matrix.h

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/*! \file
    \brief Defines layout functions used by TensorRef and derived classes. 

    Layout functions map logical coordinates to linear memory. They often require additional
    data to describe strides between elements.

    Layout functions must implement all members in the public interface of IdentityTensorLayout<>
    defined in cutlass/tensor_ref.h.
*/
#pragma once

#include "cute/layout.hpp"

#include "cutlass/cutlass.h"
#include "cutlass/fast_math.h"
#include "cutlass/matrix_coord.h"
#include "cutlass/pitch_linear_coord.h"

namespace cutlass {
namespace layout {

/////////////////////////////////////////////////////////////////////////////////////////////////
//
// Defines data layouts of various matrix formats usable by TensorRef and other classes.
//
/////////////////////////////////////////////////////////////////////////////////////////////////

/// Mapping function for row-major matrices.
class RowMajor {
public:
  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Constructor
  CUTLASS_HOST_DEVICE
  RowMajor(LongIndex ldm = 0): stride_(ldm) { }

  /// Ctor
  CUTLASS_HOST_DEVICE
  RowMajor(Stride stride): stride_(stride) { }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static RowMajor packed(MatrixCoord const &extent) {
    return RowMajor(extent.column());
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    return LongIndex(coord.row()) * LongIndex(stride_[0]) + coord.column();
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {
    return MatrixCoord(Index(offset / stride_[0]), Index(offset % stride_[0]));
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return LongIndex(extent.row()) * LongIndex(stride_[0]);
  }

  CUTLASS_HOST_DEVICE
  cute::Layout<cute::Shape<int, int>, cute::Stride<int64_t, cute::Int<1> > > 
  to_cute_layout(MatrixCoord const &extent) const {
    return cute::Layout<cute::Shape<int, int>, cute::Stride<int64_t, cute::Int<1> > >{
      {extent[0], extent[1]},
      {stride(0), cute::Int<1>{}}
    };
  }
};

/// Mapping function for column-major matrices.
class ColumnMajor {
public:
  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  ColumnMajor(LongIndex ldm = 0): stride_(ldm) { }
  
  /// Ctor
  CUTLASS_HOST_DEVICE
  ColumnMajor(Stride stride): stride_(stride) { }


  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static ColumnMajor packed(MatrixCoord const &extent) {
    return ColumnMajor(extent.row());
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    return LongIndex(coord.column()) * LongIndex(stride_[0]) + coord.row();
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {
    return MatrixCoord(Index(offset % stride_[0]), Index(offset / stride_[0]));
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return LongIndex(extent.column()) * LongIndex(stride_[0]);
  }

  CUTLASS_HOST_DEVICE
  cute::Layout<cute::Shape<int, int>, cute::Stride< cute::Int<1>, int64_t> > 
  to_cute_layout(MatrixCoord const &extent) const {
    return cute::Layout<cute::Shape<int, int>, cute::Stride<cute::Int<1>, int64_t> >{
      {extent[0], extent[1]},
      {cute::Int<1>{}, stride(0)}
    };
  }
};

/// Mapping function for interleaved matrices. Matrix is structured
/// as row-major arrangement of fixed-size columns.
template <int Interleave>
struct RowMajorInterleaved {
  
  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

  /// Size of interleaved columns
  static int const kInterleave = Interleave;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  RowMajorInterleaved(LongIndex ldm = 0): stride_(ldm) { }
  
  /// Ctor
  CUTLASS_HOST_DEVICE
  RowMajorInterleaved(Stride stride): stride_(stride) { }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static RowMajorInterleaved packed(MatrixCoord const &extent) {
    return RowMajorInterleaved(extent.column() * kInterleave);
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    Index row_major = coord.row() / kInterleave;
    Index row_minor = coord.row() % kInterleave;
    return LongIndex(row_major) * LongIndex(stride_[0]) + LongIndex(coord.column()) * kInterleave + row_minor;
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {

    Index row_major = Index(offset / stride_[0]);
    Index residual = Index(offset % stride_[0]);

    Index column = residual / kInterleave;
    Index row_minor =  residual % kInterleave;

    return MatrixCoord(row_major * kInterleave + row_minor, column);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return (extent.row() + kInterleave - 1) / kInterleave * stride_[0];
  }
};

/// Mapping function for interleaved matrices. Matrix is structured
/// as column-major arrangement of fixed-size rows.
template <int Interleave>
struct ColumnMajorInterleaved {
  
  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

  /// Size of interleaved columns
  static int const kInterleave = Interleave;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  ColumnMajorInterleaved(LongIndex ldm = 0): stride_(ldm) { }
  
  /// Ctor
  CUTLASS_HOST_DEVICE
  ColumnMajorInterleaved(Stride stride): stride_(stride) { }


  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static ColumnMajorInterleaved packed(MatrixCoord const &extent) {
    return ColumnMajorInterleaved(extent.row() * kInterleave);
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    Index column_major = coord.column() / kInterleave;
    Index column_minor = coord.column() % kInterleave;
    return LongIndex(column_major) * LongIndex(stride_[0]) + LongIndex(coord.row()) * kInterleave + column_minor;
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {

    Index column_major = Index(offset / stride_[0]);
    Index residual = Index(offset % stride_[0]);

    Index row = residual / kInterleave;
    Index column_minor =  residual % kInterleave;

    return MatrixCoord(row, column_major * kInterleave + column_minor);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return (extent.column() + kInterleave - 1) / kInterleave * stride_[0];
  }
};

/// Enumerated type for canonical pitch-linear matrix layouts
enum class Matrix {
  kColumnMajor,       ///< leading dimension refers to stride between columns; stride along rows is 1
  kRowMajor           ///< leading dimension refers to stride between rows; stride along columns is 1
};

/// Mapping function for scenario in which layout is row-major or column-major but this information
/// is only available at runtime.
struct ContiguousMatrix {

  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

  /// Enumerated type indicating canonical matrix layout
  Matrix layout_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  ContiguousMatrix(
    Index ldm = 0, 
    Matrix layout = Matrix::kColumnMajor
  ):
    stride_(ldm), layout_(layout) { }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static ContiguousMatrix packed(
    MatrixCoord const &extent, 
    Matrix layout = Matrix::kColumnMajor) {

    Index ldm = 0;
    if (layout == Matrix::kColumnMajor) {
      ldm = extent.row();
    }
    else if (layout == Matrix::kRowMajor) {
      ldm = extent.column();
    }
    return ContiguousMatrix(ldm, layout);
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    if (layout_ == Matrix::kColumnMajor) {
      return coord.row() + coord.column() * stride_[0];
    }
    else if (layout_ == Matrix::kRowMajor) {
      return coord.row() * stride_[0] + coord.column();
    }
    else {
      // degenerate case
      return 0;
    }
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {
    // TODO
    return MatrixCoord(0, 0);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    if (layout_ == Matrix::kColumnMajor) {
      return stride_[0] * extent.column();
    }
    else if (layout_ == Matrix::kRowMajor) {
      return stride_[0] * extent.row();
    }
    else {
      // degenerate case
      return 0;
    }
  }
};

/////////////////////////////////////////////////////////////////////////////////////////////////

/// Mapping function for scenario in which both rows and columns are separated by a stride.
template <int Rank>
struct AffineRankN {

  /// Logical rank of tensor
  static int const kRank = Rank;

  /// Rank of stride vector
  static int const kStrideRank = kRank;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = Coord<kRank, Index>;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRankN(
    Stride const &stride = Stride()
  ):
    stride_(stride) { }

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRankN(
    Coord<kRank/2, LongIndex> const &stride_m,
    Coord<kRank/2, LongIndex> const &stride_n
  ) { 

    // Concatenate the strides
    CUTLASS_PRAGMA_UNROLL
    for (int m = 0; m < kRank/2; ++m) {
      stride_[m] = stride_m[m];
    }

    CUTLASS_PRAGMA_UNROLL
    for (int n = 0; n < kRank/2; ++n) {
      stride_[n + kRank/2] = stride_n[n];
    }
  }

  /// Ctor for N = 2
  CUTLASS_HOST_DEVICE
  AffineRankN(
    LongIndex const &stride_m,
    LongIndex const &stride_n
  ) { 
      stride_[0] = stride_m;
      stride_[1] = stride_n;
  }

  /// Ctor for N = 2
  CUTLASS_HOST_DEVICE
  AffineRankN(
    LongIndex const &stride
  ) { 
      stride_[0] = stride;
      stride_[1] = 1;
  }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static AffineRankN packed(TensorCoord const &extent) {
    
    AffineRankN layout;
    layout.stride_[kRank - 1] = 1;

    CUTLASS_PRAGMA_UNROLL
    for (int i = kRank - 1; i > 0; --i) {
      layout.stride_[i - 1] = layout.stride_[i] * extent[i];
    }

    return layout;
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(TensorCoord const &coord) const {
    return dot(coord, stride_);
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  TensorCoord inverse(LongIndex offset) const {
    // TODO
    return TensorCoord();
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(TensorCoord const &extent) const {
    int idx = stride_.max_dim_index();
    return extent[idx] * stride_[idx];
  }
};

/// Mapping function for scenario in which both rows and columns are separated by a stride.
/// Row stride is smaller than column stride in AffineRank2ColumnMajor.
struct AffineRank2ColumnMajor {

  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 2;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRank2ColumnMajor(
    Stride const &stride = Stride()
  ):
    stride_(stride) { }

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRank2ColumnMajor(
    LongIndex row_stride,           ///< stride between elements in consecutive rows
    LongIndex column_stride         ///< stride between elements in consecutive columns
  )
    { stride_[0] = row_stride; stride_[1] = column_stride;}

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRank2ColumnMajor(
    LongIndex stride
  )
    { stride_[0] = 1; stride_[1] = stride;}

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static AffineRank2ColumnMajor packed(MatrixCoord const &extent) {
    return AffineRank2ColumnMajor(1, extent.row());
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    return dot(coord, stride_);
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {
    // TODO
    return MatrixCoord(0, 0);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return extent.column() * stride_[1];
  }
};

/// Mapping function for scenario in which both rows and columns are separated by a stride.
/// Column stride is smaller than row stride in AffineRank2RowMajor.
struct AffineRank2RowMajor {

  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 2;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRank2RowMajor(
    Stride const &stride = Stride()
  ):
    stride_(stride) { }

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRank2RowMajor(
    LongIndex row_stride,           ///< stride between elements in consecutive rows
    LongIndex column_stride         ///< stride between elements in consecutive columns
  ) { stride_[0] = row_stride; stride_[1] = column_stride;}

  /// Ctor
  CUTLASS_HOST_DEVICE
  AffineRank2RowMajor(
    LongIndex stride
  ) { stride_[0] = stride; stride_[1] = 1;}

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static AffineRank2RowMajor packed(MatrixCoord const &extent) {
    return AffineRank2RowMajor(1, extent.row());
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    return dot(coord, stride_);
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {
    // TODO
    return MatrixCoord(0, 0);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return extent.row() * stride_[0];
  }
};

/////////////////////////////////////////////////////////////////////////////////////////////////

// Utility functions to convert stride_factor to the strides used by the Affine2 layout.
//
// stride_factor is the logical distance between two coorinates.
//
// All Coodinates used here are matrix coordinates.  stride[0] and extent[0] are for the
// rows.  stride[1] and extent[1] are for the columns.
template <typename Affine2Layout>
  struct Affine2Layout_Factory {
  CUTLASS_HOST_DEVICE
  static Affine2Layout layout_factory(cutlass::Coord<2> const &extent, typename Affine2Layout::Stride stride_factor) {
    return Affine2Layout::packed(extent);
  }
};

template <>
struct Affine2Layout_Factory<cutlass::layout::AffineRank2ColumnMajor> {
CUTLASS_HOST_DEVICE
static cutlass::layout::AffineRank2ColumnMajor layout_factory(
  cutlass::Coord<2> const &extent,
  typename cutlass::layout::AffineRank2ColumnMajor::Stride stride_factor) {
    return cutlass::layout::AffineRank2ColumnMajor({ stride_factor[0], stride_factor[0] * stride_factor[1] * extent[0] });
  }
};

template <>
struct Affine2Layout_Factory<cutlass::layout::AffineRank2RowMajor> {
CUTLASS_HOST_DEVICE
static cutlass::layout::AffineRank2RowMajor layout_factory(
  cutlass::Coord<2> const &extent,
  typename cutlass::layout::AffineRank2RowMajor::Stride stride_factor) {
    return cutlass::layout::AffineRank2RowMajor({ stride_factor[0] * stride_factor[1] * extent[1], stride_factor[1] });
  }
};

// The base layout cutlass::layout::AffineRankN<2> is similar to AffineRank2ColumnMajor
template <>
struct Affine2Layout_Factory<cutlass::layout::AffineRankN<2>> {
CUTLASS_HOST_DEVICE
static cutlass::layout::AffineRankN<2> layout_factory(
  cutlass::Coord<2> const &extent,
  typename cutlass::layout::AffineRankN<2>::Stride stride_factor) {
    return cutlass::layout::AffineRankN<2>({ stride_factor[0], stride_factor[0] * stride_factor[1] * extent[0] });
  }
};

/////////////////////////////////////////////////////////////////////////////////////////////////

/// Mapping function for block-linear matrices. Matrix is structured
/// as column-major arrangement of 2D tiles (that are column-major).
template <int BlockRows, int BlockColumns>
struct ColumnMajorBlockLinear {
  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

  /// Size of a block in rows
  static int const kBlockRows = BlockRows;

  /// Size of a block in columns
  static int const kBlockColumns = BlockColumns;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  ColumnMajorBlockLinear(Index ldm = 0): stride_(ldm) { }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static ColumnMajorBlockLinear packed(MatrixCoord const &extent) {
    return ColumnMajorBlockLinear(extent.row() * kBlockRows * kBlockColumns);
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    return 
      (coord.row() % kBlockRows) + 
      (coord.column() % kBlockColumns) * kBlockRows +
      (coord.row() / kBlockRows) * kBlockRows * kBlockColumns +
      (coord.column() / kBlockColumns) * stride_[0];
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {

    // TODO
    return MatrixCoord(0, 0);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }

  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return (extent.column() + kBlockColumns - 1) / kBlockColumns * stride_[0];
  }
};

/// Mapping function for block-linear matrices. Matrix is structured
/// as row-major arrangement of 2D tiles (that are row-major)
template <int BlockRows, int BlockColumns>
struct RowMajorBlockLinear {
  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 1;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, LongIndex>;

  /// Size of a block in rows
  static int const kBlockRows = BlockRows;

  /// Size of a block in columns
  static int const kBlockColumns = BlockColumns;

private:
  //
  // Data members
  //

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  RowMajorBlockLinear(Index ldm = 0): stride_(ldm) { }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static RowMajorBlockLinear packed(MatrixCoord const &extent) {
    return RowMajorBlockLinear(extent.column() * kBlockRows * kBlockColumns);
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    return 
      (coord.column() % kBlockColumns) +
      (coord.row() % kBlockRows) * kBlockColumns +
      (coord.column() / kBlockColumns) * kBlockRows * kBlockColumns +
      (coord.row() / kBlockRows) * stride_[0];
  }

  /// Inverse of layout function, mapping linear offset to logical coordinate
  CUTLASS_HOST_DEVICE
  MatrixCoord inverse(LongIndex offset) const {
    // TODO
    return MatrixCoord(0, 0);
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }
  
  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    return (extent.row() + kBlockRows - 1) / kBlockRows * stride_[0];
  }
};

/////////////////////////////////////////////////////////////////////////////////////////////////

struct GeneralMatrix {

  /// Logical rank of tensor
  static int const kRank = 2;

  /// Rank of stride vector
  static int const kStrideRank = 2;

  /// Index type used for coordinates
  using Index = int32_t;

  /// Long index type used for offsets
  using LongIndex = int64_t;

  /// Logical coordinate
  using TensorCoord = MatrixCoord;

  /// Stride vector
  using Stride = Coord<kStrideRank, Index>;

private:
  //
  // Data members
  //

  Matrix layout_id_;

  /// Stride data member
  Stride stride_;

public:
  //
  // Methods
  //

  /// Ctor
  CUTLASS_HOST_DEVICE
  GeneralMatrix(): layout_id_(Matrix::kColumnMajor), stride_(make_Coord(0, 1)) { }

  /// Ctor
  CUTLASS_HOST_DEVICE
  GeneralMatrix(
    Matrix layout_id, 
    Index ldm, 
    Index interleave): layout_id_(layout_id), stride_(make_Coord(ldm, interleave)) { }

  /// Helper returns a layout to a tightly packed tensor
  CUTLASS_HOST_DEVICE
  static GeneralMatrix packed(
    MatrixCoord const &extent, 
    Matrix layout_id = Matrix::kColumnMajor, 
    Index interleave = 1) {

    Index c;
    if (layout_id == Matrix::kRowMajor) {
      c = extent.column();
    }
    else {
      c = extent.row();
    }

    Index ldm = c * interleave;

    return GeneralMatrix(layout_id, ldm, interleave);
  }

  /// Returns the offset of a coordinate in linear memory. 
  /// Assumes coordinate has convention (row, column)
  CUTLASS_HOST_DEVICE
  LongIndex operator()(MatrixCoord const &coord) const {
    Index c, s;
    if (layout_id_ == Matrix::kRowMajor) {
      c = coord.column();
      s = coord.row();
    }
    else {
      s = coord.column();
      c = coord.row();
    }

    Index v = s / stride_[1];
    Index residual = (s % stride_[1]);

    return LongIndex(c) * LongIndex(stride_[1]) + LongIndex(v) * LongIndex(stride_[0]) + residual;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride stride() const {
    return stride_;
  }

  CUTLASS_HOST_DEVICE
  Matrix layout_id() const {
    return layout_id_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  Stride & stride() {
    return stride_;
  }

  CUTLASS_HOST_DEVICE
  Matrix & layout_id() {
    return layout_id_;
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index stride(int idx) const {
    return stride_[idx];
  }

  /// Returns the stride of the layout
  CUTLASS_HOST_DEVICE
  typename Stride::Index & stride(int idx) {
    return stride_[idx];
  }
  
  /// Compute the number of contiguous elements needed to store a tensor with the given size
  CUTLASS_HOST_DEVICE
  LongIndex capacity(MatrixCoord const &extent) const {
    Index s;
    if (layout_id_ == Matrix::kRowMajor) {
      s = extent.row();
    }
    else {
      s = extent.column();
    }

    Index v = Index((s + stride_[1] - 1) / stride_[1]);
    return LongIndex(v) * LongIndex(stride_[0]);
  }
};

/////////////////////////////////////////////////////////////////////////////////////////////////

/// Defines transposes of matrix layouts
template <typename Layout>
struct LayoutTranspose;

/// Transpose of row-major is column-major
template <>
struct LayoutTranspose<layout::RowMajor> {
  using type = layout::ColumnMajor;
};

/// Transpose of column-major is row-major
template <>
struct LayoutTranspose<layout::ColumnMajor> {
  using type = layout::RowMajor;
};

/////////////////////////////////////////////////////////////////////////////////////////////////

} // namespace layout
} // namespace cutlass