /// and a and b are constants.
731     /// Returns true if any possible dependence is disproved.
732     /// Marks the result as inconsistent.
733     /// Works in some cases that symbolicRDIVtest doesn't,
734     /// and vice versa.
735     bool exactRDIVtest(const SCEV *SrcCoeff,
736                        const SCEV *DstCoeff,
737                        const SCEV *SrcConst,
738                        const SCEV *DstConst,
739                        const Loop *SrcLoop,
740                        const Loop *DstLoop,
741                        FullDependence &Result) const;
742 
743     /// symbolicRDIVtest - Tests the RDIV subscript pair for dependence.
744     /// Things of the form [c1 + a*i] and [c2 + b*j],
745     /// where i and j are induction variable, c1 and c2 are loop invariant,
746     /// and a and b are constants.
747     /// Returns true if any possible dependence is disproved.
748     /// Marks the result as inconsistent.
749     /// Works in some cases that exactRDIVtest doesn't,
750     /// and vice versa. Can also be used as a backup for
751     /// ordinary SIV tests.
752     bool symbolicRDIVtest(const SCEV *SrcCoeff,
753                           const SCEV *DstCoeff,
754                           const SCEV *SrcConst,
755                           const SCEV *DstConst,
756                           const Loop *SrcLoop,
757                           const Loop *DstLoop) const;
758 
759     /// gcdMIVtest - Tests an MIV subscript pair for dependence.
760     /// Returns true if any possible dependence is disproved.
761     /// Marks the result as inconsistent.
762     /// Can sometimes disprove the equal direction for 1 or more loops.
763     //  Can handle some symbolics that even the SIV tests don't get,
764     /// so we use it as a backup for everything.
765     bool gcdMIVtest(const SCEV *Src,
766                     const SCEV *Dst,
767                     FullDependence &Result) const;
768 
769     /// banerjeeMIVtest - Tests an MIV subscript pair for dependence.
770     /// Returns true if any possible dependence is disproved.
771     /// Marks the result as inconsistent.
772     /// Computes directions.
773     bool banerjeeMIVtest(const SCEV *Src,
774                          const SCEV *Dst,
775                          const SmallBitVector &Loops,
776                          FullDependence &Result) const;
777 
778     /// collectCoefficientInfo - Walks through the subscript,
779     /// collecting each coefficient, the associated loop bounds,
780     /// and recording its positive and negative parts for later use.
781     CoefficientInfo *collectCoeffInfo(const SCEV *Subscript,
782                                       bool SrcFlag,
783                                       const SCEV *&Constant) const;
784 
785     /// getPositivePart - X^+ = max(X, 0).
786     ///
787     const SCEV *getPositivePart(const SCEV *X) const;
788 
789     /// getNegativePart - X^- = min(X, 0).
790     ///
791     const SCEV *getNegativePart(const SCEV *X) const;
792 
793     /// getLowerBound - Looks through all the bounds info and
794     /// computes the lower bound given the current direction settings
795     /// at each level.
796     const SCEV *getLowerBound(BoundInfo *Bound) const;
797 
798     /// getUpperBound - Looks through all the bounds info and
799     /// computes the upper bound given the current direction settings
800     /// at each level.
801     const SCEV *getUpperBound(BoundInfo *Bound) const;
802 
803     /// exploreDirections - Hierarchically expands the direction vector
804     /// search space, combining the directions of discovered dependences
805     /// in the DirSet field of Bound. Returns the number of distinct
806     /// dependences discovered. If the dependence is disproved,
807     /// it will return 0.
808     unsigned exploreDirections(unsigned Level,
809                                CoefficientInfo *A,
810                                CoefficientInfo *B,
811                                BoundInfo *Bound,
812                                const SmallBitVector &Loops,
813                                unsigned &DepthExpanded,
814                                const SCEV *Delta) const;
815 
816     /// testBounds - Returns true iff the current bounds are plausible.
817     bool testBounds(unsigned char DirKind,
818                     unsigned Level,
819                     BoundInfo *Bound,
820                     const SCEV *Delta) const;
821 
822     /// findBoundsALL - Computes the upper and lower bounds for level K
823     /// using the * direction. Records them in Bound.
824     void findBoundsALL(CoefficientInfo *A,
825                        CoefficientInfo *B,
826                        BoundInfo *Bound,
827                        unsigned K) const;
828 
829     /// findBoundsLT - Computes the upper and lower bounds for level K
830     /// using the < direction. Records them in Bound.
831     void findBoundsLT(CoefficientInfo *A,
832                       CoefficientInfo *B,
833                       BoundInfo *Bound,
834                       unsigned K) const;
835 
836     /// findBoundsGT - Computes the upper and lower bounds for level K
837     /// using the > direction. Records them in Bound.
838     void findBoundsGT(CoefficientInfo *A,
839                       CoefficientInfo *B,
840                       BoundInfo *Bound,
841                       unsigned K) const;
842 
843     /// findBoundsEQ - Computes the upper and lower bounds for level K
844     /// using the = direction. Records them in Bound.
845     void findBoundsEQ(CoefficientInfo *A,
846                       CoefficientInfo *B,
847                       BoundInfo *Bound,
848                       unsigned K) const;
849 
850     /// intersectConstraints - Updates X with the intersection
851     /// of the Constraints X and Y. Returns true if X has changed.
852     bool intersectConstraints(Constraint *X,
853                               const Constraint *Y);
854 
855     /// propagate - Review the constraints, looking for opportunities
856     /// to simplify a subscript pair (Src and Dst).
857     /// Return true if some simplification occurs.
858     /// If the simplification isn't exact (that is, if it is conservative
859     /// in terms of dependence), set consistent to false.
860     bool propagate(const SCEV *&Src,
861                    const SCEV *&Dst,
862                    SmallBitVector &Loops,
863                    SmallVectorImpl<Constraint> &Constraints,
864                    bool &Consistent);
865 
866     /// propagateDistance - Attempt to propagate a distance
867     /// constraint into a subscript pair (Src and Dst).
868     /// Return true if some simplification occurs.
869     /// If the simplification isn't exact (that is, if it is conservative
870     /// in terms of dependence), set consistent to false.
871     bool propagateDistance(const SCEV *&Src,
872                            const SCEV *&Dst,
873                            Constraint &CurConstraint,
874                            bool &Consistent);
875 
876     /// propagatePoint - Attempt to propagate a point
877     /// constraint into a subscript pair (Src and Dst).
878     /// Return true if some simplification occurs.
879     bool propagatePoint(const SCEV *&Src,
880                         const SCEV *&Dst,
881                         Constraint &CurConstraint);
882 
883     /// propagateLine - Attempt to propagate a line
884     /// constraint into a subscript pair (Src and Dst).
885     /// Return true if some simplification occurs.
886     /// If the simplification isn't exact (that is, if it is conservative
887     /// in terms of dependence), set consistent to false.
888     bool propagateLine(const SCEV *&Src,
889                        const SCEV *&Dst,
890                        Constraint &CurConstraint,
891                        bool &Consistent);
892 
893     /// findCoefficient - Given a linear SCEV,
894     /// return the coefficient corresponding to specified loop.
895     /// If there isn't one, return the SCEV constant 0.
896     /// For example, given a*i + b*j + c*k, returning the coefficient
897     /// corresponding to the j loop would yield b.
898     const SCEV *findCoefficient(const SCEV *Expr,
899                                 const Loop *TargetLoop) const;
900 
901     /// zeroCoefficient - Given a linear SCEV,
902     /// return the SCEV given by zeroing out the coefficient
903     /// corresponding to the specified loop.
904     /// For example, given a*i + b*j + c*k, zeroing the coefficient
905     /// corresponding to the j loop would yield a*i + c*k.
906     const SCEV *zeroCoefficient(const SCEV *Expr,
907                                 const Loop *TargetLoop) const;
908 
909     /// addToCoefficient - Given a linear SCEV Expr,
910     /// return the SCEV given by adding some Value to the
911     /// coefficient corresponding to the specified TargetLoop.
912     /// For example, given a*i + b*j + c*k, adding 1 to the coefficient
913     /// corresponding to the j loop would yield a*i + (b+1)*j + c*k.
914     const SCEV *addToCoefficient(const SCEV *Expr,
915                                  const Loop *TargetLoop,
916                                  const SCEV *Value)  const;
917 
918     /// updateDirection - Update direction vector entry
919     /// based on the current constraint.
920     void updateDirection(Dependence::DVEntry &Level,
921                          const Constraint &CurConstraint) const;
922 
923     bool tryDelinearize(Instruction *Src, Instruction *Dst,
924                         SmallVectorImpl<Subscript> &Pair);
925   }; // class DependenceInfo
926 
927   /// \brief AnalysisPass to compute dependence information in a function
928   class DependenceAnalysis : public AnalysisInfoMixin<DependenceAnalysis> {
929   public:
930     typedef DependenceInfo Result;
931     Result run(Function &F, FunctionAnalysisManager &FAM);
932 
933   private:
934     static char PassID;
935     friend struct AnalysisInfoMixin<DependenceAnalysis>;
936   }; // class DependenceAnalysis
937 
938   /// \brief Legacy pass manager pass to access dependence information
939   class DependenceAnalysisWrapperPass : public FunctionPass {
940   public:
941     static char ID; // Class identification, replacement for typeinfo
942     DependenceAnalysisWrapperPass() : FunctionPass(ID) {
943       initializeDependenceAnalysisWrapperPassPass(
944           *PassRegistry::getPassRegistry());
945     }
946 
947     bool runOnFunction(Function &F) override;
948     void releaseMemory() override;
949     void getAnalysisUsage(AnalysisUsage &) const override;
950     void print(raw_ostream &, const Module * = nullptr) const override;
951     DependenceInfo &getDI() const;
952 
953   private:
954     std::unique_ptr<DependenceInfo> info;
955   }; // class DependenceAnalysisWrapperPass
956 
957   /// createDependenceAnalysisPass - This creates an instance of the
958   /// DependenceAnalysis wrapper pass.
959   FunctionPass *createDependenceAnalysisWrapperPass();
960 
961 } // namespace llvm
962 
963 #endif
964