Simplify.cpp 27.4 KB
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
//===------ 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"
#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 int 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::add_map, 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 (isl_map_n_basic_map(PrevMap.get()) + isl_map_n_basic_map(Map.get()) <=
      SimplifyMaxDisjuncts)
    return UMap.add_map(Map);

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

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

  return UResult;
}

/// Return whether at least one simplification has been applied.
bool SimplifyVisitor::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 SimplifyVisitor::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 SimplifyVisitor::removeOverwrites() {
  for (auto &Stmt : *S) {
    isl::set Domain = Stmt.getDomain();
    isl::union_map WillBeOverwritten =
        isl::union_map::empty(S->getParamSpace());

    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 SimplifyVisitor::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->getParamSpace());

    // 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.get_space());
      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.add_map(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.add_map(AccRelValAcc);
      }
    }
  }
}

/// Remove writes that just write the same value already stored in the
/// element.
void SimplifyVisitor::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->getParamSpace());

    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.add_map(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 SimplifyVisitor::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 SimplifyVisitor::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 SimplifyVisitor::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 SimplifyVisitor::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 SimplifyVisitor::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";
}

bool SimplifyVisitor::visit(Scop &S, LoopInfo *LI) {
  // Reset statistics of last processed SCoP.
  releaseMemory();
  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;

  return false;
}

void SimplifyVisitor::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);
}

void SimplifyVisitor::releaseMemory() {
  S = nullptr;

  EmptyDomainsRemoved = 0;
  OverwritesRemoved = 0;
  WritesCoalesced = 0;
  RedundantWritesRemoved = 0;
  EmptyPartialAccessesRemoved = 0;
  DeadAccessesRemoved = 0;
  DeadInstructionsRemoved = 0;
  StmtsRemoved = 0;
}

class SimplifyLegacyPass : public ScopPass {
public:
  static char ID;
  SimplifyVisitor Imp;

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

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

  virtual bool runOnScop(Scop &S) override {
    return Imp.visit(S, &getAnalysis<LoopInfoWrapperPass>().getLoopInfo());
  }

  virtual void printScop(raw_ostream &OS, Scop &S) const override {
    Imp.printScop(OS, S);
  }

  virtual void releaseMemory() override { Imp.releaseMemory(); }
};

char SimplifyLegacyPass::ID;
} // anonymous namespace

namespace polly {
llvm::PreservedAnalyses SimplifyPass::run(Scop &S, ScopAnalysisManager &SAM,
                                          ScopStandardAnalysisResults &SAR,
                                          SPMUpdater &U) {
  if (!Imp.visit(S, &SAR.LI))
    return llvm::PreservedAnalyses::all();

  return llvm::PreservedAnalyses::none();
}

llvm::PreservedAnalyses
SimplifyPrinterPass::run(Scop &S, ScopAnalysisManager &SAM,
                         ScopStandardAnalysisResults &SAR, SPMUpdater &U) {
  bool Changed = Imp.visit(S, &SAR.LI);
  Imp.printScop(OS, S);

  if (!Changed)
    return llvm::PreservedAnalyses::all();

  return llvm::PreservedAnalyses::none();
}

SmallVector<MemoryAccess *, 32> 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;
}
} // namespace polly

Pass *polly::createSimplifyPass(int CallNo) {
  return new SimplifyLegacyPass(CallNo);
}

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