text: //===- LoopAccessAnalysis.cpp - Loop Access Analysis Implementation --------==//
  //
  // 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
  //
  //===----------------------------------------------------------------------===//
  //
  // The implementation for the loop memory dependence that was originally
  // developed for the loop vectorizer.
  //
  //===----------------------------------------------------------------------===//
  
  #include "llvm/Analysis/LoopAccessAnalysis.h"
  #include "llvm/ADT/APInt.h"
  #include "llvm/ADT/DenseMap.h"
  #include "llvm/ADT/DepthFirstIterator.h"
  #include "llvm/ADT/EquivalenceClasses.h"
  #include "llvm/ADT/PointerIntPair.h"
  #include "llvm/ADT/STLExtras.h"
  #include "llvm/ADT/SetVector.h"
  #include "llvm/ADT/SmallPtrSet.h"
  #include "llvm/ADT/SmallSet.h"
  #include "llvm/ADT/SmallVector.h"
  #include "llvm/ADT/iterator_range.h"
  #include "llvm/Analysis/AliasAnalysis.h"
  #include "llvm/Analysis/AliasSetTracker.h"
  #include "llvm/Analysis/LoopAnalysisManager.h"
  #include "llvm/Analysis/LoopInfo.h"
  #include "llvm/Analysis/MemoryLocation.h"
  #include "llvm/Analysis/OptimizationRemarkEmitter.h"
  #include "llvm/Analysis/ScalarEvolution.h"
  #include "llvm/Analysis/ScalarEvolutionExpressions.h"
  #include "llvm/Analysis/TargetLibraryInfo.h"
  #include "llvm/Analysis/ValueTracking.h"
  #include "llvm/Analysis/VectorUtils.h"
  #include "llvm/IR/BasicBlock.h"
  #include "llvm/IR/Constants.h"
  #include "llvm/IR/DataLayout.h"
  #include "llvm/IR/DebugLoc.h"
  #include "llvm/IR/DerivedTypes.h"
  #include "llvm/IR/DiagnosticInfo.h"
  #include "llvm/IR/Dominators.h"
  #include "llvm/IR/Function.h"
  #include "llvm/IR/InstrTypes.h"
  #include "llvm/IR/Instruction.h"
  #include "llvm/IR/Instructions.h"
  #include "llvm/IR/Operator.h"
  #include "llvm/IR/PassManager.h"
  #include "llvm/IR/Type.h"
  #include "llvm/IR/Value.h"
  #include "llvm/IR/ValueHandle.h"
  #include "llvm/InitializePasses.h"
  #include "llvm/Pass.h"
  #include "llvm/Support/Casting.h"
  #include "llvm/Support/CommandLine.h"
  #include "llvm/Support/Debug.h"
  #include "llvm/Support/ErrorHandling.h"
  #include "llvm/Support/raw_ostream.h"
  #include <algorithm>
  #include <cassert>
  #include <cstdint>
  #include <cstdlib>
  #include <iterator>
  #include <utility>
  #include <vector>
  
  using namespace llvm;
  
  #define DEBUG_TYPE "loop-accesses"
  
  static cl::opt<unsigned, true>
  VectorizationFactor("force-vector-width", cl::Hidden,
                      cl::desc("Sets the SIMD width. Zero is autoselect."),
                      cl::location(VectorizerParams::VectorizationFactor));
  unsigned VectorizerParams::VectorizationFactor;
  
  static cl::opt<unsigned, true>
  VectorizationInterleave("force-vector-interleave", cl::Hidden,
                          cl::desc("Sets the vectorization interleave count. "
                                   "Zero is autoselect."),
                          cl::location(
                              VectorizerParams::VectorizationInterleave));
  unsigned VectorizerParams::VectorizationInterleave;
  
  static cl::opt<unsigned, true> RuntimeMemoryCheckThreshold(
      "runtime-memory-check-threshold", cl::Hidden,
      cl::desc("When performing memory disambiguation checks at runtime do not "
               "generate more than this number of comparisons (default = 8)."),
      cl::location(VectorizerParams::RuntimeMemoryCheckThreshold), cl::init(8));
  unsigned VectorizerParams::RuntimeMemoryCheckThreshold;
  
  /// The maximum iterations used to merge memory checks
  static cl::opt<unsigned> MemoryCheckMergeThreshold(
      "memory-check-merge-threshold", cl::Hidden,
      cl::desc("Maximum number of comparisons done when trying to merge "
               "runtime memory checks. (default = 100)"),
      cl::init(100));
  
  /// Maximum SIMD width.
  const unsigned VectorizerParams::MaxVectorWidth = 64;
  
  /// We collect dependences up to this threshold.
  static cl::opt<unsigned>
      MaxDependences("max-dependences", cl::Hidden,
                     cl::desc("Maximum number of dependences collected by "
                              "loop-access analysis (default = 100)"),
                     cl::init(100));
  
  /// This enables versioning on the strides of symbolically striding memory
  /// accesses in code like the following.
  ///   for (i = 0; i < N; ++i)
  ///     A[i * Stride1] += B[i * Stride2] ...
  ///
  /// Will be roughly translated to
  ///    if (Stride1 == 1 && Stride2 == 1) {
  ///      for (i = 0; i < N; i+=4)
  ///       A[i:i+3] += ...
  ///    } else
  ///      ...
  static cl::opt<bool> EnableMemAccessVersioning(
      "enable-mem-access-versioning", cl::init(true), cl::Hidden,
      cl::desc("Enable symbolic stride memory access versioning"));
  
  /// Enable store-to-load forwarding conflict detection. This option can
  /// be disabled for correctness testing.
  static cl::opt<bool> EnableForwardingConflictDetection(
      "store-to-load-forwarding-conflict-detection", cl::Hidden,
      cl::desc("Enable conflict detection in loop-access analysis"),
      cl::init(true));
  
  bool VectorizerParams::isInterleaveForced() {
    return ::VectorizationInterleave.getNumOccurrences() > 0;
  }
  
  Value *llvm::stripIntegerCast(Value *V) {
    if (auto *CI = dyn_cast<CastInst>(V))
      if (CI->getOperand(0)->getType()->isIntegerTy())
        return CI->getOperand(0);
    return V;
  }
  
  const SCEV *llvm::replaceSymbolicStrideSCEV(PredicatedScalarEvolution &PSE,
                                              const ValueToValueMap &PtrToStride,
                                              Value *Ptr, Value *OrigPtr) {
    const SCEV *OrigSCEV = PSE.getSCEV(Ptr);
  
    // If there is an entry in the map return the SCEV of the pointer with the
    // symbolic stride replaced by one.
    ValueToValueMap::const_iterator SI =
        PtrToStride.find(OrigPtr ? OrigPtr : Ptr);
    if (SI == PtrToStride.end())
      // For a non-symbolic stride, just return the original expression.
      return OrigSCEV;
  
    Value *StrideVal = stripIntegerCast(SI->second);
  
    ScalarEvolution *SE = PSE.getSE();
    const auto *U = cast<SCEVUnknown>(SE->getSCEV(StrideVal));
    const auto *CT =
      static_cast<const SCEVConstant *>(SE->getOne(StrideVal->getType()));
  
    PSE.addPredicate(*SE->getEqualPredicate(U, CT));
    auto *Expr = PSE.getSCEV(Ptr);
  
    LLVM_DEBUG(dbgs() << "LAA: Replacing SCEV: " << *OrigSCEV
  	     << " by: " << *Expr << "\n");
    return Expr;
  }
  
  RuntimeCheckingPtrGroup::RuntimeCheckingPtrGroup(
      unsigned Index, RuntimePointerChecking &RtCheck)
      : RtCheck(RtCheck), High(RtCheck.Pointers[Index].End),
        Low(RtCheck.Pointers[Index].Start) {
    Members.push_back(Index);
  }
  
  /// Calculate Start and End points of memory access.
  /// Let's assume A is the first access and B is a memory access on N-th loop
  /// iteration. Then B is calculated as:
  ///   B = A + Step*N .
  /// Step value may be positive or negative.
  /// N is a calculated back-edge taken count:
  ///     N = (TripCount > 0) ? RoundDown(TripCount -1 , VF) : 0
  /// Start and End points are calculated in the following way:
  /// Start = UMIN(A, B) ; End = UMAX(A, B) + SizeOfElt,
  /// where SizeOfElt is the size of single memory access in bytes.
  ///
  /// There is no conflict when the intervals are disjoint:
  /// NoConflict = (P2.Start >= P1.End) || (P1.Start >= P2.End)
  void RuntimePointerChecking::insert(Loop *Lp, Value *Ptr, bool WritePtr,
                                      unsigned DepSetId, unsigned ASId,
                                      const ValueToValueMap &Strides,
                                      PredicatedScalarEvolution &PSE) {
    // Get the stride replaced scev.
    const SCEV *Sc = replaceSymbolicStrideSCEV(PSE, Strides, Ptr);
    ScalarEvolution *SE = PSE.getSE();
  
    const SCEV *ScStart;
    const SCEV *ScEnd;
  
    if (SE->isLoopInvariant(Sc, Lp))
      ScStart = ScEnd = Sc;
    else {
      const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Sc);
      assert(AR && "Invalid addrec expression");
      const SCEV *Ex = PSE.getBackedgeTakenCount();
  
      ScStart = AR->getStart();
      ScEnd = AR->evaluateAtIteration(Ex, *SE);
      const SCEV *Step = AR->getStepRecurrence(*SE);
  
      // For expressions with negative step, the upper bound is ScStart and the
      // lower bound is ScEnd.
      if (const auto *CStep = dyn_cast<SCEVConstant>(Step)) {
        if (CStep->getValue()->isNegative())
          std::swap(ScStart, ScEnd);
      } else {
        // Fallback case: the step is not constant, but we can still
        // get the upper and lower bounds of the interval by using min/max
        // expressions.
        ScStart = SE->getUMinExpr(ScStart, ScEnd);
        ScEnd = SE->getUMaxExpr(AR->getStart(), ScEnd);
      }
      // Add the size of the pointed element to ScEnd.
      auto &DL = Lp->getHeader()->getModule()->getDataLayout();
      Type *IdxTy = DL.getIndexType(Ptr->getType());
      const SCEV *EltSizeSCEV =
          SE->getStoreSizeOfExpr(IdxTy, Ptr->getType()->getPointerElementType());
      ScEnd = SE->getAddExpr(ScEnd, EltSizeSCEV);
    }
  
    Pointers.emplace_back(Ptr, ScStart, ScEnd, WritePtr, DepSetId, ASId, Sc);
  }
  
  SmallVector<RuntimePointerCheck, 4>
  RuntimePointerChecking::generateChecks() const {
    SmallVector<RuntimePointerCheck, 4> Checks;
  
    for (unsigned I = 0; I < CheckingGroups.size(); ++I) {
      for (unsigned J = I + 1; J < CheckingGroups.size(); ++J) {
        const RuntimeCheckingPtrGroup &CGI = CheckingGroups[I];
        const RuntimeCheckingPtrGroup &CGJ = CheckingGroups[J];
  
        if (needsChecking(CGI, CGJ))
          Checks.push_back(std::make_pair(&CGI, &CGJ));
      }
    }
    return Checks;
  }
  
  void RuntimePointerChecking::generateChecks(
      MemoryDepChecker::DepCandidates &DepCands, bool UseDependencies) {
    assert(Checks.empty() && "Checks is not empty");
    groupChecks(DepCands, UseDependencies);
    Checks = generateChecks();
  }
  
  bool RuntimePointerChecking::needsChecking(
      const RuntimeCheckingPtrGroup &M, const RuntimeCheckingPtrGroup &N) const {
    for (unsigned I = 0, EI = M.Members.size(); EI != I; ++I)
      for (unsigned J = 0, EJ = N.Members.size(); EJ != J; ++J)
        if (needsChecking(M.Members[I], N.Members[J]))
          return true;
    return false;
  }
  
  /// Compare \p I and \p J and return the minimum.
  /// Return nullptr in case we couldn't find an answer.
  static const SCEV *getMinFromExprs(const SCEV *I, const SCEV *J,
                                     ScalarEvolution *SE) {
    const SCEV *Diff = SE->getMinusSCEV(J, I);
    const SCEVConstant *C = dyn_cast<const SCEVConstant>(Diff);
  
    if (!C)
      return nullptr;
    if (C->getValue()->isNegative())
      return J;
    return I;
  }
  
  bool RuntimeCheckingPtrGroup::addPointer(unsigned Index) {
    const SCEV *Start = RtCheck.Pointers[Index].Start;
    const SCEV *End = RtCheck.Pointers[Index].End;
  
    // Compare the starts and ends with the known minimum and maximum
    // of this set. We need to know how we compare against the min/max
    // of the set in order to be able to emit memchecks.
    const SCEV *Min0 = getMinFromExprs(Start, Low, RtCheck.SE);
    if (!Min0)
      return false;
  
    const SCEV *Min1 = getMinFromExprs(End, High, RtCheck.SE);
    if (!Min1)
      return false;
  
    // Update the low bound  expression if we've found a new min value.
    if (Min0 == Start)
      Low = Start;
  
    // Update the high bound expression if we've found a new max value.
    if (Min1 != End)
      High = End;
  
    Members.push_back(Index);
    return true;
  }
  
  void RuntimePointerChecking::groupChecks(
      MemoryDepChecker::DepCandidates &DepCands, bool UseDependencies) {
    // We build the groups from dependency candidates equivalence classes
    // because:
    //    - We know that pointers in the same equivalence class share
    //      the same underlying object and therefore there is a chance
    //      that we can compare pointers
    //    - We wouldn't be able to merge two pointers for which we need
    //      to emit a memcheck. The classes in DepCands are already
    //      conveniently built such that no two pointers in the same
    //      class need checking against each other.
  
    // We use the following (greedy) algorithm to construct the groups
    // For every pointer in the equivalence class:
    //   For each existing group:
    //   - if the difference between this pointer and the min/max bounds
    //     of the group is a constant, then make the pointer part of the
    //     group and update the min/max bounds of that group as required.
  
    CheckingGroups.clear();
  
    // If we need to check two pointers to the same underlying object
    // with a non-constant difference, we shouldn't perform any pointer
    // grouping with those pointers. This is because we can easily get
    // into cases where the resulting check would return false, even when
    // the accesses are safe.
    //
    // The following example shows this:
    // for (i = 0; i < 1000; ++i)
    //   a[5000 + i * m] = a[i] + a[i + 9000]
    //
    // Here grouping gives a check of (5000, 5000 + 1000 * m) against
    // (0, 10000) which is always false. However, if m is 1, there is no
    // dependence. Not grouping the checks for a[i] and a[i + 9000] allows
    // us to perform an accurate check in this case.
    //
    // The above case requires that we have an UnknownDependence between
    // accesses to the same underlying object. This cannot happen unless
    // FoundNonConstantDistanceDependence is set, and therefore UseDependencies
    // is also false. In this case we will use the fallback path and create
    // separate checking groups for all pointers.
  
    // If we don't have the dependency partitions, construct a new
    // checking pointer group for each pointer. This is also required
    // for correctness, because in this case we can have checking between
    // pointers to the same underlying object.
    if (!UseDependencies) {
      for (unsigned I = 0; I < Pointers.size(); ++I)
        CheckingGroups.push_back(RuntimeCheckingPtrGroup(I, *this));
      return;
    }
  
    unsigned TotalComparisons = 0;
  
    DenseMap<Value *, unsigned> PositionMap;
    for (unsigned Index = 0; Index < Pointers.size(); ++Index)
      PositionMap[Pointers[Index].PointerValue] = Index;
  
    // We need to keep track of what pointers we've already seen so we
    // don't process them twice.
    SmallSet<unsigned, 2> Seen;
  
    // Go through all equivalence classes, get the "pointer check groups"
    // and add them to the overall solution. We use the order in which accesses
    // appear in 'Pointers' to enforce determinism.
    for (unsigned I = 0; I < Pointers.size(); ++I) {
      // We've seen this pointer before, and therefore already processed
      // its equivalence class.
      if (Seen.count(I))
        continue;
  
      MemoryDepChecker::MemAccessInfo Access(Pointers[I].PointerValue,
                                             Pointers[I].IsWritePtr);
  
      SmallVector<RuntimeCheckingPtrGroup, 2> Groups;
      auto LeaderI = DepCands.findValue(DepCands.getLeaderValue(Access));
  
      // Because DepCands is constructed by visiting accesses in the order in
      // which they appear in alias sets (which is deterministic) and the
      // iteration order within an equivalence class member is only dependent on
      // the order in which unions and insertions are performed on the
      // equivalence class, the iteration order is deterministic.
      for (auto MI = DepCands.member_begin(LeaderI), ME = DepCands.member_end();
           MI != ME; ++MI) {
        auto PointerI = PositionMap.find(MI->getPointer());
        assert(PointerI != PositionMap.end() &&
               "pointer in equivalence class not found in PositionMap");
        unsigned Pointer = PointerI->second;
        bool Merged = false;
        // Mark this pointer as seen.
        Seen.insert(Pointer);
  
        // Go through all the existing sets and see if we can find one
        // which can include this pointer.
        for (RuntimeCheckingPtrGroup &Group : Groups) {
          // Don't perform more than a certain amount of comparisons.
          // This should limit the cost of grouping the pointers to something
          // reasonable.  If we do end up hitting this threshold, the algorithm
          // will create separate groups for all remaining pointers.
          if (TotalComparisons > MemoryCheckMergeThreshold)
            break;
  
          TotalComparisons++;
  
          if (Group.addPointer(Pointer)) {
            Merged = true;
            break;
          }
        }
  
        if (!Merged)
          // We couldn't add this pointer to any existing set or the threshold
          // for the number of comparisons has been reached. Create a new group
          // to hold the current pointer.
          Groups.push_back(RuntimeCheckingPtrGroup(Pointer, *this));
      }
  
      // We've computed the grouped checks for this partition.
      // Save the results and continue with the next one.
      llvm::copy(Groups, std::back_inserter(CheckingGroups));
    }
  }
  
  bool RuntimePointerChecking::arePointersInSamePartition(
      const SmallVectorImpl<int> &PtrToPartition, unsigned PtrIdx1,
      unsigned PtrIdx2) {
    return (PtrToPartition[PtrIdx1] != -1 &&
            PtrToPartition[PtrIdx1] == PtrToPartition[PtrIdx2]);
  }
  
  bool RuntimePointerChecking::needsChecking(unsigned I, unsigned J) const {
    const PointerInfo &PointerI = Pointers[I];
    const PointerInfo &PointerJ = Pointers[J];
  
    // No need to check if two readonly pointers intersect.
    if (!PointerI.IsWritePtr && !PointerJ.IsWritePtr)
      return false;
  
    // Only need to check pointers between two different dependency sets.
    if (PointerI.DependencySetId == PointerJ.DependencySetId)
      return false;
  
    // Only need to check pointers in the same alias set.
    if (PointerI.AliasSetId != PointerJ.AliasSetId)
      return false;
  
    return true;
  }
  
  void RuntimePointerChecking::printChecks(
      raw_ostream &OS, const SmallVectorImpl<RuntimePointerCheck> &Checks,
      unsigned Depth) const {
    unsigned N = 0;
    for (const auto &Check : Checks) {
      const auto &First = Check.first->Members, &Second = Check.second->Members;
  
      OS.indent(Depth) << "Check " << N++ << ":\n";
  
      OS.indent(Depth + 2) << "Comparing group (" << Check.first << "):\n";
      for (unsigned K = 0; K < First.size(); ++K)
        OS.indent(Depth + 2) << *Pointers[First[K]].PointerValue << "\n";
  
      OS.indent(Depth + 2) << "Against group (" << Check.second << "):\n";
      for (unsigned K = 0; K < Second.size(); ++K)
        OS.indent(Depth + 2) << *Pointers[Second[K]].PointerValue << "\n";
    }
  }
  
  void RuntimePointerChecking::print(raw_ostream &OS, unsigned Depth) const {
  
    OS.indent(Depth) << "Run-time memory checks:\n";
    printChecks(OS, Checks, Depth);
  
    OS.indent(Depth) << "Grouped accesses:\n";
    for (unsigned I = 0; I < CheckingGroups.size(); ++I) {
      const auto &CG = CheckingGroups[I];
  
      OS.indent(Depth + 2) << "Group " << &CG << ":\n";
      OS.indent(Depth + 4) << "(Low: " << *CG.Low << " High: " << *CG.High
                           << ")\n";
      for (unsigned J = 0; J < CG.Members.size(); ++J) {
        OS.indent(Depth + 6) << "Member: " << *Pointers[CG.Members[J]].Expr
                             << "\n";
      }
    }
  }
  
  namespace {
  
  /// Analyses memory accesses in a loop.
  ///
  /// Checks whether run time pointer checks are needed and builds sets for data
  /// dependence checking.
  class AccessAnalysis {
  public:
    /// Read or write access location.
    typedef PointerIntPair<Value *, 1, bool> MemAccessInfo;
    typedef SmallVector<MemAccessInfo, 8> MemAccessInfoList;
  
    AccessAnalysis(Loop *TheLoop, AAResults *AA, LoopInfo *LI,
                   MemoryDepChecker::DepCandidates &DA,
                   PredicatedScalarEvolution &PSE)
        : TheLoop(TheLoop), AST(*AA), LI(LI), DepCands(DA),
          IsRTCheckAnalysisNeeded(false), PSE(PSE) {}
  
    /// Register a load  and whether it is only read from.
    void addLoad(MemoryLocation &Loc, bool IsReadOnly) {
      Value *Ptr = const_cast<Value*>(Loc.Ptr);
      AST.add(Ptr, LocationSize::beforeOrAfterPointer(), Loc.AATags);
      Accesses.insert(MemAccessInfo(Ptr, false));
      if (IsReadOnly)
        ReadOnlyPtr.insert(Ptr);
    }
  
    /// Register a store.
    void addStore(MemoryLocation &Loc) {
      Value *Ptr = const_cast<Value*>(Loc.Ptr);
      AST.add(Ptr, LocationSize::beforeOrAfterPointer(), Loc.AATags);
      Accesses.insert(MemAccessInfo(Ptr, true));
    }
  
    /// Check if we can emit a run-time no-alias check for \p Access.
    ///
    /// Returns true if we can emit a run-time no alias check for \p Access.
    /// If we can check this access, this also adds it to a dependence set and
    /// adds a run-time to check for it to \p RtCheck. If \p Assume is true,
    /// we will attempt to use additional run-time checks in order to get
    /// the bounds of the pointer.
    bool createCheckForAccess(RuntimePointerChecking &RtCheck,
                              MemAccessInfo Access,
                              const ValueToValueMap &Strides,
                              DenseMap<Value *, unsigned> &DepSetId,
                              Loop *TheLoop, unsigned &RunningDepId,
                              unsigned ASId, bool ShouldCheckStride,
                              bool Assume);
  
    /// Check whether we can check the pointers at runtime for
    /// non-intersection.
    ///
    /// Returns true if we need no check or if we do and we can generate them
    /// (i.e. the pointers have computable bounds).
    bool canCheckPtrAtRT(RuntimePointerChecking &RtCheck, ScalarEvolution *SE,
                         Loop *TheLoop, const ValueToValueMap &Strides,
                         bool ShouldCheckWrap = false);
  
    /// Goes over all memory accesses, checks whether a RT check is needed
    /// and builds sets of dependent accesses.
    void buildDependenceSets() {
      processMemAccesses();
    }
  
    /// Initial processing of memory accesses determined that we need to
    /// perform dependency checking.
    ///
    /// Note that this can later be cleared if we retry memcheck analysis without
    /// dependency checking (i.e. FoundNonConstantDistanceDependence).
    bool isDependencyCheckNeeded() { return !CheckDeps.empty(); }
  
    /// We decided that no dependence analysis would be used.  Reset the state.
    void resetDepChecks(MemoryDepChecker &DepChecker) {
      CheckDeps.clear();
      DepChecker.clearDependences();
    }
  
    MemAccessInfoList &getDependenciesToCheck() { return CheckDeps; }
  
  private:
    typedef SetVector<MemAccessInfo> PtrAccessSet;
  
    /// Go over all memory access and check whether runtime pointer checks
    /// are needed and build sets of dependency check candidates.
    void processMemAccesses();
  
    /// Set of all accesses.
    PtrAccessSet Accesses;
  
    /// The loop being checked.
    const Loop *TheLoop;
  
    /// List of accesses that need a further dependence check.
    MemAccessInfoList CheckDeps;
  
    /// Set of pointers that are read only.
    SmallPtrSet<Value*, 16> ReadOnlyPtr;
  
    /// An alias set tracker to partition the access set by underlying object and
    //intrinsic property (such as TBAA metadata).
    AliasSetTracker AST;
  
    LoopInfo *LI;
  
    /// Sets of potentially dependent accesses - members of one set share an
    /// underlying pointer. The set "CheckDeps" identfies which sets really need a
    /// dependence check.
    MemoryDepChecker::DepCandidates &DepCands;
  
    /// Initial processing of memory accesses determined that we may need
    /// to add memchecks.  Perform the analysis to determine the necessary checks.
    ///
    /// Note that, this is different from isDependencyCheckNeeded.  When we retry
    /// memcheck analysis without dependency checking
    /// (i.e. FoundNonConstantDistanceDependence), isDependencyCheckNeeded is
    /// cleared while this remains set if we have potentially dependent accesses.
    bool IsRTCheckAnalysisNeeded;
  
    /// The SCEV predicate containing all the SCEV-related assumptions.
    PredicatedScalarEvolution &PSE;
  };
  
  } // end anonymous namespace
  
  /// Check whether a pointer can participate in a runtime bounds check.
  /// If \p Assume, try harder to prove that we can compute the bounds of \p Ptr
  /// by adding run-time checks (overflow checks) if necessary.
  static bool hasComputableBounds(PredicatedScalarEvolution &PSE,
                                  const ValueToValueMap &Strides, Value *Ptr,
                                  Loop *L, bool Assume) {
    const SCEV *PtrScev = replaceSymbolicStrideSCEV(PSE, Strides, Ptr);
  
    // The bounds for loop-invariant pointer is trivial.
    if (PSE.getSE()->isLoopInvariant(PtrScev, L))
      return true;
  
    const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(PtrScev);
  
    if (!AR && Assume)
      AR = PSE.getAsAddRec(Ptr);
  
    if (!AR)
      return false;
  
    return AR->isAffine();
  }
  
  /// Check whether a pointer address cannot wrap.
  static bool isNoWrap(PredicatedScalarEvolution &PSE,
                       const ValueToValueMap &Strides, Value *Ptr, Loop *L) {
    const SCEV *PtrScev = PSE.getSCEV(Ptr);
    if (PSE.getSE()->isLoopInvariant(PtrScev, L))
      return true;
  
    int64_t Stride = getPtrStride(PSE, Ptr, L, Strides);
    if (Stride == 1 || PSE.hasNoOverflow(Ptr, SCEVWrapPredicate::IncrementNUSW))
      return true;
  
    return false;
  }
  
  bool AccessAnalysis::createCheckForAccess(RuntimePointerChecking &RtCheck,
                                            MemAccessInfo Access,
                                            const ValueToValueMap &StridesMap,
                                            DenseMap<Value *, unsigned> &DepSetId,
                                            Loop *TheLoop, unsigned &RunningDepId,
                                            unsigned ASId, bool ShouldCheckWrap,
                                            bool Assume) {
    Value *Ptr = Access.getPointer();
  
    if (!hasComputableBounds(PSE, StridesMap, Ptr, TheLoop, Assume))
      return false;
  
    // When we run after a failing dependency check we have to make sure
    // we don't have wrapping pointers.
    if (ShouldCheckWrap && !isNoWrap(PSE, StridesMap, Ptr, TheLoop)) {
      auto *Expr = PSE.getSCEV(Ptr);
      if (!Assume || !isa<SCEVAddRecExpr>(Expr))
        return false;
      PSE.setNoOverflow(Ptr, SCEVWrapPredicate::IncrementNUSW);
    }
  
    // The id of the dependence set.
    unsigned DepId;
  
    if (isDependencyCheckNeeded()) {
      Value *Leader = DepCands.getLeaderValue(Access).getPointer();
      unsigned &LeaderId = DepSetId[Leader];
      if (!LeaderId)
        LeaderId = RunningDepId++;
      DepId = LeaderId;
    } else
      // Each access has its own dependence set.
      DepId = RunningDepId++;
  
    bool IsWrite = Access.getInt();
    RtCheck.insert(TheLoop, Ptr, IsWrite, DepId, ASId, StridesMap, PSE);
    LLVM_DEBUG(dbgs() << "LAA: Found a runtime check ptr:" << *Ptr << '\n');
  
    return true;
   }
  
  bool AccessAnalysis::canCheckPtrAtRT(RuntimePointerChecking &RtCheck,
                                       ScalarEvolution *SE, Loop *TheLoop,
                                       const ValueToValueMap &StridesMap,
                                       bool ShouldCheckWrap) {
    // Find pointers with computable bounds. We are going to use this information
    // to place a runtime bound check.
    bool CanDoRT = true;
  
    bool MayNeedRTCheck = false;
    if (!IsRTCheckAnalysisNeeded) return true;
  
    bool IsDepCheckNeeded = isDependencyCheckNeeded();
  
    // We assign a consecutive id to access from different alias sets.
    // Accesses between different groups doesn't need to be checked.
    unsigned ASId = 0;
    for (auto &AS : AST) {
      int NumReadPtrChecks = 0;
      int NumWritePtrChecks = 0;
      bool CanDoAliasSetRT = true;
      ++ASId;
  
      // We assign consecutive id to access from different dependence sets.
      // Accesses within the same set don't need a runtime check.
      unsigned RunningDepId = 1;
      DenseMap<Value *, unsigned> DepSetId;
  
      SmallVector<MemAccessInfo, 4> Retries;
  
      // First, count how many write and read accesses are in the alias set. Also
      // collect MemAccessInfos for later.
      SmallVector<MemAccessInfo, 4> AccessInfos;
      for (const auto &A : AS) {
        Value *Ptr = A.getValue();
        bool IsWrite = Accesses.count(MemAccessInfo(Ptr, true));
  
        if (IsWrite)
          ++NumWritePtrChecks;
        else
          ++NumReadPtrChecks;
        AccessInfos.emplace_back(Ptr, IsWrite);
      }
  
      // We do not need runtime checks for this alias set, if there are no writes
      // or a single write and no reads.
      if (NumWritePtrChecks == 0 ||
          (NumWritePtrChecks == 1 && NumReadPtrChecks == 0)) {
        assert((AS.size() <= 1 ||
                all_of(AS,
                       [this](auto AC) {
                         MemAccessInfo AccessWrite(AC.getValue(), true);
                         return DepCands.findValue(AccessWrite) == DepCands.end();
                       })) &&
               "Can only skip updating CanDoRT below, if all entries in AS "
               "are reads or there is at most 1 entry");
        continue;
      }
  
      for (auto &Access : AccessInfos) {
        if (!createCheckForAccess(RtCheck, Access, StridesMap, DepSetId, TheLoop,
                                  RunningDepId, ASId, ShouldCheckWrap, false)) {
          LLVM_DEBUG(dbgs() << "LAA: Can't find bounds for ptr:"
                            << *Access.getPointer() << '\n');
          Retries.push_back(Access);
          CanDoAliasSetRT = false;
        }
      }
  
      // Note that this function computes CanDoRT and MayNeedRTCheck
      // independently. For example CanDoRT=false, MayNeedRTCheck=false means that
      // we have a pointer for which we couldn't find the bounds but we don't
      // actually need to emit any checks so it does not matter.
      //
      // We need runtime checks for this alias set, if there are at least 2
      // dependence sets (in which case RunningDepId > 2) or if we need to re-try
      // any bound checks (because in that case the number of dependence sets is
      // incomplete).
      bool NeedsAliasSetRTCheck = RunningDepId > 2 || !Retries.empty();
  
      // We need to perform run-time alias checks, but some pointers had bounds
      // that couldn't be checked.
      if (NeedsAliasSetRTCheck && !CanDoAliasSetRT) {
        // Reset the CanDoSetRt flag and retry all accesses that have failed.
        // We know that we need these checks, so we can now be more aggressive
        // and add further checks if required (overflow checks).
        CanDoAliasSetRT = true;
        for (auto Access : Retries)
          if (!createCheckForAccess(RtCheck, Access, StridesMap, DepSetId,
                                    TheLoop, RunningDepId, ASId,
                                    ShouldCheckWrap, /*Assume=*/true)) {
            CanDoAliasSetRT = false;
            break;
          }
      }
  
      CanDoRT &= CanDoAliasSetRT;
      MayNeedRTCheck |= NeedsAliasSetRTCheck;
      ++ASId;
    }
  
    // If the pointers that we would use for the bounds comparison have different
    // address spaces, assume the values aren't directly comparable, so we can't
    // use them for the runtime check. We also have to assume they could
    // overlap. In the future there should be metadata for whether address spaces
    // are disjoint.
    unsigned NumPointers = RtCheck.Pointers.size();
    for (unsigned i = 0; i < NumPointers; ++i) {
      for (unsigned j = i + 1; j < NumPointers; ++j) {
        // Only need to check pointers between two different dependency sets.
        if (RtCheck.Pointers[i].DependencySetId ==
            RtCheck.Pointers[j].DependencySetId)
         continue;
        // Only need to check pointers in the same alias set.
        if (RtCheck.Pointers[i].AliasSetId != RtCheck.Pointers[j].AliasSetId)
          continue;
  
        Value *PtrI = RtCheck.Pointers[i].PointerValue;
        Value *PtrJ = RtCheck.Pointers[j].PointerValue;
  
        unsigned ASi = PtrI->getType()->getPointerAddressSpace();
        unsigned ASj = PtrJ->getType()->getPointerAddressSpace();
        if (ASi != ASj) {
          LLVM_DEBUG(
              dbgs() << "LAA: Runtime check would require comparison between"
                        " different address spaces\n");
          return false;
        }
      }
    }
  
    if (MayNeedRTCheck && CanDoRT)
      RtCheck.generateChecks(DepCands, IsDepCheckNeeded);
  
    LLVM_DEBUG(dbgs() << "LAA: We need to do " << RtCheck.getNumberOfChecks()
                      << " pointer comparisons.\n");
  
    // If we can do run-time checks, but there are no checks, no runtime checks
    // are needed. This can happen when all pointers point to the same underlying
    // object for example.
    RtCheck.Need = CanDoRT ? RtCheck.getNumberOfChecks() != 0 : MayNeedRTCheck;
  
    bool CanDoRTIfNeeded = !RtCheck.Need || CanDoRT;
    if (!CanDoRTIfNeeded)
      RtCheck.reset();
    return CanDoRTIfNeeded;
  }
  
  void AccessAnalysis::processMemAccesses() {
    // We process the set twice: first we process read-write pointers, last we
    // process read-only pointers. This allows us to skip dependence tests for
    // read-only pointers.
  
    LLVM_DEBUG(dbgs() << "LAA: Processing memory accesses...\n");
    LLVM_DEBUG(dbgs() << "  AST: "; AST.dump());
    LLVM_DEBUG(dbgs() << "LAA:   Accesses(" << Accesses.size() << "):\n");
    LLVM_DEBUG({
      for (auto A : Accesses)
        dbgs() << "\t" << *A.getPointer() << " (" <<
                  (A.getInt() ? "write" : (ReadOnlyPtr.count(A.getPointer()) ?
                                           "read-only" : "read")) << ")\n";
    });
  
    // The AliasSetTracker has nicely partitioned our pointers by metadata
    // compatibility and potential for underlying-object overlap. As a result, we
    // only need to check for potential pointer dependencies within each alias
    // set.
    for (const auto &AS : AST) {
      // Note that both the alias-set tracker and the alias sets themselves used
      // linked lists internally and so the iteration order here is deterministic
      // (matching the original instruction order within each set).
  
      bool SetHasWrite = false;
  
      // Map of pointers to last access encountered.
      typedef DenseMap<const Value*, MemAccessInfo> UnderlyingObjToAccessMap;
      UnderlyingObjToAccessMap ObjToLastAccess;
  
      // Set of access to check after all writes have been processed.
      PtrAccessSet DeferredAccesses;
  
      // Iterate over each alias set twice, once to process read/write pointers,
      // and then to process read-only pointers.
      for (int SetIteration = 0; SetIteration < 2; ++SetIteration) {
        bool UseDeferred = SetIteration > 0;
        PtrAccessSet &S = UseDeferred ? DeferredAccesses : Accesses;
  
        for (const auto &AV : AS) {
          Value *Ptr = AV.getValue();
  
          // For a single memory access in AliasSetTracker, Accesses may contain
          // both read and write, and they both need to be handled for CheckDeps.
          for (const auto &AC : S) {
            if (AC.getPointer() != Ptr)
              continue;
  
            bool IsWrite = AC.getInt();
  
            // If we're using the deferred access set, then it contains only
            // reads.
            bool IsReadOnlyPtr = ReadOnlyPtr.count(Ptr) && !IsWrite;
            if (UseDeferred && !IsReadOnlyPtr)
              continue;
            // Otherwise, the pointer must be in the PtrAccessSet, either as a
            // read or a write.
            assert(((IsReadOnlyPtr && UseDeferred) || IsWrite ||
                    S.count(MemAccessInfo(Ptr, false))) &&
                   "Alias-set pointer not in the access set?");
  
            MemAccessInfo Access(Ptr, IsWrite);
            DepCands.insert(Access);
  
            // Memorize read-only pointers for later processing and skip them in
            // the first round (they need to be checked after we have seen all
            // write pointers). Note: we also mark pointer that are not
            // consecutive as "read-only" pointers (so that we check
            // "a[b[i]] +="). Hence, we need the second check for "!IsWrite".
            if (!UseDeferred && IsReadOnlyPtr) {
              DeferredAccesses.insert(Access);
              continue;
            }
  
            // If this is a write - check other reads and writes for conflicts. If
            // this is a read only check other writes for conflicts (but only if
            // there is no other write to the ptr - this is an optimization to
            // catch "a[i] = a[i] + " without having to do a dependence check).
            if ((IsWrite || IsReadOnlyPtr) && SetHasWrite) {
              CheckDeps.push_back(Access);
              IsRTCheckAnalysisNeeded = true;
            }
  
            if (IsWrite)
              SetHasWrite = true;
  
            // Create sets of pointers connected by a shared alias set and
            // underlying object.
            typedef SmallVector<const Value *, 16> ValueVector;
            ValueVector TempObjects;
  
            getUnderlyingObjects(Ptr, TempObjects, LI);
            LLVM_DEBUG(dbgs()
                       << "Underlying objects for pointer " << *Ptr << "\n");
            for (const Value *UnderlyingObj : TempObjects) {
              // nullptr never alias, don't join sets for pointer that have "null"
              // in their UnderlyingObjects list.
              if (isa<ConstantPointerNull>(UnderlyingObj) &&
                  !NullPointerIsDefined(
                      TheLoop->getHeader()->getParent(),
                      UnderlyingObj->getType()->getPointerAddressSpace()))
                continue;
  
              UnderlyingObjToAccessMap::iterator Prev =
                  ObjToLastAccess.find(UnderlyingObj);
              if (Prev != ObjToLastAccess.end())
                DepCands.unionSets(Access, Prev->second);
  
              ObjToLastAccess[UnderlyingObj] = Access;
              LLVM_DEBUG(dbgs() << "  " << *UnderlyingObj << "\n");
            }
          }
        }
      }
    }
  }
  
  static bool isInBoundsGep(Value *Ptr) {
    if (GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(Ptr))
      return GEP->isInBounds();
    return false;
  }
  
  /// Return true if an AddRec pointer \p Ptr is unsigned non-wrapping,
  /// i.e. monotonically increasing/decreasing.
  static bool isNoWrapAddRec(Value *Ptr, const SCEVAddRecExpr *AR,
                             PredicatedScalarEvolution &PSE, const Loop *L) {
    // FIXME: This should probably only return true for NUW.
    if (AR->getNoWrapFlags(SCEV::NoWrapMask))
      return true;
  
    // Scalar evolution does not propagate the non-wrapping flags to values that
    // are derived from a non-wrapping induction variable because non-wrapping
    // could be flow-sensitive.
    //
    // Look through the potentially overflowing instruction to try to prove
    // non-wrapping for the *specific* value of Ptr.
  
    // The arithmetic implied by an inbounds GEP can't overflow.
    auto *GEP = dyn_cast<GetElementPtrInst>(Ptr);
    if (!GEP || !GEP->isInBounds())
      return false;
  
    // Make sure there is only one non-const index and analyze that.
    Value *NonConstIndex = nullptr;
    for (Value *Index : make_range(GEP->idx_begin(), GEP->idx_end()))
      if (!isa<ConstantInt>(Index)) {
        if (NonConstIndex)
          return false;
        NonConstIndex = Index;
      }
    if (!NonConstIndex)
      // The recurrence is on the pointer, ignore for now.
      return false;
  
    // The index in GEP is signed.  It is non-wrapping if it's derived from a NSW
    // AddRec using a NSW operation.
    if (auto *OBO = dyn_cast<OverflowingBinaryOperator>(NonConstIndex))
      if (OBO->hasNoSignedWrap() &&
          // Assume constant for other the operand so that the AddRec can be
          // easily found.
          isa<ConstantInt>(OBO->getOperand(1))) {
        auto *OpScev = PSE.getSCEV(OBO->getOperand(0));
  
        if (auto *OpAR = dyn_cast<SCEVAddRecExpr>(OpScev))
          return OpAR->getLoop() == L && OpAR->getNoWrapFlags(SCEV::FlagNSW);
      }
  
    return false;
  }
  
  /// Check whether the access through \p Ptr has a constant stride.
  int64_t llvm::getPtrStride(PredicatedScalarEvolution &PSE, Value *Ptr,
                             const Loop *Lp, const ValueToValueMap &StridesMap,
                             bool Assume, bool ShouldCheckWrap) {
    Type *Ty = Ptr->getType();
    assert(Ty->isPointerTy() && "Unexpected non-ptr");
  
    // Make sure that the pointer does not point to aggregate types.
    auto *PtrTy = cast<PointerType>(Ty);
    if (PtrTy->getElementType()->isAggregateType()) {
      LLVM_DEBUG(dbgs() << "LAA: Bad stride - Not a pointer to a scalar type"
                        << *Ptr << "\n");
      return 0;
    }
  
    const SCEV *PtrScev = replaceSymbolicStrideSCEV(PSE, StridesMap, Ptr);
  
    const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(PtrScev);
    if (Assume && !AR)
      AR = PSE.getAsAddRec(Ptr);
  
    if (!AR) {
      LLVM_DEBUG(dbgs() << "LAA: Bad stride - Not an AddRecExpr pointer " << *Ptr
                        << " SCEV: " << *PtrScev << "\n");
      return 0;
    }
  
    // The access function must stride over the innermost loop.
    if (Lp != AR->getLoop()) {
      LLVM_DEBUG(dbgs() << "LAA: Bad stride - Not striding over innermost loop "
                        << *Ptr << " SCEV: " << *AR << "\n");
      return 0;
    }
  
    // The address calculation must not wrap. Otherwise, a dependence could be
    // inverted.
    // An inbounds getelementptr that is a AddRec with a unit stride
    // cannot wrap per definition. The unit stride requirement is checked later.
    // An getelementptr without an inbounds attribute and unit stride would have
    // to access the pointer value "0" which is undefined behavior in address
    // space 0, therefore we can also vectorize this case.
    bool IsInBoundsGEP = isInBoundsGep(Ptr);
    bool IsNoWrapAddRec = !ShouldCheckWrap ||
      PSE.hasNoOverflow(Ptr, SCEVWrapPredicate::IncrementNUSW) ||
      isNoWrapAddRec(Ptr, AR, PSE, Lp);
    if (!IsNoWrapAddRec && !IsInBoundsGEP &&
        NullPointerIsDefined(Lp->getHeader()->getParent(),
                             PtrTy->getAddressSpace())) {
      if (Assume) {
        PSE.setNoOverflow(Ptr, SCEVWrapPredicate::IncrementNUSW);
        IsNoWrapAddRec = true;
        LLVM_DEBUG(dbgs() << "LAA: Pointer may wrap in the address space:\n"
                          << "LAA:   Pointer: " << *Ptr << "\n"
                          << "LAA:   SCEV: " << *AR << "\n"
                          << "LAA:   Added an overflow assumption\n");
      } else {
        LLVM_DEBUG(
            dbgs() << "LAA: Bad stride - Pointer may wrap in the address space "
                   << *Ptr << " SCEV: " << *AR << "\n");
        return 0;
      }
    }
  
    // Check the step is constant.
    const SCEV *Step = AR->getStepRecurrence(*PSE.getSE());
  
    // Calculate the pointer stride and check if it is constant.
    const SCEVConstant *C = dyn_cast<SCEVConstant>(Step);
    if (!C) {
      LLVM_DEBUG(dbgs() << "LAA: Bad stride - Not a constant strided " << *Ptr
                        << " SCEV: " << *AR << "\n");
      return 0;
    }
  
    auto &DL = Lp->getHeader()->getModule()->getDataLayout();
    int64_t Size = DL.getTypeAllocSize(PtrTy->getElementType());
    const APInt &APStepVal = C->getAPInt();
  
    // Huge step value - give up.
    if (APStepVal.getBitWidth() > 64)
      return 0;
  
    int64_t StepVal = APStepVal.getSExtValue();
  
    // Strided access.
    int64_t Stride = StepVal / Size;
    int64_t Rem = StepVal % Size;
    if (Rem)
      return 0;
  
    // If the SCEV could wrap but we have an inbounds gep with a unit stride we
    // know we can't "wrap around the address space". In case of address space
    // zero we know that this won't happen without triggering undefined behavior.
    if (!IsNoWrapAddRec && Stride != 1 && Stride != -1 &&
        (IsInBoundsGEP || !NullPointerIsDefined(Lp->getHeader()->getParent(),
                                                PtrTy->getAddressSpace()))) {
      if (Assume) {
        // We can avoid this case by adding a run-time check.
        LLVM_DEBUG(dbgs() << "LAA: Non unit strided pointer which is not either "
                          << "inbounds or in address space 0 may wrap:\n"
                          << "LAA:   Pointer: " << *Ptr << "\n"
                          << "LAA:   SCEV: " << *AR << "\n"
                          << "LAA:   Added an overflow assumption\n");
        PSE.setNoOverflow(Ptr, SCEVWrapPredicate::IncrementNUSW);
      } else
        return 0;
    }
  
    return Stride;
  }
  
  bool llvm::sortPtrAccesses(ArrayRef<Value *> VL, const DataLayout &DL,
                             ScalarEvolution &SE,
                             SmallVectorImpl<unsigned> &SortedIndices) {
    assert(llvm::all_of(
               VL, [](const Value *V) { return V->getType()->isPointerTy(); }) &&
           "Expected list of pointer operands.");
    SmallVector<std::pair<int64_t, Value *>, 4> OffValPairs;
    OffValPairs.reserve(VL.size());
  
    // Walk over the pointers, and map each of them to an offset relative to
    // first pointer in the array.
    Value *Ptr0 = VL[0];
    const SCEV *Scev0 = SE.getSCEV(Ptr0);
    Value *Obj0 = getUnderlyingObject(Ptr0);
  
    llvm::SmallSet<int64_t, 4> Offsets;
    for (auto *Ptr : VL) {
      // TODO: Outline this code as a special, more time consuming, version of
      // computeConstantDifference() function.
      if (Ptr->getType()->getPointerAddressSpace() !=
          Ptr0->getType()->getPointerAddressSpace())
        return false;
      // If a pointer refers to a different underlying object, bail - the
      // pointers are by definition incomparable.
      Value *CurrObj = getUnderlyingObject(Ptr);
      if (CurrObj != Obj0)
        return false;
  
      const SCEV *Scev = SE.getSCEV(Ptr);
      const auto *Diff = dyn_cast<SCEVConstant>(SE.getMinusSCEV(Scev, Scev0));
      // The pointers may not have a constant offset from each other, or SCEV
      // may just not be smart enough to figure out they do. Regardless,
      // there's nothing we can do.
      if (!Diff)
        return false;
  
      // Check if the pointer with the same offset is found.
      int64_t Offset = Diff->getAPInt().getSExtValue();
      if (!Offsets.insert(Offset).second)
        return false;
      OffValPairs.emplace_back(Offset, Ptr);
    }
    SortedIndices.clear();
    SortedIndices.resize(VL.size());
    std::iota(SortedIndices.begin(), SortedIndices.end(), 0);
  
    // Sort the memory accesses and keep the order of their uses in UseOrder.
    llvm::stable_sort(SortedIndices, [&](unsigned Left, unsigned Right) {
      return OffValPairs[Left].first < OffValPairs[Right].first;
    });
  
    // Check if the order is consecutive already.
    if (llvm::all_of(SortedIndices, [&SortedIndices](const unsigned I) {
          return I == SortedIndices[I];
        }))
      SortedIndices.clear();
  
    return true;
  }
  
  /// Take the address space operand from the Load/Store instruction.
  /// Returns -1 if this is not a valid Load/Store instruction.
  static unsigned getAddressSpaceOperand(Value *I) {
    if (LoadInst *L = dyn_cast<LoadInst>(I))
      return L->getPointerAddressSpace();
    if (StoreInst *S = dyn_cast<StoreInst>(I))
      return S->getPointerAddressSpace();
    return -1;
  }
  
  /// Returns true if the memory operations \p A and \p B are consecutive.
  bool llvm::isConsecutiveAccess(Value *A, Value *B, const DataLayout &DL,
                                 ScalarEvolution &SE, bool CheckType) {
    Value *PtrA = getLoadStorePointerOperand(A);
    Value *PtrB = getLoadStorePointerOperand(B);
    unsigned ASA = getAddressSpaceOperand(A);
    unsigned ASB = getAddressSpaceOperand(B);
  
    // Check that the address spaces match and that the pointers are valid.
    if (!PtrA || !PtrB || (ASA != ASB))
      return false;
  
    // Make sure that A and B are different pointers.
    if (PtrA == PtrB)
      return false;
  
    // Make sure that A and B have the same type if required.
    if (CheckType && PtrA->getType() != PtrB->getType())
      return false;
  
    unsigned IdxWidth = DL.getIndexSizeInBits(ASA);
    Type *Ty = cast<PointerType>(PtrA->getType())->getElementType();
  
    APInt OffsetA(IdxWidth, 0), OffsetB(IdxWidth, 0);
    PtrA = PtrA->stripAndAccumulateInBoundsConstantOffsets(DL, OffsetA);
    PtrB = PtrB->stripAndAccumulateInBoundsConstantOffsets(DL, OffsetB);
  
    // Retrieve the address space again as pointer stripping now tracks through
    // `addrspacecast`.
    ASA = cast<PointerType>(PtrA->getType())->getAddressSpace();
    ASB = cast<PointerType>(PtrB->getType())->getAddressSpace();
    // Check that the address spaces match and that the pointers are valid.
    if (ASA != ASB)
      return false;
  
    IdxWidth = DL.getIndexSizeInBits(ASA);
    OffsetA = OffsetA.sextOrTrunc(IdxWidth);
    OffsetB = OffsetB.sextOrTrunc(IdxWidth);
  
    APInt Size(IdxWidth, DL.getTypeStoreSize(Ty));
  
    //  OffsetDelta = OffsetB - OffsetA;
    const SCEV *OffsetSCEVA = SE.getConstant(OffsetA);
    const SCEV *OffsetSCEVB = SE.getConstant(OffsetB);
    const SCEV *OffsetDeltaSCEV = SE.getMinusSCEV(OffsetSCEVB, OffsetSCEVA);
    const APInt &OffsetDelta = cast<SCEVConstant>(OffsetDeltaSCEV)->getAPInt();
  
    // Check if they are based on the same pointer. That makes the offsets
    // sufficient.
    if (PtrA == PtrB)
      return OffsetDelta == Size;
  
    // Compute the necessary base pointer delta to have the necessary final delta
    // equal to the size.
    // BaseDelta = Size - OffsetDelta;
    const SCEV *SizeSCEV = SE.getConstant(Size);
    const SCEV *BaseDelta = SE.getMinusSCEV(SizeSCEV, OffsetDeltaSCEV);
  
    // Otherwise compute the distance with SCEV between the base pointers.
    const SCEV *PtrSCEVA = SE.getSCEV(PtrA);
    const SCEV *PtrSCEVB = SE.getSCEV(PtrB);
    const SCEV *X = SE.getAddExpr(PtrSCEVA, BaseDelta);
    return X == PtrSCEVB;
  }
  
  MemoryDepChecker::VectorizationSafetyStatus
  MemoryDepChecker::Dependence::isSafeForVectorization(DepType Type) {
    switch (Type) {
    case NoDep:
    case Forward:
    case BackwardVectorizable:
      return VectorizationSafetyStatus::Safe;
  
    case Unknown:
      return VectorizationSafetyStatus::PossiblySafeWithRtChecks;
    case ForwardButPreventsForwarding:
    case Backward:
    case BackwardVectorizableButPreventsForwarding:
      return VectorizationSafetyStatus::Unsafe;
    }
    llvm_unreachable("unexpected DepType!");
  }
  
  bool MemoryDepChecker::Dependence::isBackward() const {
    switch (Type) {
    case NoDep:
    case Forward:
    case ForwardButPreventsForwarding:
    case Unknown:
      return false;
  
    case BackwardVectorizable:
    case Backward:
    case BackwardVectorizableButPreventsForwarding:
      return true;
    }
    llvm_unreachable("unexpected DepType!");
  }
  
  bool MemoryDepChecker::Dependence::isPossiblyBackward() const {
    return isBackward() || Type == Unknown;
  }
  
  bool MemoryDepChecker::Dependence::isForward() const {
    switch (Type) {
    case Forward:
    case ForwardButPreventsForwarding:
      return true;
  
    case NoDep:
    case Unknown:
    case BackwardVectorizable:
    case Backward:
    case BackwardVectorizableButPreventsForwarding:
      return false;
    }
    llvm_unreachable("unexpected DepType!");
  }
  
  bool MemoryDepChecker::couldPreventStoreLoadForward(uint64_t Distance,
                                                      uint64_t TypeByteSize) {
    // If loads occur at a distance that is not a multiple of a feasible vector
    // factor store-load forwarding does not take place.
    // Positive dependences might cause troubles because vectorizing them might
    // prevent store-load forwarding making vectorized code run a lot slower.
    //   a[i] = a[i-3] ^ a[i-8];
    //   The stores to a[i:i+1] don't align with the stores to a[i-3:i-2] and
    //   hence on your typical architecture store-load forwarding does not take
    //   place. Vectorizing in such cases does not make sense.
    // Store-load forwarding distance.
  
    // After this many iterations store-to-load forwarding conflicts should not
    // cause any slowdowns.
    const uint64_t NumItersForStoreLoadThroughMemory = 8 * TypeByteSize;
    // Maximum vector factor.
    uint64_t MaxVFWithoutSLForwardIssues = std::min(
        VectorizerParams::MaxVectorWidth * TypeByteSize, MaxSafeDepDistBytes);
  
    // Compute the smallest VF at which the store and load would be misaligned.
    for (uint64_t VF = 2 * TypeByteSize; VF <= MaxVFWithoutSLForwardIssues;
         VF *= 2) {
      // If the number of vector iteration between the store and the load are
      // small we could incur conflicts.
      if (Distance % VF && Distance / VF < NumItersForStoreLoadThroughMemory) {
        MaxVFWithoutSLForwardIssues = (VF >>= 1);
        break;
      }
    }
  
    if (MaxVFWithoutSLForwardIssues < 2 * TypeByteSize) {
      LLVM_DEBUG(
          dbgs() << "LAA: Distance " << Distance
                 << " that could cause a store-load forwarding conflict\n");
      return true;
    }
  
    if (MaxVFWithoutSLForwardIssues < MaxSafeDepDistBytes &&
        MaxVFWithoutSLForwardIssues !=
            VectorizerParams::MaxVectorWidth * TypeByteSize)
      MaxSafeDepDistBytes = MaxVFWithoutSLForwardIssues;
    return false;
  }
  
  void MemoryDepChecker::mergeInStatus(VectorizationSafetyStatus S) {
    if (Status < S)
      Status = S;
  }
  
  /// Given a non-constant (unknown) dependence-distance \p Dist between two
  /// memory accesses, that have the same stride whose absolute value is given
  /// in \p Stride, and that have the same type size \p TypeByteSize,
  /// in a loop whose takenCount is \p BackedgeTakenCount, check if it is
  /// possible to prove statically that the dependence distance is larger
  /// than the range that the accesses will travel through the execution of
  /// the loop. If so, return true; false otherwise. This is useful for
  /// example in loops such as the following (PR31098):
  ///     for (i = 0; i < D; ++i) {
  ///                = out[i];
  ///       out[i+D] =
  ///     }
  static bool isSafeDependenceDistance(const DataLayout &DL, ScalarEvolution &SE,
                                       const SCEV &BackedgeTakenCount,
                                       const SCEV &Dist, uint64_t Stride,
                                       uint64_t TypeByteSize) {
  
    // If we can prove that
    //      (**) |Dist| > BackedgeTakenCount * Step
    // where Step is the absolute stride of the memory accesses in bytes,
    // then there is no dependence.
    //
    // Rationale:
    // We basically want to check if the absolute distance (|Dist/Step|)
    // is >= the loop iteration count (or > BackedgeTakenCount).
    // This is equivalent to the Strong SIV Test (Practical Dependence Testing,
    // Section 4.2.1); Note, that for vectorization it is sufficient to prove
    // that the dependence distance is >= VF; This is checked elsewhere.
    // But in some cases we can prune unknown dependence distances early, and
    // even before selecting the VF, and without a runtime test, by comparing
    // the distance against the loop iteration count. Since the vectorized code
    // will be executed only if LoopCount >= VF, proving distance >= LoopCount
    // also guarantees that distance >= VF.
    //
    const uint64_t ByteStride = Stride * TypeByteSize;
    const SCEV *Step = SE.getConstant(BackedgeTakenCount.getType(), ByteStride);
    const SCEV *Product = SE.getMulExpr(&BackedgeTakenCount, Step);
  
    const SCEV *CastedDist = &Dist;
    const SCEV *CastedProduct = Product;
    uint64_t DistTypeSize = DL.getTypeAllocSize(Dist.getType());
    uint64_t ProductTypeSize = DL.getTypeAllocSize(Product->getType());
  
    // The dependence distance can be positive/negative, so we sign extend Dist;
    // The multiplication of the absolute stride in bytes and the
    // backedgeTakenCount is non-negative, so we zero extend Product.
    if (DistTypeSize > ProductTypeSize)
      CastedProduct = SE.getZeroExtendExpr(Product, Dist.getType());
    else
      CastedDist = SE.getNoopOrSignExtend(&Dist, Product->getType());
  
    // Is  Dist - (BackedgeTakenCount * Step) > 0 ?
    // (If so, then we have proven (**) because |Dist| >= Dist)
    const SCEV *Minus = SE.getMinusSCEV(CastedDist, CastedProduct);
    if (SE.isKnownPositive(Minus))
      return true;
  
    // Second try: Is  -Dist - (BackedgeTakenCount * Step) > 0 ?
    // (If so, then we have proven (**) because |Dist| >= -1*Dist)
    const SCEV *NegDist = SE.getNegativeSCEV(CastedDist);
    Minus = SE.getMinusSCEV(NegDist, CastedProduct);
    if (SE.isKnownPositive(Minus))
      return true;
  
    return false;
  }
  
  /// Check the dependence for two accesses with the same stride \p Stride.
  /// \p Distance is the positive distance and \p TypeByteSize is type size in
  /// bytes.
  ///
  /// \returns true if they are independent.
  static bool areStridedAccessesIndependent(uint64_t Distance, uint64_t Stride,
                                            uint64_t TypeByteSize) {
    assert(Stride > 1 && "The stride must be greater than 1");
    assert(TypeByteSize > 0 && "The type size in byte must be non-zero");
    assert(Distance > 0 && "The distance must be non-zero");
  
    // Skip if the distance is not multiple of type byte size.
    if (Distance % TypeByteSize)
      return false;
  
    uint64_t ScaledDist = Distance / TypeByteSize;
  
    // No dependence if the scaled distance is not multiple of the stride.
    // E.g.
    //      for (i = 0; i < 1024 ; i += 4)
    //        A[i+2] = A[i] + 1;
    //
    // Two accesses in memory (scaled distance is 2, stride is 4):
    //     | A[0] |      |      |      | A[4] |      |      |      |
    //     |      |      | A[2] |      |      |      | A[6] |      |
    //
    // E.g.
    //      for (i = 0; i < 1024 ; i += 3)
    //        A[i+4] = A[i] + 1;
    //
    // Two accesses in memory (scaled distance is 4, stride is 3):
    //     | A[0] |      |      | A[3] |      |      | A[6] |      |      |
    //     |      |      |      |      | A[4] |      |      | A[7] |      |
    return ScaledDist % Stride;
  }
  
  MemoryDepChecker::Dependence::DepType
  MemoryDepChecker::isDependent(const MemAccessInfo &A, unsigned AIdx,
                                const MemAccessInfo &B, unsigned BIdx,
                                const ValueToValueMap &Strides) {
    assert (AIdx < BIdx && "Must pass arguments in program order");
  
    Value *APtr = A.getPointer();
    Value *BPtr = B.getPointer();
    bool AIsWrite = A.getInt();
    bool BIsWrite = B.getInt();
  
    // Two reads are independent.
    if (!AIsWrite && !BIsWrite)
      return Dependence::NoDep;
  
    // We cannot check pointers in different address spaces.
    if (APtr->getType()->getPointerAddressSpace() !=
        BPtr->getType()->getPointerAddressSpace())
      return Dependence::Unknown;
  
    int64_t StrideAPtr = getPtrStride(PSE, APtr, InnermostLoop, Strides, true);
    int64_t StrideBPtr = getPtrStride(PSE, BPtr, InnermostLoop, Strides, true);
  
    const SCEV *Src = PSE.getSCEV(APtr);
    const SCEV *Sink = PSE.getSCEV(BPtr);
  
    // If the induction step is negative we have to invert source and sink of the
    // dependence.
    if (StrideAPtr < 0) {
      std::swap(APtr, BPtr);
      std::swap(Src, Sink);
      std::swap(AIsWrite, BIsWrite);
      std::swap(AIdx, BIdx);
      std::swap(StrideAPtr, StrideBPtr);
    }
  
    const SCEV *Dist = PSE.getSE()->getMinusSCEV(Sink, Src);
  
    LLVM_DEBUG(dbgs() << "LAA: Src Scev: " << *Src << "Sink Scev: " << *Sink
                      << "(Induction step: " << StrideAPtr << ")\n");
    LLVM_DEBUG(dbgs() << "LAA: Distance for " << *InstMap[AIdx] << " to "
                      << *InstMap[BIdx] << ": " << *Dist << "\n");
  
    // Need accesses with constant stride. We don't want to vectorize
    // "A[B[i]] += ..." and similar code or pointer arithmetic that could wrap in
    // the address space.
    if (!StrideAPtr || !StrideBPtr || StrideAPtr != StrideBPtr){
      LLVM_DEBUG(dbgs() << "Pointer access with non-constant stride\n");
      return Dependence::Unknown;
    }
  
    Type *ATy = APtr->getType()->getPointerElementType();
    Type *BTy = BPtr->getType()->getPointerElementType();
    auto &DL = InnermostLoop->getHeader()->getModule()->getDataLayout();
    uint64_t TypeByteSize = DL.getTypeAllocSize(ATy);
    uint64_t Stride = std::abs(StrideAPtr);
    const SCEVConstant *C = dyn_cast<SCEVConstant>(Dist);
    if (!C) {
      if (TypeByteSize == DL.getTypeAllocSize(BTy) &&
          isSafeDependenceDistance(DL, *(PSE.getSE()),
                                   *(PSE.getBackedgeTakenCount()), *Dist, Stride,
                                   TypeByteSize))
        return Dependence::NoDep;
  
      LLVM_DEBUG(dbgs() << "LAA: Dependence because of non-constant distance\n");
      FoundNonConstantDistanceDependence = true;
      return Dependence::Unknown;
    }
  
    const APInt &Val = C->getAPInt();
    int64_t Distance = Val.getSExtValue();
  
    // Attempt to prove strided accesses independent.
    if (std::abs(Distance) > 0 && Stride > 1 && ATy == BTy &&
        areStridedAccessesIndependent(std::abs(Distance), Stride, TypeByteSize)) {
      LLVM_DEBUG(dbgs() << "LAA: Strided accesses are independent\n");
      return Dependence::NoDep;
    }
  
    // Negative distances are not plausible dependencies.
    if (Val.isNegative()) {
      bool IsTrueDataDependence = (AIsWrite && !BIsWrite);
      if (IsTrueDataDependence && EnableForwardingConflictDetection &&
          (couldPreventStoreLoadForward(Val.abs().getZExtValue(), TypeByteSize) ||
           ATy != BTy)) {
        LLVM_DEBUG(dbgs() << "LAA: Forward but may prevent st->ld forwarding\n");
        return Dependence::ForwardButPreventsForwarding;
      }
  
      LLVM_DEBUG(dbgs() << "LAA: Dependence is negative\n");
      return Dependence::Forward;
    }
  
    // Write to the same location with the same size.
    // Could be improved to assert type sizes are the same (i32 == float, etc).
    if (Val == 0) {
      if (ATy == BTy)
        return Dependence::Forward;
      LLVM_DEBUG(
          dbgs() << "LAA: Zero dependence difference but different types\n");
      return Dependence::Unknown;
    }
  
    assert(Val.isStrictlyPositive() && "Expect a positive value");
  
    if (ATy != BTy) {
      LLVM_DEBUG(
          dbgs()
          << "LAA: ReadWrite-Write positive dependency with different types\n");
      return Dependence::Unknown;
    }
  
    // Bail out early if passed-in parameters make vectorization not feasible.
    unsigned ForcedFactor = (VectorizerParams::VectorizationFactor ?
                             VectorizerParams::VectorizationFactor : 1);
    unsigned ForcedUnroll = (VectorizerParams::VectorizationInterleave ?
                             VectorizerParams::VectorizationInterleave : 1);
    // The minimum number of iterations for a vectorized/unrolled version.
    unsigned MinNumIter = std::max(ForcedFactor * ForcedUnroll, 2U);
  
    // It's not vectorizable if the distance is smaller than the minimum distance
    // needed for a vectroized/unrolled version. Vectorizing one iteration in
    // front needs TypeByteSize * Stride. Vectorizing the last iteration needs
    // TypeByteSize (No need to plus the last gap distance).
    //
    // E.g. Assume one char is 1 byte in memory and one int is 4 bytes.
    //      foo(int *A) {
    //        int *B = (int *)((char *)A + 14);
    //        for (i = 0 ; i < 1024 ; i += 2)
    //          B[i] = A[i] + 1;
    //      }
    //
    // Two accesses in memory (stride is 2):
    //     | A[0] |      | A[2] |      | A[4] |      | A[6] |      |
    //                              | B[0] |      | B[2] |      | B[4] |
    //
    // Distance needs for vectorizing iterations except the last iteration:
    // 4 * 2 * (MinNumIter - 1). Distance needs for the last iteration: 4.
    // So the minimum distance needed is: 4 * 2 * (MinNumIter - 1) + 4.
    //
    // If MinNumIter is 2, it is vectorizable as the minimum distance needed is
    // 12, which is less than distance.
    //
    // If MinNumIter is 4 (Say if a user forces the vectorization factor to be 4),
    // the minimum distance needed is 28, which is greater than distance. It is
    // not safe to do vectorization.
    uint64_t MinDistanceNeeded =
        TypeByteSize * Stride * (MinNumIter - 1) + TypeByteSize;
    if (MinDistanceNeeded > static_cast<uint64_t>(Distance)) {
      LLVM_DEBUG(dbgs() << "LAA: Failure because of positive distance "
                        << Distance << '\n');
      return Dependence::Backward;
    }
  
    // Unsafe if the minimum distance needed is greater than max safe distance.
    if (MinDistanceNeeded > MaxSafeDepDistBytes) {
      LLVM_DEBUG(dbgs() << "LAA: Failure because it needs at least "
                        << MinDistanceNeeded << " size in bytes");
      return Dependence::Backward;
    }
  
    // Positive distance bigger than max vectorization factor.
    // FIXME: Should use max factor instead of max distance in bytes, which could
    // not handle different types.
    // E.g. Assume one char is 1 byte in memory and one int is 4 bytes.
    //      void foo (int *A, char *B) {
    //        for (unsigned i = 0; i < 1024; i++) {
    //          A[i+2] = A[i] + 1;
    //          B[i+2] = B[i] + 1;
    //        }
    //      }
    //
    // This case is currently unsafe according to the max safe distance. If we
    // analyze the two accesses on array B, the max safe dependence distance
    // is 2. Then we analyze the accesses on array A, the minimum distance needed
    // is 8, which is less than 2 and forbidden vectorization, But actually
    // both A and B could be vectorized by 2 iterations.
    MaxSafeDepDistBytes =
        std::min(static_cast<uint64_t>(Distance), MaxSafeDepDistBytes);
  
    bool IsTrueDataDependence = (!AIsWrite && BIsWrite);
    if (IsTrueDataDependence && EnableForwardingConflictDetection &&
        couldPreventStoreLoadForward(Distance, TypeByteSize))
      return Dependence::BackwardVectorizableButPreventsForwarding;
  
    uint64_t MaxVF = MaxSafeDepDistBytes / (TypeByteSize * Stride);
    LLVM_DEBUG(dbgs() << "LAA: Positive distance " << Val.getSExtValue()
                      << " with max VF = " << MaxVF << '\n');
    uint64_t MaxVFInBits = MaxVF * TypeByteSize * 8;
    MaxSafeVectorWidthInBits = std::min(MaxSafeVectorWidthInBits, MaxVFInBits);
    return Dependence::BackwardVectorizable;
  }
  
  bool MemoryDepChecker::areDepsSafe(DepCandidates &AccessSets,
                                     MemAccessInfoList &CheckDeps,
                                     const ValueToValueMap &Strides) {
  
    MaxSafeDepDistBytes = -1;
    SmallPtrSet<MemAccessInfo, 8> Visited;
    for (MemAccessInfo CurAccess : CheckDeps) {
      if (Visited.count(CurAccess))
        continue;
  
      // Get the relevant memory access set.
      EquivalenceClasses<MemAccessInfo>::iterator I =
        AccessSets.findValue(AccessSets.getLeaderValue(CurAccess));
  
      // Check accesses within this set.
      EquivalenceClasses<MemAccessInfo>::member_iterator AI =
          AccessSets.member_begin(I);
      EquivalenceClasses<MemAccessInfo>::member_iterator AE =
          AccessSets.member_end();
  
      // Check every access pair.
      while (AI != AE) {
        Visited.insert(*AI);
        bool AIIsWrite = AI->getInt();
        // Check loads only against next equivalent class, but stores also against
        // other stores in the same equivalence class - to the same address.
        EquivalenceClasses<MemAccessInfo>::member_iterator OI =
            (AIIsWrite ? AI : std::next(AI));
        while (OI != AE) {
          // Check every accessing instruction pair in program order.
          for (std::vector<unsigned>::iterator I1 = Accesses[*AI].begin(),
               I1E = Accesses[*AI].end(); I1 != I1E; ++I1)
            // Scan all accesses of another equivalence class, but only the next
            // accesses of the same equivalent class.
            for (std::vector<unsigned>::iterator
                     I2 = (OI == AI ? std::next(I1) : Accesses[*OI].begin()),
                     I2E = (OI == AI ? I1E : Accesses[*OI].end());
                 I2 != I2E; ++I2) {
              auto A = std::make_pair(&*AI, *I1);
              auto B = std::make_pair(&*OI, *I2);
  
              assert(*I1 != *I2);
              if (*I1 > *I2)
                std::swap(A, B);
  
              Dependence::DepType Type =
                  isDependent(*A.first, A.second, *B.first, B.second, Strides);
              mergeInStatus(Dependence::isSafeForVectorization(Type));
  
              // Gather dependences unless we accumulated MaxDependences
              // dependences.  In that case return as soon as we find the first
              // unsafe dependence.  This puts a limit on this quadratic
              // algorithm.
              if (RecordDependences) {
                if (Type != Dependence::NoDep)
                  Dependences.push_back(Dependence(A.second, B.second, Type));
  
                if (Dependences.size() >= MaxDependences) {
                  RecordDependences = false;
                  Dependences.clear();
                  LLVM_DEBUG(dbgs()
                             << "Too many dependences, stopped recording\n");
                }
              }
              if (!RecordDependences && !isSafeForVectorization())
                return false;
            }
          ++OI;
        }
        AI++;
      }
    }
  
    LLVM_DEBUG(dbgs() << "Total Dependences: " << Dependences.size() << "\n");
    return isSafeForVectorization();
  }
  
  SmallVector<Instruction *, 4>
  MemoryDepChecker::getInstructionsForAccess(Value *Ptr, bool isWrite) const {
    MemAccessInfo Access(Ptr, isWrite);
    auto &IndexVector = Accesses.find(Access)->second;
  
    SmallVector<Instruction *, 4> Insts;
    transform(IndexVector,
                   std::back_inserter(Insts),
                   [&](unsigned Idx) { return this->InstMap[Idx]; });
    return Insts;
  }
  
  const char *MemoryDepChecker::Dependence::DepName[] = {
      "NoDep", "Unknown", "Forward", "ForwardButPreventsForwarding", "Backward",
      "BackwardVectorizable", "BackwardVectorizableButPreventsForwarding"};
  
  void MemoryDepChecker::Dependence::print(
      raw_ostream &OS, unsigned Depth,
      const SmallVectorImpl<Instruction *> &Instrs) const {
    OS.indent(Depth) << DepName[Type] << ":\n";
    OS.indent(Depth + 2) << *Instrs[Source] << " -> \n";
    OS.indent(Depth + 2) << *Instrs[Destination] << "\n";
  }
  
  bool LoopAccessInfo::canAnalyzeLoop() {
    // We need to have a loop header.
    LLVM_DEBUG(dbgs() << "LAA: Found a loop in "
                      << TheLoop->getHeader()->getParent()->getName() << ": "
                      << TheLoop->getHeader()->getName() << '\n');
  
    // We can only analyze innermost loops.
    if (!TheLoop->isInnermost()) {
      LLVM_DEBUG(dbgs() << "LAA: loop is not the innermost loop\n");
      recordAnalysis("NotInnerMostLoop") << "loop is not the innermost loop";
      return false;
    }
  
    // We must have a single backedge.
    if (TheLoop->getNumBackEdges() != 1) {
      LLVM_DEBUG(
          dbgs() << "LAA: loop control flow is not understood by analyzer\n");
      recordAnalysis("CFGNotUnderstood")
          << "loop control flow is not understood by analyzer";
      return false;
    }
  
    // ScalarEvolution needs to be able to find the exit count.
    const SCEV *ExitCount = PSE->getBackedgeTakenCount();
    if (isa<SCEVCouldNotCompute>(ExitCount)) {
      recordAnalysis("CantComputeNumberOfIterations")
          << "could not determine number of loop iterations";
      LLVM_DEBUG(dbgs() << "LAA: SCEV could not compute the loop exit count.\n");
      return false;
    }
  
    return true;
  }
  
  void LoopAccessInfo::analyzeLoop(AAResults *AA, LoopInfo *LI,
                                   const TargetLibraryInfo *TLI,
                                   DominatorTree *DT) {
    typedef SmallPtrSet<Value*, 16> ValueSet;
  
    // Holds the Load and Store instructions.
    SmallVector<LoadInst *, 16> Loads;
    SmallVector<StoreInst *, 16> Stores;
  
    // Holds all the different accesses in the loop.
    unsigned NumReads = 0;
    unsigned NumReadWrites = 0;
  
    bool HasComplexMemInst = false;
  
    // A runtime check is only legal to insert if there are no convergent calls.
    HasConvergentOp = false;
  
    PtrRtChecking->Pointers.clear();
    PtrRtChecking->Need = false;
  
    const bool IsAnnotatedParallel = TheLoop->isAnnotatedParallel();
  
    const bool EnableMemAccessVersioningOfLoop =
        EnableMemAccessVersioning &&
        !TheLoop->getHeader()->getParent()->hasOptSize();
  
    // For each block.
    for (BasicBlock *BB : TheLoop->blocks()) {
      // Scan the BB and collect legal loads and stores. Also detect any
      // convergent instructions.
      for (Instruction &I : *BB) {
        if (auto *Call = dyn_cast<CallBase>(&I)) {
          if (Call->isConvergent())
            HasConvergentOp = true;
        }
  
        // With both a non-vectorizable memory instruction and a convergent
        // operation, found in this loop, no reason to continue the search.
        if (HasComplexMemInst && HasConvergentOp) {
          CanVecMem = false;
          return;
        }
  
        // Avoid hitting recordAnalysis multiple times.
        if (HasComplexMemInst)
          continue;
  
        // If this is a load, save it. If this instruction can read from memory
        // but is not a load, then we quit. Notice that we don't handle function
        // calls that read or write.
        if (I.mayReadFromMemory()) {
          // Many math library functions read the rounding mode. We will only
          // vectorize a loop if it contains known function calls that don't set
          // the flag. Therefore, it is safe to ignore this read from memory.
          auto *Call = dyn_cast<CallInst>(&I);
          if (Call && getVectorIntrinsicIDForCall(Call, TLI))
            continue;
  
          // If the function has an explicit vectorized counterpart, we can safely
          // assume that it can be vectorized.
          if (Call && !Call->isNoBuiltin() && Call->getCalledFunction() &&
              !VFDatabase::getMappings(*Call).empty())
            continue;
  
          auto *Ld = dyn_cast<LoadInst>(&I);
          if (!Ld) {
            recordAnalysis("CantVectorizeInstruction", Ld)
              << "instruction cannot be vectorized";
            HasComplexMemInst = true;
            continue;
          }
          if (!Ld->isSimple() && !IsAnnotatedParallel) {
            recordAnalysis("NonSimpleLoad", Ld)
                << "read with atomic ordering or volatile read";
            LLVM_DEBUG(dbgs() << "LAA: Found a non-simple load.\n");
            HasComplexMemInst = true;
            continue;
          }
          NumLoads++;
          Loads.push_back(Ld);
          DepChecker->addAccess(Ld);
          if (EnableMemAccessVersioningOfLoop)
            collectStridedAccess(Ld);
          continue;
        }
  
        // Save 'store' instructions. Abort if other instructions write to memory.
        if (I.mayWriteToMemory()) {
          auto *St = dyn_cast<StoreInst>(&I);
          if (!St) {
            recordAnalysis("CantVectorizeInstruction", St)
                << "instruction cannot be vectorized";
            HasComplexMemInst = true;
            continue;
          }
          if (!St->isSimple() && !IsAnnotatedParallel) {
            recordAnalysis("NonSimpleStore", St)
                << "write with atomic ordering or volatile write";
            LLVM_DEBUG(dbgs() << "LAA: Found a non-simple store.\n");
            HasComplexMemInst = true;
            continue;
          }
          NumStores++;
          Stores.push_back(St);
          DepChecker->addAccess(St);
          if (EnableMemAccessVersioningOfLoop)
            collectStridedAccess(St);
        }
      } // Next instr.
    } // Next block.
  
    if (HasComplexMemInst) {
      CanVecMem = false;
      return;
    }
  
    // Now we have two lists that hold the loads and the stores.
    // Next, we find the pointers that they use.
  
    // Check if we see any stores. If there are no stores, then we don't
    // care if the pointers are *restrict*.
    if (!Stores.size()) {
      LLVM_DEBUG(dbgs() << "LAA: Found a read-only loop!\n");
      CanVecMem = true;
      return;
    }
  
    MemoryDepChecker::DepCandidates DependentAccesses;
    AccessAnalysis Accesses(TheLoop, AA, LI, DependentAccesses, *PSE);
  
    // Holds the analyzed pointers. We don't want to call getUnderlyingObjects
    // multiple times on the same object. If the ptr is accessed twice, once
    // for read and once for write, it will only appear once (on the write
    // list). This is okay, since we are going to check for conflicts between
    // writes and between reads and writes, but not between reads and reads.
    ValueSet Seen;
  
    // Record uniform store addresses to identify if we have multiple stores
    // to the same address.
    ValueSet UniformStores;
  
    for (StoreInst *ST : Stores) {
      Value *Ptr = ST->getPointerOperand();
  
      if (isUniform(Ptr))
        HasDependenceInvolvingLoopInvariantAddress |=
            !UniformStores.insert(Ptr).second;
  
      // If we did *not* see this pointer before, insert it to  the read-write
      // list. At this phase it is only a 'write' list.
      if (Seen.insert(Ptr).second) {
        ++NumReadWrites;
  
        MemoryLocation Loc = MemoryLocation::get(ST);
        // The TBAA metadata could have a control dependency on the predication
        // condition, so we cannot rely on it when determining whether or not we
        // need runtime pointer checks.
        if (blockNeedsPredication(ST->getParent(), TheLoop, DT))
          Loc.AATags.TBAA = nullptr;
  
        Accesses.addStore(Loc);
      }
    }
  
    if (IsAnnotatedParallel) {
      LLVM_DEBUG(
          dbgs() << "LAA: A loop annotated parallel, ignore memory dependency "
                 << "checks.\n");
      CanVecMem = true;
      return;
    }
  
    for (LoadInst *LD : Loads) {
      Value *Ptr = LD->getPointerOperand();
      // If we did *not* see this pointer before, insert it to the
      // read list. If we *did* see it before, then it is already in
      // the read-write list. This allows us to vectorize expressions
      // such as A[i] += x;  Because the address of A[i] is a read-write
      // pointer. This only works if the index of A[i] is consecutive.
      // If the address of i is unknown (for example A[B[i]]) then we may
      // read a few words, modify, and write a few words, and some of the
      // words may be written to the same address.
      bool IsReadOnlyPtr = false;
      if (Seen.insert(Ptr).second ||
          !getPtrStride(*PSE, Ptr, TheLoop, SymbolicStrides)) {
        ++NumReads;
        IsReadOnlyPtr = true;
      }
  
      // See if there is an unsafe dependency between a load to a uniform address and
      // store to the same uniform address.
      if (UniformStores.count(Ptr)) {
        LLVM_DEBUG(dbgs() << "LAA: Found an unsafe dependency between a uniform "
                             "load and uniform store to the same address!\n");
        HasDependenceInvolvingLoopInvariantAddress = true;
      }
  
      MemoryLocation Loc = MemoryLocation::get(LD);
      // The TBAA metadata could have a control dependency on the predication
      // condition, so we cannot rely on it when determining whether or not we
      // need runtime pointer checks.
      if (blockNeedsPredication(LD->getParent(), TheLoop, DT))
        Loc.AATags.TBAA = nullptr;
  
      Accesses.addLoad(Loc, IsReadOnlyPtr);
    }
  
    // If we write (or read-write) to a single destination and there are no
    // other reads in this loop then is it safe to vectorize.
    if (NumReadWrites == 1 && NumReads == 0) {
      LLVM_DEBUG(dbgs() << "LAA: Found a write-only loop!\n");
      CanVecMem = true;
      return;
    }
  
    // Build dependence sets and check whether we need a runtime pointer bounds
    // check.
    Accesses.buildDependenceSets();
  
    // Find pointers with computable bounds. We are going to use this information
    // to place a runtime bound check.
    bool CanDoRTIfNeeded = Accesses.canCheckPtrAtRT(*PtrRtChecking, PSE->getSE(),
                                                    TheLoop, SymbolicStrides);
    if (!CanDoRTIfNeeded) {
      recordAnalysis("CantIdentifyArrayBounds") << "cannot identify array bounds";
      LLVM_DEBUG(dbgs() << "LAA: We can't vectorize because we can't find "
                        << "the array bounds.\n");
      CanVecMem = false;
      return;
    }
  
    LLVM_DEBUG(
      dbgs() << "LAA: May be able to perform a memory runtime check if needed.\n");
  
    CanVecMem = true;
    if (Accesses.isDependencyCheckNeeded()) {
      LLVM_DEBUG(dbgs() << "LAA: Checking memory dependencies\n");
      CanVecMem = DepChecker->areDepsSafe(
          DependentAccesses, Accesses.getDependenciesToCheck(), SymbolicStrides);
      MaxSafeDepDistBytes = DepChecker->getMaxSafeDepDistBytes();
  
      if (!CanVecMem && DepChecker->shouldRetryWithRuntimeCheck()) {
        LLVM_DEBUG(dbgs() << "LAA: Retrying with memory checks\n");
  
        // Clear the dependency checks. We assume they are not needed.
        Accesses.resetDepChecks(*DepChecker);
  
        PtrRtChecking->reset();
        PtrRtChecking->Need = true;
  
        auto *SE = PSE->getSE();
        CanDoRTIfNeeded = Accesses.canCheckPtrAtRT(*PtrRtChecking, SE, TheLoop,
                                                   SymbolicStrides, true);
  
        // Check that we found the bounds for the pointer.
        if (!CanDoRTIfNeeded) {
          recordAnalysis("CantCheckMemDepsAtRunTime")
              << "cannot check memory dependencies at runtime";
          LLVM_DEBUG(dbgs() << "LAA: Can't vectorize with memory checks\n");
          CanVecMem = false;
          return;
        }
  
        CanVecMem = true;
      }
    }
  
    if (HasConvergentOp) {
      recordAnalysis("CantInsertRuntimeCheckWithConvergent")
        << "cannot add control dependency to convergent operation";
      LLVM_DEBUG(dbgs() << "LAA: We can't vectorize because a runtime check "
                           "would be needed with a convergent operation\n");
      CanVecMem = false;
      return;
    }
  
    if (CanVecMem)
      LLVM_DEBUG(
          dbgs() << "LAA: No unsafe dependent memory operations in loop.  We"
                 << (PtrRtChecking->Need ? "" : " don't")
                 << " need runtime memory checks.\n");
    else {
      recordAnalysis("UnsafeMemDep")
          << "unsafe dependent memory operations in loop. Use "
             "#pragma loop distribute(enable) to allow loop distribution "
             "to attempt to isolate the offending operations into a separate "
             "loop";
      LLVM_DEBUG(dbgs() << "LAA: unsafe dependent memory operations in loop\n");
    }
  }
  
  bool LoopAccessInfo::blockNeedsPredication(BasicBlock *BB, Loop *TheLoop,
                                             DominatorTree *DT)  {
    assert(TheLoop->contains(BB) && "Unknown block used");
  
    // Blocks that do not dominate the latch need predication.
    BasicBlock* Latch = TheLoop->getLoopLatch();
    return !DT->dominates(BB, Latch);
  }
  
  OptimizationRemarkAnalysis &LoopAccessInfo::recordAnalysis(StringRef RemarkName,
                                                             Instruction *I) {
    assert(!Report && "Multiple reports generated");
  
    Value *CodeRegion = TheLoop->getHeader();
    DebugLoc DL = TheLoop->getStartLoc();
  
    if (I) {
      CodeRegion = I->getParent();
      // If there is no debug location attached to the instruction, revert back to
      // using the loop's.
      if (I->getDebugLoc())
        DL = I->getDebugLoc();
    }
  
    Report = std::make_unique<OptimizationRemarkAnalysis>(DEBUG_TYPE, RemarkName, DL,
                                                     CodeRegion);
    return *Report;
  }
  
  bool LoopAccessInfo::isUniform(Value *V) const {
    auto *SE = PSE->getSE();
    // Since we rely on SCEV for uniformity, if the type is not SCEVable, it is
    // never considered uniform.
    // TODO: Is this really what we want? Even without FP SCEV, we may want some
    // trivially loop-invariant FP values to be considered uniform.
    if (!SE->isSCEVable(V->getType()))
      return false;
    return (SE->isLoopInvariant(SE->getSCEV(V), TheLoop));
  }
  
  void LoopAccessInfo::collectStridedAccess(Value *MemAccess) {
    Value *Ptr = getLoadStorePointerOperand(MemAccess);
    if (!Ptr)
      return;
  
    Value *Stride = getStrideFromPointer(Ptr, PSE->getSE(), TheLoop);
    if (!Stride)
      return;
  
    LLVM_DEBUG(dbgs() << "LAA: Found a strided access that is a candidate for "
                         "versioning:");
    LLVM_DEBUG(dbgs() << "  Ptr: " << *Ptr << " Stride: " << *Stride << "\n");
  
    // Avoid adding the "Stride == 1" predicate when we know that
    // Stride >= Trip-Count. Such a predicate will effectively optimize a single
    // or zero iteration loop, as Trip-Count <= Stride == 1.
    //
    // TODO: We are currently not making a very informed decision on when it is
    // beneficial to apply stride versioning. It might make more sense that the
    // users of this analysis (such as the vectorizer) will trigger it, based on
    // their specific cost considerations; For example, in cases where stride
    // versioning does  not help resolving memory accesses/dependences, the
    // vectorizer should evaluate the cost of the runtime test, and the benefit
    // of various possible stride specializations, considering the alternatives
    // of using gather/scatters (if available).
  
    const SCEV *StrideExpr = PSE->getSCEV(Stride);
    const SCEV *BETakenCount = PSE->getBackedgeTakenCount();
  
    // Match the types so we can compare the stride and the BETakenCount.
    // The Stride can be positive/negative, so we sign extend Stride;
    // The backedgeTakenCount is non-negative, so we zero extend BETakenCount.
    const DataLayout &DL = TheLoop->getHeader()->getModule()->getDataLayout();
    uint64_t StrideTypeSize = DL.getTypeAllocSize(StrideExpr->getType());
    uint64_t BETypeSize = DL.getTypeAllocSize(BETakenCount->getType());
    const SCEV *CastedStride = StrideExpr;
    const SCEV *CastedBECount = BETakenCount;
    ScalarEvolution *SE = PSE->getSE();
    if (BETypeSize >= StrideTypeSize)
      CastedStride = SE->getNoopOrSignExtend(StrideExpr, BETakenCount->getType());
    else
      CastedBECount = SE->getZeroExtendExpr(BETakenCount, StrideExpr->getType());
    const SCEV *StrideMinusBETaken = SE->getMinusSCEV(CastedStride, CastedBECount);
    // Since TripCount == BackEdgeTakenCount + 1, checking:
    // "Stride >= TripCount" is equivalent to checking:
    // Stride - BETakenCount > 0
    if (SE->isKnownPositive(StrideMinusBETaken)) {
      LLVM_DEBUG(
          dbgs() << "LAA: Stride>=TripCount; No point in versioning as the "
                    "Stride==1 predicate will imply that the loop executes "
                    "at most once.\n");
      return;
    }
    LLVM_DEBUG(dbgs() << "LAA: Found a strided access that we can version.");
  
    SymbolicStrides[Ptr] = Stride;
    StrideSet.insert(Stride);
  }
  
  LoopAccessInfo::LoopAccessInfo(Loop *L, ScalarEvolution *SE,
                                 const TargetLibraryInfo *TLI, AAResults *AA,
                                 DominatorTree *DT, LoopInfo *LI)
      : PSE(std::make_unique<PredicatedScalarEvolution>(*SE, *L)),
        PtrRtChecking(std::make_unique<RuntimePointerChecking>(SE)),
        DepChecker(std::make_unique<MemoryDepChecker>(*PSE, L)), TheLoop(L),
        NumLoads(0), NumStores(0), MaxSafeDepDistBytes(-1), CanVecMem(false),
        HasConvergentOp(false),
        HasDependenceInvolvingLoopInvariantAddress(false) {
    if (canAnalyzeLoop())
      analyzeLoop(AA, LI, TLI, DT);
  }
  
  void LoopAccessInfo::print(raw_ostream &OS, unsigned Depth) const {
    if (CanVecMem) {
      OS.indent(Depth) << "Memory dependences are safe";
      if (MaxSafeDepDistBytes != -1ULL)
        OS << " with a maximum dependence distance of " << MaxSafeDepDistBytes
           << " bytes";
      if (PtrRtChecking->Need)
        OS << " with run-time checks";
      OS << "\n";
    }
  
    if (HasConvergentOp)
      OS.indent(Depth) << "Has convergent operation in loop\n";
  
    if (Report)
      OS.indent(Depth) << "Report: " << Report->getMsg() << "\n";
  
    if (auto *Dependences = DepChecker->getDependences()) {
      OS.indent(Depth) << "Dependences:\n";
      for (auto &Dep : *Dependences) {
        Dep.print(OS, Depth + 2, DepChecker->getMemoryInstructions());
        OS << "\n";
      }
    } else
      OS.indent(Depth) << "Too many dependences, not recorded\n";
  
    // List the pair of accesses need run-time checks to prove independence.
    PtrRtChecking->print(OS, Depth);
    OS << "\n";
  
    OS.indent(Depth) << "Non vectorizable stores to invariant address were "
                     << (HasDependenceInvolvingLoopInvariantAddress ? "" : "not ")
                     << "found in loop.\n";
  
    OS.indent(Depth) << "SCEV assumptions:\n";
    PSE->getUnionPredicate().print(OS, Depth);
  
    OS << "\n";
  
    OS.indent(Depth) << "Expressions re-written:\n";
    PSE->print(OS, Depth);
  }
  
  LoopAccessLegacyAnalysis::LoopAccessLegacyAnalysis() : FunctionPass(ID) {
    initializeLoopAccessLegacyAnalysisPass(*PassRegistry::getPassRegistry());
  }
  
  const LoopAccessInfo &LoopAccessLegacyAnalysis::getInfo(Loop *L) {
    auto &LAI = LoopAccessInfoMap[L];
  
    if (!LAI)
      LAI = std::make_unique<LoopAccessInfo>(L, SE, TLI, AA, DT, LI);
  
    return *LAI.get();
  }
  
  void LoopAccessLegacyAnalysis::print(raw_ostream &OS, const Module *M) const {
    LoopAccessLegacyAnalysis &LAA = *const_cast<LoopAccessLegacyAnalysis *>(this);
  
    for (Loop *TopLevelLoop : *LI)
      for (Loop *L : depth_first(TopLevelLoop)) {
        OS.indent(2) << L->getHeader()->getName() << ":\n";
        auto &LAI = LAA.getInfo(L);
        LAI.print(OS, 4);
      }
  }
  
  bool LoopAccessLegacyAnalysis::runOnFunction(Function &F) {
    SE = &getAnalysis<ScalarEvolutionWrapperPass>().getSE();
    auto *TLIP = getAnalysisIfAvailable<TargetLibraryInfoWrapperPass>();
    TLI = TLIP ? &TLIP->getTLI(F) : nullptr;
    AA = &getAnalysis<AAResultsWrapperPass>().getAAResults();
    DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
    LI = &getAnalysis<LoopInfoWrapperPass>().getLoopInfo();
  
    return false;
  }
  
  void LoopAccessLegacyAnalysis::getAnalysisUsage(AnalysisUsage &AU) const {
      AU.addRequired<ScalarEvolutionWrapperPass>();
      AU.addRequired<AAResultsWrapperPass>();
      AU.addRequired<DominatorTreeWrapperPass>();
      AU.addRequired<LoopInfoWrapperPass>();
  
      AU.setPreservesAll();
  }
  
  char LoopAccessLegacyAnalysis::ID = 0;
  static const char laa_name[] = "Loop Access Analysis";
  #define LAA_NAME "loop-accesses"
  
  INITIALIZE_PASS_BEGIN(LoopAccessLegacyAnalysis, LAA_NAME, laa_name, false, true)
  INITIALIZE_PASS_DEPENDENCY(AAResultsWrapperPass)
  INITIALIZE_PASS_DEPENDENCY(ScalarEvolutionWrapperPass)
  INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
  INITIALIZE_PASS_DEPENDENCY(LoopInfoWrapperPass)
  INITIALIZE_PASS_END(LoopAccessLegacyAnalysis, LAA_NAME, laa_name, false, true)
  
  AnalysisKey LoopAccessAnalysis::Key;
  
  LoopAccessInfo LoopAccessAnalysis::run(Loop &L, LoopAnalysisManager &AM,
                                         LoopStandardAnalysisResults &AR) {
    return LoopAccessInfo(&L, &AR.SE, &AR.TLI, &AR.AA, &AR.DT, &AR.LI);
  }
  
  namespace llvm {
  
    Pass *createLAAPass() {
      return new LoopAccessLegacyAnalysis();
    }
  
  } // end namespace llvm
  