default_mma.h

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/*! \file
    \brief Template for a pipelined GEMM kernel. Does not compute batching or support split-K.
*/

#pragma once

#include "cutlass/cutlass.h"
#include "cutlass/numeric_types.h"
#include "cutlass/arch/arch.h"
#include "cutlass/arch/wmma.h"

#include "cutlass/layout/matrix.h"
#include "cutlass/transform/threadblock/predicated_tile_iterator.h"
#include "cutlass/transform/threadblock/predicated_tile_iterator_2dthreadtile.h"

#include "cutlass/gemm/gemm.h"
#include "cutlass/gemm/threadblock/default_mma_core_simt.h"
#include "cutlass/gemm/threadblock/default_mma_core_sm70.h"
#include "cutlass/gemm/threadblock/default_mma_core_sm75.h"
#include "cutlass/gemm/threadblock/default_mma_core_sm80.h"

#if defined(CUTLASS_ARCH_WMMA_ENABLED)
#include "cutlass/gemm/threadblock/default_mma_core_wmma.h"
#endif //CUTLASS_ARCH_WMMA_ENABLED

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

namespace cutlass {
namespace gemm {
namespace threadblock {

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

template <
    /// Element type for A matrix operand
    typename ElementA_,
    /// Layout type for A matrix operand
    typename LayoutA_,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB_,
    /// Layout type for B matrix operand
    typename LayoutB_,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator_,
    /// Layout type for C and D matrix operands
    typename LayoutC_,
    /// Operator class tag
    typename OperatorClass_,
    /// Tag indicating architecture to tune for
    typename ArchTag_,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape_,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape_,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape_,
    /// Number of stages used in the pipelined mainloop
    int Stages,
    /// Operation perfomed by GEMM
    typename Operator,
    /// Store the accumulators in row major or column major.  Row major is used
    /// when output layout is interleaved.
    bool AccumulatorsInRowMajor = false,
    /// Use zfill or predicate for out-of-bound cp.async
    SharedMemoryClearOption SharedMemoryClear = SharedMemoryClearOption::kNone,
    /// Gather operand A by using an index array
    bool GatherA = false,
    /// Gather operand B by using an index array
    bool GatherB = false
    >
struct DefaultMma;

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

/// Specialization for row-major output (OperatorClass Simt)
template <
    /// Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Layout type for C and D matrix operand
    typename LayoutC,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Operation performed by GEMM
    typename Operator,
    /// Gather operand A by using an index array
    bool GatherA,
    /// Gather operand B by using an index array
    bool GatherB
    >
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator, LayoutC,
                  arch::OpClassSimt, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, 2, Operator, false, SharedMemoryClearOption::kNone,
                  GatherA, GatherB> {

  static_assert(platform::is_same<LayoutC, layout::RowMajor>::value
             || platform::is_same<LayoutC, layout::AffineRankN<2>>::value,
             "simt epilogue must be row major");

  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, LayoutC,
      arch::OpClassSimt, 2, Operator>;

  // Define iterators over tiles from the A operand
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>,
          ElementA, LayoutA, 1, typename MmaCore::IteratorThreadMapA, kAlignmentA, GatherA>;

  // Define iterators over tiles from the B operand
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>,
          ElementB, LayoutB, 0, typename MmaCore::IteratorThreadMapB, kAlignmentB, GatherB>;

  // Define the threadblock-scoped pipelined matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaPipelined<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, ElementAccumulator,
      LayoutC, typename MmaCore::MmaPolicy>;
};

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

/// Specialization for row-major output (OperatorClass TensorOp)
template <
    /// Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Operation performed by GEMM
    typename Operator,
    /// Use zfill or predicate for out-of-bound cp.async
    SharedMemoryClearOption SharedMemoryClear,
    /// Gather operand A by using an index array
    bool GatherA,
    /// Gather operand B by using an index array
    bool GatherB
    >
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator, layout::RowMajor,
                  arch::OpClassTensorOp, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, 2, Operator, false, SharedMemoryClear,
                  GatherA, GatherB> {
  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, layout::RowMajor,
      arch::OpClassTensorOp, 2, Operator>;

  // Define iterators over tiles from the A operand
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>,
          ElementA, LayoutA, 1, typename MmaCore::IteratorThreadMapA, kAlignmentA,
          GatherA>;

  // Define iterators over tiles from the B operand
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>,
          ElementB, LayoutB, 0, typename MmaCore::IteratorThreadMapB, kAlignmentB,
          GatherB>;

  // Define the threadblock-scoped pipelined matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaPipelined<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, ElementAccumulator,
      layout::RowMajor, typename MmaCore::MmaPolicy>;
};

////////////////////////////////////////////////////////////////////////////////
/// Specialization for row-major output (OperatorClass TensorOp)
template <
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Operation performed by GEMM
    typename Operator,
    /// Gather operand A by using an index array
    bool GatherA,
    /// Gather operand B by using an index array
    bool GatherB
    >
struct DefaultMma<float, LayoutA, kAlignmentA, float, LayoutB,
                  kAlignmentB, float, layout::RowMajor,
                  arch::OpClassTensorOp, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, 2, Operator, false, SharedMemoryClearOption::kNone,
                  GatherA, GatherB> {
  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, float, LayoutA, float,
      LayoutB, float, layout::RowMajor, arch::OpClassTensorOp, 2,
      arch::OpMultiplyAddFastF16>;

  // Define iterators over tiles from the A operand
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>,
          float, LayoutA, 1, typename MmaCore::IteratorThreadMapA, kAlignmentA, GatherA>;

  // Define iterators over tiles from the B operand
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>,
          float, LayoutB, 0, typename MmaCore::IteratorThreadMapB, kAlignmentB, GatherB>;

  // Define the threadblock-scoped pipelined matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaPipelined<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, float,
      layout::RowMajor, typename MmaCore::MmaPolicy>;
};

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

/// Specialization for column-major-interleaved output
template <
    /// Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Tag indicating architecture to tune for
    typename OperatorClass,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Operation performed by GEMM
    typename Operator,
    /// Number of Interleaved K
    int InterleavedK>
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator,
                  layout::ColumnMajorInterleaved<InterleavedK>, OperatorClass,
                  ArchTag, ThreadblockShape, WarpShape, InstructionShape, 2,
                  Operator, true, SharedMemoryClearOption::kNone, false, false> {
  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator,
      layout::ColumnMajorInterleaved<InterleavedK>, OperatorClass, 2, Operator,
      true>;

  static_assert(kAlignmentA == 128 / sizeof_bits<ElementA>::value, 
    "Alignment must match thread data map's vector length");

  static_assert(kAlignmentB ==128 / sizeof_bits<ElementB>::value,
    "Alignment must match thread data map's vector length");

  // Define iterators over tiles from the A operand
  using IteratorA = cutlass::transform::threadblock::PredicatedTileIterator<
      cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>, ElementA,
      LayoutA, 1, typename MmaCore::IteratorThreadMapA>;

  // Define iterators over tiles from the B operand
  using IteratorB = cutlass::transform::threadblock::PredicatedTileIterator<
      cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>, ElementB,
      LayoutB, 0, typename MmaCore::IteratorThreadMapB>;

  // Define the threadblock-scoped pipelined matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaPipelined<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, ElementAccumulator,
      layout::ColumnMajorInterleaved<InterleavedK>,
      typename MmaCore::MmaPolicy>;
};

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

/// Specialization for row-major output
template <
    /// Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Layout type for C and D matrix operand
    typename LayoutC,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Number of stages used in the multistage mainloop
    int Stages,
    /// Operation perfomed by GEMM
    typename Operator,
    /// Gather operand A by using an index array
    bool GatherA,
    /// Gather operand B by using an index array
    bool GatherB
    >
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator, LayoutC,
                  arch::OpClassSimt, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, Stages, Operator, false, SharedMemoryClearOption::kNone,
                  GatherA, GatherB> {

  static_assert(platform::is_same<LayoutC, layout::RowMajor>::value
             || platform::is_same<LayoutC, layout::AffineRankN<2>>::value,
             "simt epilogue must be row major");

  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, LayoutC, arch::OpClassSimt,
      Stages, Operator>;

  // Define iterators over tiles from the A operand
  using ThreadMapA = typename MmaCore::IteratorThreadMapA;
  using AccessTypeA = cutlass::Array<ElementA, kAlignmentA>;
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileAccessIterator<
          cutlass::MatrixShape<ThreadblockShape::kM, ThreadblockShape::kK>,
          ElementA, LayoutA, 1, ThreadMapA, AccessTypeA, GatherA>;

  // Define iterators over tiles from the B operand
  using ThreadMapB = typename MmaCore::IteratorThreadMapB;
  using AccessTypeB = cutlass::Array<ElementB, kAlignmentB>;
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileAccessIterator<
          cutlass::MatrixShape<ThreadblockShape::kK, ThreadblockShape::kN>,
          ElementB, LayoutB, 0, ThreadMapB, AccessTypeB, GatherB>;

  // Define the threadblock-scoped multistage matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaMultistage<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      MmaCore::kCacheOpA, IteratorB, typename MmaCore::SmemIteratorB,
      MmaCore::kCacheOpB, ElementAccumulator, LayoutC,
      typename MmaCore::MmaPolicy, Stages>;
};

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

/// Specialization for row-major output (OperatorClass TensorOp)
template <
    /// Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Layout type for C and D matrix operand
    typename LayoutC,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Number of stages used in the multistage mainloop
    int Stages,
    /// Operation perfomed by GEMM
    typename Operator,
    /// Use zfill or predicate for out-of-bound cp.async
    SharedMemoryClearOption SharedMemoryClear,
    /// Gather operand A by using an index array
    bool GatherA,
    /// Gather operand B by using an index array
    bool GatherB
    >
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator, LayoutC,
                  arch::OpClassTensorOp, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, Stages, Operator, false, SharedMemoryClear,
                  GatherA, GatherB> {

  static_assert(platform::is_same<LayoutC, layout::RowMajor>::value
             || platform::is_same<LayoutC, layout::AffineRankN<2>>::value,
             "simt epilogue must be row major");

  static cutlass::arch::CacheOperation::Kind const CacheOpA =
      ((sizeof_bits<ElementA>::value * kAlignmentA) == 128)
          ? cutlass::arch::CacheOperation::Global
          : cutlass::arch::CacheOperation::Always;

  static cutlass::arch::CacheOperation::Kind const CacheOpB =
      ((sizeof_bits<ElementB>::value * kAlignmentB) == 128)
          ? cutlass::arch::CacheOperation::Global
          : cutlass::arch::CacheOperation::Always;

  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, LayoutC, arch::OpClassTensorOp,
      Stages, Operator, false, CacheOpA, CacheOpB>;

  // Define iterators over tiles from the A operand
  using ThreadMapA = typename MmaCore::IteratorThreadMapA;
  using AccessTypeA = cutlass::Array<ElementA, kAlignmentA>;
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileAccessIterator<
          cutlass::MatrixShape<ThreadblockShape::kM, ThreadblockShape::kK>,
          ElementA, LayoutA, 1, ThreadMapA, AccessTypeA, GatherA>;

  // Define iterators over tiles from the B operand
  using ThreadMapB = typename MmaCore::IteratorThreadMapB;
  using AccessTypeB = cutlass::Array<ElementB, kAlignmentB>;
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileAccessIterator<
          cutlass::MatrixShape<ThreadblockShape::kK, ThreadblockShape::kN>,
          ElementB, LayoutB, 0, ThreadMapB, AccessTypeB, GatherB>;

  // Define the threadblock-scoped multistage matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaMultistage<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      MmaCore::kCacheOpA, IteratorB, typename MmaCore::SmemIteratorB,
      MmaCore::kCacheOpB, ElementAccumulator, LayoutC,
      typename MmaCore::MmaPolicy, Stages, SharedMemoryClear>;
};

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

/// Specialization for column-major-interleaved output
template <
    /// Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Tag indicating architecture to tune for
    typename OperatorClass,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Number of stages used in the multistage mainloop
    int Stages,
    /// Operation performed by GEMM
    typename Operator,
    /// Number of Interleaved K
    int InterleavedK>
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator,
                  layout::ColumnMajorInterleaved<InterleavedK>, OperatorClass,
                  ArchTag, ThreadblockShape, WarpShape, InstructionShape,
                  Stages, Operator, true, SharedMemoryClearOption::kNone, false, false> {
  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator,
      layout::ColumnMajorInterleaved<InterleavedK>, OperatorClass, Stages,
      Operator, true>;

  // Define iterators over tiles from the A operand
  using ThreadMapA = typename MmaCore::IteratorThreadMapA;
  using AccessTypeA = cutlass::Array<ElementA, kAlignmentA>;
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileAccessIterator<
          cutlass::MatrixShape<ThreadblockShape::kM, ThreadblockShape::kK>,
          ElementA, LayoutA, 1, ThreadMapA, AccessTypeA>;

  // Define iterators over tiles from the B operand
  using ThreadMapB = typename MmaCore::IteratorThreadMapB;
  using AccessTypeB = cutlass::Array<ElementB, kAlignmentB>;
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileAccessIterator<
          cutlass::MatrixShape<ThreadblockShape::kK, ThreadblockShape::kN>,
          ElementB, LayoutB, 0, ThreadMapB, AccessTypeB>;

  // Define the threadblock-scoped multistage matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaMultistage<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      MmaCore::kCacheOpA, IteratorB, typename MmaCore::SmemIteratorB,
      MmaCore::kCacheOpB, ElementAccumulator, layout::RowMajor,
      typename MmaCore::MmaPolicy, Stages>;
};

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

/// Specialization for SIMT IDP4A Kernels
template <
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Operation performed by GEMM
    typename Operator,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape>
struct DefaultMma<int8_t, LayoutA, kAlignmentA, int8_t, LayoutB, kAlignmentB,
                  ElementAccumulator, layout::RowMajor, arch::OpClassSimt,
                  ArchTag, ThreadblockShape, WarpShape, GemmShape<1, 1, 4>, 2,
                  Operator, false, SharedMemoryClearOption::kNone, false, false> {
  using InstructionShape = GemmShape<1, 1, 4>;
  using ElementA = int8_t;
  using ElementB = int8_t;
  using OperatorClass =  arch::OpClassSimt;

  static const bool transposeA = platform::is_same< LayoutA, layout::ColumnMajor >::value;
  static const bool transposeB = platform::is_same< LayoutB, layout::RowMajor >::value;

  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, layout::RowMajor,
      OperatorClass, 2, Operator>;

  // Define iterators over tiles from the A operand
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileIterator2dThreadTile<
          cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>,
          ElementA, LayoutA, 1, typename MmaCore::IteratorThreadMapA, transposeA>;

  // Define iterators over tiles from the B operand
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileIterator2dThreadTile<
          cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>,
          ElementB, LayoutB, 0, typename MmaCore::IteratorThreadMapB, transposeB>;

  // Define the threadblock-scoped pipelined matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaPipelined<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, ElementAccumulator,
      layout::RowMajor, typename MmaCore::MmaPolicy>;
};

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

#if defined(CUTLASS_ARCH_WMMA_ENABLED)
/// Specialization for Wmma TensorOp operator with 2 staged pipeline
template <
    ///< Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Layout type for C and D matrix operands
    typename LayoutC,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Operation performed by GEMM
    typename Operator>
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator, LayoutC,
                  arch::OpClassWmmaTensorOp, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, 2, Operator, false, SharedMemoryClearOption::kNone,
                  false, false> {
  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, LayoutC,
      arch::OpClassWmmaTensorOp, 2, Operator>;

  // Define iterators over tiles from the A operand
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>,
          ElementA, LayoutA, 1, typename MmaCore::IteratorThreadMapA, kAlignmentA>;

  // Define iterators over tiles from the B operand
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>,
          ElementB, LayoutB, 0, typename MmaCore::IteratorThreadMapB, kAlignmentB>;

  // Define the threadblock-scoped pipelined matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaPipelined<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, ElementAccumulator,
      LayoutC, typename MmaCore::MmaPolicy>;
};

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

/// Specialization for Wmma TensorOp operator with 1 staged pipeline
template <
    ///< Element type for A matrix operand
    typename ElementA,
    /// Layout type for A matrix operand
    typename LayoutA,
    /// Access granularity of A matrix in units of elements
    int kAlignmentA,
    /// Element type for B matrix operand
    typename ElementB,
    /// Layout type for B matrix operand
    typename LayoutB,
    /// Access granularity of B matrix in units of elements
    int kAlignmentB,
    /// Element type for internal accumulation
    typename ElementAccumulator,
    /// Layout type for C and D matrix operands
    typename LayoutC,
    /// Tag indicating architecture to tune for
    typename ArchTag,
    /// Threadblock-level tile size (concept: GemmShape)
    typename ThreadblockShape,
    /// Warp-level tile size (concept: GemmShape)
    typename WarpShape,
    /// Instruction-level tile size (concept: GemmShape)
    typename InstructionShape,
    /// Operation performed by GEMM
    typename Operator>
struct DefaultMma<ElementA, LayoutA, kAlignmentA, ElementB, LayoutB,
                  kAlignmentB, ElementAccumulator, LayoutC,
                  arch::OpClassWmmaTensorOp, ArchTag, ThreadblockShape, WarpShape,
                  InstructionShape, 1, Operator, false, SharedMemoryClearOption::kNone,
                  false, false> {
  // Define the MmaCore components
  using MmaCore = typename cutlass::gemm::threadblock::DefaultMmaCore<
      ThreadblockShape, WarpShape, InstructionShape, ElementA, LayoutA,
      ElementB, LayoutB, ElementAccumulator, LayoutC,
      arch::OpClassWmmaTensorOp, 1, Operator>; 

  // Define iterators over tiles from the A operand
  using IteratorA =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kM, MmaCore::Shape::kK>,
          ElementA, LayoutA, 1, typename MmaCore::IteratorThreadMapA, kAlignmentA>;

  // Define iterators over tiles from the B operand
  using IteratorB =
      cutlass::transform::threadblock::PredicatedTileIterator<
          cutlass::MatrixShape<MmaCore::Shape::kK, MmaCore::Shape::kN>,
          ElementB, LayoutB, 0, typename MmaCore::IteratorThreadMapB, kAlignmentB>;

  // Define the threadblock-scoped singlestage matrix multiply
  using ThreadblockMma = cutlass::gemm::threadblock::MmaSingleStage<
      typename MmaCore::Shape, IteratorA, typename MmaCore::SmemIteratorA,
      IteratorB, typename MmaCore::SmemIteratorB, ElementAccumulator,
      LayoutC, typename MmaCore::MmaPolicy>;
};

////////////////////////////////////////////////////////////////////////////////
#endif //CUTLASS_ARCH_WMMA_ENABLED

} // namespace threadblock
} // namespace gemm
} // namespace cutlass 

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