summaryrefslogtreecommitdiff
path: root/polly/lib/Transform/Simplify.cpp
blob: 41a155a41de83d1071b0ff228031c39d5218513b (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
//===------ Simplify.cpp ----------------------------------------*- C++ -*-===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
//
// Simplify a SCoP by removing unnecessary statements and accesses.
//
//===----------------------------------------------------------------------===//

#include "polly/Simplify.h"
#include "polly/ScopInfo.h"
#include "polly/ScopPass.h"
#include "polly/Support/GICHelper.h"
#include "polly/Support/ISLOStream.h"
#include "polly/Support/ISLTools.h"
#include "polly/Support/VirtualInstruction.h"
#include "llvm/ADT/Statistic.h"
#include "llvm/InitializePasses.h"
#include "llvm/Support/Debug.h"
#include <optional>

#define DEBUG_TYPE "polly-simplify"

using namespace llvm;
using namespace polly;

namespace {

#define TWO_STATISTICS(VARNAME, DESC)                                          \
  static llvm::Statistic VARNAME[2] = {                                        \
      {DEBUG_TYPE, #VARNAME "0", DESC " (first)"},                             \
      {DEBUG_TYPE, #VARNAME "1", DESC " (second)"}}

/// Number of max disjuncts we allow in removeOverwrites(). This is to avoid
/// that the analysis of accesses in a statement is becoming too complex. Chosen
/// to be relatively small because all the common cases should access only few
/// array elements per statement.
static unsigned const SimplifyMaxDisjuncts = 4;

TWO_STATISTICS(ScopsProcessed, "Number of SCoPs processed");
TWO_STATISTICS(ScopsModified, "Number of SCoPs simplified");

TWO_STATISTICS(TotalEmptyDomainsRemoved,
               "Number of statement with empty domains removed in any SCoP");
TWO_STATISTICS(TotalOverwritesRemoved, "Number of removed overwritten writes");
TWO_STATISTICS(TotalWritesCoalesced, "Number of writes coalesced with another");
TWO_STATISTICS(TotalRedundantWritesRemoved,
               "Number of writes of same value removed in any SCoP");
TWO_STATISTICS(TotalEmptyPartialAccessesRemoved,
               "Number of empty partial accesses removed");
TWO_STATISTICS(TotalDeadAccessesRemoved, "Number of dead accesses removed");
TWO_STATISTICS(TotalDeadInstructionsRemoved,
               "Number of unused instructions removed");
TWO_STATISTICS(TotalStmtsRemoved, "Number of statements removed in any SCoP");

TWO_STATISTICS(NumValueWrites, "Number of scalar value writes after Simplify");
TWO_STATISTICS(
    NumValueWritesInLoops,
    "Number of scalar value writes nested in affine loops after Simplify");
TWO_STATISTICS(NumPHIWrites,
               "Number of scalar phi writes after the first simplification");
TWO_STATISTICS(
    NumPHIWritesInLoops,
    "Number of scalar phi writes nested in affine loops after Simplify");
TWO_STATISTICS(NumSingletonWrites, "Number of singleton writes after Simplify");
TWO_STATISTICS(
    NumSingletonWritesInLoops,
    "Number of singleton writes nested in affine loops after Simplify");

static bool isImplicitRead(MemoryAccess *MA) {
  return MA->isRead() && MA->isOriginalScalarKind();
}

static bool isExplicitAccess(MemoryAccess *MA) {
  return MA->isOriginalArrayKind();
}

static bool isImplicitWrite(MemoryAccess *MA) {
  return MA->isWrite() && MA->isOriginalScalarKind();
}

/// Like isl::union_map::unite, but may also return an underapproximated
/// result if getting too complex.
///
/// This is implemented by adding disjuncts to the results until the limit is
/// reached.
static isl::union_map underapproximatedAddMap(isl::union_map UMap,
                                              isl::map Map) {
  if (UMap.is_null() || Map.is_null())
    return {};

  isl::map PrevMap = UMap.extract_map(Map.get_space());

  // Fast path: If known that we cannot exceed the disjunct limit, just add
  // them.
  if (unsignedFromIslSize(PrevMap.n_basic_map()) +
          unsignedFromIslSize(Map.n_basic_map()) <=
      SimplifyMaxDisjuncts)
    return UMap.unite(Map);

  isl::map Result = isl::map::empty(PrevMap.get_space());
  for (isl::basic_map BMap : PrevMap.get_basic_map_list()) {
    if (unsignedFromIslSize(Result.n_basic_map()) > SimplifyMaxDisjuncts)
      break;
    Result = Result.unite(BMap);
  }
  for (isl::basic_map BMap : Map.get_basic_map_list()) {
    if (unsignedFromIslSize(Result.n_basic_map()) > SimplifyMaxDisjuncts)
      break;
    Result = Result.unite(BMap);
  }

  isl::union_map UResult =
      UMap.subtract(isl::map::universe(PrevMap.get_space()));
  UResult.unite(Result);

  return UResult;
}

class SimplifyImpl final {
private:
  /// The invocation id (if there are multiple instances in the pass manager's
  /// pipeline) to determine which statistics to update.
  int CallNo;

  /// The last/current SCoP that is/has been processed.
  Scop *S = nullptr;

  /// Number of statements with empty domains removed from the SCoP.
  int EmptyDomainsRemoved = 0;

  /// Number of writes that are overwritten anyway.
  int OverwritesRemoved = 0;

  /// Number of combined writes.
  int WritesCoalesced = 0;

  /// Number of redundant writes removed from this SCoP.
  int RedundantWritesRemoved = 0;

  /// Number of writes with empty access domain removed.
  int EmptyPartialAccessesRemoved = 0;

  /// Number of unused accesses removed from this SCoP.
  int DeadAccessesRemoved = 0;

  /// Number of unused instructions removed from this SCoP.
  int DeadInstructionsRemoved = 0;

  /// Number of unnecessary statements removed from the SCoP.
  int StmtsRemoved = 0;

  /// Remove statements that are never executed due to their domains being
  /// empty.
  ///
  /// In contrast to Scop::simplifySCoP, this removes based on the SCoP's
  /// effective domain, i.e. including the SCoP's context as used by some other
  /// simplification methods in this pass. This is necessary because the
  /// analysis on empty domains is unreliable, e.g. remove a scalar value
  /// definition MemoryAccesses, but not its use.
  void removeEmptyDomainStmts();

  /// Remove writes that are overwritten unconditionally later in the same
  /// statement.
  ///
  /// There must be no read of the same value between the write (that is to be
  /// removed) and the overwrite.
  void removeOverwrites();

  /// Combine writes that write the same value if possible.
  ///
  /// This function is able to combine:
  /// - Partial writes with disjoint domain.
  /// - Writes that write to the same array element.
  ///
  /// In all cases, both writes must write the same values.
  void coalesceWrites();

  /// Remove writes that just write the same value already stored in the
  /// element.
  void removeRedundantWrites();

  /// Remove statements without side effects.
  void removeUnnecessaryStmts();

  /// Remove accesses that have an empty domain.
  void removeEmptyPartialAccesses();

  /// Mark all reachable instructions and access, and sweep those that are not
  /// reachable.
  void markAndSweep(LoopInfo *LI);

  /// Print simplification statistics to @p OS.
  void printStatistics(llvm::raw_ostream &OS, int Indent = 0) const;

  /// Print the current state of all MemoryAccesses to @p OS.
  void printAccesses(llvm::raw_ostream &OS, int Indent = 0) const;

public:
  explicit SimplifyImpl(int CallNo = 0) : CallNo(CallNo) {}

  void run(Scop &S, LoopInfo *LI);

  void printScop(raw_ostream &OS, Scop &S) const;

  /// Return whether at least one simplification has been applied.
  bool isModified() const;
};

/// Return whether at least one simplification has been applied.
bool SimplifyImpl::isModified() const {
  return EmptyDomainsRemoved > 0 || OverwritesRemoved > 0 ||
         WritesCoalesced > 0 || RedundantWritesRemoved > 0 ||
         EmptyPartialAccessesRemoved > 0 || DeadAccessesRemoved > 0 ||
         DeadInstructionsRemoved > 0 || StmtsRemoved > 0;
}

/// Remove statements that are never executed due to their domains being
/// empty.
///
/// In contrast to Scop::simplifySCoP, this removes based on the SCoP's
/// effective domain, i.e. including the SCoP's context as used by some other
/// simplification methods in this pass. This is necessary because the
/// analysis on empty domains is unreliable, e.g. remove a scalar value
/// definition MemoryAccesses, but not its use.
void SimplifyImpl::removeEmptyDomainStmts() {
  size_t NumStmtsBefore = S->getSize();

  S->removeStmts([](ScopStmt &Stmt) -> bool {
    auto EffectiveDomain =
        Stmt.getDomain().intersect_params(Stmt.getParent()->getContext());
    return EffectiveDomain.is_empty();
  });

  assert(NumStmtsBefore >= S->getSize());
  EmptyDomainsRemoved = NumStmtsBefore - S->getSize();
  LLVM_DEBUG(dbgs() << "Removed " << EmptyDomainsRemoved << " (of "
                    << NumStmtsBefore << ") statements with empty domains \n");
  TotalEmptyDomainsRemoved[CallNo] += EmptyDomainsRemoved;
}

/// Remove writes that are overwritten unconditionally later in the same
/// statement.
///
/// There must be no read of the same value between the write (that is to be
/// removed) and the overwrite.
void SimplifyImpl::removeOverwrites() {
  for (auto &Stmt : *S) {
    isl::set Domain = Stmt.getDomain();
    isl::union_map WillBeOverwritten = isl::union_map::empty(S->getIslCtx());

    SmallVector<MemoryAccess *, 32> Accesses(getAccessesInOrder(Stmt));

    // Iterate in reverse order, so the overwrite comes before the write that
    // is to be removed.
    for (auto *MA : reverse(Accesses)) {

      // In region statements, the explicit accesses can be in blocks that are
      // can be executed in any order. We therefore process only the implicit
      // writes and stop after that.
      if (Stmt.isRegionStmt() && isExplicitAccess(MA))
        break;

      auto AccRel = MA->getAccessRelation();
      AccRel = AccRel.intersect_domain(Domain);
      AccRel = AccRel.intersect_params(S->getContext());

      // If a value is read in-between, do not consider it as overwritten.
      if (MA->isRead()) {
        // Invalidate all overwrites for the array it accesses to avoid too
        // complex isl sets.
        isl::map AccRelUniv = isl::map::universe(AccRel.get_space());
        WillBeOverwritten = WillBeOverwritten.subtract(AccRelUniv);
        continue;
      }

      // If all of a write's elements are overwritten, remove it.
      isl::union_map AccRelUnion = AccRel;
      if (AccRelUnion.is_subset(WillBeOverwritten)) {
        LLVM_DEBUG(dbgs() << "Removing " << MA
                          << " which will be overwritten anyway\n");

        Stmt.removeSingleMemoryAccess(MA);
        OverwritesRemoved++;
        TotalOverwritesRemoved[CallNo]++;
      }

      // Unconditional writes overwrite other values.
      if (MA->isMustWrite()) {
        // Avoid too complex isl sets. If necessary, throw away some of the
        // knowledge.
        WillBeOverwritten = underapproximatedAddMap(WillBeOverwritten, AccRel);
      }
    }
  }
}

/// Combine writes that write the same value if possible.
///
/// This function is able to combine:
/// - Partial writes with disjoint domain.
/// - Writes that write to the same array element.
///
/// In all cases, both writes must write the same values.
void SimplifyImpl::coalesceWrites() {
  for (auto &Stmt : *S) {
    isl::set Domain = Stmt.getDomain().intersect_params(S->getContext());

    // We let isl do the lookup for the same-value condition. For this, we
    // wrap llvm::Value into an isl::set such that isl can do the lookup in
    // its hashtable implementation. llvm::Values are only compared within a
    // ScopStmt, so the map can be local to this scope. TODO: Refactor with
    // ZoneAlgorithm::makeValueSet()
    SmallDenseMap<Value *, isl::set> ValueSets;
    auto makeValueSet = [&ValueSets, this](Value *V) -> isl::set {
      assert(V);
      isl::set &Result = ValueSets[V];
      if (Result.is_null()) {
        isl::ctx Ctx = S->getIslCtx();
        std::string Name = getIslCompatibleName(
            "Val", V, ValueSets.size() - 1, std::string(), UseInstructionNames);
        isl::id Id = isl::id::alloc(Ctx, Name, V);
        Result = isl::set::universe(
            isl::space(Ctx, 0, 0).set_tuple_id(isl::dim::set, Id));
      }
      return Result;
    };

    // List of all eligible (for coalescing) writes of the future.
    // { [Domain[] -> Element[]] -> [Value[] -> MemoryAccess[]] }
    isl::union_map FutureWrites = isl::union_map::empty(S->getIslCtx());

    // Iterate over accesses from the last to the first.
    SmallVector<MemoryAccess *, 32> Accesses(getAccessesInOrder(Stmt));
    for (MemoryAccess *MA : reverse(Accesses)) {
      // In region statements, the explicit accesses can be in blocks that can
      // be executed in any order. We therefore process only the implicit
      // writes and stop after that.
      if (Stmt.isRegionStmt() && isExplicitAccess(MA))
        break;

      // { Domain[] -> Element[] }
      isl::map AccRel = MA->getLatestAccessRelation().intersect_domain(Domain);

      // { [Domain[] -> Element[]] }
      isl::set AccRelWrapped = AccRel.wrap();

      // { Value[] }
      isl::set ValSet;

      if (MA->isMustWrite() && (MA->isOriginalScalarKind() ||
                                isa<StoreInst>(MA->getAccessInstruction()))) {
        // Normally, tryGetValueStored() should be used to determine which
        // element is written, but it can return nullptr; For PHI accesses,
        // getAccessValue() returns the PHI instead of the PHI's incoming
        // value. In this case, where we only compare values of a single
        // statement, this is fine, because within a statement, a PHI in a
        // successor block has always the same value as the incoming write. We
        // still preferably use the incoming value directly so we also catch
        // direct uses of that.
        Value *StoredVal = MA->tryGetValueStored();
        if (!StoredVal)
          StoredVal = MA->getAccessValue();
        ValSet = makeValueSet(StoredVal);

        // { Domain[] }
        isl::set AccDomain = AccRel.domain();

        // Parts of the statement's domain that is not written by this access.
        isl::set UndefDomain = Domain.subtract(AccDomain);

        // { Element[] }
        isl::set ElementUniverse =
            isl::set::universe(AccRel.get_space().range());

        // { Domain[] -> Element[] }
        isl::map UndefAnything =
            isl::map::from_domain_and_range(UndefDomain, ElementUniverse);

        // We are looking a compatible write access. The other write can
        // access these elements...
        isl::map AllowedAccesses = AccRel.unite(UndefAnything);

        // ... and must write the same value.
        // { [Domain[] -> Element[]] -> Value[] }
        isl::map Filter =
            isl::map::from_domain_and_range(AllowedAccesses.wrap(), ValSet);

        // Lookup future write that fulfills these conditions.
        // { [[Domain[] -> Element[]] -> Value[]] -> MemoryAccess[] }
        isl::union_map Filtered =
            FutureWrites.uncurry().intersect_domain(Filter.wrap());

        // Iterate through the candidates.
        for (isl::map Map : Filtered.get_map_list()) {
          MemoryAccess *OtherMA = (MemoryAccess *)Map.get_space()
                                      .get_tuple_id(isl::dim::out)
                                      .get_user();

          isl::map OtherAccRel =
              OtherMA->getLatestAccessRelation().intersect_domain(Domain);

          // The filter only guaranteed that some of OtherMA's accessed
          // elements are allowed. Verify that it only accesses allowed
          // elements. Otherwise, continue with the next candidate.
          if (!OtherAccRel.is_subset(AllowedAccesses).is_true())
            continue;

          // The combined access relation.
          // { Domain[] -> Element[] }
          isl::map NewAccRel = AccRel.unite(OtherAccRel);
          simplify(NewAccRel);

          // Carry out the coalescing.
          Stmt.removeSingleMemoryAccess(MA);
          OtherMA->setNewAccessRelation(NewAccRel);

          // We removed MA, OtherMA takes its role.
          MA = OtherMA;

          TotalWritesCoalesced[CallNo]++;
          WritesCoalesced++;

          // Don't look for more candidates.
          break;
        }
      }

      // Two writes cannot be coalesced if there is another access (to some of
      // the written elements) between them. Remove all visited write accesses
      // from the list of eligible writes. Don't just remove the accessed
      // elements, but any MemoryAccess that touches any of the invalidated
      // elements.
      SmallPtrSet<MemoryAccess *, 2> TouchedAccesses;
      for (isl::map Map :
           FutureWrites.intersect_domain(AccRelWrapped).get_map_list()) {
        MemoryAccess *MA = (MemoryAccess *)Map.get_space()
                               .range()
                               .unwrap()
                               .get_tuple_id(isl::dim::out)
                               .get_user();
        TouchedAccesses.insert(MA);
      }
      isl::union_map NewFutureWrites =
          isl::union_map::empty(FutureWrites.ctx());
      for (isl::map FutureWrite : FutureWrites.get_map_list()) {
        MemoryAccess *MA = (MemoryAccess *)FutureWrite.get_space()
                               .range()
                               .unwrap()
                               .get_tuple_id(isl::dim::out)
                               .get_user();
        if (!TouchedAccesses.count(MA))
          NewFutureWrites = NewFutureWrites.unite(FutureWrite);
      }
      FutureWrites = NewFutureWrites;

      if (MA->isMustWrite() && !ValSet.is_null()) {
        // { MemoryAccess[] }
        auto AccSet =
            isl::set::universe(isl::space(S->getIslCtx(), 0, 0)
                                   .set_tuple_id(isl::dim::set, MA->getId()));

        // { Val[] -> MemoryAccess[] }
        isl::map ValAccSet = isl::map::from_domain_and_range(ValSet, AccSet);

        // { [Domain[] -> Element[]] -> [Value[] -> MemoryAccess[]] }
        isl::map AccRelValAcc =
            isl::map::from_domain_and_range(AccRelWrapped, ValAccSet.wrap());
        FutureWrites = FutureWrites.unite(AccRelValAcc);
      }
    }
  }
}

/// Remove writes that just write the same value already stored in the
/// element.
void SimplifyImpl::removeRedundantWrites() {
  for (auto &Stmt : *S) {
    SmallDenseMap<Value *, isl::set> ValueSets;
    auto makeValueSet = [&ValueSets, this](Value *V) -> isl::set {
      assert(V);
      isl::set &Result = ValueSets[V];
      if (Result.is_null()) {
        isl_ctx *Ctx = S->getIslCtx().get();
        std::string Name = getIslCompatibleName(
            "Val", V, ValueSets.size() - 1, std::string(), UseInstructionNames);
        isl::id Id = isl::manage(isl_id_alloc(Ctx, Name.c_str(), V));
        Result = isl::set::universe(
            isl::space(Ctx, 0, 0).set_tuple_id(isl::dim::set, Id));
      }
      return Result;
    };

    isl::set Domain = Stmt.getDomain();
    Domain = Domain.intersect_params(S->getContext());

    // List of element reads that still have the same value while iterating
    // through the MemoryAccesses.
    // { [Domain[] -> Element[]] -> Val[] }
    isl::union_map Known = isl::union_map::empty(S->getIslCtx());

    SmallVector<MemoryAccess *, 32> Accesses(getAccessesInOrder(Stmt));
    for (MemoryAccess *MA : Accesses) {
      // Is the memory access in a defined order relative to the other
      // accesses? In region statements, only the first and the last accesses
      // have defined order. Execution of those in the middle may depend on
      // runtime conditions an therefore cannot be modified.
      bool IsOrdered =
          Stmt.isBlockStmt() || MA->isOriginalScalarKind() ||
          (!S->getBoxedLoops().size() && MA->getAccessInstruction() &&
           Stmt.getEntryBlock() == MA->getAccessInstruction()->getParent());

      isl::map AccRel = MA->getAccessRelation();
      AccRel = AccRel.intersect_domain(Domain);
      isl::set AccRelWrapped = AccRel.wrap();

      // Determine whether a write is redundant (stores only values that are
      // already present in the written array elements) and remove it if this
      // is the case.
      if (IsOrdered && MA->isMustWrite() &&
          (isa<StoreInst>(MA->getAccessInstruction()) ||
           MA->isOriginalScalarKind())) {
        Value *StoredVal = MA->tryGetValueStored();
        if (!StoredVal)
          StoredVal = MA->getAccessValue();

        if (StoredVal) {
          // Lookup in the set of known values.
          isl::map AccRelStoredVal = isl::map::from_domain_and_range(
              AccRelWrapped, makeValueSet(StoredVal));
          if (isl::union_map(AccRelStoredVal).is_subset(Known)) {
            LLVM_DEBUG(dbgs() << "Cleanup of " << MA << ":\n");
            LLVM_DEBUG(dbgs() << "      Scalar: " << *StoredVal << "\n");
            LLVM_DEBUG(dbgs() << "      AccRel: " << AccRel << "\n");

            Stmt.removeSingleMemoryAccess(MA);

            RedundantWritesRemoved++;
            TotalRedundantWritesRemoved[CallNo]++;
          }
        }
      }

      // Update the know values set.
      if (MA->isRead()) {
        // Loaded values are the currently known values of the array element
        // it was loaded from.
        Value *LoadedVal = MA->getAccessValue();
        if (LoadedVal && IsOrdered) {
          isl::map AccRelVal = isl::map::from_domain_and_range(
              AccRelWrapped, makeValueSet(LoadedVal));

          Known = Known.unite(AccRelVal);
        }
      } else if (MA->isWrite()) {
        // Remove (possibly) overwritten values from the known elements set.
        // We remove all elements of the accessed array to avoid too complex
        // isl sets.
        isl::set AccRelUniv = isl::set::universe(AccRelWrapped.get_space());
        Known = Known.subtract_domain(AccRelUniv);

        // At this point, we could add the written value of must-writes.
        // However, writing same values is already handled by
        // coalesceWrites().
      }
    }
  }
}

/// Remove statements without side effects.
void SimplifyImpl::removeUnnecessaryStmts() {
  auto NumStmtsBefore = S->getSize();
  S->simplifySCoP(true);
  assert(NumStmtsBefore >= S->getSize());
  StmtsRemoved = NumStmtsBefore - S->getSize();
  LLVM_DEBUG(dbgs() << "Removed " << StmtsRemoved << " (of " << NumStmtsBefore
                    << ") statements\n");
  TotalStmtsRemoved[CallNo] += StmtsRemoved;
}

/// Remove accesses that have an empty domain.
void SimplifyImpl::removeEmptyPartialAccesses() {
  for (ScopStmt &Stmt : *S) {
    // Defer the actual removal to not invalidate iterators.
    SmallVector<MemoryAccess *, 8> DeferredRemove;

    for (MemoryAccess *MA : Stmt) {
      if (!MA->isWrite())
        continue;

      isl::map AccRel = MA->getAccessRelation();
      if (!AccRel.is_empty().is_true())
        continue;

      LLVM_DEBUG(
          dbgs() << "Removing " << MA
                 << " because it's a partial access that never occurs\n");
      DeferredRemove.push_back(MA);
    }

    for (MemoryAccess *MA : DeferredRemove) {
      Stmt.removeSingleMemoryAccess(MA);
      EmptyPartialAccessesRemoved++;
      TotalEmptyPartialAccessesRemoved[CallNo]++;
    }
  }
}

/// Mark all reachable instructions and access, and sweep those that are not
/// reachable.
void SimplifyImpl::markAndSweep(LoopInfo *LI) {
  DenseSet<MemoryAccess *> UsedMA;
  DenseSet<VirtualInstruction> UsedInsts;

  // Get all reachable instructions and accesses.
  markReachable(S, LI, UsedInsts, UsedMA);

  // Remove all non-reachable accesses.
  // We need get all MemoryAccesses first, in order to not invalidate the
  // iterators when removing them.
  SmallVector<MemoryAccess *, 64> AllMAs;
  for (ScopStmt &Stmt : *S)
    AllMAs.append(Stmt.begin(), Stmt.end());

  for (MemoryAccess *MA : AllMAs) {
    if (UsedMA.count(MA))
      continue;
    LLVM_DEBUG(dbgs() << "Removing " << MA
                      << " because its value is not used\n");
    ScopStmt *Stmt = MA->getStatement();
    Stmt->removeSingleMemoryAccess(MA);

    DeadAccessesRemoved++;
    TotalDeadAccessesRemoved[CallNo]++;
  }

  // Remove all non-reachable instructions.
  for (ScopStmt &Stmt : *S) {
    // Note that for region statements, we can only remove the non-terminator
    // instructions of the entry block. All other instructions are not in the
    // instructions list, but implicitly always part of the statement.

    SmallVector<Instruction *, 32> AllInsts(Stmt.insts_begin(),
                                            Stmt.insts_end());
    SmallVector<Instruction *, 32> RemainInsts;

    for (Instruction *Inst : AllInsts) {
      auto It = UsedInsts.find({&Stmt, Inst});
      if (It == UsedInsts.end()) {
        LLVM_DEBUG(dbgs() << "Removing "; Inst->print(dbgs());
                   dbgs() << " because it is not used\n");
        DeadInstructionsRemoved++;
        TotalDeadInstructionsRemoved[CallNo]++;
        continue;
      }

      RemainInsts.push_back(Inst);

      // If instructions appear multiple times, keep only the first.
      UsedInsts.erase(It);
    }

    // Set the new instruction list to be only those we did not remove.
    Stmt.setInstructions(RemainInsts);
  }
}

/// Print simplification statistics to @p OS.
void SimplifyImpl::printStatistics(llvm::raw_ostream &OS, int Indent) const {
  OS.indent(Indent) << "Statistics {\n";
  OS.indent(Indent + 4) << "Empty domains removed: " << EmptyDomainsRemoved
                        << '\n';
  OS.indent(Indent + 4) << "Overwrites removed: " << OverwritesRemoved << '\n';
  OS.indent(Indent + 4) << "Partial writes coalesced: " << WritesCoalesced
                        << "\n";
  OS.indent(Indent + 4) << "Redundant writes removed: "
                        << RedundantWritesRemoved << "\n";
  OS.indent(Indent + 4) << "Accesses with empty domains removed: "
                        << EmptyPartialAccessesRemoved << "\n";
  OS.indent(Indent + 4) << "Dead accesses removed: " << DeadAccessesRemoved
                        << '\n';
  OS.indent(Indent + 4) << "Dead instructions removed: "
                        << DeadInstructionsRemoved << '\n';
  OS.indent(Indent + 4) << "Stmts removed: " << StmtsRemoved << "\n";
  OS.indent(Indent) << "}\n";
}

/// Print the current state of all MemoryAccesses to @p OS.
void SimplifyImpl::printAccesses(llvm::raw_ostream &OS, int Indent) const {
  OS.indent(Indent) << "After accesses {\n";
  for (auto &Stmt : *S) {
    OS.indent(Indent + 4) << Stmt.getBaseName() << "\n";
    for (auto *MA : Stmt)
      MA->print(OS);
  }
  OS.indent(Indent) << "}\n";
}

void SimplifyImpl::run(Scop &S, LoopInfo *LI) {
  // Must not have run before.
  assert(!this->S);
  assert(!isModified());

  // Prepare processing of this SCoP.
  this->S = &S;
  ScopsProcessed[CallNo]++;

  LLVM_DEBUG(dbgs() << "Removing statements that are never executed...\n");
  removeEmptyDomainStmts();

  LLVM_DEBUG(dbgs() << "Removing partial writes that never happen...\n");
  removeEmptyPartialAccesses();

  LLVM_DEBUG(dbgs() << "Removing overwrites...\n");
  removeOverwrites();

  LLVM_DEBUG(dbgs() << "Coalesce partial writes...\n");
  coalesceWrites();

  LLVM_DEBUG(dbgs() << "Removing redundant writes...\n");
  removeRedundantWrites();

  LLVM_DEBUG(dbgs() << "Cleanup unused accesses...\n");
  markAndSweep(LI);

  LLVM_DEBUG(dbgs() << "Removing statements without side effects...\n");
  removeUnnecessaryStmts();

  if (isModified())
    ScopsModified[CallNo]++;
  LLVM_DEBUG(dbgs() << "\nFinal Scop:\n");
  LLVM_DEBUG(dbgs() << S);

  auto ScopStats = S.getStatistics();
  NumValueWrites[CallNo] += ScopStats.NumValueWrites;
  NumValueWritesInLoops[CallNo] += ScopStats.NumValueWritesInLoops;
  NumPHIWrites[CallNo] += ScopStats.NumPHIWrites;
  NumPHIWritesInLoops[CallNo] += ScopStats.NumPHIWritesInLoops;
  NumSingletonWrites[CallNo] += ScopStats.NumSingletonWrites;
  NumSingletonWritesInLoops[CallNo] += ScopStats.NumSingletonWritesInLoops;
}

void SimplifyImpl::printScop(raw_ostream &OS, Scop &S) const {
  assert(&S == this->S &&
         "Can only print analysis for the last processed SCoP");
  printStatistics(OS);

  if (!isModified()) {
    OS << "SCoP could not be simplified\n";
    return;
  }
  printAccesses(OS);
}

class SimplifyWrapperPass final : public ScopPass {
public:
  static char ID;
  int CallNo;
  std::optional<SimplifyImpl> Impl;

  explicit SimplifyWrapperPass(int CallNo = 0) : ScopPass(ID), CallNo(CallNo) {}

  void getAnalysisUsage(AnalysisUsage &AU) const override {
    AU.addRequiredTransitive<ScopInfoRegionPass>();
    AU.addRequired<LoopInfoWrapperPass>();
    AU.setPreservesAll();
  }

  bool runOnScop(Scop &S) override {
    LoopInfo *LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();

    Impl.emplace(CallNo);
    Impl->run(S, LI);

    return false;
  }

  void printScop(raw_ostream &OS, Scop &S) const override {
    if (Impl)
      Impl->printScop(OS, S);
  }

  void releaseMemory() override { Impl.reset(); }
};

char SimplifyWrapperPass::ID;

static llvm::PreservedAnalyses
runSimplifyUsingNPM(Scop &S, ScopAnalysisManager &SAM,
                    ScopStandardAnalysisResults &SAR, SPMUpdater &U, int CallNo,
                    raw_ostream *OS) {
  SimplifyImpl Impl(CallNo);
  Impl.run(S, &SAR.LI);
  if (OS) {
    *OS << "Printing analysis 'Polly - Simplify' for region: '" << S.getName()
        << "' in function '" << S.getFunction().getName() << "':\n";
    Impl.printScop(*OS, S);
  }

  if (!Impl.isModified())
    return llvm::PreservedAnalyses::all();

  PreservedAnalyses PA;
  PA.preserveSet<AllAnalysesOn<Module>>();
  PA.preserveSet<AllAnalysesOn<Function>>();
  PA.preserveSet<AllAnalysesOn<Loop>>();
  return PA;
}

} // anonymous namespace

llvm::PreservedAnalyses SimplifyPass::run(Scop &S, ScopAnalysisManager &SAM,
                                          ScopStandardAnalysisResults &SAR,
                                          SPMUpdater &U) {
  return runSimplifyUsingNPM(S, SAM, SAR, U, CallNo, nullptr);
}

llvm::PreservedAnalyses
SimplifyPrinterPass::run(Scop &S, ScopAnalysisManager &SAM,
                         ScopStandardAnalysisResults &SAR, SPMUpdater &U) {
  return runSimplifyUsingNPM(S, SAM, SAR, U, CallNo, &OS);
}

SmallVector<MemoryAccess *, 32> polly::getAccessesInOrder(ScopStmt &Stmt) {
  SmallVector<MemoryAccess *, 32> Accesses;

  for (MemoryAccess *MemAcc : Stmt)
    if (isImplicitRead(MemAcc))
      Accesses.push_back(MemAcc);

  for (MemoryAccess *MemAcc : Stmt)
    if (isExplicitAccess(MemAcc))
      Accesses.push_back(MemAcc);

  for (MemoryAccess *MemAcc : Stmt)
    if (isImplicitWrite(MemAcc))
      Accesses.push_back(MemAcc);

  return Accesses;
}

Pass *polly::createSimplifyWrapperPass(int CallNo) {
  return new SimplifyWrapperPass(CallNo);
}

INITIALIZE_PASS_BEGIN(SimplifyWrapperPass, "polly-simplify", "Polly - Simplify",
                      false, false)
INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
INITIALIZE_PASS_END(SimplifyWrapperPass, "polly-simplify", "Polly - Simplify",
                    false, false)

//===----------------------------------------------------------------------===//

namespace {
/// Print result from SimplifyWrapperPass.
class SimplifyPrinterLegacyPass final : public ScopPass {
public:
  static char ID;

  SimplifyPrinterLegacyPass() : SimplifyPrinterLegacyPass(outs()) {}
  explicit SimplifyPrinterLegacyPass(llvm::raw_ostream &OS)
      : ScopPass(ID), OS(OS) {}

  bool runOnScop(Scop &S) override {
    SimplifyWrapperPass &P = getAnalysis<SimplifyWrapperPass>();

    OS << "Printing analysis '" << P.getPassName() << "' for region: '"
       << S.getRegion().getNameStr() << "' in function '"
       << S.getFunction().getName() << "':\n";
    P.printScop(OS, S);

    return false;
  }

  void getAnalysisUsage(AnalysisUsage &AU) const override {
    ScopPass::getAnalysisUsage(AU);
    AU.addRequired<SimplifyWrapperPass>();
    AU.setPreservesAll();
  }

private:
  llvm::raw_ostream &OS;
};

char SimplifyPrinterLegacyPass::ID = 0;
} // namespace

Pass *polly::createSimplifyPrinterLegacyPass(raw_ostream &OS) {
  return new SimplifyPrinterLegacyPass(OS);
}

INITIALIZE_PASS_BEGIN(SimplifyPrinterLegacyPass, "polly-print-simplify",
                      "Polly - Print Simplify actions", false, false)
INITIALIZE_PASS_DEPENDENCY(SimplifyWrapperPass)
INITIALIZE_PASS_END(SimplifyPrinterLegacyPass, "polly-print-simplify",
                    "Polly - Print Simplify actions", false, false)