mma_tensor_op_tile_iterator.h

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#pragma once

#include "cutlass/cutlass.h"

#include "cutlass/array.h"
#include "cutlass/numeric_types.h"
#include "cutlass/tensor_ref.h"
#include "cutlass/matrix_shape.h"

#include "cutlass/arch/memory_sm75.h"
#include "cutlass/gemm/gemm.h"

#include "cutlass/layout/matrix.h"
#include "cutlass/layout/tensor.h"
#include "cutlass/layout/pitch_linear.h"
#include "cutlass/layout/tensor_op_multiplicand_sm75.h"

#include "cutlass/platform/platform.h"
#include "cutlass/fast_math.h"


namespace cutlass {
namespace gemm {
namespace warp {


template <
    typename Shape_,
    Operand Operand,
    typename Element_,
    typename Layout_,
    typename InstructionShape_,
    int OpDelta_,
    int Threads,
    int PartitionsK_ = 1>
class MmaTensorOpMultiplicandTileIterator;


template <
    typename Shape_,
    Operand Operand_,
    typename Element_,
    typename InstructionShape_,
    int OpDelta_,
    int PartitionsK_>
class MmaTensorOpMultiplicandTileIterator<
    Shape_, Operand_, Element_,
    cutlass::layout::TensorOpMultiplicandCongruous<sizeof_bits<Element_>::value,
                                                   64>,
    InstructionShape_, OpDelta_, 32, PartitionsK_> {
 public:

  using Shape = Shape_;

  static Operand const kOperand = Operand_;

  static_assert(kOperand == Operand::kA || kOperand== Operand::kB,
    "MmaTensorOpMultiplicandIterator may only be instantiated for A or B operands to warp-level Mma.");

  using Element = Element_;

  using Layout = cutlass::layout::TensorOpMultiplicandCongruous<
      sizeof_bits<Element_>::value, 64>;

  using InstructionShape = InstructionShape_;

  static int const kOpDelta = OpDelta_;

  static int const kThreads = 32;

  static int const kPartitionsK = PartitionsK_;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  struct Policy {
    static_assert(
        !(Shape::kContiguous % InstructionShape::kContiguous),
        "Shape of warp-level Mma must be divisible by operator shape.");

    // Determine number of elements along outer dimension per individual LDSM op
    static int const kLdsmOpOuter = Layout::kElementsPerAccess;
    static int const kLdsmOpInner = 8;

    static_assert(!(Shape::kContiguous % kLdsmOpOuter),
      "Shape of warp-level mma must be divisible by LDSM's fundamental tile size.");

    static_assert(!(Shape::kStrided % kLdsmOpInner), 
      "Shape of warp-level mma must be divisible by LDSM's fundamental tile size.");

    static int const LdsmShapeStrided =
        InstructionShape::kStrided / kLdsmOpInner;
    static int const LdsmShapeContiguous = 4 / LdsmShapeStrided;
    using LdsmShape =
        layout::PitchLinearShape<LdsmShapeContiguous, LdsmShapeStrided>;

    using LdsmIterations = layout::PitchLinearShape<
        Shape::kContiguous / Layout::kElementsPerAccess / LdsmShapeContiguous,
        1>;

    static int const kGroupsPerTile =
        Shape::kStrided / InstructionShape::kStrided;
  };

private:

  static_assert(kOpDelta == 1,
    "Alternative arrangements not supported at present.");

  static int const kPointerCount =
      Layout::TileShape::kContiguous / Policy::LdsmShape::kContiguous;

  using AccessType = Array<Element, Layout::kElementsPerAccess>;

  int k_group_idx_;

public:

  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

private:

  Index stride_;

  AccessType const *pointer_[kPointerCount];

  Index byte_offset_;

public:
  
  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator(): stride_(0), byte_offset_(0) { }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator(
    TensorRef const &ref, 
    int lane_id
  ):
    stride_(ref.stride(0) / Layout::kElementsPerAccess), byte_offset_(0),
    k_group_idx_(0) {
      
    int quad_pair = (lane_id >> 3);
    int lane_in_quad = (lane_id & 3);
    int lane_in_quad_pair = (lane_id & 7);
    CUTLASS_PRAGMA_UNROLL
    for (int i = 0; i < kPointerCount; ++i) {
      int partition_contiguous_idx = -1;
      int access_contiguous_idx = -1;
      int access_strided_idx = -1;

      if (Policy::LdsmShape::kContiguous == 4) {
        partition_contiguous_idx = ((lane_in_quad_pair >> 2) ^ i);
        access_contiguous_idx = (quad_pair ^ lane_in_quad);
        access_strided_idx = lane_in_quad_pair;
      }
      int access_contiguous =
          partition_contiguous_idx * Layout::PartitionShape::kContiguous +
          access_contiguous_idx;

      int access_strided = access_strided_idx;

      pointer_[i] = reinterpret_cast<AccessType const *>(ref.data()) +
                    access_contiguous + access_strided * stride_;
    }
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_pointer_offset(LongIndex offset) {

    byte_offset_ += offset * sizeof(Element);

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_tile_offset(TensorCoord const &tile_offset) {

    int contiguous_offset = tile_offset.contiguous();
    if (Shape::kContiguous ==
        Layout::PartitionShape::kContiguous * Layout::kElementsPerAccess) {
      if (tile_offset.contiguous() % 2) {
        CUTLASS_PRAGMA_UNROLL
        for (int i = 0; i < kPointerCount / 2; ++i) {
          AccessType const *tmp_pointer = pointer_[i];
          pointer_[i] = pointer_[i + kPointerCount / 2];
          pointer_[i + kPointerCount / 2] = tmp_pointer;
        }
      }
      contiguous_offset = (tile_offset.contiguous() >> 1) << 1;
    }

    int offset = (tile_offset.strided() * InstructionShape::kStrided) *
                     stride_ * Layout::kElementsPerAccess +
                 contiguous_offset * Shape::kContiguous;

    add_pointer_offset(offset);

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator++() {

    add_tile_offset({0, 1});

    if (kPartitionsK > 1) {
      ++k_group_idx_;
      // Jump to next stage
      if (k_group_idx_ == Policy::kGroupsPerTile) {
        k_group_idx_ = 0;
        add_tile_offset(
            {0, ((kPartitionsK - 1) * Policy::kGroupsPerTile)});
      }
    }

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator--() {
    byte_offset_ -= stride_ * InstructionShape::kStrided * sizeof(Element) *
                    Layout::kElementsPerAccess;

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator+=(TensorCoord const &tile_offset) {
    add_tile_offset(tile_offset);
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator-=(TensorCoord const &tile_offset) {
    add_tile_offset(-tile_offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const {

    load_with_byte_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      Index byte_offset) const {

    Array<unsigned, Policy::LdsmShape::kCount> *fetch_ptr = 
      reinterpret_cast<Array<unsigned, Policy::LdsmShape::kCount> *>(&frag);

    CUTLASS_PRAGMA_UNROLL
    for (int s = 0; s < Policy::LdsmIterations::kStrided; ++s) {

      CUTLASS_PRAGMA_UNROLL
      for (int c = 0; c < Policy::LdsmIterations::kContiguous; ++c) {

        int access_idx = c + s * Policy::LdsmIterations::kContiguous;

        AccessType const *source_ptr =
            pointer_[c % kPointerCount] +
            Layout::TileShape::kContiguous * (c / kPointerCount) +
            Policy::LdsmShape::kStrided * s * stride_;

        char const *source_byte_ptr = reinterpret_cast<char const *>(source_ptr) + byte_offset + byte_offset_;

        cutlass::arch::ldsm<layout::ColumnMajor, Policy::LdsmShape::kCount>(
          fetch_ptr[access_idx],
          source_byte_ptr
        );
      }
    }
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
      Fragment &frag,
      Index pointer_offset) const {
    load_with_byte_offset(frag, pointer_offset * sizeof(Element));
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset) const {
    load_with_byte_offset(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    load_with_byte_offset(frag, tile_offset, pointer_offset * sizeof(Element));
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index byte_offset) const {
    Index pointer_offset = 
      tile_offset.contiguous() * Shape::kContiguous / Layout::kElementsPerAccess + 
      tile_offset.strided() * InstructionShape::kStrided * stride_;

    byte_offset += sizeof(AccessType) * pointer_offset;

    load_with_byte_offset(frag, byte_offset);
  }

  CUTLASS_DEVICE
  void set_kgroup_index(int k_group) {
    // no op
  }
};

template <
    typename Shape_,
    Operand Operand_,
    typename Element_,
    typename InstructionShape_,
    int OpDelta_,
    int PartitionsK_>
class MmaTensorOpMultiplicandTileIterator<
    Shape_, Operand_, Element_,
    cutlass::layout::ColumnMajorTensorOpMultiplicandCongruous<
        sizeof_bits<Element_>::value, int(128 / sizeof(Element_))>,
    InstructionShape_, OpDelta_, 32, PartitionsK_> {
 public:

  using Shape = Shape_;

  static Operand const kOperand = Operand_;

  static_assert(kOperand == Operand::kA,
                "MmaTensorOpMultiplicandIterator for ColumnMajor Congruous may "
                "only be instantiated for A operand to warp-level Mma.");

  using Element = Element_;

  using Layout = cutlass::layout::ColumnMajorTensorOpMultiplicandCongruous<
      sizeof_bits<Element_>::value, int(128 / sizeof(Element_))>;

  using InstructionShape = InstructionShape_;

  static int const kOpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  using Base = MmaTensorOpMultiplicandTileIterator<
      layout::PitchLinearShape<Shape::kRow, Shape::kColumn>, kOperand, Element,
      layout::TensorOpMultiplicandCongruous<sizeof_bits<Element_>::value,
                                            int(128 / sizeof(Element_))>,
      layout::PitchLinearShape<InstructionShape::kRow,
                               InstructionShape::kColumn>,
      kOpDelta, kThreads, PartitionsK_>;

 public:

  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

private:

  Base iterator_;

public:
  
  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator() { }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator(
    TensorRef const &ref, 
    int lane_id
  ): iterator_({ref.data(), ref.stride()}, lane_id) {
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_pointer_offset(LongIndex offset) {

    iterator_.add_pointer_offset(offset);

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_tile_offset(TensorCoord const &tile_offset) {

    iterator_.add_tile_offset({tile_offset.row(), tile_offset.column()});

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator++() {

    ++iterator_;

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator--() {

    --iterator_;

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator+=(TensorCoord const &tile_offset) {
    add_tile_offset(PitchLinearCoord(tile_offset.row(), tile_offset.column()));
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator-=(TensorCoord const &tile_offset) {
    add_tile_offset(-PitchLinearCoord(tile_offset.row(), tile_offset.column()));
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const {

    iterator_.load(frag);
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
      Fragment &frag,
      Index pointer_offset) const {
    iterator_.load_with_pointer_offset(frag, pointer_offset);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(frag, byte_offset);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset) const {
    // TODO
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    // TODO
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(
      frag,
      {tile_offset.contiguous(), tile_offset.strided()},
      byte_offset);
  }

  CUTLASS_DEVICE
  void set_kgroup_index(int k_group) {
    iterator_.set_kgroup_index(k_group); 
  }
};


template <
    typename Shape_,
    Operand Operand_,
    typename Element_,
    typename InstructionShape_,
    int OpDelta_,
    int PartitionsK_>
class MmaTensorOpMultiplicandTileIterator<
    Shape_, Operand_, Element_,
    cutlass::layout::RowMajorTensorOpMultiplicandCongruous<
        sizeof_bits<Element_>::value, int(128 / sizeof(Element_))>,
    InstructionShape_, OpDelta_, 32, PartitionsK_> {
 public:

  using Shape = Shape_;

  static Operand const kOperand = Operand_;

  static_assert(kOperand == Operand::kB,
                "MmaTensorOpMultiplicandIterator for RowMajor Congruous may "
                "only be instantiated for B operand to warp-level Mma.");

  using Element = Element_;

  using Layout = cutlass::layout::RowMajorTensorOpMultiplicandCongruous<
      sizeof_bits<Element_>::value, int(128 / sizeof(Element_))>;

  using InstructionShape = InstructionShape_;

  static int const kOpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  using Base = MmaTensorOpMultiplicandTileIterator<
      layout::PitchLinearShape<Shape::kColumn, Shape::kRow>, kOperand, Element,
      layout::TensorOpMultiplicandCongruous<sizeof_bits<Element_>::value,
                                            int(128 / sizeof(Element_))>,
      layout::PitchLinearShape<InstructionShape::kColumn,
                               InstructionShape::kRow>,
      kOpDelta, kThreads, PartitionsK_>;

 public:

  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

private:

  Base iterator_;

public:
  
  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator() { }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator(
    TensorRef const &ref, 
    int lane_id
  ): iterator_({ref.data(), ref.stride()}, lane_id) {
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_pointer_offset(LongIndex offset) {

    iterator_.add_pointer_offset(offset);

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_tile_offset(TensorCoord const &tile_offset) {

    iterator_.add_tile_offset({tile_offset.column(), tile_offset.row()});

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator++() {

    ++iterator_;

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator--() {

    --iterator_;

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator+=(TensorCoord const &tile_offset) {
    add_tile_offset(PitchLinearCoord(tile_offset.column(), tile_offset.row()));
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator & operator-=(TensorCoord const &tile_offset) {
    add_tile_offset(-PitchLinearCoord(tile_offset.column(), tile_offset.row()));
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const {

    iterator_.load(frag);
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
      Fragment &frag,
      Index pointer_offset) const {
    iterator_.load_with_pointer_offset(frag, pointer_offset);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(frag, byte_offset);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset) const {
    // TODO
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    // TODO
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(
      frag,
      {tile_offset.strided(), tile_offset.contiguous()},
      byte_offset);
  }

  CUTLASS_DEVICE
  void set_kgroup_index(int k_group) {
    iterator_.set_kgroup_index(k_group); 
  }
};


template <
    typename Shape_,
    Operand Operand_,
    typename Element_,
    typename InstructionShape_,
    int OpDelta_,
    int Crosswise,
    int PartitionsK_>
class MmaTensorOpMultiplicandTileIterator<
    Shape_, Operand_, Element_,
    cutlass::layout::TensorOpMultiplicandCrosswise<sizeof_bits<Element_>::value,
                                                   Crosswise>,
    InstructionShape_, OpDelta_, 32, PartitionsK_> {
 public:
  using Shape = Shape_;

  static Operand const kOperand = Operand_;

  static_assert(kOperand == Operand::kA || kOperand == Operand::kB,
                "MmaTensorOpMultiplicandIterator may only be instantiated for "
                "A or B operands to warp-level Mma.");

  using Element = Element_;

  static int const kCrosswise = Crosswise;

  using Layout = cutlass::layout::TensorOpMultiplicandCrosswise<
      sizeof_bits<Element_>::value, kCrosswise>;

  using InstructionShape = InstructionShape_;

  static int const kOpDelta = OpDelta_;

  static int const kThreads = 32;

  static int const kPartitionsK = PartitionsK_;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  struct Policy {
    static_assert(
        !(Shape::kContiguous % InstructionShape::kContiguous),
        "Shape of warp-level Mma must be divisible by operator shape.");

    // Determine number of elements along outer dimension per individual LDSM op
    static int const kLdsmOpOuter = Layout::kElementsPerAccess;
    static int const kLdsmOpInner = 8;

    static_assert(!(Shape::kContiguous % kLdsmOpOuter),
                  "Shape of warp-level mma must be divisible by LDSM's "
                  "fundamental tile size.");

    static_assert(!(Shape::kStrided % kLdsmOpInner),
                  "Shape of warp-level mma must be divisible by LDSM's "
                  "fundamental tile size.");

    static int const LdsmShapeContiguous =
        InstructionShape::kContiguous / kLdsmOpOuter;
    static int const LdsmShapeStrided =
        ((4 / LdsmShapeContiguous * kLdsmOpInner) > Shape::kStrided)
            ? (Shape::kStrided / kLdsmOpInner)
            : (4 / LdsmShapeContiguous);
    using LdsmShape =
        layout::PitchLinearShape<LdsmShapeContiguous, LdsmShapeStrided>;

    using LdsmIterations =
        layout::PitchLinearShape<1, Shape::kStrided / kLdsmOpInner /
                                        LdsmShape::kStrided>;

    static int const kGroupsPerTile = Layout::TileShape::kContiguous /
                                      Layout::kFactor / LdsmShape::kContiguous;
  };

 private:
  static_assert(kOpDelta == 1,
                "Alternative arrangements not supported at present.");

  using AccessType = Array<Element, Layout::kElementsPerAccess>;

 public:
  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

 private:

  int sections_;

  Index stride_;

  AccessType const *pointer_;

  Index byte_offset_;

  int k_group_idx_;

 public:
  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator()
      : pointer_(nullptr),
        sections_(0),
        stride_(0),
        byte_offset_(0),
        k_group_idx_(0) {}

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator(TensorRef const &ref, int lane_id)
      : pointer_(reinterpret_cast<AccessType const *>(ref.data())),
        sections_(ref.stride(0) / kCrosswise),
        // stride_ = kCrosswise x sections_ x kFactor
        stride_(ref.stride(0) * Layout::kFactor / Layout::kElementsPerAccess),
        byte_offset_(0),
        k_group_idx_(0) {
    // Warp level iterator at most use double buffer to hide latency.  If there
    // are more than 2 sections, every stage should have more than 1 section.
    // TODO: refactor code after every case is implemented

    // Turing silicon requires all 32 threads in a warp provide valid addresses
    // even for LDSM.1 and LDSM.2
#if (defined(__CUDA_ARCH__) && (__CUDA_ARCH__ == 750))
    lane_id = lane_id % (Policy::LdsmShape::kCount * Policy::kLdsmOpInner);
#endif

    int lane_in_pair = (lane_id & 1);
    int lane_in_quad = (lane_id & 3);
    int lane_in_quad_pair = (lane_id & 7);
    int lane_in_quad_quad = (lane_id & 15);

    int partition_contiguous_idx = -1;
    int access_contiguous_idx = -1;
    int access_strided_idx = -1;

    if (Layout::kFactor == 4) {
      // Super Integer matrix multiply Interleaved-32

      int factor_in_partition =
          (Layout::PartitionShape::kContiguous * Layout::kFactor /
           Layout::TileShape::kContiguous);

      if (Policy::LdsmShape::kStrided == Policy::LdsmShape::kCount) {
        // Integer matrix multiply 8816  A/B
        partition_contiguous_idx = lane_in_quad / factor_in_partition;
        access_contiguous_idx = ((lane_in_pair * factor_in_partition) ^
                                 (lane_in_quad_quad / Layout::kFactor));
        access_strided_idx = lane_id / Layout::kFactor;
      }
    } else if (Layout::kFactor == 2) {
      // Super Matrix multiply kBlock = 32
      if (Policy::LdsmShape::kStrided == Policy::LdsmShape::kCount) {
        // (Q stands for 1 8x128bit block).
        // Q0
        // Q1
        // Q2
        // Q3
        // Four blocks are next to each other in the strided dimension.
        partition_contiguous_idx = (lane_id % Layout::kFactor);
        access_contiguous_idx = (lane_in_quad_pair / Layout::kFactor);
        access_strided_idx = lane_id / Layout::kFactor;
      }
    } else if (Layout::kFactor == 1) {
      // Super Matrix multiply kBlock = 64
      if (Policy::LdsmShape::kStrided == Policy::LdsmShape::kCount) {
        // Q0
        // Q1
        // Q2
        // Q3
        partition_contiguous_idx = (lane_in_quad_pair >> 2);
        access_contiguous_idx = lane_in_quad;
        access_strided_idx = lane_id;
      }
    }

    int access_contiguous =
        partition_contiguous_idx * Layout::PartitionShape::kContiguous +
        access_contiguous_idx;

    int access_strided = access_strided_idx;

    byte_offset_ = (access_contiguous + access_strided * stride_) *
                   sizeof_bits<Element>::value * Layout::kElementsPerAccess / 8;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_pointer_offset(LongIndex offset) {
    byte_offset_ += offset * sizeof_bits<Element>::value / 8;

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_tile_offset(
      TensorCoord const &tile_offset) {
    int whole_tiles = tile_offset.contiguous() / Policy::kGroupsPerTile;
    int k_groups_delta = tile_offset.contiguous() % Policy::kGroupsPerTile;

    byte_offset_ ^= k_groups_delta * sizeof_bits<Element>::value *
                    Layout::kElementsPerAccess / 8;
    pointer_ +=
        tile_offset.strided() * stride_ * Shape::kStrided / Layout::kFactor +
        whole_tiles * stride_ / sections_;
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator++() {

    // Integer matrix multiply 8816  Interleaved-32
    //   ^1 ^1
    // Matrix multiply 1688 kblock=32 || Integer matrix multiply 8816 kblock=64
    //   ^1 ^3 ^1 ^3
    // Matrix multiply 1688 kblock=64
    //   ^1 ^3 ^1 ^7 ^1 ^3 ^1 ^7
    if ((Policy::kGroupsPerTile / kPartitionsK) > 1) {
      int mask = ((Policy::kGroupsPerTile / kPartitionsK) == 8)
                     ? 3
                     : (((Policy::kGroupsPerTile / kPartitionsK) == 4) ? 1 : 0);

      if (((k_group_idx_ & mask) % 2) == 0)
        byte_offset_ ^= 1 * Policy::LdsmShape::kContiguous *
                        sizeof_bits<Element>::value *
                        Layout::kElementsPerAccess / 8;
      else if ((k_group_idx_ & mask) == 1)
        byte_offset_ ^= 3 * Policy::LdsmShape::kContiguous *
                        sizeof_bits<Element>::value *
                        Layout::kElementsPerAccess / 8;
      else if ((k_group_idx_ & mask) == 3)
        byte_offset_ ^= 7 * Policy::LdsmShape::kContiguous *
                        sizeof_bits<Element>::value *
                        Layout::kElementsPerAccess / 8;
    }

    k_group_idx_++;

    if (k_group_idx_ == (Policy::kGroupsPerTile / kPartitionsK)) {
      k_group_idx_ = 0;
      add_tile_offset({Policy::kGroupsPerTile, 0});
    }

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator--() { assert(0); }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator+=(
      TensorCoord const &tile_offset) {
    add_tile_offset(tile_offset);
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator-=(
      TensorCoord const &tile_offset) {
    add_tile_offset(-tile_offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const { load_with_byte_offset(frag, 0); }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      Index byte_offset) const {
    Array<unsigned, Policy::LdsmShape::kCount> *fetch_ptr =
        reinterpret_cast<Array<unsigned, Policy::LdsmShape::kCount> *>(&frag);

    CUTLASS_PRAGMA_UNROLL
    for (int s = 0; s < Policy::LdsmIterations::kStrided; ++s) {
      CUTLASS_PRAGMA_UNROLL
      for (int c = 0; c < Policy::LdsmIterations::kContiguous; ++c) {
        int access_idx = c + s * Policy::LdsmIterations::kContiguous;

        AccessType const *source_ptr =
            pointer_ + Policy::LdsmShape::kContiguous * c +
            Policy::kLdsmOpInner / Layout::kFactor *
                Policy::LdsmShape::kStrided * s * stride_;

        char const *source_byte_ptr =
            reinterpret_cast<char const *>(source_ptr) + byte_offset +
            byte_offset_;

        cutlass::arch::ldsm<layout::RowMajor, Policy::LdsmShape::kCount>(
            fetch_ptr[access_idx], source_byte_ptr);
      }
    }
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
      Fragment &frag,
      Index pointer_offset) const {
    load_with_byte_offset(frag, pointer_offset * sizeof(Element));
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset) const {
    load_with_byte_offset(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    load_with_byte_offset(frag, tile_offset, pointer_offset * sizeof(Element));
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index byte_offset) const {
    Index pointer_offset = tile_offset.contiguous() *
                               InstructionShape::kContiguous /
                               Layout::kElementsPerAccess +
                           tile_offset.strided() * Shape::kStrided * stride_;

    byte_offset += sizeof_bits<AccessType>::value * pointer_offset / 8;

    load_with_byte_offset(frag, byte_offset);
  }

  CUTLASS_DEVICE
  void set_kgroup_index(int k_group) {
    k_group_idx_ = k_group % (Policy::kGroupsPerTile / kPartitionsK);
  }
};


template <
    typename Shape_,
    Operand Operand_,
    typename Element_,
    typename InstructionShape_,
    int OpDelta_,
    int Crosswise,
    int PartitionsK_>
class MmaTensorOpMultiplicandTileIterator<
    Shape_, Operand_, Element_,
    cutlass::layout::ColumnMajorTensorOpMultiplicandCrosswise<
        sizeof_bits<Element_>::value, Crosswise>,
    InstructionShape_, OpDelta_, 32, PartitionsK_> {
 public:
  using Shape = Shape_;

  static Operand const kOperand = Operand_;

  static_assert(kOperand == Operand::kB,
                "MmaTensorOpMultiplicandIterator for ColumnMajor Crosswise may "
                "only be instantiated for B operand to warp-level Mma.");

  using Element = Element_;

  static int const kCrosswise = Crosswise;

  using Layout = cutlass::layout::ColumnMajorTensorOpMultiplicandCrosswise<
      sizeof_bits<Element_>::value, kCrosswise>;

  using InstructionShape = InstructionShape_;

  static int const kOpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  using Base = MmaTensorOpMultiplicandTileIterator<
      layout::PitchLinearShape<Shape::kRow, Shape::kColumn>, kOperand, Element,
      layout::TensorOpMultiplicandCrosswise<sizeof_bits<Element_>::value,
                                            kCrosswise>,
      layout::PitchLinearShape<InstructionShape::kRow,
                               InstructionShape::kColumn>,
      kOpDelta, kThreads, PartitionsK_>;

 public:
  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

 private:
  Base iterator_;

 public:
  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator() {}

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator(TensorRef const &ref, int lane_id)
      : iterator_({ref.data(), ref.stride()}, lane_id) {}

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_pointer_offset(LongIndex offset) {
    iterator_.add_pointer_offset(offset);

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_tile_offset(
      TensorCoord const &tile_offset) {
    iterator_.add_tile_offset({tile_offset.row(), tile_offset.column()});

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator++() {
    ++iterator_;

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator--() {
    --iterator_;

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator+=(
      TensorCoord const &tile_offset) {
    add_tile_offset(PitchLinearCoord(tile_offset.row(), tile_offset.column()));
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator-=(
      TensorCoord const &tile_offset) {
    add_tile_offset(-PitchLinearCoord(tile_offset.row(), tile_offset.column()));
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const { iterator_.load(frag); }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
      Fragment &frag,
      Index pointer_offset) const {
    iterator_.load_with_pointer_offset(frag, pointer_offset);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(frag, byte_offset);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset) const {
    // TODO
    assert(0);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    // TODO
    assert(0);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(
        frag, {tile_offset.contiguous(), tile_offset.strided()}, byte_offset);
  }

  CUTLASS_DEVICE
  void set_kgroup_index(int k_group) {
    iterator_.set_kgroup_index(k_group); 
  }
};


template <
    typename Shape_,
    Operand Operand_,
    typename Element_,
    typename InstructionShape_,
    int OpDelta_,
    int Crosswise,
    int PartitionsK_>
class MmaTensorOpMultiplicandTileIterator<
    Shape_, Operand_, Element_,
    cutlass::layout::RowMajorTensorOpMultiplicandCrosswise<
        sizeof_bits<Element_>::value, Crosswise>,
    InstructionShape_, OpDelta_, 32, PartitionsK_> {
 public:
  using Shape = Shape_;

  static Operand const kOperand = Operand_;

  static_assert(kOperand == Operand::kA,
                "MmaTensorOpMultiplicandIterator for RowMajor Crosswise may "
                "only be instantiated for A operand to warp-level Mma.");

  using Element = Element_;

  static int const kCrosswise = Crosswise;

  using Layout = cutlass::layout::RowMajorTensorOpMultiplicandCrosswise<
      sizeof_bits<Element_>::value, kCrosswise>;

  using InstructionShape = InstructionShape_;

  static int const kOpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  using Base = MmaTensorOpMultiplicandTileIterator<
      layout::PitchLinearShape<Shape::kColumn, Shape::kRow>, kOperand, Element,
      layout::TensorOpMultiplicandCrosswise<sizeof_bits<Element_>::value,
                                            kCrosswise>,
      layout::PitchLinearShape<InstructionShape::kColumn,
                               InstructionShape::kRow>,
      kOpDelta, kThreads, PartitionsK_>;

 public:
  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

 private:
  Base iterator_;

 public:
  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator() {}

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator(TensorRef const &ref, int lane_id)
      : iterator_({ref.data(), ref.stride()}, lane_id) {}

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_pointer_offset(LongIndex offset) {
    iterator_.add_pointer_offset(offset);

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &add_tile_offset(
      TensorCoord const &tile_offset) {
    iterator_.add_tile_offset({tile_offset.column(), tile_offset.row()});

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator++() {
    ++iterator_;

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator--() {
    --iterator_;

    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator+=(
      TensorCoord const &tile_offset) {
    add_tile_offset(PitchLinearCoord(tile_offset.column(), tile_offset.row()));
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpMultiplicandTileIterator &operator-=(
      TensorCoord const &tile_offset) {
    add_tile_offset(-PitchLinearCoord(tile_offset.column(), tile_offset.row()));
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const { iterator_.load(frag); }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
      Fragment &frag,
      Index pointer_offset) const {
    iterator_.load_with_pointer_offset(frag, pointer_offset);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(frag, byte_offset);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset) const {
    // TODO
    assert(0);
  }

  CUTLASS_DEVICE
  void load(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    // TODO
    assert(0);
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
      Fragment &frag,
      TensorCoord const &tile_offset,
      Index byte_offset) const {
    iterator_.load_with_byte_offset(
        frag, {tile_offset.strided(), tile_offset.contiguous()}, byte_offset);
  }

  CUTLASS_DEVICE
  void set_kgroup_index(int k_group) {
    iterator_.set_kgroup_index(k_group); 
  }
};

template <
    typename Shape_,
    typename Element_,
    typename Layout_,
    typename InstructionShape_,
    typename OpDelta_>
class MmaTensorOpAccumulatorTileIterator;


template <
    typename Shape_,
    typename Element_,
    typename InstructionShape_,
    typename OpDelta_>
class MmaTensorOpAccumulatorTileIterator<
    Shape_, Element_, cutlass::layout::RowMajor, InstructionShape_, OpDelta_> {
 public:

  using Shape = Shape_;

  static Operand const kOperand = Operand::kC;

  using Element = Element_;

  using Layout = cutlass::layout::RowMajor;

  using InstructionShape = InstructionShape_;

  using OpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  struct Policy {
    static_assert(
        !(Shape::kRow % InstructionShape::kM) &&
            !(Shape::kColumn % InstructionShape::kN),
        "Shape of warp-level Mma must be divisible by operator shape.");

    static_assert(platform::is_same<TensorCoord, MatrixCoord>::value,
      "Layouts must be defined for logical MatrixCoord coordinate space.");

    using MmaIterations = MatrixShape<Shape::kRow / InstructionShape::kM,
                                      Shape::kColumn / InstructionShape::kN>;
  };

private:

  // Assume accumulator tile is an arrangement of 8-by-8 tiles replicated over the entire
  // shape, with each quad mapped to one row and each thread mapped to 1/4 of the elements
  // of that row. The accumulators within one row are assumed to be consecutive.
 static int const kElementsPerAccess = InstructionShape::kN / 4;
 static int const kRowsPerTile = 8;
 static int const kAccumulatorRows = InstructionShape::kM / kRowsPerTile;

public:

  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

private:

  TensorRef ref_;

public:
  
  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator() { }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator(
    TensorRef const &ref, 
    int lane_id
  ):
    ref_(ref) {

    int quad = (lane_id >> 2);
    int lane_in_quad = (lane_id & 3);

    MatrixCoord lane_offset(quad, lane_in_quad * kElementsPerAccess);

    ref_.add_coord_offset(lane_offset);
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator &add_pointer_offset(LongIndex offset) {
    ref_.add_pointer_offset(offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator &add_tile_offset(TensorCoord const &tile_offset) {

    ref_.add_coord_offset(tile_offset * make_Coord(Shape::kRow, Shape::kColumn));

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator++() {
    // deliberate no-op
    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator--() {
    // deliberate no-op
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator+=(TensorCoord const &tile_offset) {
    add_tile_offset(tile_offset);
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator-=(TensorCoord const &tile_offset) {
    add_tile_offset(-tile_offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const {
    load_with_pointer_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
    Fragment &frag,                             
    Index pointer_offset) const {               
  
    TensorRef offset_ref(ref_);
    offset_ref.add_pointer_offset(pointer_offset);

    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Policy::MmaIterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int mma_m = 0; mma_m < Policy::MmaIterations::kRow; ++mma_m) {
        
        int mma_accum_start = kAccumulatorRows * kElementsPerAccess * 
          (mma_n * Policy::MmaIterations::kRow + mma_m);

        CUTLASS_PRAGMA_UNROLL
        for (int row = 0; row < kAccumulatorRows; ++row) {
          CUTLASS_PRAGMA_UNROLL
          for (int col = 0; col < kElementsPerAccess; ++col) {
            int accum_m = mma_m * InstructionShape::kM * OpDelta::kRow +
                          row * kRowsPerTile;
            int accum_n = mma_n * InstructionShape::kN * OpDelta::kColumn + col;

            frag[mma_accum_start + row * kElementsPerAccess + col] = offset_ref.at({accum_m, accum_n});
          }
        }
      }
    }
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
    Fragment &frag,                             
    Index byte_offset) const {                  

    load_with_pointer_offset(byte_offset / sizeof(Element));
  }

  CUTLASS_DEVICE
  void load(
    Fragment &frag,                             
    TensorCoord const &tile_offset) const {     

    load(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void load(
    Fragment &frag,                             
    TensorCoord const &tile_offset,             
    Index pointer_offset) const {               

    load_with_pointer_offset(frag, ref_.offset(tile_offset) + pointer_offset);
  }

  CUTLASS_HOST_DEVICE
  void store(Fragment const &frag) const {
    store_with_pointer_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void store_with_pointer_offset(
    Fragment const &frag,                       
    Index pointer_offset) const {               
  
    TensorRef offset_ref(ref_);
    offset_ref.add_pointer_offset(pointer_offset);

    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Policy::MmaIterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int mma_m = 0; mma_m < Policy::MmaIterations::kRow; ++mma_m) {
        
        int mma_accum_start = kAccumulatorRows * kElementsPerAccess * 
          (mma_n * Policy::MmaIterations::kRow + mma_m);

        CUTLASS_PRAGMA_UNROLL
        for (int row = 0; row < kAccumulatorRows; ++row) {
          CUTLASS_PRAGMA_UNROLL
          for (int col = 0; col < kElementsPerAccess; ++col) {
            int accum_m = mma_m * InstructionShape::kM * OpDelta::kRow +
                          row * kRowsPerTile;
            int accum_n = mma_n * InstructionShape::kN * OpDelta::kColumn + col;
            int idx = mma_accum_start + row * kElementsPerAccess + col;

            offset_ref.at({accum_m, accum_n}) = frag[idx];
          }
        }
      }
    }
  }

  CUTLASS_DEVICE
  void store_with_byte_offset(
    Fragment const &frag,                       
    Index byte_offset) const {                  

    store_with_pointer_offset(byte_offset / sizeof(Element));
  }

  CUTLASS_DEVICE
  void store(
    Fragment &frag,                             
    TensorCoord const &tile_offset) const {     

    store(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void store(
      Fragment const &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    store_with_pointer_offset(frag, ref_.offset(tile_offset) + pointer_offset);
  }
};


template <
    typename Shape_,
    typename Element_,
    typename InstructionShape_,
    typename OpDelta_>
class MmaTensorOpAccumulatorTileIterator<Shape_, Element_,
                                         cutlass::layout::ColumnMajor,
                                         InstructionShape_, OpDelta_> {
 public:

  using Shape = Shape_;

  static Operand const kOperand = Operand::kC;

  using Element = Element_;

  using Layout = cutlass::layout::ColumnMajor;

  using InstructionShape = InstructionShape_;

  using OpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  struct Policy {
    static_assert(
        !(Shape::kRow % InstructionShape::kM) &&
            !(Shape::kColumn % InstructionShape::kN),
        "Shape of warp-level Mma must be divisible by operator shape.");

    static_assert(platform::is_same<TensorCoord, MatrixCoord>::value,
      "Layouts must be defined for logical MatrixCoord coordinate space.");

    using MmaIterations = MatrixShape<Shape::kRow / InstructionShape::kM,
                                      Shape::kColumn / InstructionShape::kN>;
  };

private:

  // Assume accumulator tile is an arrangement of 8-by-8 tiles replicated over the entire
  // shape, with each quad mapped to one row and each thread mapped to 1/4 of the elements
  // of that row. The accumulators within one row are assumed to be consecutive.
 static int const kElementsPerAccess = InstructionShape::kN / 4;
 static int const kRowsPerTile = 8;
 static int const kAccumulatorRows = InstructionShape::kM / kRowsPerTile;

public:

  //
  // Derived quantities
  //

  using Fragment = Array<Element, Shape::kCount / kThreads>;

private:

  TensorRef ref_;

public:
  
  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator() { }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator(
    TensorRef const &ref, 
    int lane_id
  ):
    ref_(ref) {

    int quad = (lane_id >> 2);
    int lane_in_quad = (lane_id & 3);

    MatrixCoord lane_offset(quad, lane_in_quad * kElementsPerAccess);

    ref_.add_coord_offset(lane_offset);
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator &add_pointer_offset(LongIndex offset) {
    ref_.add_pointer_offset(offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator &add_tile_offset(TensorCoord const &tile_offset) {

    ref_.add_coord_offset(tile_offset * make_Coord(Shape::kRow, Shape::kColumn));

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator++() {
    // deliberate no-op
    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator--() {
    // deliberate no-op
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator+=(TensorCoord const &tile_offset) {
    add_tile_offset(tile_offset);
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator-=(TensorCoord const &tile_offset) {
    add_tile_offset(-tile_offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const {
    load_with_pointer_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
    Fragment &frag,                             
    Index pointer_offset) const {               
  
    TensorRef offset_ref(ref_);
    offset_ref.add_pointer_offset(pointer_offset);

    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Policy::MmaIterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int mma_m = 0; mma_m < Policy::MmaIterations::kRow; ++mma_m) {
        
        int mma_accum_start = kAccumulatorRows * kElementsPerAccess * 
          (mma_n * Policy::MmaIterations::kRow + mma_m);

        CUTLASS_PRAGMA_UNROLL
        for (int row = 0; row < kAccumulatorRows; ++row) {
          CUTLASS_PRAGMA_UNROLL
          for (int col = 0; col < kElementsPerAccess; ++col) {
            int accum_m = mma_m * InstructionShape::kM * OpDelta::kRow +
                          row * kRowsPerTile;
            int accum_n = mma_n * InstructionShape::kN * OpDelta::kColumn + col;
            int idx = mma_accum_start + row * kElementsPerAccess + col;

            frag[idx] = offset_ref.at({accum_m, accum_n});
          }
        }
      }
    }
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
    Fragment &frag,                             
    Index byte_offset) const {                  

    load_with_pointer_offset(byte_offset / sizeof(Element));
  }

  CUTLASS_DEVICE
  void load(
    Fragment &frag,                             
    TensorCoord const &tile_offset) const {     

    load(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void load(
    Fragment &frag,                             
    TensorCoord const &tile_offset,             
    Index pointer_offset) const {               

    load_with_pointer_offset(frag, ref_.offset(tile_offset) + pointer_offset);
  }

  CUTLASS_HOST_DEVICE
  void store(Fragment const &frag) const {
    store_with_pointer_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void store_with_pointer_offset(
    Fragment const &frag,                       
    Index pointer_offset) const {               
  
    TensorRef offset_ref(ref_);
    offset_ref.add_pointer_offset(pointer_offset);

    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Policy::MmaIterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int mma_m = 0; mma_m < Policy::MmaIterations::kRow; ++mma_m) {
        
        int mma_accum_start = kAccumulatorRows * kElementsPerAccess * 
          (mma_n * Policy::MmaIterations::kRow + mma_m);

        CUTLASS_PRAGMA_UNROLL
        for (int row = 0; row < kAccumulatorRows; ++row) {
          CUTLASS_PRAGMA_UNROLL
          for (int col = 0; col < kElementsPerAccess; ++col) {
            int accum_m = mma_m * InstructionShape::kM * OpDelta::kRow +
                          row * kRowsPerTile;
            int accum_n = mma_n * InstructionShape::kN * OpDelta::kColumn + col;
            int idx = mma_accum_start + row * kElementsPerAccess + col;
            
            offset_ref.at({accum_m, accum_n}) = frag[idx];
          }
        }
      }
    }
  }

  CUTLASS_DEVICE
  void store_with_byte_offset(
    Fragment const &frag,                       
    Index byte_offset) const {                  

    store_with_pointer_offset(byte_offset / sizeof(Element));
  }

  CUTLASS_DEVICE
  void store(
    Fragment &frag,                             
    TensorCoord const &tile_offset) const {     

    store(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void store(
      Fragment const &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    store_with_pointer_offset(frag, ref_.offset(tile_offset) + pointer_offset);
  }
};



template <
    typename Shape_,
    typename Element_,
    typename InstructionShape_,
    typename OpDelta_,
    int InterleavedN>
class MmaTensorOpAccumulatorTileIterator<
    Shape_, Element_, cutlass::layout::ColumnMajorInterleaved<InterleavedN>,
    InstructionShape_, OpDelta_> {
 public:

  using Shape = Shape_;

  static Operand const kOperand = Operand::kC;

  using Element = Element_;

  using Layout = cutlass::layout::ColumnMajorInterleaved<InterleavedN>;

  using InstructionShape = InstructionShape_;

  using OpDelta = OpDelta_;

  static int const kThreads = 32;

  using TensorRef = TensorRef<Element, Layout>;

  using Index = typename TensorRef::Index;

  using LongIndex = typename TensorRef::LongIndex;

  using TensorCoord = typename TensorRef::TensorCoord;

  struct Policy {
    static_assert(
        !(Shape::kRow % InstructionShape::kM) &&
            !(Shape::kColumn % InstructionShape::kN),
        "Shape of warp-level Mma must be divisible by operator shape.");

    static_assert(platform::is_same<TensorCoord, MatrixCoord>::value,
      "Layouts must be defined for logical MatrixCoord coordinate space.");

    using MmaIterations = MatrixShape<Shape::kRow / InstructionShape::kM,
                                      Shape::kColumn / InstructionShape::kN>;
  };

private:

  static int const kElementsPerAccess = 2;

public:

  //
  // Derived quantities
  //

  using AccessType = Array<Element, kElementsPerAccess>;

  using Fragment = Array<Element, Shape::kCount / kThreads>;

private:

  TensorRef ref_;

public:
  
  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator() { }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator(
    TensorRef const &ref, 
    int lane_id
  ):
    ref_(ref) {

    int quad = (lane_id >> 2);
    int lane_in_quad = (lane_id & 3);

    MatrixCoord lane_offset(quad, lane_in_quad * kElementsPerAccess);

    ref_.add_coord_offset(lane_offset);
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator &add_pointer_offset(LongIndex offset) {
    ref_.add_pointer_offset(offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator &add_tile_offset(TensorCoord const &tile_offset) {

    ref_.add_coord_offset(tile_offset * make_Coord(Shape::kRow, Shape::kColumn));

    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator++() {
    // deliberate no-op
    return *this;
  }

  CUTLASS_HOST_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator--() {
    // deliberate no-op
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator+=(TensorCoord const &tile_offset) {
    add_tile_offset(tile_offset);
    return *this;
  }

  CUTLASS_DEVICE
  MmaTensorOpAccumulatorTileIterator & operator-=(TensorCoord const &tile_offset) {
    add_tile_offset(-tile_offset);
    return *this;
  }

  CUTLASS_HOST_DEVICE
  void load(Fragment &frag) const {
    load_with_pointer_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void load_with_pointer_offset(
    Fragment &frag,                             
    Index pointer_offset) const {               
  
    TensorRef offset_ref(ref_);
    offset_ref.add_pointer_offset(pointer_offset);

    AccessType* frag_ptr = reinterpret_cast<AccessType *>(&frag);

    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Policy::MmaIterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int mma_m = 0; mma_m < Policy::MmaIterations::kRow; ++mma_m) {
        int accum_m = mma_m * InstructionShape::kM;
        int accum_n = mma_n * InstructionShape::kN;

        int idx = mma_m + mma_n * Policy::MmaIterations::kRow;

        AccessType* access_ptr = reinterpret_cast<AccessType *>(offset_ref.data() +
          offset_ref.offset(TensorCoord(accum_m, accum_n)));

        frag_ptr[idx] = access_ptr[0];
      }
    }
  }

  CUTLASS_DEVICE
  void load_with_byte_offset(
    Fragment &frag,                             
    Index byte_offset) const {                  

    load_with_pointer_offset(byte_offset / sizeof(Element));
  }

  CUTLASS_DEVICE
  void load(
    Fragment &frag,                             
    TensorCoord const &tile_offset) const {     

    load(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void load(
    Fragment &frag,                             
    TensorCoord const &tile_offset,             
    Index pointer_offset) const {               

    load_with_pointer_offset(frag, ref_.offset(tile_offset) + pointer_offset);
  }

  CUTLASS_HOST_DEVICE
  void store(Fragment const &frag) const {
    store_with_pointer_offset(frag, 0);
  }

  CUTLASS_DEVICE
  void store_with_pointer_offset(
    Fragment const &frag,                       
    Index pointer_offset) const {               
  
    TensorRef offset_ref(ref_);
    offset_ref.add_pointer_offset(pointer_offset);

    AccessType const *frag_ptr = reinterpret_cast<AccessType const*>(&frag);

    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Policy::MmaIterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int mma_m = 0; mma_m < Policy::MmaIterations::kRow; ++mma_m) {
        int accum_m = mma_m * InstructionShape::kM;
        int accum_n = mma_n * InstructionShape::kN;

        int idx = mma_m + mma_n * Policy::MmaIterations::kRow;

  AccessType* access_ptr = reinterpret_cast<AccessType *>(offset_ref.data() +
         offset_ref.offset(TensorCoord(accum_m, accum_n)));

        access_ptr[0] = frag_ptr[idx];         
      }
    }
  }

  CUTLASS_DEVICE
  void store_with_byte_offset(
    Fragment const &frag,                       
    Index byte_offset) const {                  

    store_with_pointer_offset(byte_offset / sizeof(Element));
  }

  CUTLASS_DEVICE
  void store(
    Fragment &frag,                             
    TensorCoord const &tile_offset) const {     

    store(frag, tile_offset, 0);
  }

  CUTLASS_DEVICE
  void store(
      Fragment const &frag,
      TensorCoord const &tile_offset,
      Index pointer_offset) const {
    store_with_pointer_offset(frag, ref_.offset(tile_offset) + pointer_offset);
  }
};

} // namespace warp
} // namespace gemm
} // namespace cutlass