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/*! \file
    \brief Tools and utils to store a GEMM output in shmem, and to use that
   output as operandA for another GEMM back-to-back
*/

#pragma once

#include "cutlass/aligned_buffer.h"
#include "cutlass/arch/memory.h"
#include "cutlass/array.h"
#include "cutlass/cutlass.h"
#include "cutlass/epilogue/thread/linear_combination.h"
#include "cutlass/epilogue/threadblock/default_epilogue_simt.h"
#include "cutlass/epilogue/threadblock/default_epilogue_tensor_op.h"
#include "cutlass/epilogue/threadblock/default_epilogue_volta_tensor_op.h"
#include "cutlass/functional.h"
#include "cutlass/gemm/gemm.h"
#include "cutlass/gemm/warp/mma_tensor_op_fragment_iterator.h"
#include "cutlass/matrix_shape.h"
#include "cutlass/numeric_conversion.h"
#include "cutlass/numeric_types.h"
#include "cutlass/platform/platform.h"
#include "cutlass/transform/threadblock/vector_iterator.h"

#include "../epilogue/epilogue_thread_apply_logsumexp.h"
#include "../gemm/mma_accum_lambda_iterator.h"
#include "../gemm_kernel_utils.h"
#include "../iterators/default_warp_iterator_from_smem.h"
#include "../iterators/make_residual_last.h"
#include "../iterators/transpose_warp_iterator.h"
#include "../iterators/warp_iterator_from_smem.h"
#include "cutlass/epilogue/threadblock/epilogue_smem_accumulator.h"
#include "cutlass/gemm/threadblock/mma_base.h"
#include "cutlass/gemm/threadblock/mma_multistage.h"
#include "cutlass/gemm/threadblock/mma_pipelined.h"
#include "cutlass/gemm/warp/mma_tensor_op_tile_access_iterator.h"

namespace cutlass {
namespace gemm {
namespace threadblock {

/// Shared storage object needed by accumulator
/// From 13_two_tensor_op_fusion/threadblock/b2b_mma_base_smem_accumulator.h
template <
    typename Shape_,
    typename Element_,
    typename Layout_,
    typename Padding_>
class AccumulatorSharedStorage {
 public:
  //
  // Type definitions
  //
  using Shape = Shape_;
  using Element = Element_;
  using Layout = Layout_;
  using Padding = Padding_;

  /// Tensor reference to the accumulator
  using TensorRefAccum = cutlass::TensorRef<Element, Layout>;

  /// Shape of the accumulator matrix in shared memory
  using ShapeAccum = cutlass::
      MatrixShape<Shape::kM + Padding::kRow, Shape::kN + Padding::kColumn>;

 public:
  //
  // Data members
  //

  /// Buffer for accumulator
  cutlass::AlignedBuffer<Element, ShapeAccum::kCount> accum;

 public:
  //
  // Methods
  //

  /// Returns a layout object for the Accum matrix
  CUTLASS_DEVICE
  static Layout LayoutAccum() {
    return Layout::packed({ShapeAccum::kRow, ShapeAccum::kColumn});
  }

  /// Returns a TensorRef to the Accumulator
  CUTLASS_HOST_DEVICE
  TensorRefAccum accum_ref() {
    return TensorRefAccum{accum.data(), LayoutAccum()};
  }
};

////////////////////////////////////////////////////////////////////////////////
// Taken from
// https://github.com/NVIDIA/cutlass/blob/master/examples/13_two_tensor_op_fusion/threadblock/b2b_mma_base_smem_accumulator.h
////////////////////////////////////////////////////////////////////////////////

/// Structure to compute the matrix product targeting CUDA cores and SIMT math
/// instructions.
template <
    /// Size of the Gemm problem - concept: gemm::GemmShape<>
    typename Shape_,
    // Maximum K dimension - also the dimension of the shared-memory
    // holding `OperandA`
    int kMaxK_,
    /// Policy describing tuning details (concept: MmaPolicy)
    typename Policy_,
    /// Number of stages,
    int Stages,
    /// Layout in shared-memory of operand A
    typename SmemLayoutA,
    /// Used for partial specialization
    typename Enable = bool>
class MmaBaseFromSharedMemory {
 public:
  ///< Size of the Gemm problem - concept: gemm::GemmShape<>
  using Shape = Shape_;
  static constexpr int kMaxK = kMaxK_;

  ///< Policy describing tuning details
  using Policy = Policy_;

  //
  // Dependent types
  //

  /// Warp-level Mma
  using Operator = typename Policy::Operator;

  /// Shape describing the overall GEMM computed from shared memory
  /// by each warp.
  using WarpGemm = typename Policy::Operator::Shape;

  /// Shape describing the number of warps filling the CTA
  using WarpCount = GemmShape<
      Shape::kM / WarpGemm::kM,
      Shape::kN / WarpGemm::kN,
      Shape::kK / WarpGemm::kK>;
  using WarpCount1 = WarpCount;

  /// Number of warp-level GEMM oeprations
  static int const kWarpGemmIterations =
      (WarpGemm::kK / Operator::Policy::MmaShape::kK);
  static int const kWarpGemmIterations1 = kWarpGemmIterations;

  /// Number of stages
  static int const kStages = Stages;

  /// If this is true, we fill the entire shmem buffer at start
  /// and don't need to iterate through it in a circular fashion
  static bool const kSmemContainsEntireB = kMaxK <= Shape::kK * kStages;

  /// Tensor reference to the A operand
  using TensorRefA = TensorRef<typename Operator::ElementA, SmemLayoutA>;

  /// Tensor reference to the B operand
  using TensorRefB =
      TensorRef<typename Operator::ElementB, typename Operator::LayoutB>;

  //
  // Nested structs
  //

  /// Shared storage object needed by threadblock-scoped GEMM
  class SharedStorage {
   public:
    //
    // Type definitions
    //

    /// Shape of the B matrix operand in shared memory
    using ShapeB = MatrixShape<
        Shape::kK * kStages + Policy::SmemPaddingB::kRow,
        Shape::kN + Policy::SmemPaddingB::kColumn>;

   public:
    //
    // Data members
    //

    /// Buffer for B operand
    AlignedBuffer<typename Operator::ElementB, ShapeB::kCount> operand_B;

   public:
    //
    // Methods
    //

    /// Returns a layout object for the B matrix
    CUTLASS_HOST_DEVICE
    static typename Operator::LayoutB LayoutB() {
      return Operator::LayoutB::packed({ShapeB::kRow, ShapeB::kColumn});
    }

    /// Returns a TensorRef to the B operand
    CUTLASS_HOST_DEVICE
    TensorRefB operand_B_ref() {
      return TensorRefB{operand_B.data(), LayoutB()};
    }
  };

 protected:
  //
  // Data members
  //

  // /// Iterator to load a warp-scoped tile of A operand from shared memory
  // typename Operator::IteratorA warp_tile_iterator_A_;

  /// Iterator to load a warp-scoped tile of B operand from shared memory
  typename Operator::IteratorB warp_tile_iterator_B_;

 public:
  /// Construct from tensor references
  CUTLASS_DEVICE
  MmaBaseFromSharedMemory(
      ///< Shared storage needed for internal use by threadblock-scoped GEMM
      TensorRefB& b_tile,
      ///< ID within the threadblock
      int thread_idx,
      ///< ID of warp
      int warp_idx,
      ///< ID of each thread within a warp
      int lane_idx)
      : warp_tile_iterator_B_(b_tile, lane_idx) {}
};

namespace {

// has necessary trait compliance with WarpIteratorFromSmem but doesn't do
// anything, can be default initialized, and uses fragment that takes up
// (almost) no space. this warp iterator is selected at compile time when
// elementwise on-the-fly scaling for operand A is disabled, in which case
// operations related to loading scale factors for operand A get wiped out by
// the compiler.
template <typename TensorRef>
class NoOpWarpIteratorScale {
 public:
  // in pipelined+multistage MMA implementations we keep an array of fragments.
  // if we aren't using scaling we don't want to waste registers on fragments
  // of scale elements, so ideally this would be sized 0.
  // Since arrays of zero-sized objects are not allowed, using size as 1.
  // The compiler will most likely wipe it out anyways.
  using Fragment = cutlass::Array<char, 1>;

  CUTLASS_HOST_DEVICE
  NoOpWarpIteratorScale() {}

  CUTLASS_HOST_DEVICE
  NoOpWarpIteratorScale(TensorRef const&, int) {}

  CUTLASS_HOST_DEVICE
  NoOpWarpIteratorScale& add_tile_offset(
      typename TensorRef::TensorCoord const&) {
    return *this;
  }

  CUTLASS_HOST_DEVICE
  NoOpWarpIteratorScale& operator++() {
    return *this;
  }

  CUTLASS_DEVICE
  void load(Fragment&) const {}
};

// if scaling is enabled, performs fragment elementwise multiplication between
// fragment and its scaling factor.
template <typename Fragment, typename FragmentScale, bool ScalingEnabled>
class FragmentElementwiseScaler;

// specialization for scaling being enabled.
template <typename Fragment, typename FragmentScale>
class FragmentElementwiseScaler<Fragment, FragmentScale, true> {
 public:
  // cast scale_frag to correct type then apply elementwise to fragment
  CUTLASS_DEVICE
  static Fragment apply(Fragment frag, FragmentScale const& scale_frag) {
    Fragment converted_scale_frag = cutlass::NumericArrayConverter<
        typename Fragment::Element,
        typename FragmentScale::Element,
        FragmentScale::kElements>()(scale_frag);
    return cutlass::multiplies<Fragment>()(frag, converted_scale_frag);
  }
};

// specialization for scaling being disabled. doesn't do anything and should
// just get wiped out by the compiler.
template <typename Fragment, typename FragmentScale>
class FragmentElementwiseScaler<Fragment, FragmentScale, false> {
 public:
  CUTLASS_DEVICE
  static Fragment apply(Fragment frag, FragmentScale const&) {
    return frag;
  }
};
} // namespace

////////////////////////////////////////////////////////////////////////////////
// Taken from
// https://github.com/NVIDIA/cutlass/blob/master/examples/13_two_tensor_op_fusion/threadblock/b2b_mma_pipelined_smem_accumulator.h
////////////////////////////////////////////////////////////////////////////////

/// Structure to compute the matrix product targeting CUDA cores and SIMT math
/// instructions.
template <
    /// Size of the Gemm problem - concept: gemm::GemmShape<>
    typename Shape_,
    // BEGIN smem
    /// Iterates over the intermediate accumulator tile in shared memory
    typename WarpIteratorA_,
    /// whether or not to perform elementwise multiplication of A
    //  by another matrix (A_scale) that is also kept in shared memory prior
    //  to matmul A @ B
    bool ScaleOperandA_,
    /// Max GEMM problem size in K dimension
    int MaxK,
    /// Iterates over tiles of B operand in global memory
    //  (concept: ReadableTileIterator | ForwardTileIterator |
    //  MaskedTileIterator)
    typename IteratorB_,
    /// Iterates over tiles of B operand in shared memory
    /// (concept: WriteableTileIterator | RandomAccessTileIterator)
    typename SmemIteratorB_,
    /// Data type of accumulator matrix
    typename ElementC_,
    /// Data type of accumulator matrix
    typename LayoutC_,
    /// Policy describing tuning details (concept: MmaPolicy)
    typename Policy_,
    /// Transformation applied to B operand
    typename TransformB_ = NumericArrayConverter<
        typename SmemIteratorB_::Element,
        typename IteratorB_::Element,
        IteratorB_::Fragment::kElements>,
    /// Used for partial specialization
    typename Enable = bool>
class MmaPipelinedFromSharedMemory : public MmaBaseFromSharedMemory<
                                         Shape_,
                                         MaxK,
                                         Policy_,
                                         2,
                                         typename WarpIteratorA_::Layout> {
 public:
  ///< Base class
  using Base = MmaBaseFromSharedMemory<
      Shape_,
      MaxK,
      Policy_,
      2,
      typename WarpIteratorA_::Layout>;

  using Shape =
      Shape_; ///< Size of the Gemm problem - concept: gemm::GemmShape<>
  static constexpr bool ScaleOperandA = ScaleOperandA_;

  using WarpIteratorA = WarpIteratorA_;
  ///< loads fragments of A_scale from shared memory if operand A scaling is
  ///< enabled. otherwise no-op.
  using WarpIteratorAScale = typename cutlass::platform::conditional<
      ScaleOperandA,
      WarpIteratorA,
      NoOpWarpIteratorScale<typename WarpIteratorA::TensorRef>>::type;

  using IteratorB =
      IteratorB_; ///< Iterates over tiles of B operand in global memory
  using ElementC = ElementC_; ///< Data type of accumulator matrix
  using LayoutC = LayoutC_; ///< Layout of accumulator matrix
  using Policy = Policy_; ///< Policy describing tuning details

  using SmemIteratorB = SmemIteratorB_;

  using TransformB = TransformB_;

  //
  // Dependent types
  //

  /// Fragment of operand B loaded from global memory
  using FragmentB = typename IteratorB::Fragment;

  /// Fragment of accumulator tile
  using FragmentC = typename Policy::Operator::FragmentC;

  /// Warp-level Mma
  using Operator = typename Policy::Operator;

  /// Obtain the arch tag from the warp-level operator
  using ArchTag = typename Policy::Operator::ArchTag;

  /// Complex transform on B operand
  static ComplexTransform const kTransformB = Operator::kTransformB;

  // staticaly assert kStages for MmaPipelined is two (Double-buffered pipeline)
  static_assert(
      (Base::kStages == 2),
      "MmaPipelined requires kStages set to value 2");

 private:
  using WarpFragmentA = typename Operator::FragmentA;

  /// fragment type of OperandA elementwise scaling matrix. (almost) empty
  /// if operand A scaling is disabled.
  using WarpFragmentAScale = typename WarpIteratorAScale::Fragment;

  using WarpFragmentB = typename Operator::FragmentB;

  /// applies scaling factor to operand A fragment if operand A scaling is
  /// enabled. otherwise no-op.
  using FragmentAScaler = FragmentElementwiseScaler<
      WarpFragmentA,
      WarpFragmentAScale,
      ScaleOperandA>;

 protected:
  // /// Iterator to write threadblock-scoped tile of A operand to shared memory
  // SmemIteratorA smem_iterator_A_;

  /// Iterator to write threadblock-scoped tile of B operand to shared memory
  SmemIteratorB smem_iterator_B_;

  /// Iterator to load a warp-scoped tile of A operand from intermediate
  /// accumulator tile
  WarpIteratorA warp_tile_iterator_A_;

  /// Iterator to load a warp-scoped tile of A_scale from intermediate
  /// accumulator tile (only used if ScaleOperandA_ is true)
  WarpIteratorAScale warp_tile_iterator_A_scale_;

 public:
  /// constructor for MMA with operand A scaling enabled.
  CUTLASS_DEVICE
  MmaPipelinedFromSharedMemory(
      typename Base::TensorRefA a, // Operand A in shared memory
      typename Base::TensorRefA a_scale, // Operand A_scale in shared memory
      typename Base::TensorRefB
          b_staging, // staging memory for loading tiles of B
      int thread_idx,
      int warp_idx,
      int lane_idx)
      : Base(b_staging, thread_idx, warp_idx, lane_idx),
        warp_tile_iterator_A_(a, lane_idx),
        warp_tile_iterator_A_scale_(a_scale, lane_idx),
        smem_iterator_B_(b_staging, thread_idx) {
    // Compute warp location within threadblock tile by mapping the warp_id to
    // three coordinates:
    //   _m: the warp's position within the threadblock along the M dimension
    //   _n: the warp's position within the threadblock along the N dimension
    //   _k: the warp's position within the threadblock along the K dimension
    int warp_idx_mn = warp_idx % (Base::WarpCount::kM * Base::WarpCount::kN);
    int warp_idx_k = warp_idx / (Base::WarpCount::kM * Base::WarpCount::kN);
    int warp_idx_m = warp_idx_mn % Base::WarpCount::kM;
    int warp_idx_n = warp_idx_mn / Base::WarpCount::kM;

    // Add per-warp offsets in units of warp-level tiles
    this->warp_tile_iterator_A_.add_tile_offset(
        {warp_idx_m, Base::kWarpGemmIterations * warp_idx_k});
    this->warp_tile_iterator_A_scale_.add_tile_offset(
        {warp_idx_m, Base::kWarpGemmIterations * warp_idx_k});
    this->warp_tile_iterator_B_.add_tile_offset(
        {Base::kWarpGemmIterations * warp_idx_k, warp_idx_n});
  }

  /// Construct from tensor references
  CUTLASS_DEVICE
  MmaPipelinedFromSharedMemory(
      typename Base::TensorRefA a, ///< Operand A in shared memory
      typename Base::TensorRefB b_staging, ///< staging memory for loading B
      int thread_idx, ///< ID within the threadblock
      int warp_idx, ///< ID of warp
      int lane_idx) ///< ID of each thread within a warp
      : Base(b_staging, thread_idx, warp_idx, lane_idx),
        warp_tile_iterator_A_(a, lane_idx),
        smem_iterator_B_(b_staging, thread_idx) {
    // Compute warp location within threadblock tile by mapping the warp_id to
    // three coordinates:
    //   _m: the warp's position within the threadblock along the M dimension
    //   _n: the warp's position within the threadblock along the N dimension
    //   _k: the warp's position within the threadblock along the K dimension

    int warp_idx_mn = warp_idx % (Base::WarpCount::kM * Base::WarpCount::kN);
    int warp_idx_k = warp_idx / (Base::WarpCount::kM * Base::WarpCount::kN);

    int warp_idx_m = warp_idx_mn % Base::WarpCount::kM;
    int warp_idx_n = warp_idx_mn / Base::WarpCount::kM;

    // Add per-warp offsets in units of warp-level tiles
    this->warp_tile_iterator_A_.add_tile_offset(
        {warp_idx_m, Base::kWarpGemmIterations * warp_idx_k});
    this->warp_tile_iterator_B_.add_tile_offset(
        {Base::kWarpGemmIterations * warp_idx_k, warp_idx_n});
  }

  // For API compatibility with MmaMultistageFromSharedMemory
  // but not supported as it worsens perf: older gpus < sm80 don't
  // support async tranfers and have to waste registers
  CUTLASS_DEVICE
  void set_prologue_done(bool value) {}
  CUTLASS_DEVICE
  static void prologue(
      typename Base::SharedStorage& shared_storage,
      IteratorB iterator_B1,
      int thread_idx,
      int problem_size_0_n) {}

  CUTLASS_DEVICE
  static void drain_cp_asyncs() {}

  /// Perform a threadblock-scoped matrix multiply-accumulate
  CUTLASS_DEVICE
  void operator()(
      int gemm_k_iterations, ///< number of iterations of the mainloop
      FragmentC& accum, ///< destination accumulator tile
      // IteratorA iterator_A,                             ///< iterator over A
      // operand in global memory
      IteratorB iterator_B, ///< iterator over B operand in global memory
      FragmentC const& src_accum, ///< source accumulator tile
      // TransformA transform_A = TransformA(),            ///< transformation
      // applied to A fragment
      TransformB transform_B =
          TransformB()) { ///< transformation applied to B fragment

    //
    // Prologue
    //

    // Perform accumulation in the 'd' output operand
    accum = src_accum;

    FragmentB tb_frag_B;

    tb_frag_B.clear();

    // The last kblock is loaded in the prolog
    iterator_B.set_residual_tile(gemm_k_iterations == 1);
    iterator_B.load(tb_frag_B);

    ++iterator_B;

    this->smem_iterator_B_.store(transform_B(tb_frag_B));

    ++this->smem_iterator_B_;

    __syncthreads();

    // remember that WarpFragmentAScale and WarpIteratorAScale are empty/no-op
    // if scaling is disabled.

    // Pair of fragments used to overlap shared memory loads and math
    // instructions
    WarpFragmentA warp_frag_A[2];
    WarpFragmentAScale warp_frag_A_scale[2];
    WarpFragmentB warp_frag_B[2];
    warp_frag_A[0].clear();
    warp_frag_A_scale[0].clear();
    warp_frag_B[0].clear();

    this->warp_tile_iterator_B_.set_kgroup_index(0);

    this->warp_tile_iterator_A_.load(warp_frag_A[0]);
    this->warp_tile_iterator_A_scale_.load(warp_frag_A_scale[0]);
    this->warp_tile_iterator_B_.load(warp_frag_B[0]);

    ++this->warp_tile_iterator_A_;
    ++this->warp_tile_iterator_A_scale_;
    ++this->warp_tile_iterator_B_;

    Operator warp_mma;

    int smem_write_stage_idx = 1;

    // Avoid reading out of bounds
    iterator_B.set_residual_tile(gemm_k_iterations == 2);
    iterator_B.clear_mask(gemm_k_iterations <= 1);

    // Issue loads during the first warp-level matrix multiply-add *AFTER*
    // issuing shared memory loads (which have the tightest latency
    // requirement).

    //
    // Mainloop
    //

    // Note: The main loop does not support Base::kWarpGemmIterations == 2.
    CUTLASS_GEMM_LOOP
    for (; gemm_k_iterations > 0; --gemm_k_iterations) {
      //
      // Loop over GEMM K dimension
      //

      CUTLASS_PRAGMA_UNROLL
      for (int warp_mma_k = 0; warp_mma_k < Base::kWarpGemmIterations;
           ++warp_mma_k) {
        // Load warp-level tiles from shared memory, wrapping to k offset if
        // this is the last group as the case may be.
        bool hasNext = true;

        if (warp_mma_k == Base::kWarpGemmIterations - 1) {
          if (gemm_k_iterations > 1) {
            // Write fragments to shared memory
            this->smem_iterator_B_.store(transform_B(tb_frag_B));
          }

          __syncthreads();

          ++this->smem_iterator_B_;

          // Add negative offsets to return iterators to the 'start' of the
          // circular buffer in shared memory SMEM: Don't reset iterator A, as
          // we are continuing our iteration at this point
          if (smem_write_stage_idx == 1) {
            this->smem_iterator_B_.add_tile_offset({-Base::kStages, 0});
          } else {
            this->warp_tile_iterator_B_.add_tile_offset(
                {-Base::kStages * Policy::kPartitionsK *
                     Base::kWarpGemmIterations,
                 0});
          }

          smem_write_stage_idx ^= 1;
          hasNext = gemm_k_iterations > 1;
        }

        // Only read the next if we need to
        if (hasNext) {
          this->warp_tile_iterator_B_.set_kgroup_index(
              (warp_mma_k + 1) % Base::kWarpGemmIterations);

          this->warp_tile_iterator_A_.load(warp_frag_A[(warp_mma_k + 1) % 2]);
          this->warp_tile_iterator_A_scale_.load(
              warp_frag_A_scale[(warp_mma_k + 1) % 2]);
          this->warp_tile_iterator_B_.load(warp_frag_B[(warp_mma_k + 1) % 2]);

          ++this->warp_tile_iterator_A_;
          ++this->warp_tile_iterator_A_scale_;
          ++this->warp_tile_iterator_B_;

          if (warp_mma_k == 0) {
            iterator_B.load(tb_frag_B);

            ++iterator_B;

            // Avoid reading out of bounds if this was the last loop iteration
            iterator_B.set_residual_tile(gemm_k_iterations == 3);
            iterator_B.clear_mask(gemm_k_iterations <= 2);
          }
        }

        warp_mma(
            accum,
            FragmentAScaler::apply(
                warp_frag_A[warp_mma_k % 2], warp_frag_A_scale[warp_mma_k % 2]),
            warp_frag_B[warp_mma_k % 2],
            accum);
      }
    }
  }
};

////////////////////////////////////////////////////////////////////////////////
// Taken from
// https://github.com/NVIDIA/cutlass/blob/master/examples/13_two_tensor_op_fusion/threadblock/b2b_mma_multistage_smem_accumulator.h
////////////////////////////////////////////////////////////////////////////////

/// Structure to compute the matrix product targeting CUDA cores and SIMT math
/// instructions.
template <
    /// Size of the Gemm problem - concept: gemm::GemmShape<>
    typename Shape1_,
    /// Iterates over the intermediate accumulator tile in shared memory
    typename WarpIteratorA1_,
    /// whether or not to perform elementwise multiplication of A
    //  by another matrix (A_scale) that is also kept in shared memory prior
    //  to matmul A @ B
    bool ScaleOperandA_,
    /// Iterates over tiles of B operand in global memory
    //  (concept: ReadableTileIterator | ForwardTileIterator |
    //  MaskedTileIterator)
    typename IteratorB1_,
    /// Iterates over tiles of B operand in shared memory
    /// (concept: WriteableTileIterator | RandomAccessTileIterator)
    typename SmemIteratorB1_,
    /// Cache operation for operand B
    cutlass::arch::CacheOperation::Kind CacheOpB1,
    /// Data type of accumulator matrix
    typename ElementC_,
    /// Data type of accumulator matrix
    typename LayoutC_,
    /// Policy describing tuning details (concept: MmaPolicy)
    typename Policy1_,
    /// Number of stages,
    int Stages_,
    int kMaxK_,
    /// Used for partial specialization
    typename Enable = bool>
class MmaMultistageFromSharedMemory : public MmaBaseFromSharedMemory<
                                          Shape1_,
                                          kMaxK_,
                                          Policy1_,
                                          Stages_,
                                          typename WarpIteratorA1_::Layout> {
 public:
  ///< Base class
  using Base = MmaBaseFromSharedMemory<
      Shape1_,
      kMaxK_,
      Policy1_,
      Stages_,
      typename WarpIteratorA1_::Layout>;

  ///< Size of the Gemm problem - concept: gemm::GemmShape<>
  using Shape1 = Shape1_;
  ///< Iterates over tiles of B operand in global memory
  using IteratorB1 = IteratorB1_;
  using IteratorB = IteratorB1;
  ///< Policy describing tuning details
  using Policy1 = Policy1_;

  using SmemIteratorB1 = SmemIteratorB1_;
  using WarpIteratorA1 = WarpIteratorA1_; ///< Iterates over the intermediate
                                          ///< accumulator tile in shared memory
  static constexpr bool ScaleOperandA = ScaleOperandA_;

  ///< warp level iterator over A_scale matrix tile kept in shared memory.
  ///< if elementwise A scaling is disabled then everything this does is no-op.
  using WarpIteratorAScale = typename cutlass::platform::conditional<
      ScaleOperandA,
      WarpIteratorA1,
      NoOpWarpIteratorScale<typename WarpIteratorA1::TensorRef>>::type;
  ///< Data type of accumulator matrix
  using ElementC = ElementC_;
  ///< Layout of accumulator matrix
  using LayoutC = LayoutC_;

  static cutlass::arch::CacheOperation::Kind const kCacheOpB1 = CacheOpB1;
  static constexpr bool kSmemContainsEntireB = Base::kSmemContainsEntireB;

  //
  // Dependent types
  //

  /// Fragment of accumulator tile
  using FragmentC1 = typename Policy1::Operator::FragmentC;
  using FragmentC = FragmentC1;

  /// Warp-level Mma
  using Operator1 = typename Policy1::Operator;

  /// Minimum architecture is Sm80 to support cp.async
  using ArchTag = arch::Sm80;

  /// Complex transform on B operand
  static ComplexTransform const kTransformB1 = Operator1::kTransformB;

  /// Internal structure exposed for introspection.
  struct Detail {
    static_assert(
        Base::kWarpGemmIterations1 > 1,
        "The pipelined structure requires at least two warp-level "
        "GEMM operations.");

    /// Number of cp.async instructions to load one stage of operand B
    static int const TBLoadIterationsB1 =
        IteratorB1::ThreadMap::Iterations::kCount;

    /// Number of cp.async instructions to load on group of operand B
    static int const kAccessesPerGroupB1 =
        (TBLoadIterationsB1 + Base::kWarpGemmIterations1 - 1) /
        Base::kWarpGemmIterations1;
  };

  static constexpr int kNumStagesConcurrentLoad =
      kSmemContainsEntireB ? Base::kStages : Base::kStages - 1;

 private:
  using WarpLoadedFragmentA1 = typename Operator1::FragmentA;
  /// fragment of OperandA scale matrix. if operand A scaling is disabled this
  /// is (almost) empty.
  using WarpLoadedFragmentA1Scale = typename WarpIteratorAScale::Fragment;
  using WarpLoadedFragmentB1 = typename Operator1::FragmentB;
  using WarpTransformedFragmentA1 = typename Operator1::TransformedFragmentA;
  using WarpTransformedFragmentB1 = typename Operator1::TransformedFragmentB;

  /// applies elementwise scaling to fragment of A. if operand A scaling is
  /// disabled this is a no-op.
  using FragmentAScaler = FragmentElementwiseScaler<
      WarpLoadedFragmentA1,
      WarpLoadedFragmentA1Scale,
      ScaleOperandA>;

 private:
  //
  // Data members
  //

  /// Iterator to load a warp-scoped tile of A1 operand from intermediate
  /// accumulator tile
  WarpIteratorA1 warp_tile_iterator_A1_;

  /// Iterator to load a warp-scoped tile of A1_scale operand from shared memory
  /// if operand A scaling is disabled everything this does is a no-op.
  WarpIteratorAScale warp_tile_iterator_A1_scale_;

  /// Iterator to write threadblock-scoped tile of B operand to shared memory
  SmemIteratorB1 smem_iterator_B1_;

  bool prologue_done_;

 public:
  /// constructor for MMA with operand A scaling enabled.
  CUTLASS_DEVICE
  MmaMultistageFromSharedMemory(
      typename Base::TensorRefA a,
      typename Base::TensorRefA a_scale,
      typename Base::TensorRefB b_tile,
      int thread_idx,
      int warp_idx,
      int lane_idx)
      : Base(b_tile, thread_idx, warp_idx, lane_idx),
        warp_tile_iterator_A1_(a, lane_idx),
        warp_tile_iterator_A1_scale_(a_scale, lane_idx),
        smem_iterator_B1_(b_tile, thread_idx),
        prologue_done_(false) {
    // Compute warp location within threadblock tile by mapping the warp_id to
    // three coordinates:
    //   _m: the warp's position within the threadblock along the M dimension
    //   _n: the warp's position within the threadblock along the N dimension
    //   _k: the warp's position within the threadblock along the K dimension
    int warp_idx_mn_1 =
        warp_idx % (Base::WarpCount1::kM * Base::WarpCount1::kN);
    int warp_idx_k_1 = warp_idx / (Base::WarpCount1::kM * Base::WarpCount1::kN);
    int warp_idx_m_1 = warp_idx_mn_1 % Base::WarpCount1::kM;
    int warp_idx_n_1 = warp_idx_mn_1 / Base::WarpCount1::kM;

    // Add per-warp offsets in units of warp-level tiles
    warp_tile_iterator_A1_.add_tile_offset(
        {warp_idx_m_1, Base::kWarpGemmIterations1 * warp_idx_k_1});
    warp_tile_iterator_A1_scale_.add_tile_offset(
        {warp_idx_m_1, Base::kWarpGemmIterations1 * warp_idx_k_1});
    this->warp_tile_iterator_B_.add_tile_offset(
        {Base::kWarpGemmIterations1 * warp_idx_k_1, warp_idx_n_1});
  }

  /// Construct from tensor references
  CUTLASS_DEVICE
  MmaMultistageFromSharedMemory(
      typename Base::TensorRefA a,
      typename Base::TensorRefB b_tile,
      ///< ID within the threadblock
      int thread_idx,
      ///< ID of warp
      int warp_idx,
      ///< ID of each thread within a warp
      int lane_idx)
      : Base(b_tile, thread_idx, warp_idx, lane_idx),
        warp_tile_iterator_A1_(a, lane_idx),
        smem_iterator_B1_(b_tile, thread_idx),
        prologue_done_(false) {
    // Compute warp location within threadblock tile by mapping the warp_id to
    // three coordinates:
    //   _m: the warp's position within the threadblock along the M dimension
    //   _n: the warp's position within the threadblock along the N dimension
    //   _k: the warp's position within the threadblock along the K dimension

    int warp_idx_mn_1 =
        warp_idx % (Base::WarpCount1::kM * Base::WarpCount1::kN);
    int warp_idx_k_1 = warp_idx / (Base::WarpCount1::kM * Base::WarpCount1::kN);

    int warp_idx_m_1 = warp_idx_mn_1 % Base::WarpCount1::kM;
    int warp_idx_n_1 = warp_idx_mn_1 / Base::WarpCount1::kM;

    // Add per-warp offsets in units of warp-level tiles
    warp_tile_iterator_A1_.add_tile_offset(
        {warp_idx_m_1, Base::kWarpGemmIterations1 * warp_idx_k_1});
    this->warp_tile_iterator_B_.add_tile_offset(
        {Base::kWarpGemmIterations1 * warp_idx_k_1, warp_idx_n_1});
  }

  CUTLASS_DEVICE
  void set_prologue_done(bool value) {
    prologue_done_ = value;
  }

  CUTLASS_DEVICE
  static void prologue(
      typename Base::SharedStorage& shared_storage,
      IteratorB iterator_B1,
      int thread_idx,
      int problem_size_0_n) {
    SmemIteratorB1 smem_iterator_B1(shared_storage.operand_B_ref(), thread_idx);
    _prologue(
        iterator_B1,
        (problem_size_0_n + Base::Shape::kK - 1) / Base::Shape::kK,
        smem_iterator_B1);
  }

  CUTLASS_DEVICE
  static void drain_cp_asyncs() {
    // commit and drain all pending and predicated cp.async pnz from the GEMM
    // mainloop
    cutlass::arch::cp_async_fence();
    cutlass::arch::cp_async_wait<0>();
    __syncthreads();
  }

  CUTLASS_DEVICE
  void copy_tiles_and_advance_1(
      IteratorB1& iterator_B1,
      int group_start_B1 = 0) {
    iterator_B1.set_iteration_index(
        group_start_B1 * IteratorB1::kAccessesPerVector);
    this->smem_iterator_B1_.set_iteration_index(group_start_B1);

    // Load for operand B
    CUTLASS_PRAGMA_UNROLL
    for (int j = 0; j < Detail::kAccessesPerGroupB1; ++j) {
      if (group_start_B1 + j < Detail::TBLoadIterationsB1) {
        typename IteratorB1::AccessType* dst_ptr =
            reinterpret_cast<typename IteratorB1::AccessType*>(
                this->smem_iterator_B1_.get());

        int const kSrcBytes = sizeof_bits<typename IteratorB1::Element>::value *
            IteratorB1::ThreadMap::kElementsPerAccess /
            IteratorB1::kAccessesPerVector / 8;

        CUTLASS_PRAGMA_UNROLL
        for (int v = 0; v < IteratorB1::kAccessesPerVector; ++v) {
          auto gmem_ptr = iterator_B1.get();

          cutlass::arch::cp_async_zfill<kSrcBytes, kCacheOpB1>(
              dst_ptr + v, gmem_ptr, iterator_B1.valid());

          ++iterator_B1;
        }
        ++this->smem_iterator_B1_;
      }
    }
  }

  CUTLASS_DEVICE
  static void _prologue(
      IteratorB& iterator_B1,
      int32_t gemm_k_iterations_1,
      SmemIteratorB1& smem_iterator_B1_) {
    // Issue several complete stages
    CUTLASS_PRAGMA_UNROLL
    for (int stage = 0; stage < kNumStagesConcurrentLoad;
         ++stage, --gemm_k_iterations_1) {
      iterator_B1.set_residual_tile(gemm_k_iterations_1 == 1);
      iterator_B1.clear_mask(gemm_k_iterations_1 == 0);

      iterator_B1.set_iteration_index(0);
      smem_iterator_B1_.set_iteration_index(0);

      // Load for operand B
      CUTLASS_PRAGMA_UNROLL
      for (int j = 0; j < Detail::TBLoadIterationsB1; ++j) {
        typename IteratorB1::AccessType* dst_ptr =
            reinterpret_cast<typename IteratorB1::AccessType*>(
                smem_iterator_B1_.get());

        CUTLASS_PRAGMA_UNROLL
        for (int v = 0; v < IteratorB1::kAccessesPerVector; ++v) {
          int const kSrcBytes =
              sizeof_bits<typename IteratorB1::Element>::value *
              IteratorB1::ThreadMap::kElementsPerAccess /
              IteratorB1::kAccessesPerVector / 8;

          cutlass::arch::cp_async_zfill<kSrcBytes, kCacheOpB1>(
              dst_ptr + v, iterator_B1.get(), iterator_B1.valid());

          ++iterator_B1;
        }

        ++smem_iterator_B1_;
      }

      // Move to the next stage
      iterator_B1.add_tile_offset({1, 0});

      smem_iterator_B1_.add_tile_offset({1, 0});

      // Defines the boundary of a stage of cp.async.
      cutlass::arch::cp_async_fence();
    }
    iterator_B1.set_residual_tile(gemm_k_iterations_1 == 1);
    iterator_B1.clear_mask(gemm_k_iterations_1 == 0);
  }

  /// Perform a threadblock-scoped matrix multiply-accumulate
  CUTLASS_DEVICE
  void operator()(
      ///< problem size of GEMM
      int gemm_k_iterations_1_,
      ///< destination accumulator tile
      FragmentC1& accum,
      ///< iterator over B1 operand in global memory
      IteratorB1 iterator_B1,
      ///< initial value of accumulator
      FragmentC1 const& src_accum) {
    // 2nd Gemm

    //
    // Prologue
    //
    // Perform accumulation in the 'd' output operand
    accum = src_accum;

    if (!prologue_done_) {
      _prologue(iterator_B1, gemm_k_iterations_1_, smem_iterator_B1_);
    } else if (!kSmemContainsEntireB) {
      // Restore the iterators increments

      int gemm_k_iterations_1 = gemm_k_iterations_1_;
      // Issue several complete stages
      CUTLASS_PRAGMA_UNROLL
      for (int stage = 0; stage < kNumStagesConcurrentLoad;
           ++stage, --gemm_k_iterations_1) {
        iterator_B1.set_iteration_index(0);
        this->smem_iterator_B1_.set_iteration_index(0);

        // Load for operand B
        CUTLASS_PRAGMA_UNROLL
        for (int j = 0; j < Detail::TBLoadIterationsB1; ++j) {
          CUTLASS_PRAGMA_UNROLL
          for (int v = 0; v < IteratorB1::kAccessesPerVector; ++v) {
            ++iterator_B1;
          }
          ++this->smem_iterator_B1_;
        }
        iterator_B1.add_tile_offset({1, 0});
        this->smem_iterator_B1_.add_tile_offset({1, 0});
      }
      iterator_B1.set_residual_tile(gemm_k_iterations_1 <= 1);
      iterator_B1.clear_mask(gemm_k_iterations_1 <= 0);
    }

    // DEPBAR+SYNC
    cutlass::arch::cp_async_wait<kNumStagesConcurrentLoad - 1>();
    __syncthreads();

    // remember that WarpFragmentAScale and WarpIteratorAScale are no-op/empty
    // if scaling is disabled.

    // Pair of fragments used to overlap shared memory loads and math
    // instructions
    WarpLoadedFragmentA1 warp_loaded_frag_A1[2];
    WarpLoadedFragmentA1Scale warp_loaded_frag_A1_scale[2];
    WarpLoadedFragmentB1 warp_loaded_frag_B1[2];
    WarpTransformedFragmentA1 warp_transformed_frag_A1[2];
    WarpTransformedFragmentB1 warp_transformed_frag_B1[2];

    Operator1 warp_mma1;

    warp_tile_iterator_A1_.load(warp_loaded_frag_A1[0]);
    ++warp_tile_iterator_A1_;

    warp_tile_iterator_A1_scale_.load(warp_loaded_frag_A1_scale[0]);
    ++warp_tile_iterator_A1_scale_;

    this->warp_tile_iterator_B_.set_kgroup_index(0);
    this->warp_tile_iterator_B_.load(warp_loaded_frag_B1[0]);
    ++this->warp_tile_iterator_B_;

    int smem_write_stage_idx = Base::kStages - 1;
    int smem_read_stage_idx = 0;

    warp_mma1.transform(
        warp_transformed_frag_A1[0],
        warp_transformed_frag_B1[0],
        FragmentAScaler::apply(
            warp_loaded_frag_A1[0], warp_loaded_frag_A1_scale[0]),
        warp_loaded_frag_B1[0]);

    // tf32x3 kernels use staging accumulation. warp_mma uses a temporary
    // accumulator and this temporary accumulator is added to the final
    // accumulator once in every mainloop iteration.
    plus<FragmentC1> plus_accum;

    FragmentC1 tmp_accum;

    if (platform::is_same<
            typename Operator1::MathOperator,
            arch::OpMultiplyAddFastF32>::value ||
        platform::is_same<
            typename Operator1::MathOperator,
            arch::OpMultiplyAddComplexFastF32>::value) {
      tmp_accum.clear();
    }

    //
    // Mainloop
    //

    CUTLASS_PRAGMA_UNROLL
    for (int gemm_k_iterations_1 = gemm_k_iterations_1_ - (Base::kStages - 1);
         gemm_k_iterations_1 > (-Base::kStages + 1);
         gemm_k_iterations_1--) {
      //
      // Loop over GEMM K dimension
      //

      // Computes a warp-level GEMM on data held in shared memory
      // Each "warp_mma_k" refers to a warp-level matrix multiply-accumulate
      CUTLASS_PRAGMA_UNROLL
      for (int warp_mma_k = 0; warp_mma_k < Base::kWarpGemmIterations1;
           ++warp_mma_k) {
        // Load warp-level tile from accumulator fragment (A)
        // or shared memory (operand B)
        this->warp_tile_iterator_B_.set_kgroup_index(
            (warp_mma_k + 1) % Base::kWarpGemmIterations1);
        // skip warp tile loading for the last kgroup (we are out of the buf)
        if (gemm_k_iterations_1 > (-Base::kStages + 2) ||
            warp_mma_k < Base::kWarpGemmIterations1 - 1) {
          warp_tile_iterator_A1_.load(
              warp_loaded_frag_A1[(warp_mma_k + 1) % 2]);
          warp_tile_iterator_A1_scale_.load(
              warp_loaded_frag_A1_scale[(warp_mma_k + 1) % 2]);
          this->warp_tile_iterator_B_.load(
              warp_loaded_frag_B1[(warp_mma_k + 1) % 2]);
        }
        ++warp_tile_iterator_A1_;
        ++warp_tile_iterator_A1_scale_;
        ++this->warp_tile_iterator_B_;

        if (warp_mma_k > 0)
          warp_mma1.transform(
              warp_transformed_frag_A1[warp_mma_k % 2],
              warp_transformed_frag_B1[warp_mma_k % 2],
              FragmentAScaler::apply(
                  warp_loaded_frag_A1[warp_mma_k % 2],
                  warp_loaded_frag_A1_scale[warp_mma_k % 2]),
              warp_loaded_frag_B1[warp_mma_k % 2]);

        if (platform::is_same<
                typename Operator1::MathOperator,
                arch::OpMultiplyAddFastF32>::value ||
            platform::is_same<
                typename Operator1::MathOperator,
                arch::OpMultiplyAddComplexFastF32>::value) {
          warp_mma1(
              tmp_accum,
              warp_transformed_frag_A1[warp_mma_k % 2],
              warp_transformed_frag_B1[warp_mma_k % 2],
              tmp_accum);

          if (warp_mma_k == 0) {
            accum = plus_accum(accum, tmp_accum);
            tmp_accum.clear();
          }
        } else {
          warp_mma1(
              accum,
              warp_transformed_frag_A1[warp_mma_k % 2],
              warp_transformed_frag_B1[warp_mma_k % 2],
              accum);
        }

        // Issue global->shared copies for the this stage
        if (warp_mma_k < Base::kWarpGemmIterations1 - 1) {
          int group_start_iteration_B1;

          group_start_iteration_B1 = warp_mma_k * Detail::kAccessesPerGroupB1;

          if (!kSmemContainsEntireB) {
            copy_tiles_and_advance_1(iterator_B1, group_start_iteration_B1);
          }
        }

        if (warp_mma_k + 2 == Base::kWarpGemmIterations1) {
          int group_start_iteration_B1;
          group_start_iteration_B1 =
              (warp_mma_k + 1) * Detail::kAccessesPerGroupB1;

          if (!kSmemContainsEntireB) {
            copy_tiles_and_advance_1(iterator_B1, group_start_iteration_B1);
          }

          // Inserts a memory fence between stages of cp.async instructions.
          cutlass::arch::cp_async_fence();

          // Waits until kStages-2 stages have committed.
          arch::cp_async_wait<kNumStagesConcurrentLoad - 1>();
          __syncthreads();

          // Move to the next stage
          iterator_B1.add_tile_offset({1, 0});

          this->smem_iterator_B1_.add_tile_offset({1, 0});

          // Add negative offsets to return iterators to the 'start' of the
          // circular buffer in shared memory
          if (!kSmemContainsEntireB) {
            if (smem_write_stage_idx == (Base::kStages - 1)) {
              this->smem_iterator_B1_.add_tile_offset({-Base::kStages, 0});
              smem_write_stage_idx = 0;
            } else {
              ++smem_write_stage_idx;
            }

            if (smem_read_stage_idx == (Base::kStages - 1)) {
              this->warp_tile_iterator_B_.add_tile_offset(
                  {-Base::kStages * Policy1::kPartitionsK *
                       Base::kWarpGemmIterations1,
                   0});
              smem_read_stage_idx = 0;
            } else {
              ++smem_read_stage_idx;
            }
          }

          iterator_B1.set_residual_tile(gemm_k_iterations_1 == 2);
          iterator_B1.clear_mask(gemm_k_iterations_1 == 1);
        }

        // Do any conversions feeding the first stage at the end of the loop so
        // we can start right away on mma instructions
        if (warp_mma_k + 1 == Base::kWarpGemmIterations1)
          warp_mma1.transform(
              warp_transformed_frag_A1[(warp_mma_k + 1) % 2],
              warp_transformed_frag_B1[(warp_mma_k + 1) % 2],
              FragmentAScaler::apply(
                  warp_loaded_frag_A1[(warp_mma_k + 1) % 2],
                  warp_loaded_frag_A1_scale[(warp_mma_k + 1) % 2]),
              warp_loaded_frag_B1[(warp_mma_k + 1) % 2]);
      }
    }

    if (platform::is_same<
            typename Operator1::MathOperator,
            arch::OpMultiplyAddFastF32>::value ||
        platform::is_same<
            typename Operator1::MathOperator,
            arch::OpMultiplyAddComplexFastF32>::value) {
      accum = plus_accum(accum, tmp_accum);
    }
  }
};

// Converts a "regular" Mma into their counterpart from shared memory
template <
    typename Mma_,
    int kMaxK,
    typename WarpIteratorA_,
    /// whether or not to apply elementwise multiplication of operand A by
    /// another matrix in shared memory before usage in A @ B
    bool kScaleOperandA,
    bool kTransposeA = false>
struct DefaultMmaFromSharedMemory;

// Mma pipelined
template <
    /// Size of the Gemm problem - concept: gemm::GemmShape<>
    typename Shape_,
    /// Iterates over tiles of A operand in global memory
    //  (concept: ReadableTileIterator | ForwardTileIterator |
    //  MaskedTileIterator)
    typename IteratorA_,
    /// Iterates over tiles of A operand in shared memory
    /// (concept: WriteableTileIterator | RandomAccessTileIterator)
    typename SmemIteratorA_,
    typename WarpIteratorA_,
    /// Iterates over tiles of B operand in global memory
    //  (concept: ReadableTileIterator | ForwardTileIterator |
    //  MaskedTileIterator)
    typename IteratorB_,
    /// Iterates over tiles of B operand in shared memory
    /// (concept: WriteableTileIterator | RandomAccessTileIterator)
    typename SmemIteratorB_,
    /// Data type of accumulator matrix
    typename ElementC_,
    /// Data type of accumulator matrix
    typename LayoutC_,
    /// Policy describing tuning details (concept: MmaPolicy)
    typename Policy_,
    /// Transformation applied to A operand
    typename TransformA_,
    /// Transformation applied to B operand
    typename TransformB_,
    // Max MMA problem size K
    int kMaxK,
    /// whether or not to apply elementwise multiplication of operand A by
    /// another matrix in shared memory before usage in A @ B
    bool kScaleOperandA,
    bool kTransposeA>
struct DefaultMmaFromSharedMemory<
    MmaPipelined<
        Shape_,
        IteratorA_,
        SmemIteratorA_,
        IteratorB_,
        SmemIteratorB_,
        ElementC_,
        LayoutC_,
        Policy_,
        TransformA_,
        TransformB_>,
    kMaxK,
    WarpIteratorA_,
    kScaleOperandA,
    kTransposeA> {
  using RegularMma = MmaPipelined<
      Shape_,
      IteratorA_,
      SmemIteratorA_,
      IteratorB_,
      SmemIteratorB_,
      ElementC_,
      LayoutC_,
      Policy_,
      TransformA_,
      TransformB_>;

  using WarpShape = typename Policy_::Operator::Shape;
  using InstructionShape = typename Policy_::Operator::InstructionShape;
  using ArchMmaOperator = typename Policy_::Operator;

  static constexpr bool kIsTransposedA = false;
  using WarpIteratorA = WarpIteratorA_;
  using IteratorB =
      typename cutlass::transform::threadblock::MakeIteratorResidualLast<
          IteratorB_>::Iterator;

  using Mma = typename cutlass::gemm::threadblock::MmaPipelinedFromSharedMemory<
      Shape_,
      WarpIteratorA,
      kScaleOperandA,
      kMaxK,
      IteratorB,
      SmemIteratorB_,
      ElementC_,
      LayoutC_,
      Policy_>;
};

template <
    /// Size of the Gemm problem - concept: gemm::GemmShape<>
    typename Shape_,
    /// Iterates over tiles of A operand in global memory
    //  (concept: ReadableTileIterator | ForwardTileIterator |
    //  MaskedTileIterator)
    typename IteratorA_,
    /// Iterates over tiles of A operand in shared memory
    /// (concept: WriteableTileIterator | RandomAccessTileIterator)
    typename SmemIteratorA_,
    typename WarpIteratorA_,
    /// Cache operation for operand A
    cutlass::arch::CacheOperation::Kind CacheOpA,
    /// Iterates over tiles of B operand in global memory
    //  (concept: ReadableTileIterator | ForwardTileIterator |
    //  MaskedTileIterator)
    typename IteratorB_,
    /// Iterates over tiles of B operand in shared memory
    /// (concept: WriteableTileIterator | RandomAccessTileIterator)
    typename SmemIteratorB_,
    /// Cache operation for operand B
    cutlass::arch::CacheOperation::Kind CacheOpB,
    /// Data type of accumulator matrix
    typename ElementC_,
    /// Data type of accumulator matrix
    typename LayoutC_,
    /// Policy describing tuning details (concept: MmaPolicy)
    typename Policy_,
    /// Number of stages,
    int Stages,
    /// Use zfill or predicate for out-of-bound cp.async
    SharedMemoryClearOption SharedMemoryClear,
    int kMaxK,
    /// whether or not to apply elementwise multiplication of operand A by
    /// another matrix in shared memory before usage in A @ B
    bool kScaleOperandA,
    bool kTransposeA>
struct DefaultMmaFromSharedMemory<
    MmaMultistage<
        Shape_,
        IteratorA_,
        SmemIteratorA_,
        CacheOpA,
        IteratorB_,
        SmemIteratorB_,
        CacheOpB,
        ElementC_,
        LayoutC_,
        Policy_,
        Stages,
        SharedMemoryClear>,
    kMaxK,
    WarpIteratorA_,
    kScaleOperandA,
    kTransposeA> {
  using RegularMma = MmaMultistage<
      Shape_,
      IteratorA_,
      SmemIteratorA_,
      CacheOpA,
      IteratorB_,
      SmemIteratorB_,
      CacheOpB,
      ElementC_,
      LayoutC_,
      Policy_,
      Stages,
      SharedMemoryClear>;

  using WarpShape = typename Policy_::Operator::Shape;
  using InstructionShape = typename Policy_::Operator::InstructionShape;
  using WarpIteratorTranspose = TransposeWarpIterator<WarpIteratorA_>;
  static constexpr bool kIsTransposedA =
      WarpIteratorTranspose::kSupportsTranspose && kTransposeA;
  using WarpIteratorA = typename platform::conditional<
      kIsTransposedA,
      typename WarpIteratorTranspose::Iterator,
      WarpIteratorA_>::type;

  // Reduce the number of stages if we don't need that many
  static int constexpr kStagesMax =
      (kMaxK + int(Shape_::kK) - 1) / int(Shape_::kK);
  static int constexpr kStages = cutlass::const_min(Stages, kStagesMax);

  using IteratorB =
      typename cutlass::transform::threadblock::MakeIteratorResidualLast<
          IteratorB_>::Iterator;
  using Mma =
      typename cutlass::gemm::threadblock::MmaMultistageFromSharedMemory<
          Shape_,
          WarpIteratorA,
          kScaleOperandA,
          IteratorB,
          SmemIteratorB_,
          RegularMma::kCacheOpB,
          ElementC_,
          LayoutC_,
          Policy_,
          kStages,
          kMaxK>;
};

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

template <
    typename IteratorC,
    typename Operator,
    typename scalar_t,
    typename WarpShape_,
    typename ThreadblockShape_>
struct B2bGemm;

// Tensor Cores >= Sm75 specialization (Ampere ...)
template < /// Size of the matrix to load (concept: MatrixShape)
    typename Shape_,
    /// Element type
    typename Element_,
    /// Layout of operand in memory
    typename Layout_,
    /// Shape of one matrix product operation (concept: MatrixShape)
    typename InstructionShape_,
    /// Interval between adjacent *MMA instructions (in units of MMA
    /// instructions, concept: MatrixShape)
    typename OpDelta_,
    typename Operator,
    typename scalar_t,
    typename WarpShape_,
    typename ThreadblockShape_>
struct B2bGemm<
    cutlass::gemm::warp::MmaTensorOpAccumulatorTileIterator<
        Shape_,
        Element_,
        Layout_,
        InstructionShape_,
        OpDelta_>,
    Operator,
    scalar_t,
    WarpShape_,
    ThreadblockShape_> {
  using IteratorC =
      typename cutlass::gemm::warp::MmaTensorOpAccumulatorTileIterator<
          Shape_,
          Element_,
          Layout_,
          InstructionShape_,
          OpDelta_>;
  using FragmentC = typename IteratorC::Fragment;
  using InstructionShape = InstructionShape_;
  using WarpShape = WarpShape_;
  using ThreadblockShape = ThreadblockShape_;
  using accum_t = Element_;
  using lse_scalar_t = float;

  using SmemAccumulatorLayout = cutlass::layout::RowMajor;

  // Iterator to load accumulators (results of matmul in registers)
  using FragmentIteratorAccumulator =
      cutlass::epilogue::warp::FragmentIteratorTensorOp<
          WarpShape,
          InstructionShape,
          accum_t,
          typename Operator::Policy::Operator::FragmentC,
          cutlass::layout::RowMajor>;

  // Iterator to store to shared-memory
  using SmemIteratorD0 = typename cutlass::epilogue::warp::TileIteratorTensorOp<
      WarpShape,
      InstructionShape,
      scalar_t, // accum_t,
      SmemAccumulatorLayout>;
  using AccumulatorSharedStorage =
      cutlass::gemm::threadblock::AccumulatorSharedStorage<
          ThreadblockShape,
          typename SmemIteratorD0::Element,
          typename SmemIteratorD0::TensorLayout,
          typename SmemIteratorD0::Padding>;
  // We need to provide an operation for the epilogue. Let's create an
  // operation that does nothing (ScaleType::Nothing), just converts
  // from accum_t (float) -> scalar_t (can be half)
  using OutputOpNoOp = cutlass::epilogue::thread::LinearCombination<
      typename SmemIteratorD0::Element, // ElementOutput
      FragmentIteratorAccumulator::Fragment::kElements,
      accum_t, // ElementAccumulator
      typename SmemIteratorD0::Element, // ElementCompute
      cutlass::epilogue::thread::ScaleType::Nothing>;
  using Epilogue = cutlass::epilogue::threadblock::EpilogueSmemAccumulator<
      SmemIteratorD0,
      FragmentIteratorAccumulator,
      SmemIteratorD0, // ScaleBiasIterator - not used
      OutputOpNoOp>;

  // Epilogue 2: with LSE (for backwards pass)
  static int const kElementsPerAccess = 2; // TODO: Why 2?
  using IteratorAccumulatorLSE =
      cutlass::transform::threadblock::VectorIterator<
          cutlass::transform::threadblock::PredicatedVectorAccessIterator<
              // Shape
              cutlass::MatrixShape<ThreadblockShape::kM, ThreadblockShape::kN>,
              // WarpShape
              cutlass::MatrixShape<WarpShape::kM, WarpShape::kN>,
              lse_scalar_t,
              cutlass::layout::RowMajor,
              kElementsPerAccess>>;
  using EpilogueOpApplyLSE = cutlass::epilogue::thread::ApplyLogSumExp<
      scalar_t, // ElementOutput_
      lse_scalar_t, // ElementLSE_
      accum_t, // ElementAccumulator_
      accum_t, // ElementCompute_
      128 / cutlass::sizeof_bits<scalar_t>::value
      // FragmentIteratorAccumulator::Fragment::kElements
      // InstructionShape::kM * InstructionShape::kN / 32
      >;
  using EpilogueWithLSE =
      cutlass::epilogue::threadblock::EpilogueSmemAccumulator<
          SmemIteratorD0,
          FragmentIteratorAccumulator,
          IteratorAccumulatorLSE,
          EpilogueOpApplyLSE>;

  static void CUTLASS_DEVICE accumToSmem(
      AccumulatorSharedStorage& shared_storage,
      FragmentC const& accum,
      int lane_id,
      cutlass::MatrixCoord const& tile_coords) {
    SmemIteratorD0 smem_iterator_attn(shared_storage.accum_ref(), lane_id);
    smem_iterator_attn.add_tile_offset(
        tile_coords *
        cutlass::MatrixCoord{
            SmemIteratorD0::TileIterations::kRow,
            SmemIteratorD0::TileIterations::kColumn});
    Epilogue epilogue;
    epilogue(OutputOpNoOp({}), smem_iterator_attn, accum);
  }

  static void CUTLASS_DEVICE accumApplyLSEToSmem(
      AccumulatorSharedStorage& shared_storage,
      FragmentC& accum,
      lse_scalar_t const* lse,
      int32_t lse_extents,
      int thread_id,
      int warp_id,
      int lane_id,
      cutlass::MatrixCoord const& tile_coords) {
    constexpr int32_t kAlignLSE = 32;
    IteratorAccumulatorLSE iterator_lse(
        lse,
        {(int32_t)0, (int32_t)ceil_div(lse_extents, kAlignLSE) * kAlignLSE},
        thread_id,
        warp_id,
        cutlass::MatrixCoord{0, 0} // offset
    );

    SmemIteratorD0 smem_iterator_attn(shared_storage.accum_ref(), lane_id);
    smem_iterator_attn.add_tile_offset(
        tile_coords *
        cutlass::MatrixCoord{
            SmemIteratorD0::TileIterations::kRow,
            SmemIteratorD0::TileIterations::kColumn});
    EpilogueWithLSE epilogue;
    EpilogueOpApplyLSE minus_lse_exp({});
    epilogue(
        minus_lse_exp,
        smem_iterator_attn,
        accum,
        // scale - unused
        iterator_lse,
        // bias
        iterator_lse);
  }
};

// Volta Specialization
// only supported for f16
template <typename Operator, typename WarpShape_, typename ThreadblockShape_>
struct B2bGemm<
    cutlass::gemm::warp::MmaVoltaTensorOpAccumulatorTileIterator<
        cutlass::MatrixShape<32, 32>,
        float,
        cutlass::layout::RowMajor,
        cutlass::gemm::GemmShape<16, 16, 4>,
        cutlass::MatrixShape<1, 1>>,
    Operator,
    cutlass::half_t,
    WarpShape_,
    ThreadblockShape_> {
  using IteratorC =
      cutlass::gemm::warp::MmaVoltaTensorOpAccumulatorTileIterator<
          cutlass::MatrixShape<32, 32>,
          float,
          cutlass::layout::RowMajor,
          cutlass::gemm::GemmShape<16, 16, 4>,
          cutlass::MatrixShape<1, 1>>;
  using scalar_t = cutlass::half_t;
  using accum_t = IteratorC::Element;
  using WarpShape = WarpShape_;
  using ThreadblockShape = ThreadblockShape_;
  using FragmentC = IteratorC::Fragment;
  using lse_scalar_t = float;

  // Storage in shared-memory for Q.Kt
  using SmemAccumulatorLayout =
      cutlass::layout::RowMajorVoltaTensorOpMultiplicandCrosswise<16, 32>;
  using AccumulatorSharedStorage =
      cutlass::gemm::threadblock::AccumulatorSharedStorage<
          ThreadblockShape,
          scalar_t,
          SmemAccumulatorLayout,
          cutlass::MatrixShape<0, 0> // Padding
          >;
  using TensorRef = cutlass::TensorRef<scalar_t, SmemAccumulatorLayout>;
  using Policy = typename IteratorC::Policy;
  using Element = accum_t;
  // Those are MmaVoltaTensorOpAccumulatorTileIterator private fields
  // Let's copy their values
  static int const kElementsPerPartial = 4;
  using EleShapePerPatial = typename cutlass::platform::conditional<
      cutlass::platform::is_same<Element, float>::value,
      cutlass::MatrixShape<2, 2>,
      cutlass::MatrixShape<1, 4>>::type;
  static int const kElementsPerMma = 8;
  static int const kAccumulatorPatials = 2;
  using QuadShapePerPatialMma = cutlass::MatrixShape<4, 4>;

  static void CUTLASS_DEVICE accumToSmem(
      AccumulatorSharedStorage& shared_storage,
      FragmentC const& accum,
      int lane_id,
      cutlass::MatrixCoord const& tile_coords) {
    // ctor - from MmaVoltaTensorOpAccumulatorTileIterator
    TensorRef ref_(shared_storage.accum_ref());
    int quad = (lane_id >> 2);
    int lane_in_quad = (lane_id & 3);
    int accum_m, accum_n;

    if (cutlass::platform::is_same<Element, float>::value) {
      // (quad[2],quad[0])+lane_in_quad[0]
      accum_m = (((quad & 0x4) >> 1) + (quad & 0x1)) * 8 + (lane_in_quad & 1);
      // (quad[1])+lane_in_quad[1]
      accum_n =
          ((quad >> 1) & 0x1) * kElementsPerPartial * kAccumulatorPatials +
          (lane_in_quad & 2);
    } else {
      accum_m = (((quad & 0x4) >> 1) + (quad & 0x1)) * 8 +
          lane_in_quad; // (quad[2],quad[0])
      accum_n = ((quad >> 1) & 0x1) * kElementsPerPartial * kAccumulatorPatials;
    }
    cutlass::MatrixCoord lane_offset(accum_m, accum_n);

    // Tile offset
    ref_.add_coord_offset(
        tile_coords *
        cutlass::MatrixCoord(
            {IteratorC::Shape::kRow, IteratorC::Shape::kColumn}));

    using AccessType = cutlass::Array<scalar_t, EleShapePerPatial::kColumn>;

    // store - from MmaVoltaTensorOpAccumulatorTileIterator
    CUTLASS_PRAGMA_UNROLL
    for (int tile_n = 0; tile_n < Policy::TileIterations::kColumn; ++tile_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int tile_m = 0; tile_m < Policy::TileIterations::kRow; ++tile_m) {
        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 =
                (((tile_n * Policy::TileIterations::kRow + tile_m) *
                      Policy::MmaIterations::kColumn +
                  mma_n) *
                     Policy::MmaIterations::kRow +
                 mma_m) *
                kElementsPerMma;

            CUTLASS_PRAGMA_UNROLL
            for (int p = 0; p < kAccumulatorPatials; ++p) {
              CUTLASS_PRAGMA_UNROLL
              for (int m = 0; m < EleShapePerPatial::kRow; ++m) {
                int accum_m = tile_m * Policy::InterleavedTile::kRow +
                    mma_m * QuadShapePerPatialMma::kRow + m * 2;
                int accum_n = tile_n * Policy::InterleavedTile::kColumn +
                    mma_n * QuadShapePerPatialMma::kColumn +
                    p * Policy::InterleavedTile::kColumn / 2;
                int r = (accum_m + lane_offset.row());
                AccessType to_store;
                CUTLASS_PRAGMA_UNROLL
                for (int n = 0; n < EleShapePerPatial::kColumn; ++n) {
                  int idx = mma_accum_start + p * kElementsPerPartial +
                      m * EleShapePerPatial::kColumn + n;
                  int c = (accum_n + n + lane_offset.column());
                  to_store[n] = scalar_t(accum[idx]);
                }
                int c = (accum_n + lane_offset.column());
                assert(r < 32);
                assert(c < 32);
                *reinterpret_cast<AccessType*>(
                    ref_.data() + ref_.offset({r, c})) = to_store;
              }
            }
          }
        }
      }
    }
  }

  static void CUTLASS_DEVICE accumApplyLSEToSmem(
      AccumulatorSharedStorage& shared_storage,
      typename IteratorC::Fragment& accum,
      lse_scalar_t const* lse,
      int lse_extent,
      int thread_id,
      int warp_id,
      int lane_id,
      cutlass::MatrixCoord const& tile_coords) {
    // Non-optimized way to apply LSE to registers
    // NOTE: accum is attn.T
    // TODO: Optimize for each architecture
    static constexpr int WarpSize = 32;
    using AccumLambdaIterator =
        typename DefaultMmaAccumLambdaIterator<IteratorC, accum_t, WarpSize>::
            Iterator;
    auto lane_offset =
        AccumLambdaIterator::get_lane_offset(lane_id, warp_id, tile_coords);

    cutlass::Array<lse_scalar_t, IteratorC::Fragment::kElements> lse_prefetched;
    lse_prefetched.clear();
    int rowIdx = 0;
    int colIdx = 0;
    AccumLambdaIterator::iterateRows(
        lane_offset,
        [&](int accum_m) {
          ++rowIdx;
          colIdx = 0;
        },
        [&](int accum_m, int accum_n, int idx) {
          if (rowIdx == 1) {
            lse_prefetched[colIdx] = accum_n < lse_extent
                ? lse[accum_n]
                : platform::numeric_limits<accum_t>::infinity();
          }
          accum[idx] = expf(accum[idx] - lse_prefetched[colIdx]);
          ++colIdx;
        },
        [&](int accum_m) {});
    accumToSmem(shared_storage, accum, lane_id, tile_coords);
  }
};

// Simt Specialization
// for f32 on Sm70-Sm75 and f16/f32 below

template <
    typename Operator,
    typename OperatorPolicy,
    typename scalar_t,
    typename WarpShape_,
    typename ThreadblockShape_>
struct B2bGemm<
    cutlass::gemm::warp::MmaSimtTileIterator<
        cutlass::MatrixShape<32, 32>,
        cutlass::gemm::Operand::kC,
        float,
        cutlass::layout::RowMajor,
        OperatorPolicy,
        1,
        1>,
    Operator,
    scalar_t,
    WarpShape_,
    ThreadblockShape_> {
  using IteratorC = cutlass::gemm::warp::MmaSimtTileIterator<
      cutlass::MatrixShape<32, 32>,
      cutlass::gemm::Operand::kC,
      float,
      cutlass::layout::RowMajor,
      OperatorPolicy,
      1,
      1>;
  using accum_t = typename IteratorC::Element;
  using WarpShape = WarpShape_;
  using ThreadblockShape = ThreadblockShape_;
  using FragmentC = typename IteratorC::Fragment;
  using lse_scalar_t = float;

  // Storage in shared-memory for Q.Kt
  using AccumulatorSharedStorage =
      cutlass::gemm::threadblock::AccumulatorSharedStorage<
          ThreadblockShape,
          scalar_t,
          cutlass::layout::ColumnMajor,
          cutlass::MatrixShape<0, 0> // Padding
          >;

  static void CUTLASS_DEVICE accumToSmem(
      AccumulatorSharedStorage& shared_storage,
      FragmentC const& accum,
      int lane_id,
      cutlass::MatrixCoord const& tile_coords) {
    using Policy = typename IteratorC::Policy;
    using Element = typename IteratorC::Element;
    using Iterations = typename IteratorC::Iterations;
    using Delta = typename IteratorC::Delta;

    auto ref_ = shared_storage.accum_ref();
    // ctor - MmaSimtTileIterator
    // compute offset based on thread ID and lane layout
    typename Policy::LaneLayout lane_layout = Policy::get_lane_layout();

    MatrixCoord lane_offset = lane_layout.inverse(lane_id) *
        MatrixCoord(Policy::LaneMmaShape::kM, Policy::LaneMmaShape::kN);

    ref_.add_coord_offset(lane_offset);

    // Tile offset
    ref_.add_coord_offset(
        tile_coords *
        cutlass::MatrixCoord(
            {IteratorC::Shape::kRow, IteratorC::Shape::kColumn}));

    // store - MmaSimtTileIterator
    CUTLASS_PRAGMA_UNROLL
    for (int mma_n = 0; mma_n < Iterations::kColumn; ++mma_n) {
      CUTLASS_PRAGMA_UNROLL
      for (int n = 0; n < Policy::LaneMmaShape::kN; ++n) {
        CUTLASS_PRAGMA_UNROLL
        for (int mma_m = 0; mma_m < Iterations::kRow; ++mma_m) {
          CUTLASS_PRAGMA_UNROLL
          for (int m = 0; m < Policy::LaneMmaShape::kM; ++m) {
            int r =
                Policy::LaneMmaShape::kM * (mma_m * Policy::WarpShape::kRow) +
                m;
            int c = mma_n * Delta::kColumn + n;
            int idx = n +
                Policy::LaneMmaShape::kN *
                    (mma_n +
                     Iterations::kColumn *
                         (m + mma_m * Policy::LaneMmaShape::kM));
            ref_.at({r, c}) = scalar_t(accum[idx]);
          }
        }
      }
    }
  }

  static void CUTLASS_DEVICE accumApplyLSEToSmem(
      AccumulatorSharedStorage& shared_storage,
      typename IteratorC::Fragment& accum,
      lse_scalar_t const* lse,
      int lse_extent,
      int thread_id,
      int warp_id,
      int lane_id,
      cutlass::MatrixCoord const& tile_coords) {
    // Non-optimized way to apply LSE to registers
    // NOTE: accum is attn.T
    // TODO: Optimize for each architecture
    static constexpr int WarpSize = 32;
    using AccumLambdaIterator =
        typename DefaultMmaAccumLambdaIterator<IteratorC, accum_t, WarpSize>::
            Iterator;
    auto lane_offset =
        AccumLambdaIterator::get_lane_offset(lane_id, warp_id, tile_coords);

    cutlass::Array<lse_scalar_t, IteratorC::Fragment::kElements> lse_prefetched;
    lse_prefetched.clear();
    int rowIdx = 0;
    int colIdx = 0;
    AccumLambdaIterator::iterateRows(
        lane_offset,
        [&](int accum_m) {
          ++rowIdx;
          colIdx = 0;
        },
        [&](int accum_m, int accum_n, int idx) {
          if (rowIdx == 1) {
            lse_prefetched[colIdx] = accum_n < lse_extent
                ? lse[accum_n]
                : platform::numeric_limits<accum_t>::infinity();
          }
          accum[idx] = expf(accum[idx] - lse_prefetched[colIdx]);
          ++colIdx;
        },
        [&](int accum_m) {});
    accumToSmem(shared_storage, accum, lane_id, tile_coords);
  }
};

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

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