add splitk gridwise

include/ck/tensor_operation/gpu/grid/gridwise_gemm_multiple_d_xdl_splitk_cshuffle.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/multi_index_transform_helper.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/tensor_descriptor_helper.hpp"
+#include "ck/tensor_operation/gpu/grid/block_to_ctile_map.hpp"
+#include "ck/tensor_operation/gpu/grid/gridwise_gemm_pipeline_selector.hpp"
+#include "ck/tensor_operation/gpu/block/blockwise_gemm_xdlops.hpp"
+#include "ck/tensor_operation/gpu/block/thread_group_tensor_slice_transfer_v4r1.hpp"
+#include "ck/tensor_operation/gpu/block/thread_group_tensor_slice_transfer_v7.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+
+namespace ck {
+
+// GEMM:
+//   input : A[M, K]
+//   input : B[N, K]
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+// Assume:
+//   D0, D1, ... and E have the same layout
+template <typename ABDataType, // FIXME: don't assume A/B have same datatype
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          InMemoryDataOperationEnum EGlobalMemoryDataOperation,
+          index_t NumGemmKPrefetchStage,
+          index_t BlockSize,
+          index_t MPerBlock,
+          index_t NPerBlock,
+          index_t KPerBlock,
+          index_t AK1Value,
+          index_t BK1Value,
+          index_t MPerXdl,
+          index_t NPerXdl,
+          index_t MXdlPerWave,
+          index_t NXdlPerWave,
+          typename ABlockTransferThreadClusterLengths_KBatch_AK0_M_AK1,
+          typename ABlockTransferThreadClusterArrangeOrder,
+          typename ABlockTransferSrcAccessOrder,
+          index_t ABlockTransferSrcVectorDim,
+          index_t ABlockTransferSrcScalarPerVector,
+          index_t ABlockTransferDstScalarPerVector_AK1,
+          bool AThreadTransferSrcResetCoordinateAfterRun,
+          index_t ABlockLdsExtraM,
+          typename BBlockTransferThreadClusterLengths_KBatch_BK0_N_BK1,
+          typename BBlockTransferThreadClusterArrangeOrder,
+          typename BBlockTransferSrcAccessOrder,
+          index_t BBlockTransferSrcVectorDim,
+          index_t BBlockTransferSrcScalarPerVector,
+          index_t BBlockTransferDstScalarPerVector_BK1,
+          bool BThreadTransferSrcResetCoordinateAfterRun,
+          index_t BBlockLdsExtraN,
+          index_t CShuffleMXdlPerWavePerShuffle,
+          index_t CShuffleNXdlPerWavePerShuffle,
+          typename CDEBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
+          index_t CDEShuffleBlockTransferScalarPerVector_NPerBlock,
+          LoopScheduler LoopSched,
+          PipelineVersion PipelineVer = PipelineVersion::v1>
+struct GridwiseGemmMultipleD_xdl_splitk_cshuffle
+{
+    static constexpr index_t NumDTensor = DsDataType::Size();
+
+    using GemmSpecialization = ck::tensor_operation::device::GemmSpecialization;
+
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+    static constexpr auto I4 = Number<4>{};
+    static constexpr auto I5 = Number<5>{};
+    static constexpr auto I6 = Number<6>{};
+    static constexpr auto I7 = Number<7>{};
+
+    // K1 should be Number<...>
+    static constexpr auto AK1         = Number<AK1Value>{};
+    static constexpr auto BK1         = Number<BK1Value>{};
+    static constexpr auto AK0PerBlock = Number<KPerBlock / AK1Value>{};
+    static constexpr auto BK0PerBlock = Number<KPerBlock / BK1Value>{};
+
+    using ThisThreadBlock = ThisThreadBlock<BlockSize>;
+
+    using GridwiseGemmPipe = remove_cvref_t<decltype(
+        GridwiseGemmPipeline_Selector<PipelineVer, NumGemmKPrefetchStage, LoopSched>())>;
+
+    // denorm test fix, required to work around fp16 mfma issue
+    // we convert fp16->fp32->bf16 and execute bf16 mfma instruction
+    // when mfma if fixed, remove this section and update
+    // ABDataTypeAdjusted -> ABDataType throughout this file
+#if CK_WORKAROUND_DENORM_FIX
+    using ABDataTypeAdjusted =
+        conditional_t<is_same_v<ABDataType, ck::half_t>, ck::bhalf_t, ABDataType>;
+#else
+    using ABDataTypeAdjusted = ABDataType;
+#endif
+
+    __host__ __device__ static constexpr auto GetABlockDescriptor_KBatch_AK0PerBlock_MPerBlock_AK1()
+    {
+        // A matrix in LDS memory, dst of blockwise copy
+        return make_naive_tensor_descriptor(
+            make_tuple(I1, AK0PerBlock, Number<MPerBlock>{}, AK1),
+            make_tuple(AK0PerBlock * Number<MPerBlock + ABlockLdsExtraM>{} * AK1, Number<MPerBlock + ABlockLdsExtraM>{} * AK1, AK1, I1));
+    }
+
+    __host__ __device__ static constexpr auto GetBBlockDescriptor_KBatch_BK0PerBlock_NPerBlock_BK1()
+    {
+        // B matrix in LDS memory, dst of blockwise copy
+        return make_naive_tensor_descriptor(
+            make_tuple(I1, BK0PerBlock, Number<NPerBlock>{}, BK1),
+            make_tuple(BK0PerBlock * Number<NPerBlock + BBlockLdsExtraN>{} * BK1, Number<NPerBlock + BBlockLdsExtraN>{} * BK1, BK1, I1));
+    }
+
+    __host__ __device__ static constexpr auto GetABlockDescriptor_AK0PerBlock_MPerBlock_AK1()
+    {
+        // A matrix in LDS memory, dst of blockwise copy
+        return make_naive_tensor_descriptor(
+            make_tuple(AK0PerBlock, Number<MPerBlock>{}, AK1),
+            make_tuple(Number<MPerBlock + ABlockLdsExtraM>{} * AK1, AK1, I1));
+    }
+
+    __host__ __device__ static constexpr auto GetBBlockDescriptor_BK0PerBlock_NPerBlock_BK1()
+    {
+        // B matrix in LDS memory, dst of blockwise copy
+        return make_naive_tensor_descriptor(
+            make_tuple(BK0PerBlock, Number<NPerBlock>{}, BK1),
+            make_tuple(Number<NPerBlock + BBlockLdsExtraN>{} * BK1, BK1, I1));
+    }
+
+    __host__ __device__ static constexpr auto
+    GetCShuffleBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock()
+    {
+        constexpr index_t MWave = MPerBlock / (MXdlPerWave * MPerXdl);
+        constexpr index_t NWave = NPerBlock / (NXdlPerWave * NPerXdl);
+
+        constexpr auto c_shuffle_block_desc_mblock_mperblock_nblock_nperblock =
+            make_naive_tensor_descriptor_packed(
+                make_tuple(I1,
+                           Number<CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl>{},
+                           I1,
+                           Number<CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>{}));
+
+        return c_shuffle_block_desc_mblock_mperblock_nblock_nperblock;
+    }
+
+    // ck::Tuple<const D0DataType*, const D1DataType*, ...>
+    static constexpr auto MakeDsGridPointer()
+    {
+        return generate_tuple(
+            [&](auto i) {
+                using DDataType = remove_cvref_t<tuple_element_t<i.value, DsDataType>>;
+
+                return static_cast<const DDataType*>(nullptr);
+            },
+            Number<NumDTensor>{});
+    }
+
+    __host__ __device__ static constexpr index_t GetSharedMemoryNumberOfByte()
+    {
+        // LDS allocation for A and B: be careful of alignment
+        constexpr auto a_block_desc_ak0_m_ak1 = GetABlockDescriptor_AK0PerBlock_MPerBlock_AK1();
+        constexpr auto b_block_desc_bk0_n_bk1 = GetBBlockDescriptor_BK0PerBlock_NPerBlock_BK1();
+
+        // lds max alignment
+        constexpr auto max_lds_align = math::lcm(AK1, BK1);
+
+        constexpr auto a_block_space_size_aligned = math::integer_least_multiple(
+            a_block_desc_ak0_m_ak1.GetElementSpaceSize(), max_lds_align);
+
+        constexpr auto b_block_space_size_aligned = math::integer_least_multiple(
+            b_block_desc_bk0_n_bk1.GetElementSpaceSize(), max_lds_align);
+
+        // LDS allocation for C shuffle in LDS
+        constexpr auto c_shuffle_block_desc_mblock_mperblock_nblock_nperblock =
+            GetCShuffleBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock();
+
+        constexpr auto c_block_size =
+            c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize();
+
+        return math::max((a_block_space_size_aligned + b_block_space_size_aligned) *
+                             sizeof(ABDataType),
+                         c_block_size * sizeof(CShuffleDataType));
+    }
+
+    // A desc for source in blockwise copy
+    template <typename AGridDesc_M_K>
+    __host__ __device__ static constexpr auto
+    MakeDefaultAGridDescriptor_AK0_M_AK1(const AGridDesc_M_K& a_grid_desc_m_k)
+    {
+        const auto M = a_grid_desc_m_k.GetLength(I0);
+        const auto K = a_grid_desc_m_k.GetLength(I1);
+
+        const auto AK0 = K / AK1;
+
+        return transform_tensor_descriptor(a_grid_desc_m_k,
+                                           make_tuple(make_unmerge_transform(make_tuple(AK0, AK1)),
+                                                      make_pass_through_transform(M)),
+                                           make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                           make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+    }
+
+    // B desc for source in blockwise copy
+    template <typename BGridDesc_N_K>
+    __host__ __device__ static constexpr auto
+    MakeDefaultBGridDescriptor_BK0_N_BK1(const BGridDesc_N_K& b_grid_desc_n_k)
+    {
+        const auto N = b_grid_desc_n_k.GetLength(I0);
+        const auto K = b_grid_desc_n_k.GetLength(I1);
+
+        const auto BK0 = K / BK1;
+
+        return transform_tensor_descriptor(b_grid_desc_n_k,
+                                           make_tuple(make_unmerge_transform(make_tuple(BK0, BK1)),
+                                                      make_pass_through_transform(N)),
+                                           make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                           make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+    }
+
+    // prefer this to be called on host
+    __host__ __device__ static auto CalculateMPadded(index_t M)
+    {
+        return math::integer_least_multiple(M, MPerBlock);
+    }
+
+    __host__ __device__ static auto CalculateNPadded(index_t N)
+    {
+        return math::integer_least_multiple(N, NPerBlock);
+    }
+
+    __host__ __device__ static auto CalculateKPadded(index_t K, index_t K_Batch = 1)
+    {
+        return math::integer_least_multiple(K, KPerBlock * K_Batch);
+    }
+
+    template <typename ALayout, GemmSpecialization GemmSpec>
+    __host__ __device__ static auto MakeAGridDescriptor_KBatch_AK0_M_AK1(index_t M,
+                                                                       index_t K,
+                                                                       index_t StrideA,
+                                                                       index_t KBatch)
+    {
+        const auto a_grid_desc_m_k = [&]() {
+            if constexpr(is_same<tensor_layout::gemm::RowMajor, ALayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(M, K), make_tuple(StrideA, I1));
+            }
+            else if constexpr(is_same<tensor_layout::gemm::ColumnMajor, ALayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(M, K), make_tuple(I1, StrideA));
+            }
+        }();
+
+        const auto MPad = CalculateMPadded(M);
+        const auto KPad = CalculateKPadded(K, KBatch);
+
+        const auto a_grid_desc_m_kpad = transform_tensor_descriptor(
+            a_grid_desc_m_k,
+            make_tuple(make_pass_through_transform(M), make_right_pad_transform(K, KPad - K)),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+        const auto AK0 = KPad / (KBatch * AK1);
+
+        if constexpr(GemmSpec == tensor_operation::device::GemmSpecialization::MPadding ||
+                     GemmSpec == tensor_operation::device::GemmSpecialization::MNPadding ||
+                     GemmSpec == tensor_operation::device::GemmSpecialization::MKPadding ||
+                     GemmSpec == tensor_operation::device::GemmSpecialization::MNKPadding)
+        {
+            // const auto PadM = (MPerBlock - M % MPerBlock) % MPerBlock;
+            return transform_tensor_descriptor(
+                a_grid_desc_m_kpad,
+                make_tuple(make_unmerge_transform(make_tuple(KBatch, AK0, AK1)),
+                           make_right_pad_transform(M, MPad - M)),
+                make_tuple(Sequence<1>{}, Sequence<0>{}),
+                make_tuple(Sequence<0, 1, 3>{}, Sequence<2>{}));
+        }
+        else
+        {
+            return transform_tensor_descriptor(
+                a_grid_desc_m_kpad,
+                make_tuple(make_unmerge_transform(make_tuple(KBatch, AK0, AK1)),
+                           make_pass_through_transform(M)),
+                make_tuple(Sequence<1>{}, Sequence<0>{}),
+                make_tuple(Sequence<0, 1, 3>{}, Sequence<2>{}));
+        }
+    }
+
+    template <typename BLayout, GemmSpecialization GemmSpec>
+    __host__ __device__ static auto MakeBGridDescriptor_KBatch_BK0_N_BK1(index_t K,
+                                                                       index_t N,
+                                                                       index_t StrideB,
+                                                                       index_t KBatch)
+    {
+        const auto b_grid_desc_k_n = [&]() {
+            if constexpr(is_same<tensor_layout::gemm::RowMajor, BLayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(K, N), make_tuple(StrideB, I1));
+            }
+            else if constexpr(is_same<tensor_layout::gemm::ColumnMajor, BLayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(K, N), make_tuple(I1, StrideB));
+            }
+        }();
+
+        const auto NPad = CalculateNPadded(N);
+        const auto KPad = CalculateKPadded(K, KBatch);
+
+        const auto b_grid_desc_kpad_n = transform_tensor_descriptor(
+            b_grid_desc_k_n,
+            make_tuple(make_right_pad_transform(K, KPad - K), make_pass_through_transform(N)),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+        const auto BK0 = KPad / (KBatch * BK1);
+
+        if constexpr(GemmSpec == tensor_operation::device::GemmSpecialization::NPadding ||
+                     GemmSpec == tensor_operation::device::GemmSpecialization::MNPadding ||
+                     GemmSpec == tensor_operation::device::GemmSpecialization::NKPadding ||
+                     GemmSpec == tensor_operation::device::GemmSpecialization::MNKPadding)
+        {
+            // const auto PadN = (NPerBlock - N % NPerBlock) % NPerBlock;
+            return transform_tensor_descriptor(
+                b_grid_desc_kpad_n,
+                make_tuple(make_unmerge_transform(make_tuple(KBatch, BK0, BK1)),
+                           make_right_pad_transform(N, NPad - N)),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0, 1, 3>{}, Sequence<2>{}));
+        }
+        else
+        {
+            return transform_tensor_descriptor(
+                b_grid_desc_kpad_n,
+                make_tuple(make_unmerge_transform(make_tuple(KBatch, BK0, BK1)),
+                           make_pass_through_transform(N)),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0, 1, 3>{}, Sequence<2>{}));
+        }
+    }
+
+
+    // E desc for destination in blockwise copy
+    template <typename EGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(const EGridDesc_M_N& e_grid_desc_m_n)
+    {
+        const auto M = e_grid_desc_m_n.GetLength(I0);
+        const auto N = e_grid_desc_m_n.GetLength(I1);
+
+        const auto MBlock = M / MPerBlock;
+        const auto NBlock = N / NPerBlock;
+
+        const auto e_grid_desc_mblock_mperblock_nblock_nperblock = transform_tensor_descriptor(
+            e_grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(MBlock, Number<MPerBlock>{})),
+                       make_unmerge_transform(make_tuple(NBlock, Number<NPerBlock>{}))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 1>{}, Sequence<2, 3>{}));
+
+        return e_grid_desc_mblock_mperblock_nblock_nperblock;
+    }
+
+    // Ds desc for source in blockwise copy
+    template <typename DsGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeDsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(const DsGridDesc_M_N& ds_grid_desc_m_n)
+    {
+        return generate_tuple(
+            [&](auto i) {
+                return MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(ds_grid_desc_m_n[i]);
+            },
+            Number<NumDTensor>{});
+    }
+
+    // return block_id to E matrix tile idx (m0, n0) mapping
+    template <typename EGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeDefaultBlock2ETileMap(const EGridDesc_M_N& e_grid_desc_m_n)
+    {
+        return BlockToCTileMap_M00_N0_M01Adapt<MPerBlock, NPerBlock, EGridDesc_M_N>(
+            e_grid_desc_m_n);
+    }
+
+    // block_id to matrix tile idx (m0, n0) mapping are controlled by {M01, N01}
+    template <typename AGridDesc_M_K,
+              typename BGridDesc_N_K,
+              typename DsGridDesc_M_N,
+              typename EGridDesc_M_N,
+              typename Block2ETileMap>
+    __host__ __device__ static constexpr bool CheckValidity(const AGridDesc_M_K& a_grid_desc_m_k,
+                                                            const BGridDesc_N_K& b_grid_desc_n_k,
+                                                            const DsGridDesc_M_N& ds_grid_desc_m_n,
+                                                            const EGridDesc_M_N& e_grid_desc_m_n,
+                                                            const Block2ETileMap& block_2_etile_map)
+    {
+        static_assert((MPerBlock % (MPerXdl * MXdlPerWave) == 0) &&
+                          (NPerBlock % (NXdlPerWave * NPerXdl)) == 0,
+                      "Invalid tuning param!");
+
+        const auto M = a_grid_desc_m_k.GetLength(I0);
+        const auto N = b_grid_desc_n_k.GetLength(I0);
+        const auto K = a_grid_desc_m_k.GetLength(I1);
+
+        // check consistency of desc
+        if(!(M == e_grid_desc_m_n.GetLength(I0) && N == e_grid_desc_m_n.GetLength(I1)))
+        {
+            return false;
+        }
+
+        bool valid = true;
+
+        static_for<0, NumDTensor, 1>{}([&](auto i) {
+            valid = valid && (M == ds_grid_desc_m_n[i].GetLength(I0) &&
+                              N == ds_grid_desc_m_n[i].GetLength(I1));
+        });
+
+        if(!valid)
+        {
+            return false;
+        }
+
+        // check tile size
+        if(!(M % MPerBlock == 0 && N % NPerBlock == 0 && K % KPerBlock == 0))
+        {
+            return false;
+        }
+
+        // check gridwise gemm pipeline
+        const auto num_k_loop = K / KPerBlock;
+
+        if(!GridwiseGemmPipe::IsSupported(num_k_loop))
+        {
+            return false;
+        }
+
+        // check block-to-E-tile
+        if(!block_2_etile_map.CheckValidity(e_grid_desc_m_n))
+        {
+            return false;
+        }
+
+        // TODO: also check validity of all components (blockwise-copy, threadwise-copy, etc)
+        // check tensor size: cannot be larger than 2GB each
+        constexpr long_index_t TwoGB = (long_index_t{1} << 31);
+
+        if(!(a_grid_desc_m_k.GetElementSpaceSize() * sizeof(ABDataType) <= TwoGB &&
+             b_grid_desc_n_k.GetElementSpaceSize() * sizeof(ABDataType) <= TwoGB &&
+             e_grid_desc_m_n.GetElementSpaceSize() * sizeof(EDataType) <= TwoGB))
+        {
+            return false;
+        }
+
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool CalculateHasMainKBlockLoop(index_t K)
+    {
+        const index_t num_loop = K / KPerBlock;
+
+        return GridwiseGemmPipe::CalculateHasMainLoop(num_loop);
+    }
+
+    using DsGridPointer = decltype(MakeDsGridPointer());
+
+#if 0
+    template <typename ALayout, GemmSpecialization GemmSpec>
+    __host__ __device__ static auto
+    MakeAGridDescriptor_M_K(index_t MRaw, index_t KRaw, index_t StrideA)
+    {
+        constexpr auto matrix_padder =
+            ck::tensor_operation::device::MatrixPadder<GemmSpec, index_t, index_t, index_t>{
+                MPerBlock, NPerBlock, KPerBlock};
+
+        const auto a_grid_desc_mraw_kraw = [&]() {
+            if constexpr(is_same_v<tensor_layout::gemm::RowMajor, ALayout>)
+            {
+                return make_naive_tensor_descriptor(make_tuple(MRaw, KRaw),
+                                                    make_tuple(StrideA, I1));
+            }
+            else if constexpr(is_same_v<tensor_layout::gemm::ColumnMajor, ALayout>)
+            {
+                return make_naive_tensor_descriptor(make_tuple(MRaw, KRaw),
+                                                    make_tuple(I1, StrideA));
+            }
+        }();
+
+        return matrix_padder.PadADescriptor_M_K(a_grid_desc_mraw_kraw);
+    }
+
+    template <typename BLayout, GemmSpecialization GemmSpec>
+    __host__ __device__ static auto
+    MakeBGridDescriptor_N_K(index_t KRaw, index_t NRaw, index_t StrideB)
+    {
+        constexpr auto matrix_padder =
+            ck::tensor_operation::device::MatrixPadder<GemmSpec, index_t, index_t, index_t>{
+                MPerBlock, NPerBlock, KPerBlock};
+
+        const auto b_grid_desc_nraw_kraw = [&]() {
+            if constexpr(is_same<tensor_layout::gemm::RowMajor, BLayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(NRaw, KRaw),
+                                                    make_tuple(I1, StrideB));
+            }
+            else if constexpr(is_same<tensor_layout::gemm::ColumnMajor, BLayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(NRaw, KRaw),
+                                                    make_tuple(StrideB, I1));
+            }
+        }();
+
+        return matrix_padder.PadBDescriptor_N_K(b_grid_desc_nraw_kraw);
+    }
+#endif
+
+    template <typename ELayout, GemmSpecialization GemmSpec>
+    __host__ __device__ static auto
+    MakeEGridDescriptor_M_N(index_t MRaw, index_t NRaw, index_t StrideE)
+    {
+        constexpr auto matrix_padder =
+            ck::tensor_operation::device::MatrixPadder<GemmSpec, index_t, index_t, index_t>{
+                MPerBlock, NPerBlock, KPerBlock};
+        const auto e_grid_desc_mraw_nraw = [&]() {
+            if constexpr(is_same<tensor_layout::gemm::RowMajor, ELayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(MRaw, NRaw),
+                                                    make_tuple(StrideE, I1));
+            }
+            else if constexpr(is_same<tensor_layout::gemm::ColumnMajor, ELayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(MRaw, NRaw),
+                                                    make_tuple(I1, StrideE));
+            }
+        }();
+
+        return matrix_padder.PadCDescriptor_M_N(e_grid_desc_mraw_nraw);
+    }
+
+    template <typename DsLayout, GemmSpecialization GemmSpec>
+    __host__ __device__ static auto
+    MakeDsGridDescriptor_M_N(const std::array<index_t, NumDTensor>& MRaws,
+                             const std::array<index_t, NumDTensor>& NRaws,
+                             const std::array<index_t, NumDTensor>& DsStride)
+    {
+        return generate_tuple(
+            [&](auto i) {
+                using DLayout = remove_cvref_t<tuple_element_t<i.value, DsLayout>>;
+
+                return MakeEGridDescriptor_M_N<DLayout, GemmSpec>(MRaws[i], NRaws[i], DsStride[i]);
+            },
+            Number<NumDTensor>{});
+    }
+
+    __device__ __host__ static constexpr auto GetMPerBlock() { return MPerBlock; }
+
+    template <bool HasMainKBlockLoop,
+              typename AGridDesc_KBatch_AK0_M_AK1,
+              typename BGridDesc_KBatch_BK0_N_BK1,
+              typename DsGridDesc_MBlock_MPerBlock_NBlock_NPerBlock,
+              typename EGridDesc_MBlock_MPerBlock_NBlock_NPerBlock,
+              typename Block2ETileMap>
+    __device__ static void Run(const ABDataType* __restrict__ p_a_grid,
+                               const ABDataType* __restrict__ p_b_grid,
+                               DsGridPointer p_ds_grid,
+                               EDataType* __restrict__ p_e_grid,
+                               void* __restrict__ p_shared,
+                               const AElementwiseOperation& a_element_op,
+                               const BElementwiseOperation& b_element_op,
+                               const CDEElementwiseOperation& cde_element_op,
+                               const AGridDesc_KBatch_AK0_M_AK1& a_grid_desc_kbatch_ak0_m_ak1,
+                               const BGridDesc_KBatch_BK0_N_BK1& b_grid_desc_kbatch_bk0_n_bk1,
+                               const DsGridDesc_MBlock_MPerBlock_NBlock_NPerBlock&
+                                   ds_grid_desc_mblock_mperblock_nblock_nperblock,
+                               const EGridDesc_MBlock_MPerBlock_NBlock_NPerBlock&
+                                   e_grid_desc_mblock_mperblock_nblock_nperblock,
+                               const Block2ETileMap& block_2_etile_map)
+    {
+        const auto a_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_a_grid, a_grid_desc_kbatch_ak0_m_ak1.GetElementSpaceSize());
+
+        const auto b_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_b_grid, b_grid_desc_kbatch_bk0_n_bk1.GetElementSpaceSize());
+
+        const auto ds_grid_buf = generate_tuple(
+            [&](auto i) {
+                return make_dynamic_buffer<AddressSpaceEnum::Global>(
+                    p_ds_grid[i],
+                    ds_grid_desc_mblock_mperblock_nblock_nperblock[i].GetElementSpaceSize());
+            },
+            Number<NumDTensor>{});
+
+        auto e_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_e_grid, e_grid_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize());
+
+        // divide block work by [M, N]
+        const auto block_work_idx =
+            block_2_etile_map.CalculateBottomIndex(make_multi_index(get_block_1d_id()));
+
+        if(!block_2_etile_map.ValidCTileIndex(
+               block_work_idx,
+               make_tuple(e_grid_desc_mblock_mperblock_nblock_nperblock.GetLength(I0),
+                          e_grid_desc_mblock_mperblock_nblock_nperblock.GetLength(I2))))
+        {
+            return;
+        }
+
+        // HACK: this force m/n_block_data_idx_on_grid into SGPR
+        const index_t m_block_data_idx_on_grid =
+            __builtin_amdgcn_readfirstlane(block_work_idx[I0] * MPerBlock);
+
+        const index_t n_block_data_idx_on_grid =
+            __builtin_amdgcn_readfirstlane(block_work_idx[I1] * NPerBlock);
+
+        // lds max alignment
+        constexpr auto max_lds_align = math::lcm(AK1, BK1);
+
+        // A matrix in LDS memory, dst of blockwise copy
+        constexpr auto a_block_desc_kbatch_ak0_m_ak1 = GetABlockDescriptor_KBatch_AK0PerBlock_MPerBlock_AK1();
+
+        // B matrix in LDS memory, dst of blockwise copy
+        constexpr auto b_block_desc_kbatch_bk0_n_bk1 = GetBBlockDescriptor_KBatch_BK0PerBlock_NPerBlock_BK1();
+
+        const index_t kbatch_id = 0;
+
+        // A matrix blockwise copy
+        auto a_blockwise_copy =
+            ThreadGroupTensorSliceTransfer_v4r1<ThisThreadBlock,
+                                                AElementwiseOperation,
+                                                ck::tensor_operation::element_wise::PassThrough,
+                                                InMemoryDataOperationEnum::Set,
+                                                Sequence<1, AK0PerBlock, MPerBlock, AK1>,
+                                                ABlockTransferThreadClusterLengths_KBatch_AK0_M_AK1,
+                                                ABlockTransferThreadClusterArrangeOrder,
+                                                ABDataType,
+                                                ABDataTypeAdjusted,
+                                                decltype(a_grid_desc_kbatch_ak0_m_ak1),
+                                                decltype(a_block_desc_kbatch_ak0_m_ak1),
+                                                ABlockTransferSrcAccessOrder,
+                                                Sequence<2, 0, 1, 3>,
+                                                ABlockTransferSrcVectorDim,
+                                                3,
+                                                ABlockTransferSrcScalarPerVector,
+                                                ABlockTransferDstScalarPerVector_AK1,
+                                                1,
+                                                1,
+                                                AThreadTransferSrcResetCoordinateAfterRun,
+                                                true,
+                                                NumGemmKPrefetchStage>(
+                a_grid_desc_kbatch_ak0_m_ak1,
+                make_multi_index(kbatch_id, 0, m_block_data_idx_on_grid, 0),
+                a_element_op,
+                a_block_desc_kbatch_ak0_m_ak1,
+                make_multi_index(0, 0, 0, 0),
+                ck::tensor_operation::element_wise::PassThrough{});
+
+        // B matrix blockwise copy
+        auto b_blockwise_copy =
+            ThreadGroupTensorSliceTransfer_v4r1<ThisThreadBlock,
+                                                BElementwiseOperation,
+                                                ck::tensor_operation::element_wise::PassThrough,
+                                                InMemoryDataOperationEnum::Set,
+                                                Sequence<1, BK0PerBlock, NPerBlock, BK1>,
+                                                BBlockTransferThreadClusterLengths_KBatch_BK0_N_BK1,
+                                                BBlockTransferThreadClusterArrangeOrder,
+                                                ABDataType,
+                                                ABDataTypeAdjusted,
+                                                decltype(b_grid_desc_kbatch_bk0_n_bk1),
+                                                decltype(b_block_desc_kbatch_bk0_n_bk1),
+                                                BBlockTransferSrcAccessOrder,
+                                                Sequence<2, 0, 1, 3>,
+                                                BBlockTransferSrcVectorDim,
+                                                3,
+                                                BBlockTransferSrcScalarPerVector,
+                                                BBlockTransferDstScalarPerVector_BK1,
+                                                1,
+                                                1,
+                                                BThreadTransferSrcResetCoordinateAfterRun,
+                                                true,
+                                                NumGemmKPrefetchStage>(
+                b_grid_desc_kbatch_bk0_n_bk1,
+                make_multi_index(kbatch_id, 0, n_block_data_idx_on_grid, 0),
+                b_element_op,
+                b_block_desc_kbatch_bk0_n_bk1,
+                make_multi_index(0, 0, 0, 0),
+                ck::tensor_operation::element_wise::PassThrough{});
+
+
+        // A matrix in LDS memory, dst of blockwise copy
+        constexpr auto a_block_desc_ak0_m_ak1 = GetABlockDescriptor_AK0PerBlock_MPerBlock_AK1();
+
+        // B matrix in LDS memory, dst of blockwise copy
+        constexpr auto b_block_desc_bk0_n_bk1 = GetBBlockDescriptor_BK0PerBlock_NPerBlock_BK1();
+
+        // GEMM definition
+        //   c_mtx += transpose(a_mtx) * b_mtx
+        //     a_mtx[K0PerBlock, MPerBlock] is in LDS
+        //     b_mtx[K0PerBlock, NPerBlock] is in LDS
+        //     c_mtx[MPerBlock, NPerBlock] is distributed among threads, and saved in
+        //       register
+        // sanity check
+        constexpr index_t KPack =
+            math::max(math::lcm(AK1, BK1),
+                      MfmaSelector<ABDataTypeAdjusted, MPerXdl, NPerXdl>::selected_mfma.k_per_blk);
+
+        auto blockwise_gemm = BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_Selector<
+            BlockSize,
+            ABDataTypeAdjusted,
+            AccDataType,
+            decltype(a_block_desc_ak0_m_ak1),
+            decltype(b_block_desc_bk0_n_bk1),
+            MPerXdl,
+            NPerXdl,
+            MXdlPerWave,
+            NXdlPerWave,
+            KPack,
+            LoopSched>();
+
+        auto c_thread_buf = blockwise_gemm.GetCThreadBuffer();
+
+        // LDS allocation for A and B: be careful of alignment
+        constexpr auto a_block_space_size_aligned = math::integer_least_multiple(
+            a_block_desc_ak0_m_ak1.GetElementSpaceSize(), max_lds_align);
+
+        auto a_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+            static_cast<ABDataTypeAdjusted*>(p_shared),
+            a_block_desc_ak0_m_ak1.GetElementSpaceSize());
+
+        auto b_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+            static_cast<ABDataTypeAdjusted*>(p_shared) + a_block_space_size_aligned,
+            b_block_desc_bk0_n_bk1.GetElementSpaceSize());
+
+        constexpr auto a_block_slice_copy_step = make_multi_index(0, KPerBlock / AK1, 0, 0);
+        constexpr auto b_block_slice_copy_step = make_multi_index(0, KPerBlock / BK1, 0, 0);
+
+        // gridwise GEMM pipeline
+        const auto gridwise_gemm_pipeline =
+            GridwiseGemmPipeline_Selector<PipelineVer, NumGemmKPrefetchStage, LoopSched>();
+
+        const index_t num_k_block_main_loop = __builtin_amdgcn_readfirstlane(
+            (a_grid_desc_kbatch_ak0_m_ak1.GetLength(I0) * a_grid_desc_kbatch_ak0_m_ak1.GetLength(I2)) /
+            KPerBlock);
+
+        gridwise_gemm_pipeline.template Run<HasMainKBlockLoop>(a_grid_desc_kbatch_ak0_m_ak1,
+                                                               a_block_desc_kbatch_ak0_m_ak1,
+                                                               a_blockwise_copy,
+                                                               a_grid_buf,
+                                                               a_block_buf,
+                                                               a_block_slice_copy_step,
+                                                               b_grid_desc_kbatch_bk0_n_bk1,
+                                                               b_block_desc_kbatch_bk0_n_bk1,
+                                                               b_blockwise_copy,
+                                                               b_grid_buf,
+                                                               b_block_buf,
+                                                               b_block_slice_copy_step,
+                                                               blockwise_gemm,
+                                                               c_thread_buf,
+                                                               num_k_block_main_loop);
+
+        // shuffle C and write out
+        {
+            static_assert(MXdlPerWave % CShuffleMXdlPerWavePerShuffle == 0 &&
+                              NXdlPerWave % CShuffleNXdlPerWavePerShuffle == 0,
+                          "wrong!");
+
+            constexpr index_t MWave = MPerBlock / (MXdlPerWave * MPerXdl);
+            constexpr index_t NWave = NPerBlock / (NXdlPerWave * NPerXdl);
+
+            // TODO: hacky, fix it!
+            constexpr auto c_thread_desc_m0_n0_m1_n1_m2_m3_m4_n2 =
+                blockwise_gemm.GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2();
+
+            // TODO: hacky, fix it!
+            // c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp is only used to get lengths
+            constexpr auto c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp =
+                blockwise_gemm.GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2();
+
+            constexpr auto M0 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I0);
+            constexpr auto N0 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I1);
+            constexpr auto M1 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I2);
+            constexpr auto N1 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I3);
+            constexpr auto M2 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I4);
+            constexpr auto M3 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I5);
+            constexpr auto M4 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I6);
+            constexpr auto N2 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I7);
+
+            constexpr auto c_shuffle_block_desc_mblock_mperblock_nblock_nperblock =
+                GetCShuffleBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock();
+
+            auto c_shuffle_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+                static_cast<CShuffleDataType*>(p_shared),
+                c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize());
+
+            constexpr auto c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2 = transform_tensor_descriptor(
+                c_shuffle_block_desc_mblock_mperblock_nblock_nperblock,
+                make_tuple(
+                    make_freeze_transform(I0),
+                    make_unmerge_transform(make_tuple(
+                        Number<CShuffleMXdlPerWavePerShuffle>{}, // M0 (MXdlPerWave) per shuffle
+                        M1,                                      // M1 = MWave
+                        M2,                                      // M2 * M3 * M4 = MPerXdl
+                        M3,
+                        M4)),
+                    make_freeze_transform(I0),
+                    make_unmerge_transform(make_tuple(
+                        Number<CShuffleNXdlPerWavePerShuffle>{}, // N0 (NXdlPerWave) per shuffle
+                        N1,                                      // N1 = NWave
+                        N2))),                                   // N2 = NPerXdl
+                make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
+                make_tuple(
+                    Sequence<>{}, Sequence<0, 2, 4, 5, 6>{}, Sequence<>{}, Sequence<1, 3, 7>{}));
+
+            // calculate origin of thread output tensor on global memory
+            //     blockwise GEMM c matrix starting index
+            const auto c_thread_mtx_on_block =
+                blockwise_gemm.CalculateCThreadOriginDataIndex(I0, I0, I0, I0);
+
+            const index_t m_thread_data_on_block = c_thread_mtx_on_block[I0];
+            const index_t n_thread_data_on_block = c_thread_mtx_on_block[I1];
+
+            const auto m_thread_data_on_block_to_m0_m1_m2_m3_m4_adaptor =
+                make_single_stage_tensor_adaptor(
+                    make_tuple(make_merge_transform(make_tuple(M0, M1, M2, M3, M4))),
+                    make_tuple(Sequence<0, 1, 2, 3, 4>{}),
+                    make_tuple(Sequence<0>{}));
+
+            const auto m_thread_data_on_block_idx =
+                m_thread_data_on_block_to_m0_m1_m2_m3_m4_adaptor.CalculateBottomIndex(
+                    make_multi_index(m_thread_data_on_block));
+
+            const auto n_thread_data_on_block_to_n0_n1_n2_adaptor =
+                make_single_stage_tensor_adaptor(
+                    make_tuple(make_merge_transform(make_tuple(N0, N1, N2))),
+                    make_tuple(Sequence<0, 1, 2>{}),
+                    make_tuple(Sequence<0>{}));
+
+            const auto n_thread_data_on_block_idx =
+                n_thread_data_on_block_to_n0_n1_n2_adaptor.CalculateBottomIndex(
+                    make_multi_index(n_thread_data_on_block));
+
+            // shuffle: threadwise copy C from VGPR to LDS
+            auto c_thread_copy_vgpr_to_lds =
+                ThreadwiseTensorSliceTransfer_v1r3<AccDataType,
+                                                   CShuffleDataType,
+                                                   decltype(c_thread_desc_m0_n0_m1_n1_m2_m3_m4_n2),
+                                                   decltype(c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2),
+                                                   ck::tensor_operation::element_wise::PassThrough,
+                                                   Sequence<CShuffleMXdlPerWavePerShuffle,
+                                                            CShuffleNXdlPerWavePerShuffle,
+                                                            I1,
+                                                            I1,
+                                                            M2,
+                                                            I1,
+                                                            M4,
+                                                            I1>,
+                                                   Sequence<0, 1, 2, 3, 4, 5, 6, 7>,
+                                                   7,
+                                                   1,
+                                                   InMemoryDataOperationEnum::Set,
+                                                   1,
+                                                   true>{
+                    c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2,
+                    make_multi_index(0,
+                                     0,
+                                     m_thread_data_on_block_idx[I1],
+                                     n_thread_data_on_block_idx[I1],
+                                     m_thread_data_on_block_idx[I2],
+                                     m_thread_data_on_block_idx[I3],
+                                     m_thread_data_on_block_idx[I4],
+                                     n_thread_data_on_block_idx[I2]),
+                    ck::tensor_operation::element_wise::PassThrough{}};
+
+            // tuple of reference to C/Ds tensor descriptors
+            const auto c_ds_desc_refs = concat_tuple_of_reference(
+                tie(c_shuffle_block_desc_mblock_mperblock_nblock_nperblock),
+                generate_tie(
+                    [&](auto i) -> const auto& // return type should be reference
+                    { return ds_grid_desc_mblock_mperblock_nblock_nperblock[i]; },
+                    Number<NumDTensor>{}));
+
+            // tuple of reference to C/Ds tensor descriptors
+            const auto c_ds_buf_refs = concat_tuple_of_reference(
+                tie(c_shuffle_block_buf),
+                generate_tie(
+                    [&](auto i) -> const auto& // return type should be reference
+                    { return ds_grid_buf[i]; },
+                    Number<NumDTensor>{}));
+
+            // tuple of starting index of C/Ds blockwise copy
+            const auto idx_c_ds_block_begin = container_concat(
+                make_tuple(make_multi_index(0, 0, 0, 0)),
+                generate_tuple(
+                    [&](auto) {
+                        return make_multi_index(block_work_idx[I0], 0, block_work_idx[I1], 0);
+                    },
+                    Number<NumDTensor>{}));
+
+            // blockwise copy C/D/E between LDS and global
+            auto cde_block_copy_lds_and_global = ThreadGroupTensorSliceTransfer_v7<
+                ThisThreadBlock,
+                decltype(container_concat(make_tuple(CShuffleDataType{}), DsDataType{})),
+                Tuple<EDataType>,
+                decltype(c_ds_desc_refs),
+                decltype(tie(e_grid_desc_mblock_mperblock_nblock_nperblock)),
+                CDEElementwiseOperation,
+                Sequence<static_cast<index_t>(EGlobalMemoryDataOperation)>, // FIXME: make Sequence
+                                                                            // support arbitray type
+                Sequence<1,
+                         CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl,
+                         1,
+                         CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>, // BlockSliceLengths,
+                CDEBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
+                Sequence<0, 1, 2, 3>, // typename ThreadClusterArrangeOrder,
+                Sequence<0, 1, 2, 3>, // typename DimAccessOrder,
+                3,                    // index_t VectorDim,
+                CDEShuffleBlockTransferScalarPerVector_NPerBlock,
+                sequence_merge_t<
+                    Sequence<true>,
+                    uniform_sequence_gen_t<NumDTensor,
+                                           false>>, // ThreadTransferSrcResetCoordinateAfterRunFlags
+                Sequence<false>>                    // ThreadTransferDstResetCoordinateAfterRunFlags
+                {c_ds_desc_refs,
+                 idx_c_ds_block_begin,
+                 tie(e_grid_desc_mblock_mperblock_nblock_nperblock),
+                 make_tuple(make_multi_index(block_work_idx[I0], 0, block_work_idx[I1], 0)),
+                 cde_element_op};
+
+            // space filling curve for threadwise C in VGPR before shuffle
+            constexpr auto sfc_c_vgpr =
+                SpaceFillingCurve<Sequence<MXdlPerWave, NXdlPerWave, 1, 1, M2, 1, M4, 1>,
+                                  Sequence<0, 1, 2, 3, 4, 5, 6, 7>,
+                                  Sequence<CShuffleMXdlPerWavePerShuffle,
+                                           CShuffleNXdlPerWavePerShuffle,
+                                           1,
+                                           1,
+                                           M2,
+                                           1,
+                                           M4,
+                                           1>>{};
+
+            // space filling curve for shuffled blockwise C/D/E
+            constexpr auto sfc_cde_block =
+                SpaceFillingCurve<Sequence<1, MPerBlock, 1, NPerBlock>,
+                                  Sequence<0, 2, 1, 3>,
+                                  Sequence<1,
+                                           CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl,
+                                           1,
+                                           CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>>{};
+
+            constexpr index_t num_access = sfc_c_vgpr.GetNumOfAccess();
+
+            static_assert(num_access == sfc_cde_block.GetNumOfAccess(), "wrong!");
+
+            static_for<0, num_access, 1>{}([&](auto access_id) {
+                // make sure it's safe to write to LDS
+                block_sync_lds();
+
+                // each thread write its data from VGPR to LDS
+                c_thread_copy_vgpr_to_lds.Run(c_thread_desc_m0_n0_m1_n1_m2_m3_m4_n2,
+                                              sfc_c_vgpr.GetIndexTupleOfNumber(access_id),
+                                              c_thread_buf,
+                                              c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2,
+                                              c_shuffle_block_buf);
+
+                // make sure it's safe to read from LDS
+                block_sync_lds();
+
+                // each block copy its data from LDS to global
+                cde_block_copy_lds_and_global.Run(
+                    c_ds_desc_refs,
+                    c_ds_buf_refs,
+                    tie(e_grid_desc_mblock_mperblock_nblock_nperblock),
+                    tie(e_grid_buf));
+
+                if constexpr(access_id < num_access - 1)
+                {
+                    constexpr auto cde_lds_and_global_step =
+                        sfc_cde_block.GetForwardStep(access_id);
+
+                    // move on Ds
+                    static_for<0, NumDTensor, 1>{}([&](auto i) {
+                        cde_block_copy_lds_and_global.MoveSrcSliceWindow(
+                            c_ds_desc_refs, i + I1, cde_lds_and_global_step);
+                    });
+
+                    // move on E
+                    cde_block_copy_lds_and_global.MoveDstSliceWindow(
+                        tie(e_grid_desc_mblock_mperblock_nblock_nperblock),
+                        I0,
+                        cde_lds_and_global_step);
+                }
+            });
+        }
+    }
+
+    template <bool HasMainKBlockLoop,
+              GemmSpecialization GemmSpec,
+              typename ALayout,
+              typename BLayout,
+              typename DsLayout,
+              typename ELayout,
+              typename Block2ETileMap>
+    __device__ static void Run(const void* __restrict__ p_a_grid_,
+                               const void* __restrict__ p_b_grid_,
+                               DsGridPointer p_ds_grid,
+                               void* __restrict__ p_e_grid_,
+                               void* __restrict__ p_shared,
+                               const AElementwiseOperation& a_element_op,
+                               const BElementwiseOperation& b_element_op,
+                               const CDEElementwiseOperation& cde_element_op,
+                               const index_t M,
+                               const index_t N,
+                               const index_t K,
+                               const index_t StrideA,
+                               const index_t StrideB,
+                               const std::array<index_t, NumDTensor> StrideDs,
+                               const index_t StrideE,
+                               const Block2ETileMap& block_2_etile_map)
+    {
+        const auto p_a_grid = reinterpret_cast<const ABDataType*>(p_a_grid_);
+        const auto p_b_grid = reinterpret_cast<const ABDataType*>(p_b_grid_);
+        const auto p_e_grid = reinterpret_cast<EDataType*>(p_e_grid_);
+
+        // tensor descriptors for problem definiton
+        //const auto a_grid_desc_m_k = MakeAGridDescriptor_M_K<ALayout, GemmSpec>(M, K, StrideA);
+        //const auto b_grid_desc_n_k = MakeBGridDescriptor_N_K<BLayout, GemmSpec>(K, N, StrideB);
+
+        using DsGridDesc_M_N =
+            remove_cvref_t<decltype(MakeDsGridDescriptor_M_N<DsLayout, GemmSpec>({}, {}, {}))>;
+
+        DsGridDesc_M_N ds_grid_desc_m_n;
+
+        static_for<0, NumDTensor, 1>{}([&](auto j) {
+            using DLayout = remove_cvref_t<tuple_element_t<j.value, DsLayout>>;
+
+            ds_grid_desc_m_n(j) = MakeEGridDescriptor_M_N<DLayout, GemmSpec>(M, N, StrideDs[j]);
+        });
+
+        const auto e_grid_desc_m_n = MakeEGridDescriptor_M_N<ELayout, GemmSpec>(M, N, StrideE);
+
+        // tensor descriptors for block/thread-wise copy
+        const auto a_grid_desc_kbatch_ak0_m_ak1 = MakeAGridDescriptor_KBatch_AK0_M_AK1<ALayout, GemmSpec>(M, K, StrideA, 1);
+
+        const auto b_grid_desc_kbatch_bk0_n_bk1 = MakeBGridDescriptor_KBatch_BK0_N_BK1<BLayout, GemmSpec>(K, N, StrideB, 1);
+
+        using DsGridDesc_MBlock_MPerBlock_NBlock_NPerBlock = remove_cvref_t<decltype(
+            MakeDsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(DsGridDesc_M_N{}))>;
+
+        DsGridDesc_MBlock_MPerBlock_NBlock_NPerBlock ds_grid_desc_mblock_mperblock_nblock_nperblock;
+
+        static_for<0, NumDTensor, 1>{}([&](auto j) {
+            ds_grid_desc_mblock_mperblock_nblock_nperblock(j) =
+                MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(ds_grid_desc_m_n[j]);
+        });
+
+        const auto e_grid_desc_mblock_mperblock_nblock_nperblock =
+            MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(e_grid_desc_m_n);
+
+        Run<HasMainKBlockLoop>(p_a_grid,
+                               p_b_grid,
+                               p_ds_grid,
+                               p_e_grid,
+                               p_shared,
+                               a_element_op,
+                               b_element_op,
+                               cde_element_op,
+                               a_grid_desc_kbatch_ak0_m_ak1,
+                               b_grid_desc_kbatch_bk0_n_bk1,
+                               ds_grid_desc_mblock_mperblock_nblock_nperblock,
+                               e_grid_desc_mblock_mperblock_nblock_nperblock,
+                               block_2_etile_map);
+    }
+};
+
+} // namespace ck