llvm/lib/Analysis/VectorUtils.cpp

//===----------- VectorUtils.cpp - Vectorizer utility functions -----------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//
//
// This file defines vectorizer utilities.
//
//===----------------------------------------------------------------------===//

#include "llvm/Analysis/VectorUtils.h"
#include "llvm/ADT/EquivalenceClasses.h"
#include "llvm/Analysis/DemandedBits.h"
#include "llvm/Analysis/LoopInfo.h"
#include "llvm/Analysis/LoopIterator.h"
#include "llvm/Analysis/ScalarEvolution.h"
#include "llvm/Analysis/ScalarEvolutionExpressions.h"
#include "llvm/Analysis/TargetTransformInfo.h"
#include "llvm/Analysis/ValueTracking.h"
#include "llvm/IR/Constants.h"
#include "llvm/IR/GetElementPtrTypeIterator.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Value.h"

#define DEBUG_TYPE "vectorutils"

using namespace llvm;
using namespace llvm::PatternMatch;

/// Maximum factor for an interleaved memory access.
static cl::opt<unsigned> MaxInterleaveGroupFactor(
    "max-interleave-group-factor", cl::Hidden,
    cl::desc("Maximum factor for an interleaved access group (default = 8)"),
    cl::init(8));

/// Identify if the intrinsic is trivially vectorizable.
/// This method returns true if the intrinsic's argument types are all
/// scalars for the scalar form of the intrinsic and all vectors for
/// the vector form of the intrinsic.
bool llvm::isTriviallyVectorizable(Intrinsic::ID ID) {
  switch (ID) {
  case Intrinsic::sqrt:
  case Intrinsic::sin:
  case Intrinsic::cos:
  case Intrinsic::exp:
  case Intrinsic::exp2:
  case Intrinsic::log:
  case Intrinsic::log10:
  case Intrinsic::log2:
  case Intrinsic::fabs:
  case Intrinsic::minnum:
  case Intrinsic::maxnum:
  case Intrinsic::copysign:
  case Intrinsic::floor:
  case Intrinsic::ceil:
  case Intrinsic::trunc:
  case Intrinsic::rint:
  case Intrinsic::nearbyint:
  case Intrinsic::round:
  case Intrinsic::bswap:
  case Intrinsic::bitreverse:
  case Intrinsic::ctpop:
  case Intrinsic::pow:
  case Intrinsic::fma:
  case Intrinsic::fmuladd:
  case Intrinsic::ctlz:
  case Intrinsic::cttz:
  case Intrinsic::powi:
  case Intrinsic::canonicalize:
    return true;
  default:
    return false;
  }
}

/// Identifies if the intrinsic has a scalar operand. It check for
/// ctlz,cttz and powi special intrinsics whose argument is scalar.
bool llvm::hasVectorInstrinsicScalarOpd(Intrinsic::ID ID,
                                        unsigned ScalarOpdIdx) {
  switch (ID) {
  case Intrinsic::ctlz:
  case Intrinsic::cttz:
  case Intrinsic::powi:
    return (ScalarOpdIdx == 1);
  default:
    return false;
  }
}

/// Returns intrinsic ID for call.
/// For the input call instruction it finds mapping intrinsic and returns
/// its ID, in case it does not found it return not_intrinsic.
Intrinsic::ID llvm::getVectorIntrinsicIDForCall(const CallInst *CI,
                                                const TargetLibraryInfo *TLI) {
  Intrinsic::ID ID = getIntrinsicForCallSite(CI, TLI);
  if (ID == Intrinsic::not_intrinsic)
    return Intrinsic::not_intrinsic;

  if (isTriviallyVectorizable(ID) || ID == Intrinsic::lifetime_start ||
      ID == Intrinsic::lifetime_end || ID == Intrinsic::assume ||
      ID == Intrinsic::sideeffect)
    return ID;
  return Intrinsic::not_intrinsic;
}

/// Find the operand of the GEP that should be checked for consecutive
/// stores. This ignores trailing indices that have no effect on the final
/// pointer.
unsigned llvm::getGEPInductionOperand(const GetElementPtrInst *Gep) {
  const DataLayout &DL = Gep->getModule()->getDataLayout();
  unsigned LastOperand = Gep->getNumOperands() - 1;
  unsigned GEPAllocSize = DL.getTypeAllocSize(Gep->getResultElementType());

  // Walk backwards and try to peel off zeros.
  while (LastOperand > 1 && match(Gep->getOperand(LastOperand), m_Zero())) {
    // Find the type we're currently indexing into.
    gep_type_iterator GEPTI = gep_type_begin(Gep);
    std::advance(GEPTI, LastOperand - 2);

    // If it's a type with the same allocation size as the result of the GEP we
    // can peel off the zero index.
    if (DL.getTypeAllocSize(GEPTI.getIndexedType()) != GEPAllocSize)
      break;
    --LastOperand;
  }

  return LastOperand;
}

/// If the argument is a GEP, then returns the operand identified by
/// getGEPInductionOperand. However, if there is some other non-loop-invariant
/// operand, it returns that instead.
Value *llvm::stripGetElementPtr(Value *Ptr, ScalarEvolution *SE, Loop *Lp) {
  GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(Ptr);
  if (!GEP)
    return Ptr;

  unsigned InductionOperand = getGEPInductionOperand(GEP);

  // Check that all of the gep indices are uniform except for our induction
  // operand.
  for (unsigned i = 0, e = GEP->getNumOperands(); i != e; ++i)
    if (i != InductionOperand &&
        !SE->isLoopInvariant(SE->getSCEV(GEP->getOperand(i)), Lp))
      return Ptr;
  return GEP->getOperand(InductionOperand);
}

/// If a value has only one user that is a CastInst, return it.
Value *llvm::getUniqueCastUse(Value *Ptr, Loop *Lp, Type *Ty) {
  Value *UniqueCast = nullptr;
  for (User *U : Ptr->users()) {
    CastInst *CI = dyn_cast<CastInst>(U);
    if (CI && CI->getType() == Ty) {
      if (!UniqueCast)
        UniqueCast = CI;
      else
        return nullptr;
    }
  }
  return UniqueCast;
}

/// Get the stride of a pointer access in a loop. Looks for symbolic
/// strides "a[i*stride]". Returns the symbolic stride, or null otherwise.
Value *llvm::getStrideFromPointer(Value *Ptr, ScalarEvolution *SE, Loop *Lp) {
  auto *PtrTy = dyn_cast<PointerType>(Ptr->getType());
  if (!PtrTy || PtrTy->isAggregateType())
    return nullptr;

  // Try to remove a gep instruction to make the pointer (actually index at this
  // point) easier analyzable. If OrigPtr is equal to Ptr we are analyzing the
  // pointer, otherwise, we are analyzing the index.
  Value *OrigPtr = Ptr;

  // The size of the pointer access.
  int64_t PtrAccessSize = 1;

  Ptr = stripGetElementPtr(Ptr, SE, Lp);
  const SCEV *V = SE->getSCEV(Ptr);

  if (Ptr != OrigPtr)
    // Strip off casts.
    while (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(V))
      V = C->getOperand();

  const SCEVAddRecExpr *S = dyn_cast<SCEVAddRecExpr>(V);
  if (!S)
    return nullptr;

  V = S->getStepRecurrence(*SE);
  if (!V)
    return nullptr;

  // Strip off the size of access multiplication if we are still analyzing the
  // pointer.
  if (OrigPtr == Ptr) {
    if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(V)) {
      if (M->getOperand(0)->getSCEVType() != scConstant)
        return nullptr;

      const APInt &APStepVal = cast<SCEVConstant>(M->getOperand(0))->getAPInt();

      // Huge step value - give up.
      if (APStepVal.getBitWidth() > 64)
        return nullptr;

      int64_t StepVal = APStepVal.getSExtValue();
      if (PtrAccessSize != StepVal)
        return nullptr;
      V = M->getOperand(1);
    }
  }

  // Strip off casts.
  Type *StripedOffRecurrenceCast = nullptr;
  if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(V)) {
    StripedOffRecurrenceCast = C->getType();
    V = C->getOperand();
  }

  // Look for the loop invariant symbolic value.
  const SCEVUnknown *U = dyn_cast<SCEVUnknown>(V);
  if (!U)
    return nullptr;

  Value *Stride = U->getValue();
  if (!Lp->isLoopInvariant(Stride))
    return nullptr;

  // If we have stripped off the recurrence cast we have to make sure that we
  // return the value that is used in this loop so that we can replace it later.
  if (StripedOffRecurrenceCast)
    Stride = getUniqueCastUse(Stride, Lp, StripedOffRecurrenceCast);

  return Stride;
}

/// Given a vector and an element number, see if the scalar value is
/// already around as a register, for example if it were inserted then extracted
/// from the vector.
Value *llvm::findScalarElement(Value *V, unsigned EltNo) {
  assert(V->getType()->isVectorTy() && "Not looking at a vector?");
  VectorType *VTy = cast<VectorType>(V->getType());
  unsigned Width = VTy->getNumElements();
  if (EltNo >= Width)  // Out of range access.
    return UndefValue::get(VTy->getElementType());

  if (Constant *C = dyn_cast<Constant>(V))
    return C->getAggregateElement(EltNo);

  if (InsertElementInst *III = dyn_cast<InsertElementInst>(V)) {
    // If this is an insert to a variable element, we don't know what it is.
    if (!isa<ConstantInt>(III->getOperand(2)))
      return nullptr;
    unsigned IIElt = cast<ConstantInt>(III->getOperand(2))->getZExtValue();

    // If this is an insert to the element we are looking for, return the
    // inserted value.
    if (EltNo == IIElt)
      return III->getOperand(1);

    // Otherwise, the insertelement doesn't modify the value, recurse on its
    // vector input.
    return findScalarElement(III->getOperand(0), EltNo);
  }

  if (ShuffleVectorInst *SVI = dyn_cast<ShuffleVectorInst>(V)) {
    unsigned LHSWidth = SVI->getOperand(0)->getType()->getVectorNumElements();
    int InEl = SVI->getMaskValue(EltNo);
    if (InEl < 0)
      return UndefValue::get(VTy->getElementType());
    if (InEl < (int)LHSWidth)
      return findScalarElement(SVI->getOperand(0), InEl);
    return findScalarElement(SVI->getOperand(1), InEl - LHSWidth);
  }

  // Extract a value from a vector add operation with a constant zero.
  Value *Val = nullptr; Constant *Con = nullptr;
  if (match(V, m_Add(m_Value(Val), m_Constant(Con))))
    if (Constant *Elt = Con->getAggregateElement(EltNo))
      if (Elt->isNullValue())
        return findScalarElement(Val, EltNo);

  // Otherwise, we don't know.
  return nullptr;
}

/// Get splat value if the input is a splat vector or return nullptr.
/// This function is not fully general. It checks only 2 cases:
/// the input value is (1) a splat constants vector or (2) a sequence
/// of instructions that broadcast a single value into a vector.
///
const llvm::Value *llvm::getSplatValue(const Value *V) {

  if (auto *C = dyn_cast<Constant>(V))
    if (isa<VectorType>(V->getType()))
      return C->getSplatValue();

  auto *ShuffleInst = dyn_cast<ShuffleVectorInst>(V);
  if (!ShuffleInst)
    return nullptr;
  // All-zero (or undef) shuffle mask elements.
  for (int MaskElt : ShuffleInst->getShuffleMask())
    if (MaskElt != 0 && MaskElt != -1)
      return nullptr;
  // The first shuffle source is 'insertelement' with index 0.
  auto *InsertEltInst =
    dyn_cast<InsertElementInst>(ShuffleInst->getOperand(0));
  if (!InsertEltInst || !isa<ConstantInt>(InsertEltInst->getOperand(2)) ||
      !cast<ConstantInt>(InsertEltInst->getOperand(2))->isZero())
    return nullptr;

  return InsertEltInst->getOperand(1);
}

MapVector<Instruction *, uint64_t>
llvm::computeMinimumValueSizes(ArrayRef<BasicBlock *> Blocks, DemandedBits &DB,
                               const TargetTransformInfo *TTI) {

  // DemandedBits will give us every value's live-out bits. But we want
  // to ensure no extra casts would need to be inserted, so every DAG
  // of connected values must have the same minimum bitwidth.
  EquivalenceClasses<Value *> ECs;
  SmallVector<Value *, 16> Worklist;
  SmallPtrSet<Value *, 4> Roots;
  SmallPtrSet<Value *, 16> Visited;
  DenseMap<Value *, uint64_t> DBits;
  SmallPtrSet<Instruction *, 4> InstructionSet;
  MapVector<Instruction *, uint64_t> MinBWs;

  // Determine the roots. We work bottom-up, from truncs or icmps.
  bool SeenExtFromIllegalType = false;
  for (auto *BB : Blocks)
    for (auto &I : *BB) {
      InstructionSet.insert(&I);

      if (TTI && (isa<ZExtInst>(&I) || isa<SExtInst>(&I)) &&
          !TTI->isTypeLegal(I.getOperand(0)->getType()))
        SeenExtFromIllegalType = true;

      // Only deal with non-vector integers up to 64-bits wide.
      if ((isa<TruncInst>(&I) || isa<ICmpInst>(&I)) &&
          !I.getType()->isVectorTy() &&
          I.getOperand(0)->getType()->getScalarSizeInBits() <= 64) {
        // Don't make work for ourselves. If we know the loaded type is legal,
        // don't add it to the worklist.
        if (TTI && isa<TruncInst>(&I) && TTI->isTypeLegal(I.getType()))
          continue;

        Worklist.push_back(&I);
        Roots.insert(&I);
      }
    }
  // Early exit.
  if (Worklist.empty() || (TTI && !SeenExtFromIllegalType))
    return MinBWs;

  // Now proceed breadth-first, unioning values together.
  while (!Worklist.empty()) {
    Value *Val = Worklist.pop_back_val();
    Value *Leader = ECs.getOrInsertLeaderValue(Val);

    if (Visited.count(Val))
      continue;
    Visited.insert(Val);

    // Non-instructions terminate a chain successfully.
    if (!isa<Instruction>(Val))
      continue;
    Instruction *I = cast<Instruction>(Val);

    // If we encounter a type that is larger than 64 bits, we can't represent
    // it so bail out.
    if (DB.getDemandedBits(I).getBitWidth() > 64)
      return MapVector<Instruction *, uint64_t>();

    uint64_t V = DB.getDemandedBits(I).getZExtValue();
    DBits[Leader] |= V;
    DBits[I] = V;

    // Casts, loads and instructions outside of our range terminate a chain
    // successfully.
    if (isa<SExtInst>(I) || isa<ZExtInst>(I) || isa<LoadInst>(I) ||
        !InstructionSet.count(I))
      continue;

    // Unsafe casts terminate a chain unsuccessfully. We can't do anything
    // useful with bitcasts, ptrtoints or inttoptrs and it'd be unsafe to
    // transform anything that relies on them.
    if (isa<BitCastInst>(I) || isa<PtrToIntInst>(I) || isa<IntToPtrInst>(I) ||
        !I->getType()->isIntegerTy()) {
      DBits[Leader] |= ~0ULL;
      continue;
    }

    // We don't modify the types of PHIs. Reductions will already have been
    // truncated if possible, and inductions' sizes will have been chosen by
    // indvars.
    if (isa<PHINode>(I))
      continue;

    if (DBits[Leader] == ~0ULL)
      // All bits demanded, no point continuing.
      continue;

    for (Value *O : cast<User>(I)->operands()) {
      ECs.unionSets(Leader, O);
      Worklist.push_back(O);
    }
  }

  // Now we've discovered all values, walk them to see if there are
  // any users we didn't see. If there are, we can't optimize that
  // chain.
  for (auto &I : DBits)
    for (auto *U : I.first->users())
      if (U->getType()->isIntegerTy() && DBits.count(U) == 0)
        DBits[ECs.getOrInsertLeaderValue(I.first)] |= ~0ULL;

  for (auto I = ECs.begin(), E = ECs.end(); I != E; ++I) {
    uint64_t LeaderDemandedBits = 0;
    for (auto MI = ECs.member_begin(I), ME = ECs.member_end(); MI != ME; ++MI)
      LeaderDemandedBits |= DBits[*MI];

    uint64_t MinBW = (sizeof(LeaderDemandedBits) * 8) -
                     llvm::countLeadingZeros(LeaderDemandedBits);
    // Round up to a power of 2
    if (!isPowerOf2_64((uint64_t)MinBW))
      MinBW = NextPowerOf2(MinBW);

    // We don't modify the types of PHIs. Reductions will already have been
    // truncated if possible, and inductions' sizes will have been chosen by
    // indvars.
    // If we are required to shrink a PHI, abandon this entire equivalence class.
    bool Abort = false;
    for (auto MI = ECs.member_begin(I), ME = ECs.member_end(); MI != ME; ++MI)
      if (isa<PHINode>(*MI) && MinBW < (*MI)->getType()->getScalarSizeInBits()) {
        Abort = true;
        break;
      }
    if (Abort)
      continue;

    for (auto MI = ECs.member_begin(I), ME = ECs.member_end(); MI != ME; ++MI) {
      if (!isa<Instruction>(*MI))
        continue;
      Type *Ty = (*MI)->getType();
      if (Roots.count(*MI))
        Ty = cast<Instruction>(*MI)->getOperand(0)->getType();
      if (MinBW < Ty->getScalarSizeInBits())
        MinBWs[cast<Instruction>(*MI)] = MinBW;
    }
  }

  return MinBWs;
}

/// \returns \p I after propagating metadata from \p VL.
Instruction *llvm::propagateMetadata(Instruction *Inst, ArrayRef<Value *> VL) {
  Instruction *I0 = cast<Instruction>(VL[0]);
  SmallVector<std::pair<unsigned, MDNode *>, 4> Metadata;
  I0->getAllMetadataOtherThanDebugLoc(Metadata);

  for (auto Kind :
       {LLVMContext::MD_tbaa, LLVMContext::MD_alias_scope,
        LLVMContext::MD_noalias, LLVMContext::MD_fpmath,
        LLVMContext::MD_nontemporal, LLVMContext::MD_invariant_load}) {
    MDNode *MD = I0->getMetadata(Kind);

    for (int J = 1, E = VL.size(); MD && J != E; ++J) {
      const Instruction *IJ = cast<Instruction>(VL[J]);
      MDNode *IMD = IJ->getMetadata(Kind);
      switch (Kind) {
      case LLVMContext::MD_tbaa:
        MD = MDNode::getMostGenericTBAA(MD, IMD);
        break;
      case LLVMContext::MD_alias_scope:
        MD = MDNode::getMostGenericAliasScope(MD, IMD);
        break;
      case LLVMContext::MD_fpmath:
        MD = MDNode::getMostGenericFPMath(MD, IMD);
        break;
      case LLVMContext::MD_noalias:
      case LLVMContext::MD_nontemporal:
      case LLVMContext::MD_invariant_load:
        MD = MDNode::intersect(MD, IMD);
        break;
      default:
        llvm_unreachable("unhandled metadata");
      }
    }

    Inst->setMetadata(Kind, MD);
  }

  return Inst;
}

Constant *llvm::createInterleaveMask(IRBuilder<> &Builder, unsigned VF,
                                     unsigned NumVecs) {
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    for (unsigned j = 0; j < NumVecs; j++)
      Mask.push_back(Builder.getInt32(j * VF + i));

  return ConstantVector::get(Mask);
}

Constant *llvm::createStrideMask(IRBuilder<> &Builder, unsigned Start,
                                 unsigned Stride, unsigned VF) {
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    Mask.push_back(Builder.getInt32(Start + i * Stride));

  return ConstantVector::get(Mask);
}

Constant *llvm::createSequentialMask(IRBuilder<> &Builder, unsigned Start,
                                     unsigned NumInts, unsigned NumUndefs) {
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < NumInts; i++)
    Mask.push_back(Builder.getInt32(Start + i));

  Constant *Undef = UndefValue::get(Builder.getInt32Ty());
  for (unsigned i = 0; i < NumUndefs; i++)
    Mask.push_back(Undef);

  return ConstantVector::get(Mask);
}

/// A helper function for concatenating vectors. This function concatenates two
/// vectors having the same element type. If the second vector has fewer
/// elements than the first, it is padded with undefs.
static Value *concatenateTwoVectors(IRBuilder<> &Builder, Value *V1,
                                    Value *V2) {
  VectorType *VecTy1 = dyn_cast<VectorType>(V1->getType());
  VectorType *VecTy2 = dyn_cast<VectorType>(V2->getType());
  assert(VecTy1 && VecTy2 &&
         VecTy1->getScalarType() == VecTy2->getScalarType() &&
         "Expect two vectors with the same element type");

  unsigned NumElts1 = VecTy1->getNumElements();
  unsigned NumElts2 = VecTy2->getNumElements();
  assert(NumElts1 >= NumElts2 && "Unexpect the first vector has less elements");

  if (NumElts1 > NumElts2) {
    // Extend with UNDEFs.
    Constant *ExtMask =
        createSequentialMask(Builder, 0, NumElts2, NumElts1 - NumElts2);
    V2 = Builder.CreateShuffleVector(V2, UndefValue::get(VecTy2), ExtMask);
  }

  Constant *Mask = createSequentialMask(Builder, 0, NumElts1 + NumElts2, 0);
  return Builder.CreateShuffleVector(V1, V2, Mask);
}

Value *llvm::concatenateVectors(IRBuilder<> &Builder, ArrayRef<Value *> Vecs) {
  unsigned NumVecs = Vecs.size();
  assert(NumVecs > 1 && "Should be at least two vectors");

  SmallVector<Value *, 8> ResList;
  ResList.append(Vecs.begin(), Vecs.end());
  do {
    SmallVector<Value *, 8> TmpList;
    for (unsigned i = 0; i < NumVecs - 1; i += 2) {
      Value *V0 = ResList[i], *V1 = ResList[i + 1];
      assert((V0->getType() == V1->getType() || i == NumVecs - 2) &&
             "Only the last vector may have a different type");

      TmpList.push_back(concatenateTwoVectors(Builder, V0, V1));
    }

    // Push the last vector if the total number of vectors is odd.
    if (NumVecs % 2 != 0)
      TmpList.push_back(ResList[NumVecs - 1]);

    ResList = TmpList;
    NumVecs = ResList.size();
  } while (NumVecs > 1);

  return ResList[0];
}

bool InterleavedAccessInfo::isStrided(int Stride) {
  unsigned Factor = std::abs(Stride);
  return Factor >= 2 && Factor <= MaxInterleaveGroupFactor;
}

void InterleavedAccessInfo::collectConstStrideAccesses(
    MapVector<Instruction *, StrideDescriptor> &AccessStrideInfo,
    const ValueToValueMap &Strides) {
  auto &DL = TheLoop->getHeader()->getModule()->getDataLayout();

  // Since it's desired that the load/store instructions be maintained in
  // "program order" for the interleaved access analysis, we have to visit the
  // blocks in the loop in reverse postorder (i.e., in a topological order).
  // Such an ordering will ensure that any load/store that may be executed
  // before a second load/store will precede the second load/store in
  // AccessStrideInfo.
  LoopBlocksDFS DFS(TheLoop);
  DFS.perform(LI);
  for (BasicBlock *BB : make_range(DFS.beginRPO(), DFS.endRPO()))
    for (auto &I : *BB) {
      auto *LI = dyn_cast<LoadInst>(&I);
      auto *SI = dyn_cast<StoreInst>(&I);
      if (!LI && !SI)
        continue;

      Value *Ptr = getLoadStorePointerOperand(&I);
      // We don't check wrapping here because we don't know yet if Ptr will be
      // part of a full group or a group with gaps. Checking wrapping for all
      // pointers (even those that end up in groups with no gaps) will be overly
      // conservative. For full groups, wrapping should be ok since if we would
      // wrap around the address space we would do a memory access at nullptr
      // even without the transformation. The wrapping checks are therefore
      // deferred until after we've formed the interleaved groups.
      int64_t Stride = getPtrStride(PSE, Ptr, TheLoop, Strides,
                                    /*Assume=*/true, /*ShouldCheckWrap=*/false);

      const SCEV *Scev = replaceSymbolicStrideSCEV(PSE, Strides, Ptr);
      PointerType *PtrTy = dyn_cast<PointerType>(Ptr->getType());
      uint64_t Size = DL.getTypeAllocSize(PtrTy->getElementType());

      // An alignment of 0 means target ABI alignment.
      unsigned Align = getLoadStoreAlignment(&I);
      if (!Align)
        Align = DL.getABITypeAlignment(PtrTy->getElementType());

      AccessStrideInfo[&I] = StrideDescriptor(Stride, Scev, Size, Align);
    }
}

// Analyze interleaved accesses and collect them into interleaved load and
// store groups.
//
// When generating code for an interleaved load group, we effectively hoist all
// loads in the group to the location of the first load in program order. When
// generating code for an interleaved store group, we sink all stores to the
// location of the last store. This code motion can change the order of load
// and store instructions and may break dependences.
//
// The code generation strategy mentioned above ensures that we won't violate
// any write-after-read (WAR) dependences.
//
// E.g., for the WAR dependence:  a = A[i];      // (1)
//                                A[i] = b;      // (2)
//
// The store group of (2) is always inserted at or below (2), and the load
// group of (1) is always inserted at or above (1). Thus, the instructions will
// never be reordered. All other dependences are checked to ensure the
// correctness of the instruction reordering.
//
// The algorithm visits all memory accesses in the loop in bottom-up program
// order. Program order is established by traversing the blocks in the loop in
// reverse postorder when collecting the accesses.
//
// We visit the memory accesses in bottom-up order because it can simplify the
// construction of store groups in the presence of write-after-write (WAW)
// dependences.
//
// E.g., for the WAW dependence:  A[i] = a;      // (1)
//                                A[i] = b;      // (2)
//                                A[i + 1] = c;  // (3)
//
// We will first create a store group with (3) and (2). (1) can't be added to
// this group because it and (2) are dependent. However, (1) can be grouped
// with other accesses that may precede it in program order. Note that a
// bottom-up order does not imply that WAW dependences should not be checked.
void InterleavedAccessInfo::analyzeInterleaving() {
  LLVM_DEBUG(dbgs() << "LV: Analyzing interleaved accesses...\n");
  const ValueToValueMap &Strides = LAI->getSymbolicStrides();

  // Holds all accesses with a constant stride.
  MapVector<Instruction *, StrideDescriptor> AccessStrideInfo;
  collectConstStrideAccesses(AccessStrideInfo, Strides);

  if (AccessStrideInfo.empty())
    return;

  // Collect the dependences in the loop.
  collectDependences();

  // Holds all interleaved store groups temporarily.
  SmallSetVector<InterleaveGroup *, 4> StoreGroups;
  // Holds all interleaved load groups temporarily.
  SmallSetVector<InterleaveGroup *, 4> LoadGroups;

  // Search in bottom-up program order for pairs of accesses (A and B) that can
  // form interleaved load or store groups. In the algorithm below, access A
  // precedes access B in program order. We initialize a group for B in the
  // outer loop of the algorithm, and then in the inner loop, we attempt to
  // insert each A into B's group if:
  //
  //  1. A and B have the same stride,
  //  2. A and B have the same memory object size, and
  //  3. A belongs in B's group according to its distance from B.
  //
  // Special care is taken to ensure group formation will not break any
  // dependences.
  for (auto BI = AccessStrideInfo.rbegin(), E = AccessStrideInfo.rend();
       BI != E; ++BI) {
    Instruction *B = BI->first;
    StrideDescriptor DesB = BI->second;

    // Initialize a group for B if it has an allowable stride. Even if we don't
    // create a group for B, we continue with the bottom-up algorithm to ensure
    // we don't break any of B's dependences.
    InterleaveGroup *Group = nullptr;
    if (isStrided(DesB.Stride)) {
      Group = getInterleaveGroup(B);
      if (!Group) {
        LLVM_DEBUG(dbgs() << "LV: Creating an interleave group with:" << *B
                          << '\n');
        Group = createInterleaveGroup(B, DesB.Stride, DesB.Align);
      }
      if (B->mayWriteToMemory())
        StoreGroups.insert(Group);
      else
        LoadGroups.insert(Group);
    }

    for (auto AI = std::next(BI); AI != E; ++AI) {
      Instruction *A = AI->first;
      StrideDescriptor DesA = AI->second;

      // Our code motion strategy implies that we can't have dependences
      // between accesses in an interleaved group and other accesses located
      // between the first and last member of the group. Note that this also
      // means that a group can't have more than one member at a given offset.
      // The accesses in a group can have dependences with other accesses, but
      // we must ensure we don't extend the boundaries of the group such that
      // we encompass those dependent accesses.
      //
      // For example, assume we have the sequence of accesses shown below in a
      // stride-2 loop:
      //
      //  (1, 2) is a group | A[i]   = a;  // (1)
      //                    | A[i-1] = b;  // (2) |
      //                      A[i-3] = c;  // (3)
      //                      A[i]   = d;  // (4) | (2, 4) is not a group
      //
      // Because accesses (2) and (3) are dependent, we can group (2) with (1)
      // but not with (4). If we did, the dependent access (3) would be within
      // the boundaries of the (2, 4) group.
      if (!canReorderMemAccessesForInterleavedGroups(&*AI, &*BI)) {
        // If a dependence exists and A is already in a group, we know that A
        // must be a store since A precedes B and WAR dependences are allowed.
        // Thus, A would be sunk below B. We release A's group to prevent this
        // illegal code motion. A will then be free to form another group with
        // instructions that precede it.
        if (isInterleaved(A)) {
          InterleaveGroup *StoreGroup = getInterleaveGroup(A);
          StoreGroups.remove(StoreGroup);
          releaseGroup(StoreGroup);
        }

        // If a dependence exists and A is not already in a group (or it was
        // and we just released it), B might be hoisted above A (if B is a
        // load) or another store might be sunk below A (if B is a store). In
        // either case, we can't add additional instructions to B's group. B
        // will only form a group with instructions that it precedes.
        break;
      }

      // At this point, we've checked for illegal code motion. If either A or B
      // isn't strided, there's nothing left to do.
      if (!isStrided(DesA.Stride) || !isStrided(DesB.Stride))
        continue;

      // Ignore A if it's already in a group or isn't the same kind of memory
      // operation as B.
      // Note that mayReadFromMemory() isn't mutually exclusive to
      // mayWriteToMemory in the case of atomic loads. We shouldn't see those
      // here, canVectorizeMemory() should have returned false - except for the
      // case we asked for optimization remarks.
      if (isInterleaved(A) ||
          (A->mayReadFromMemory() != B->mayReadFromMemory()) ||
          (A->mayWriteToMemory() != B->mayWriteToMemory()))
        continue;

      // Check rules 1 and 2. Ignore A if its stride or size is different from
      // that of B.
      if (DesA.Stride != DesB.Stride || DesA.Size != DesB.Size)
        continue;

      // Ignore A if the memory object of A and B don't belong to the same
      // address space
      if (getLoadStoreAddressSpace(A) != getLoadStoreAddressSpace(B))
        continue;

      // Calculate the distance from A to B.
      const SCEVConstant *DistToB = dyn_cast<SCEVConstant>(
          PSE.getSE()->getMinusSCEV(DesA.Scev, DesB.Scev));
      if (!DistToB)
        continue;
      int64_t DistanceToB = DistToB->getAPInt().getSExtValue();

      // Check rule 3. Ignore A if its distance to B is not a multiple of the
      // size.
      if (DistanceToB % static_cast<int64_t>(DesB.Size))
        continue;

      // Ignore A if either A or B is in a predicated block. Although we
      // currently prevent group formation for predicated accesses, we may be
      // able to relax this limitation in the future once we handle more
      // complicated blocks.
      if (isPredicated(A->getParent()) || isPredicated(B->getParent()))
        continue;

      // The index of A is the index of B plus A's distance to B in multiples
      // of the size.
      int IndexA =
          Group->getIndex(B) + DistanceToB / static_cast<int64_t>(DesB.Size);

      // Try to insert A into B's group.
      if (Group->insertMember(A, IndexA, DesA.Align)) {
        LLVM_DEBUG(dbgs() << "LV: Inserted:" << *A << '\n'
                          << "    into the interleave group with" << *B
                          << '\n');
        InterleaveGroupMap[A] = Group;

        // Set the first load in program order as the insert position.
        if (A->mayReadFromMemory())
          Group->setInsertPos(A);
      }
    } // Iteration over A accesses.
  }   // Iteration over B accesses.

  // Remove interleaved store groups with gaps.
  for (InterleaveGroup *Group : StoreGroups)
    if (Group->getNumMembers() != Group->getFactor()) {
      LLVM_DEBUG(
          dbgs() << "LV: Invalidate candidate interleaved store group due "
                    "to gaps.\n");
      releaseGroup(Group);
    }
  // Remove interleaved groups with gaps (currently only loads) whose memory
  // accesses may wrap around. We have to revisit the getPtrStride analysis,
  // this time with ShouldCheckWrap=true, since collectConstStrideAccesses does
  // not check wrapping (see documentation there).
  // FORNOW we use Assume=false;
  // TODO: Change to Assume=true but making sure we don't exceed the threshold
  // of runtime SCEV assumptions checks (thereby potentially failing to
  // vectorize altogether).
  // Additional optional optimizations:
  // TODO: If we are peeling the loop and we know that the first pointer doesn't
  // wrap then we can deduce that all pointers in the group don't wrap.
  // This means that we can forcefully peel the loop in order to only have to
  // check the first pointer for no-wrap. When we'll change to use Assume=true
  // we'll only need at most one runtime check per interleaved group.
  for (InterleaveGroup *Group : LoadGroups) {
    // Case 1: A full group. Can Skip the checks; For full groups, if the wide
    // load would wrap around the address space we would do a memory access at
    // nullptr even without the transformation.
    if (Group->getNumMembers() == Group->getFactor())
      continue;

    // Case 2: If first and last members of the group don't wrap this implies
    // that all the pointers in the group don't wrap.
    // So we check only group member 0 (which is always guaranteed to exist),
    // and group member Factor - 1; If the latter doesn't exist we rely on
    // peeling (if it is a non-reveresed accsess -- see Case 3).
    Value *FirstMemberPtr = getLoadStorePointerOperand(Group->getMember(0));
    if (!getPtrStride(PSE, FirstMemberPtr, TheLoop, Strides, /*Assume=*/false,
                      /*ShouldCheckWrap=*/true)) {
      LLVM_DEBUG(
          dbgs() << "LV: Invalidate candidate interleaved group due to "
                    "first group member potentially pointer-wrapping.\n");
      releaseGroup(Group);
      continue;
    }
    Instruction *LastMember = Group->getMember(Group->getFactor() - 1);
    if (LastMember) {
      Value *LastMemberPtr = getLoadStorePointerOperand(LastMember);
      if (!getPtrStride(PSE, LastMemberPtr, TheLoop, Strides, /*Assume=*/false,
                        /*ShouldCheckWrap=*/true)) {
        LLVM_DEBUG(
            dbgs() << "LV: Invalidate candidate interleaved group due to "
                      "last group member potentially pointer-wrapping.\n");
        releaseGroup(Group);
      }
    } else {
      // Case 3: A non-reversed interleaved load group with gaps: We need
      // to execute at least one scalar epilogue iteration. This will ensure
      // we don't speculatively access memory out-of-bounds. We only need
      // to look for a member at index factor - 1, since every group must have
      // a member at index zero.
      if (Group->isReverse()) {
        LLVM_DEBUG(
            dbgs() << "LV: Invalidate candidate interleaved group due to "
                      "a reverse access with gaps.\n");
        releaseGroup(Group);
        continue;
      }
      LLVM_DEBUG(
          dbgs() << "LV: Interleaved group requires epilogue iteration.\n");
      RequiresScalarEpilogue = true;
    }
  }
}