VectorUtils.cpp

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//===----------- VectorUtils.cpp - Vectorizer utility functions -----------===//
//
// 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
//
//===----------------------------------------------------------------------===//
//
// This file defines vectorizer utilities.
//
//===----------------------------------------------------------------------===//
 
#include "llvm/Analysis/VectorUtils.h"
#include "llvm/ADT/EquivalenceClasses.h"
#include "llvm/ADT/SmallVector.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/DerivedTypes.h"
#include "llvm/IR/IRBuilder.h"
#include "llvm/IR/MemoryModelRelaxationAnnotations.h"
#include "llvm/IR/PatternMatch.h"
#include "llvm/IR/Value.h"
#include "llvm/Support/CommandLine.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));
 
/// Return true if all of the intrinsic's arguments and return type are scalars
/// for the scalar form of the intrinsic, and vectors for the vector form of the
/// intrinsic (except operands that are marked as always being scalar by
/// isVectorIntrinsicWithScalarOpAtArg).
bool llvm::isTriviallyVectorizable(Intrinsic::ID ID) {
  switch (ID) {
  case Intrinsic::abs:   // Begin integer bit-manipulation.
  case Intrinsic::bswap:
  case Intrinsic::bitreverse:
  case Intrinsic::ctpop:
  case Intrinsic::ctlz:
  case Intrinsic::cttz:
  case Intrinsic::fshl:
  case Intrinsic::fshr:
  case Intrinsic::smax:
  case Intrinsic::smin:
  case Intrinsic::umax:
  case Intrinsic::umin:
  case Intrinsic::sadd_sat:
  case Intrinsic::ssub_sat:
  case Intrinsic::uadd_sat:
  case Intrinsic::usub_sat:
  case Intrinsic::smul_fix:
  case Intrinsic::smul_fix_sat:
  case Intrinsic::umul_fix:
  case Intrinsic::umul_fix_sat:
  case Intrinsic::sqrt: // Begin floating-point.
  case Intrinsic::asin:
  case Intrinsic::acos:
  case Intrinsic::atan:
  case Intrinsic::atan2:
  case Intrinsic::sin:
  case Intrinsic::cos:
  case Intrinsic::tan:
  case Intrinsic::sinh:
  case Intrinsic::cosh:
  case Intrinsic::tanh:
  case Intrinsic::exp:
  case Intrinsic::exp10:
  case Intrinsic::exp2:
  case Intrinsic::log:
  case Intrinsic::log10:
  case Intrinsic::log2:
  case Intrinsic::fabs:
  case Intrinsic::minnum:
  case Intrinsic::maxnum:
  case Intrinsic::minimum:
  case Intrinsic::maximum:
  case Intrinsic::copysign:
  case Intrinsic::floor:
  case Intrinsic::ceil:
  case Intrinsic::trunc:
  case Intrinsic::rint:
  case Intrinsic::nearbyint:
  case Intrinsic::round:
  case Intrinsic::roundeven:
  case Intrinsic::pow:
  case Intrinsic::fma:
  case Intrinsic::fmuladd:
  case Intrinsic::is_fpclass:
  case Intrinsic::powi:
  case Intrinsic::canonicalize:
  case Intrinsic::fptosi_sat:
  case Intrinsic::fptoui_sat:
  case Intrinsic::lrint:
  case Intrinsic::llrint:
  case Intrinsic::ucmp:
  case Intrinsic::scmp:
    return true;
  default:
    return false;
  }
}
 
bool llvm::isTriviallyScalarizable(Intrinsic::ID ID,
                                   const TargetTransformInfo *TTI) {
  if (isTriviallyVectorizable(ID))
    return true;
 
  if (TTI && Intrinsic::isTargetIntrinsic(ID))
    return TTI->isTargetIntrinsicTriviallyScalarizable(ID);
 
  // TODO: Move frexp to isTriviallyVectorizable.
  // https://github.com/llvm/llvm-project/issues/112408
  switch (ID) {
  case Intrinsic::frexp:
    return true;
  }
  return false;
}
 
/// Identifies if the vector form of the intrinsic has a scalar operand.
bool llvm::isVectorIntrinsicWithScalarOpAtArg(Intrinsic::ID ID,
                                              unsigned ScalarOpdIdx,
                                              const TargetTransformInfo *TTI) {
 
  if (TTI && Intrinsic::isTargetIntrinsic(ID))
    return TTI->isTargetIntrinsicWithScalarOpAtArg(ID, ScalarOpdIdx);
 
  switch (ID) {
  case Intrinsic::abs:
  case Intrinsic::vp_abs:
  case Intrinsic::ctlz:
  case Intrinsic::vp_ctlz:
  case Intrinsic::cttz:
  case Intrinsic::vp_cttz:
  case Intrinsic::is_fpclass:
  case Intrinsic::vp_is_fpclass:
  case Intrinsic::powi:
    return (ScalarOpdIdx == 1);
  case Intrinsic::smul_fix:
  case Intrinsic::smul_fix_sat:
  case Intrinsic::umul_fix:
  case Intrinsic::umul_fix_sat:
    return (ScalarOpdIdx == 2);
  default:
    return false;
  }
}
 
bool llvm::isVectorIntrinsicWithOverloadTypeAtArg(
    Intrinsic::ID ID, int OpdIdx, const TargetTransformInfo *TTI) {
  assert(ID != Intrinsic::not_intrinsic && "Not an intrinsic!");
 
  if (TTI && Intrinsic::isTargetIntrinsic(ID))
    return TTI->isTargetIntrinsicWithOverloadTypeAtArg(ID, OpdIdx);
 
  if (VPCastIntrinsic::isVPCast(ID))
    return OpdIdx == -1 || OpdIdx == 0;
 
  switch (ID) {
  case Intrinsic::fptosi_sat:
  case Intrinsic::fptoui_sat:
  case Intrinsic::lrint:
  case Intrinsic::llrint:
  case Intrinsic::vp_lrint:
  case Intrinsic::vp_llrint:
  case Intrinsic::ucmp:
  case Intrinsic::scmp:
    return OpdIdx == -1 || OpdIdx == 0;
  case Intrinsic::is_fpclass:
  case Intrinsic::vp_is_fpclass:
    return OpdIdx == 0;
  case Intrinsic::powi:
    return OpdIdx == -1 || OpdIdx == 1;
  default:
    return OpdIdx == -1;
  }
}
 
bool llvm::isVectorIntrinsicWithStructReturnOverloadAtField(
    Intrinsic::ID ID, int RetIdx, const TargetTransformInfo *TTI) {
 
  if (TTI && Intrinsic::isTargetIntrinsic(ID))
    return TTI->isTargetIntrinsicWithStructReturnOverloadAtField(ID, RetIdx);
 
  switch (ID) {
  case Intrinsic::frexp:
    return RetIdx == 0 || RetIdx == 1;
  default:
    return RetIdx == 0;
  }
}
 
/// 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::experimental_noalias_scope_decl ||
      ID == Intrinsic::sideeffect || ID == Intrinsic::pseudoprobe)
    return ID;
  return Intrinsic::not_intrinsic;
}
 
/// 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());
  // For fixed-length vector, return poison for out of range access.
  if (auto *FVTy = dyn_cast<FixedVectorType>(VTy)) {
    unsigned Width = FVTy->getNumElements();
    if (EltNo >= Width)
      return PoisonValue::get(FVTy->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);
 
    // Guard against infinite loop on malformed, unreachable IR.
    if (III == III->getOperand(0))
      return nullptr;
 
    // Otherwise, the insertelement doesn't modify the value, recurse on its
    // vector input.
    return findScalarElement(III->getOperand(0), EltNo);
  }
 
  ShuffleVectorInst *SVI = dyn_cast<ShuffleVectorInst>(V);
  // Restrict the following transformation to fixed-length vector.
  if (SVI && isa<FixedVectorType>(SVI->getType())) {
    unsigned LHSWidth =
        cast<FixedVectorType>(SVI->getOperand(0)->getType())->getNumElements();
    int InEl = SVI->getMaskValue(EltNo);
    if (InEl < 0)
      return PoisonValue::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.
  // TODO: Use getBinOpIdentity() to generalize this.
  Value *Val; Constant *C;
  if (match(V, m_Add(m_Value(Val), m_Constant(C))))
    if (Constant *Elt = C->getAggregateElement(EltNo))
      if (Elt->isNullValue())
        return findScalarElement(Val, EltNo);
 
  // If the vector is a splat then we can trivially find the scalar element.
  if (isa<ScalableVectorType>(VTy))
    if (Value *Splat = getSplatValue(V))
      if (EltNo < VTy->getElementCount().getKnownMinValue())
        return Splat;
 
  // Otherwise, we don't know.
  return nullptr;
}
 
int llvm::getSplatIndex(ArrayRef<int> Mask) {
  int SplatIndex = -1;
  for (int M : Mask) {
    // Ignore invalid (undefined) mask elements.
    if (M < 0)
      continue;
 
    // There can be only 1 non-negative mask element value if this is a splat.
    if (SplatIndex != -1 && SplatIndex != M)
      return -1;
 
    // Initialize the splat index to the 1st non-negative mask element.
    SplatIndex = M;
  }
  assert((SplatIndex == -1 || SplatIndex >= 0) && "Negative index?");
  return SplatIndex;
}
 
/// 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 constant vector or (2) a sequence
/// of instructions that broadcasts a scalar at element 0.
Value *llvm::getSplatValue(const Value *V) {
  if (isa<VectorType>(V->getType()))
    if (auto *C = dyn_cast<Constant>(V))
      return C->getSplatValue();
 
  // shuf (inselt ?, Splat, 0), ?, <0, undef, 0, ...>
  Value *Splat;
  if (match(V,
            m_Shuffle(m_InsertElt(m_Value(), m_Value(Splat), m_ZeroInt()),
                      m_Value(), m_ZeroMask())))
    return Splat;
 
  return nullptr;
}
 
bool llvm::isSplatValue(const Value *V, int Index, unsigned Depth) {
  assert(Depth <= MaxAnalysisRecursionDepth && "Limit Search Depth");
 
  if (isa<VectorType>(V->getType())) {
    if (isa<UndefValue>(V))
      return true;
    // FIXME: We can allow undefs, but if Index was specified, we may want to
    //        check that the constant is defined at that index.
    if (auto *C = dyn_cast<Constant>(V))
      return C->getSplatValue() != nullptr;
  }
 
  if (auto *Shuf = dyn_cast<ShuffleVectorInst>(V)) {
    // FIXME: We can safely allow undefs here. If Index was specified, we will
    //        check that the mask elt is defined at the required index.
    if (!all_equal(Shuf->getShuffleMask()))
      return false;
 
    // Match any index.
    if (Index == -1)
      return true;
 
    // Match a specific element. The mask should be defined at and match the
    // specified index.
    return Shuf->getMaskValue(Index) == Index;
  }
 
  // The remaining tests are all recursive, so bail out if we hit the limit.
  if (Depth++ == MaxAnalysisRecursionDepth)
    return false;
 
  // If both operands of a binop are splats, the result is a splat.
  Value *X, *Y, *Z;
  if (match(V, m_BinOp(m_Value(X), m_Value(Y))))
    return isSplatValue(X, Index, Depth) && isSplatValue(Y, Index, Depth);
 
  // If all operands of a select are splats, the result is a splat.
  if (match(V, m_Select(m_Value(X), m_Value(Y), m_Value(Z))))
    return isSplatValue(X, Index, Depth) && isSplatValue(Y, Index, Depth) &&
           isSplatValue(Z, Index, Depth);
 
  // TODO: Add support for unary ops (fneg), casts, intrinsics (overflow ops).
 
  return false;
}
 
bool llvm::getShuffleDemandedElts(int SrcWidth, ArrayRef<int> Mask,
                                  const APInt &DemandedElts, APInt &DemandedLHS,
                                  APInt &DemandedRHS, bool AllowUndefElts) {
  DemandedLHS = DemandedRHS = APInt::getZero(SrcWidth);
 
  // Early out if we don't demand any elements.
  if (DemandedElts.isZero())
    return true;
 
  // Simple case of a shuffle with zeroinitializer.
  if (all_of(Mask, [](int Elt) { return Elt == 0; })) {
    DemandedLHS.setBit(0);
    return true;
  }
 
  for (unsigned I = 0, E = Mask.size(); I != E; ++I) {
    int M = Mask[I];
    assert((-1 <= M) && (M < (SrcWidth * 2)) &&
           "Invalid shuffle mask constant");
 
    if (!DemandedElts[I] || (AllowUndefElts && (M < 0)))
      continue;
 
    // For undef elements, we don't know anything about the common state of
    // the shuffle result.
    if (M < 0)
      return false;
 
    if (M < SrcWidth)
      DemandedLHS.setBit(M);
    else
      DemandedRHS.setBit(M - SrcWidth);
  }
 
  return true;
}
 
void llvm::narrowShuffleMaskElts(int Scale, ArrayRef<int> Mask,
                                 SmallVectorImpl<int> &ScaledMask) {
  assert(Scale > 0 && "Unexpected scaling factor");
 
  // Fast-path: if no scaling, then it is just a copy.
  if (Scale == 1) {
    ScaledMask.assign(Mask.begin(), Mask.end());
    return;
  }
 
  ScaledMask.clear();
  for (int MaskElt : Mask) {
    if (MaskElt >= 0) {
      assert(((uint64_t)Scale * MaskElt + (Scale - 1)) <= INT32_MAX &&
             "Overflowed 32-bits");
    }
    for (int SliceElt = 0; SliceElt != Scale; ++SliceElt)
      ScaledMask.push_back(MaskElt < 0 ? MaskElt : Scale * MaskElt + SliceElt);
  }
}
 
bool llvm::widenShuffleMaskElts(int Scale, ArrayRef<int> Mask,
                                SmallVectorImpl<int> &ScaledMask) {
  assert(Scale > 0 && "Unexpected scaling factor");
 
  // Fast-path: if no scaling, then it is just a copy.
  if (Scale == 1) {
    ScaledMask.assign(Mask.begin(), Mask.end());
    return true;
  }
 
  // We must map the original elements down evenly to a type with less elements.
  int NumElts = Mask.size();
  if (NumElts % Scale != 0)
    return false;
 
  ScaledMask.clear();
  ScaledMask.reserve(NumElts / Scale);
 
  // Step through the input mask by splitting into Scale-sized slices.
  do {
    ArrayRef<int> MaskSlice = Mask.take_front(Scale);
    assert((int)MaskSlice.size() == Scale && "Expected Scale-sized slice.");
 
    // The first element of the slice determines how we evaluate this slice.
    int SliceFront = MaskSlice.front();
    if (SliceFront < 0) {
      // Negative values (undef or other "sentinel" values) must be equal across
      // the entire slice.
      if (!all_equal(MaskSlice))
        return false;
      ScaledMask.push_back(SliceFront);
    } else {
      // A positive mask element must be cleanly divisible.
      if (SliceFront % Scale != 0)
        return false;
      // Elements of the slice must be consecutive.
      for (int i = 1; i < Scale; ++i)
        if (MaskSlice[i] != SliceFront + i)
          return false;
      ScaledMask.push_back(SliceFront / Scale);
    }
    Mask = Mask.drop_front(Scale);
  } while (!Mask.empty());
 
  assert((int)ScaledMask.size() * Scale == NumElts && "Unexpected scaled mask");
 
  // All elements of the original mask can be scaled down to map to the elements
  // of a mask with wider elements.
  return true;
}
 
bool llvm::scaleShuffleMaskElts(unsigned NumDstElts, ArrayRef<int> Mask,
                                SmallVectorImpl<int> &ScaledMask) {
  unsigned NumSrcElts = Mask.size();
  assert(NumSrcElts > 0 && NumDstElts > 0 && "Unexpected scaling factor");
 
  // Fast-path: if no scaling, then it is just a copy.
  if (NumSrcElts == NumDstElts) {
    ScaledMask.assign(Mask.begin(), Mask.end());
    return true;
  }
 
  // Ensure we can find a whole scale factor.
  assert(((NumSrcElts % NumDstElts) == 0 || (NumDstElts % NumSrcElts) == 0) &&
         "Unexpected scaling factor");
 
  if (NumSrcElts > NumDstElts) {
    int Scale = NumSrcElts / NumDstElts;
    return widenShuffleMaskElts(Scale, Mask, ScaledMask);
  }
 
  int Scale = NumDstElts / NumSrcElts;
  narrowShuffleMaskElts(Scale, Mask, ScaledMask);
  return true;
}
 
void llvm::getShuffleMaskWithWidestElts(ArrayRef<int> Mask,
                                        SmallVectorImpl<int> &ScaledMask) {
  std::array<SmallVector<int, 16>, 2> TmpMasks;
  SmallVectorImpl<int> *Output = &TmpMasks[0], *Tmp = &TmpMasks[1];
  ArrayRef<int> InputMask = Mask;
  for (unsigned Scale = 2; Scale <= InputMask.size(); ++Scale) {
    while (widenShuffleMaskElts(Scale, InputMask, *Output)) {
      InputMask = *Output;
      std::swap(Output, Tmp);
    }
  }
  ScaledMask.assign(InputMask.begin(), InputMask.end());
}
 
void llvm::processShuffleMasks(
    ArrayRef<int> Mask, unsigned NumOfSrcRegs, unsigned NumOfDestRegs,
    unsigned NumOfUsedRegs, function_ref<void()> NoInputAction,
    function_ref<void(ArrayRef<int>, unsigned, unsigned)> SingleInputAction,
    function_ref<void(ArrayRef<int>, unsigned, unsigned)> ManyInputsAction) {
  SmallVector<SmallVector<SmallVector<int>>> Res(NumOfDestRegs);
  // Try to perform better estimation of the permutation.
  // 1. Split the source/destination vectors into real registers.
  // 2. Do the mask analysis to identify which real registers are
  // permuted.
  int Sz = Mask.size();
  unsigned SzDest = Sz / NumOfDestRegs;
  unsigned SzSrc = Sz / NumOfSrcRegs;
  for (unsigned I = 0; I < NumOfDestRegs; ++I) {
    auto &RegMasks = Res[I];
    RegMasks.assign(2 * NumOfSrcRegs, {});
    // Check that the values in dest registers are in the one src
    // register.
    for (unsigned K = 0; K < SzDest; ++K) {
      int Idx = I * SzDest + K;
      if (Idx == Sz)
        break;
      if (Mask[Idx] >= 2 * Sz || Mask[Idx] == PoisonMaskElem)
        continue;
      int MaskIdx = Mask[Idx] % Sz;
      int SrcRegIdx = MaskIdx / SzSrc + (Mask[Idx] >= Sz ? NumOfSrcRegs : 0);
      // Add a cost of PermuteTwoSrc for each new source register permute,
      // if we have more than one source registers.
      if (RegMasks[SrcRegIdx].empty())
        RegMasks[SrcRegIdx].assign(SzDest, PoisonMaskElem);
      RegMasks[SrcRegIdx][K] = MaskIdx % SzSrc;
    }
  }
  // Process split mask.
  for (unsigned I : seq<unsigned>(NumOfUsedRegs)) {
    auto &Dest = Res[I];
    int NumSrcRegs =
        count_if(Dest, [](ArrayRef<int> Mask) { return !Mask.empty(); });
    switch (NumSrcRegs) {
    case 0:
      // No input vectors were used!
      NoInputAction();
      break;
    case 1: {
      // Find the only mask with at least single undef mask elem.
      auto *It =
          find_if(Dest, [](ArrayRef<int> Mask) { return !Mask.empty(); });
      unsigned SrcReg = std::distance(Dest.begin(), It);
      SingleInputAction(*It, SrcReg, I);
      break;
    }
    default: {
      // The first mask is a permutation of a single register. Since we have >2
      // input registers to shuffle, we merge the masks for 2 first registers
      // and generate a shuffle of 2 registers rather than the reordering of the
      // first register and then shuffle with the second register. Next,
      // generate the shuffles of the resulting register + the remaining
      // registers from the list.
      auto &&CombineMasks = [](MutableArrayRef<int> FirstMask,
                               ArrayRef<int> SecondMask) {
        for (int Idx = 0, VF = FirstMask.size(); Idx < VF; ++Idx) {
          if (SecondMask[Idx] != PoisonMaskElem) {
            assert(FirstMask[Idx] == PoisonMaskElem &&
                   "Expected undefined mask element.");
            FirstMask[Idx] = SecondMask[Idx] + VF;
          }
        }
      };
      auto &&NormalizeMask = [](MutableArrayRef<int> Mask) {
        for (int Idx = 0, VF = Mask.size(); Idx < VF; ++Idx) {
          if (Mask[Idx] != PoisonMaskElem)
            Mask[Idx] = Idx;
        }
      };
      int SecondIdx;
      do {
        int FirstIdx = -1;
        SecondIdx = -1;
        MutableArrayRef<int> FirstMask, SecondMask;
        for (unsigned I : seq<unsigned>(2 * NumOfSrcRegs)) {
          SmallVectorImpl<int> &RegMask = Dest[I];
          if (RegMask.empty())
            continue;
 
          if (FirstIdx == SecondIdx) {
            FirstIdx = I;
            FirstMask = RegMask;
            continue;
          }
          SecondIdx = I;
          SecondMask = RegMask;
          CombineMasks(FirstMask, SecondMask);
          ManyInputsAction(FirstMask, FirstIdx, SecondIdx);
          NormalizeMask(FirstMask);
          RegMask.clear();
          SecondMask = FirstMask;
          SecondIdx = FirstIdx;
        }
        if (FirstIdx != SecondIdx && SecondIdx >= 0) {
          CombineMasks(SecondMask, FirstMask);
          ManyInputsAction(SecondMask, SecondIdx, FirstIdx);
          Dest[FirstIdx].clear();
          NormalizeMask(SecondMask);
        }
      } while (SecondIdx >= 0);
      break;
    }
    }
  }
}
 
void llvm::getHorizDemandedEltsForFirstOperand(unsigned VectorBitWidth,
                                               const APInt &DemandedElts,
                                               APInt &DemandedLHS,
                                               APInt &DemandedRHS) {
  assert(VectorBitWidth >= 128 && "Vectors smaller than 128 bit not supported");
  int NumLanes = VectorBitWidth / 128;
  int NumElts = DemandedElts.getBitWidth();
  int NumEltsPerLane = NumElts / NumLanes;
  int HalfEltsPerLane = NumEltsPerLane / 2;
 
  DemandedLHS = APInt::getZero(NumElts);
  DemandedRHS = APInt::getZero(NumElts);
 
  // Map DemandedElts to the horizontal operands.
  for (int Idx = 0; Idx != NumElts; ++Idx) {
    if (!DemandedElts[Idx])
      continue;
    int LaneIdx = (Idx / NumEltsPerLane) * NumEltsPerLane;
    int LocalIdx = Idx % NumEltsPerLane;
    if (LocalIdx < HalfEltsPerLane) {
      DemandedLHS.setBit(LaneIdx + 2 * LocalIdx);
    } else {
      LocalIdx -= HalfEltsPerLane;
      DemandedRHS.setBit(LaneIdx + 2 * LocalIdx);
    }
  }
}
 
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.insert(Val).second)
      continue;
 
    // 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 (Value *M : llvm::make_range(ECs.member_begin(I), ECs.member_end()))
      LeaderDemandedBits |= DBits[M];
 
    uint64_t MinBW = llvm::bit_width(LeaderDemandedBits);
    // Round up to a power of 2
    MinBW = llvm::bit_ceil(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 (Value *M : llvm::make_range(ECs.member_begin(I), ECs.member_end()))
      if (isa<PHINode>(M) && MinBW < M->getType()->getScalarSizeInBits()) {
        Abort = true;
        break;
      }
    if (Abort)
      continue;
 
    for (Value *M : llvm::make_range(ECs.member_begin(I), ECs.member_end())) {
      auto *MI = dyn_cast<Instruction>(M);
      if (!MI)
        continue;
      Type *Ty = M->getType();
      if (Roots.count(M))
        Ty = MI->getOperand(0)->getType();
 
      if (MinBW >= Ty->getScalarSizeInBits())
        continue;
 
      // If any of M's operands demand more bits than MinBW then M cannot be
      // performed safely in MinBW.
      if (any_of(MI->operands(), [&DB, MinBW](Use &U) {
            auto *CI = dyn_cast<ConstantInt>(U);
            // For constants shift amounts, check if the shift would result in
            // poison.
            if (CI &&
                isa<ShlOperator, LShrOperator, AShrOperator>(U.getUser()) &&
                U.getOperandNo() == 1)
              return CI->uge(MinBW);
            uint64_t BW = bit_width(DB.getDemandedBits(&U).getZExtValue());
            return bit_ceil(BW) > MinBW;
          }))
        continue;
 
      MinBWs[MI] = MinBW;
    }
  }
 
  return MinBWs;
}
 
/// Add all access groups in @p AccGroups to @p List.
template <typename ListT>
static void addToAccessGroupList(ListT &List, MDNode *AccGroups) {
  // Interpret an access group as a list containing itself.
  if (AccGroups->getNumOperands() == 0) {
    assert(isValidAsAccessGroup(AccGroups) && "Node must be an access group");
    List.insert(AccGroups);
    return;
  }
 
  for (const auto &AccGroupListOp : AccGroups->operands()) {
    auto *Item = cast<MDNode>(AccGroupListOp.get());
    assert(isValidAsAccessGroup(Item) && "List item must be an access group");
    List.insert(Item);
  }
}
 
MDNode *llvm::uniteAccessGroups(MDNode *AccGroups1, MDNode *AccGroups2) {
  if (!AccGroups1)
    return AccGroups2;
  if (!AccGroups2)
    return AccGroups1;
  if (AccGroups1 == AccGroups2)
    return AccGroups1;
 
  SmallSetVector<Metadata *, 4> Union;
  addToAccessGroupList(Union, AccGroups1);
  addToAccessGroupList(Union, AccGroups2);
 
  if (Union.size() == 0)
    return nullptr;
  if (Union.size() == 1)
    return cast<MDNode>(Union.front());
 
  LLVMContext &Ctx = AccGroups1->getContext();
  return MDNode::get(Ctx, Union.getArrayRef());
}
 
MDNode *llvm::intersectAccessGroups(const Instruction *Inst1,
                                    const Instruction *Inst2) {
  bool MayAccessMem1 = Inst1->mayReadOrWriteMemory();
  bool MayAccessMem2 = Inst2->mayReadOrWriteMemory();
 
  if (!MayAccessMem1 && !MayAccessMem2)
    return nullptr;
  if (!MayAccessMem1)
    return Inst2->getMetadata(LLVMContext::MD_access_group);
  if (!MayAccessMem2)
    return Inst1->getMetadata(LLVMContext::MD_access_group);
 
  MDNode *MD1 = Inst1->getMetadata(LLVMContext::MD_access_group);
  MDNode *MD2 = Inst2->getMetadata(LLVMContext::MD_access_group);
  if (!MD1 || !MD2)
    return nullptr;
  if (MD1 == MD2)
    return MD1;
 
  // Use set for scalable 'contains' check.
  SmallPtrSet<Metadata *, 4> AccGroupSet2;
  addToAccessGroupList(AccGroupSet2, MD2);
 
  SmallVector<Metadata *, 4> Intersection;
  if (MD1->getNumOperands() == 0) {
    assert(isValidAsAccessGroup(MD1) && "Node must be an access group");
    if (AccGroupSet2.count(MD1))
      Intersection.push_back(MD1);
  } else {
    for (const MDOperand &Node : MD1->operands()) {
      auto *Item = cast<MDNode>(Node.get());
      assert(isValidAsAccessGroup(Item) && "List item must be an access group");
      if (AccGroupSet2.count(Item))
        Intersection.push_back(Item);
    }
  }
 
  if (Intersection.size() == 0)
    return nullptr;
  if (Intersection.size() == 1)
    return cast<MDNode>(Intersection.front());
 
  LLVMContext &Ctx = Inst1->getContext();
  return MDNode::get(Ctx, Intersection);
}
 
/// \returns \p I after propagating metadata from \p VL.
Instruction *llvm::propagateMetadata(Instruction *Inst, ArrayRef<Value *> VL) {
  if (VL.empty())
    return Inst;
  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,
                    LLVMContext::MD_access_group, LLVMContext::MD_mmra}) {
    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_mmra: {
        MD = MMRAMetadata::combine(Inst->getContext(), MD, IMD);
        break;
      }
      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;
      case LLVMContext::MD_access_group:
        MD = intersectAccessGroups(Inst, IJ);
        break;
      default:
        llvm_unreachable("unhandled metadata");
      }
    }
 
    Inst->setMetadata(Kind, MD);
  }
 
  return Inst;
}
 
Constant *
llvm::createBitMaskForGaps(IRBuilderBase &Builder, unsigned VF,
                           const InterleaveGroup<Instruction> &Group) {
  // All 1's means mask is not needed.
  if (Group.getNumMembers() == Group.getFactor())
    return nullptr;
 
  // TODO: support reversed access.
  assert(!Group.isReverse() && "Reversed group not supported.");
 
  SmallVector<Constant *, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    for (unsigned j = 0; j < Group.getFactor(); ++j) {
      unsigned HasMember = Group.getMember(j) ? 1 : 0;
      Mask.push_back(Builder.getInt1(HasMember));
    }
 
  return ConstantVector::get(Mask);
}
 
llvm::SmallVector<int, 16>
llvm::createReplicatedMask(unsigned ReplicationFactor, unsigned VF) {
  SmallVector<int, 16> MaskVec;
  for (unsigned i = 0; i < VF; i++)
    for (unsigned j = 0; j < ReplicationFactor; j++)
      MaskVec.push_back(i);
 
  return MaskVec;
}
 
llvm::SmallVector<int, 16> llvm::createInterleaveMask(unsigned VF,
                                                      unsigned NumVecs) {
  SmallVector<int, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    for (unsigned j = 0; j < NumVecs; j++)
      Mask.push_back(j * VF + i);
 
  return Mask;
}
 
llvm::SmallVector<int, 16>
llvm::createStrideMask(unsigned Start, unsigned Stride, unsigned VF) {
  SmallVector<int, 16> Mask;
  for (unsigned i = 0; i < VF; i++)
    Mask.push_back(Start + i * Stride);
 
  return Mask;
}
 
llvm::SmallVector<int, 16> llvm::createSequentialMask(unsigned Start,
                                                      unsigned NumInts,
                                                      unsigned NumUndefs) {
  SmallVector<int, 16> Mask;
  for (unsigned i = 0; i < NumInts; i++)
    Mask.push_back(Start + i);
 
  for (unsigned i = 0; i < NumUndefs; i++)
    Mask.push_back(-1);
 
  return Mask;
}
 
llvm::SmallVector<int, 16> llvm::createUnaryMask(ArrayRef<int> Mask,
                                                 unsigned NumElts) {
  // Avoid casts in the loop and make sure we have a reasonable number.
  int NumEltsSigned = NumElts;
  assert(NumEltsSigned > 0 && "Expected smaller or non-zero element count");
 
  // If the mask chooses an element from operand 1, reduce it to choose from the
  // corresponding element of operand 0. Undef mask elements are unchanged.
  SmallVector<int, 16> UnaryMask;
  for (int MaskElt : Mask) {
    assert((MaskElt < NumEltsSigned * 2) && "Expected valid shuffle mask");
    int UnaryElt = MaskElt >= NumEltsSigned ? MaskElt - NumEltsSigned : MaskElt;
    UnaryMask.push_back(UnaryElt);
  }
  return UnaryMask;
}
 
/// 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(IRBuilderBase &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 = cast<FixedVectorType>(VecTy1)->getNumElements();
  unsigned NumElts2 = cast<FixedVectorType>(VecTy2)->getNumElements();
  assert(NumElts1 >= NumElts2 && "Unexpect the first vector has less elements");
 
  if (NumElts1 > NumElts2) {
    // Extend with UNDEFs.
    V2 = Builder.CreateShuffleVector(
        V2, createSequentialMask(0, NumElts2, NumElts1 - NumElts2));
  }
 
  return Builder.CreateShuffleVector(
      V1, V2, createSequentialMask(0, NumElts1 + NumElts2, 0));
}
 
Value *llvm::concatenateVectors(IRBuilderBase &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 llvm::maskIsAllZeroOrUndef(Value *Mask) {
  assert(isa<VectorType>(Mask->getType()) &&
         isa<IntegerType>(Mask->getType()->getScalarType()) &&
         cast<IntegerType>(Mask->getType()->getScalarType())->getBitWidth() ==
             1 &&
         "Mask must be a vector of i1");
 
  auto *ConstMask = dyn_cast<Constant>(Mask);
  if (!ConstMask)
    return false;
  if (ConstMask->isNullValue() || isa<UndefValue>(ConstMask))
    return true;
  if (isa<ScalableVectorType>(ConstMask->getType()))
    return false;
  for (unsigned
           I = 0,
           E = cast<FixedVectorType>(ConstMask->getType())->getNumElements();
       I != E; ++I) {
    if (auto *MaskElt = ConstMask->getAggregateElement(I))
      if (MaskElt->isNullValue() || isa<UndefValue>(MaskElt))
        continue;
    return false;
  }
  return true;
}
 
bool llvm::maskIsAllOneOrUndef(Value *Mask) {
  assert(isa<VectorType>(Mask->getType()) &&
         isa<IntegerType>(Mask->getType()->getScalarType()) &&
         cast<IntegerType>(Mask->getType()->getScalarType())->getBitWidth() ==
             1 &&
         "Mask must be a vector of i1");
 
  auto *ConstMask = dyn_cast<Constant>(Mask);
  if (!ConstMask)
    return false;
  if (ConstMask->isAllOnesValue() || isa<UndefValue>(ConstMask))
    return true;
  if (isa<ScalableVectorType>(ConstMask->getType()))
    return false;
  for (unsigned
           I = 0,
           E = cast<FixedVectorType>(ConstMask->getType())->getNumElements();
       I != E; ++I) {
    if (auto *MaskElt = ConstMask->getAggregateElement(I))
      if (MaskElt->isAllOnesValue() || isa<UndefValue>(MaskElt))
        continue;
    return false;
  }
  return true;
}
 
bool llvm::maskContainsAllOneOrUndef(Value *Mask) {
  assert(isa<VectorType>(Mask->getType()) &&
         isa<IntegerType>(Mask->getType()->getScalarType()) &&
         cast<IntegerType>(Mask->getType()->getScalarType())->getBitWidth() ==
             1 &&
         "Mask must be a vector of i1");
 
  auto *ConstMask = dyn_cast<Constant>(Mask);
  if (!ConstMask)
    return false;
  if (ConstMask->isAllOnesValue() || isa<UndefValue>(ConstMask))
    return true;
  if (isa<ScalableVectorType>(ConstMask->getType()))
    return false;
  for (unsigned
           I = 0,
           E = cast<FixedVectorType>(ConstMask->getType())->getNumElements();
       I != E; ++I) {
    if (auto *MaskElt = ConstMask->getAggregateElement(I))
      if (MaskElt->isAllOnesValue() || isa<UndefValue>(MaskElt))
        return true;
  }
  return false;
}
 
/// TODO: This is a lot like known bits, but for
/// vectors.  Is there something we can common this with?
APInt llvm::possiblyDemandedEltsInMask(Value *Mask) {
  assert(isa<FixedVectorType>(Mask->getType()) &&
         isa<IntegerType>(Mask->getType()->getScalarType()) &&
         cast<IntegerType>(Mask->getType()->getScalarType())->getBitWidth() ==
             1 &&
         "Mask must be a fixed width vector of i1");
 
  const unsigned VWidth =
      cast<FixedVectorType>(Mask->getType())->getNumElements();
  APInt DemandedElts = APInt::getAllOnes(VWidth);
  if (auto *CV = dyn_cast<ConstantVector>(Mask))
    for (unsigned i = 0; i < VWidth; i++)
      if (CV->getAggregateElement(i)->isNullValue())
        DemandedElts.clearBit(i);
  return DemandedElts;
}
 
bool InterleavedAccessInfo::isStrided(int Stride) {
  unsigned Factor = std::abs(Stride);
  return Factor >= 2 && Factor <= MaxInterleaveGroupFactor;
}
 
void InterleavedAccessInfo::collectConstStrideAccesses(
    MapVector<Instruction *, StrideDescriptor> &AccessStrideInfo,
    const DenseMap<Value*, const SCEV*> &Strides) {
  auto &DL = TheLoop->getHeader()->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) {
      Value *Ptr = getLoadStorePointerOperand(&I);
      if (!Ptr)
        continue;
      Type *ElementTy = getLoadStoreType(&I);
 
      // Currently, codegen doesn't support cases where the type size doesn't
      // match the alloc size. Skip them for now.
      uint64_t Size = DL.getTypeAllocSize(ElementTy);
      if (Size * 8 != DL.getTypeSizeInBits(ElementTy))
        continue;
 
      // 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, ElementTy, Ptr, TheLoop, Strides,
                     /*Assume=*/true, /*ShouldCheckWrap=*/false).value_or(0);
 
      const SCEV *Scev = replaceSymbolicStrideSCEV(PSE, Strides, Ptr);
      AccessStrideInfo[&I] = StrideDescriptor(Stride, Scev, Size,
                                              getLoadStoreAlignment(&I));
    }
}
 
// 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(
                                 bool EnablePredicatedInterleavedMemAccesses) {
  LLVM_DEBUG(dbgs() << "LV: Analyzing interleaved accesses...\n");
  const auto &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<Instruction> *, 4> StoreGroups;
  // Holds all interleaved load groups temporarily.
  SmallSetVector<InterleaveGroup<Instruction> *, 4> LoadGroups;
  // Groups added to this set cannot have new members added.
  SmallPtrSet<InterleaveGroup<Instruction> *, 4> CompletedLoadGroups;
 
  // 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<Instruction> *GroupB = nullptr;
    if (isStrided(DesB.Stride) &&
        (!isPredicated(B->getParent()) || EnablePredicatedInterleavedMemAccesses)) {
      GroupB = getInterleaveGroup(B);
      if (!GroupB) {
        LLVM_DEBUG(dbgs() << "LV: Creating an interleave group with:" << *B
                          << '\n');
        GroupB = createInterleaveGroup(B, DesB.Stride, DesB.Alignment);
        if (B->mayWriteToMemory())
          StoreGroups.insert(GroupB);
        else
          LoadGroups.insert(GroupB);
      }
    }
 
    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.
      auto DependentMember = [&](InterleaveGroup<Instruction> *Group,
                                 StrideEntry *A) -> Instruction * {
        for (uint32_t Index = 0; Index < Group->getFactor(); ++Index) {
          Instruction *MemberOfGroupB = Group->getMember(Index);
          if (MemberOfGroupB && !canReorderMemAccessesForInterleavedGroups(
                                    A, &*AccessStrideInfo.find(MemberOfGroupB)))
            return MemberOfGroupB;
        }
        return nullptr;
      };
 
      auto GroupA = getInterleaveGroup(A);
      // If A is a load, dependencies are tolerable, there's nothing to do here.
      // If both A and B belong to the same (store) group, they are independent,
      // even if dependencies have not been recorded.
      // If both GroupA and GroupB are null, there's nothing to do here.
      if (A->mayWriteToMemory() && GroupA != GroupB) {
        Instruction *DependentInst = nullptr;
        // If GroupB is a load group, we have to compare AI against all
        // members of GroupB because if any load within GroupB has a dependency
        // on AI, we need to mark GroupB as complete and also release the
        // store GroupA (if A belongs to one). The former prevents incorrect
        // hoisting of load B above store A while the latter prevents incorrect
        // sinking of store A below load B.
        if (GroupB && LoadGroups.contains(GroupB))
          DependentInst = DependentMember(GroupB, &*AI);
        else if (!canReorderMemAccessesForInterleavedGroups(&*AI, &*BI))
          DependentInst = B;
 
        if (DependentInst) {
          // A has a store dependence on B (or on some load within GroupB) and
          // is part of a store group. Release A's group to prevent illegal
          // sinking of A below B. A will then be free to form another group
          // with instructions that precede it.
          if (GroupA && StoreGroups.contains(GroupA)) {
            LLVM_DEBUG(dbgs() << "LV: Invalidated store group due to "
                                 "dependence between "
                              << *A << " and " << *DependentInst << '\n');
            StoreGroups.remove(GroupA);
            releaseGroup(GroupA);
          }
          // If B is a load and part of an interleave group, no earlier loads
          // can be added to B's interleave group, because this would mean the
          // DependentInst would move across store A. Mark the interleave group
          // as complete.
          if (GroupB && LoadGroups.contains(GroupB)) {
            LLVM_DEBUG(dbgs() << "LV: Marking interleave group for " << *B
                              << " as complete.\n");
            CompletedLoadGroups.insert(GroupB);
          }
        }
      }
      if (CompletedLoadGroups.contains(GroupB)) {
        // Skip trying to add A to B, continue to look for other conflicting A's
        // in groups to be released.
        continue;
      }
 
      // 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;
 
      // All members of a predicated interleave-group must have the same predicate,
      // and currently must reside in the same BB.
      BasicBlock *BlockA = A->getParent();
      BasicBlock *BlockB = B->getParent();
      if ((isPredicated(BlockA) || isPredicated(BlockB)) &&
          (!EnablePredicatedInterleavedMemAccesses || BlockA != BlockB))
        continue;
 
      // The index of A is the index of B plus A's distance to B in multiples
      // of the size.
      int IndexA =
          GroupB->getIndex(B) + DistanceToB / static_cast<int64_t>(DesB.Size);
 
      // Try to insert A into B's group.
      if (GroupB->insertMember(A, IndexA, DesA.Alignment)) {
        LLVM_DEBUG(dbgs() << "LV: Inserted:" << *A << '\n'
                          << "    into the interleave group with" << *B
                          << '\n');
        InterleaveGroupMap[A] = GroupB;
 
        // Set the first load in program order as the insert position.
        if (A->mayReadFromMemory())
          GroupB->setInsertPos(A);
      }
    } // Iteration over A accesses.
  }   // Iteration over B accesses.
 
  auto InvalidateGroupIfMemberMayWrap = [&](InterleaveGroup<Instruction> *Group,
                                            int Index,
                                            const char *FirstOrLast) -> bool {
    Instruction *Member = Group->getMember(Index);
    assert(Member && "Group member does not exist");
    Value *MemberPtr = getLoadStorePointerOperand(Member);
    Type *AccessTy = getLoadStoreType(Member);
    if (getPtrStride(PSE, AccessTy, MemberPtr, TheLoop, Strides,
                     /*Assume=*/false, /*ShouldCheckWrap=*/true).value_or(0))
      return false;
    LLVM_DEBUG(dbgs() << "LV: Invalidate candidate interleaved group due to "
                      << FirstOrLast
                      << " group member potentially pointer-wrapping.\n");
    releaseGroup(Group);
    return true;
  };
 
  // Remove interleaved groups with gaps 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 (auto *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-reversed access -- see Case 3).
    if (InvalidateGroupIfMemberMayWrap(Group, 0, "first"))
      continue;
    if (Group->getMember(Group->getFactor() - 1))
      InvalidateGroupIfMemberMayWrap(Group, Group->getFactor() - 1, "last");
    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;
    }
  }
 
  for (auto *Group : StoreGroups) {
    // Case 1: A full group. Can Skip the checks; For full groups, if the wide
    // store would wrap around the address space we would do a memory access at
    // nullptr even without the transformation.
    if (Group->getNumMembers() == Group->getFactor())
      continue;
 
    // Interleave-store-group with gaps is implemented using masked wide store.
    // Remove interleaved store groups with gaps if
    // masked-interleaved-accesses are not enabled by the target.
    if (!EnablePredicatedInterleavedMemAccesses) {
      LLVM_DEBUG(
          dbgs() << "LV: Invalidate candidate interleaved store group due "
                    "to gaps.\n");
      releaseGroup(Group);
      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 the last group member. Case 3 (scalar epilog) is not relevant for
    // stores with gaps, which are implemented with masked-store (rather than
    // speculative access, as in loads).
    if (InvalidateGroupIfMemberMayWrap(Group, 0, "first"))
      continue;
    for (int Index = Group->getFactor() - 1; Index > 0; Index--)
      if (Group->getMember(Index)) {
        InvalidateGroupIfMemberMayWrap(Group, Index, "last");
        break;
      }
  }
}
 
void InterleavedAccessInfo::invalidateGroupsRequiringScalarEpilogue() {
  // If no group had triggered the requirement to create an epilogue loop,
  // there is nothing to do.
  if (!requiresScalarEpilogue())
    return;
 
  // Release groups requiring scalar epilogues. Note that this also removes them
  // from InterleaveGroups.
  bool ReleasedGroup = InterleaveGroups.remove_if([&](auto *Group) {
    if (!Group->requiresScalarEpilogue())
      return false;
    LLVM_DEBUG(
        dbgs()
        << "LV: Invalidate candidate interleaved group due to gaps that "
           "require a scalar epilogue (not allowed under optsize) and cannot "
           "be masked (not enabled). \n");
    releaseGroupWithoutRemovingFromSet(Group);
    return true;
  });
  assert(ReleasedGroup && "At least one group must be invalidated, as a "
                          "scalar epilogue was required");
  (void)ReleasedGroup;
  RequiresScalarEpilogue = false;
}
 
template <typename InstT>
void InterleaveGroup<InstT>::addMetadata(InstT *NewInst) const {
  llvm_unreachable("addMetadata can only be used for Instruction");
}
 
namespace llvm {
template <>
void InterleaveGroup<Instruction>::addMetadata(Instruction *NewInst) const {
  SmallVector<Value *, 4> VL;
  std::transform(Members.begin(), Members.end(), std::back_inserter(VL),
                 [](std::pair<int, Instruction *> p) { return p.second; });
  propagateMetadata(NewInst, VL);
}
} // namespace llvm