gridwise_gemm_reduce_xdl_cshuffle_v1.hpp Source File

gridwise_gemm_reduce_xdl_cshuffle_v1.hpp Source File#

Composable Kernel: gridwise_gemm_reduce_xdl_cshuffle_v1.hpp Source File
// SPDX-License-Identifier: MIT
// Copyright (c) 2018-2025, 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_v6r1.hpp"
#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
#include "ck/tensor_operation/gpu/thread/reduction_functions_threadwise.hpp"
#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
 
namespace ck {
 
template <typename GridwiseGemm,
          typename FloatAB,
          typename FloatC,
          typename ReducePtrsGlobal,
          typename AElementwiseOperation,
          typename BElementwiseOperation,
          typename CElementwiseOperation,
          typename ReduceInElementwiseOperations,
          typename ReduceAccElementwiseOperations,
          typename AGridDesc_AK0_M_AK1,
          typename BGridDesc_BK0_N_BK1,
          typename CGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
          typename ReduceGridDescriptor_MBlock_MPerBlock,
          typename Block2CTileMap,
          bool HasMainKBlockLoop>
__global__ void
#if CK_USE_LAUNCH_BOUNDS
__launch_bounds__(CK_MAX_THREAD_PER_BLOCK, CK_MIN_BLOCK_PER_CU)
#endif
    kernel_gemm_reduce_xdl_cshuffle_v1(
        const FloatAB* __restrict__ p_a_grid,
        const FloatAB* __restrict__ p_b_grid,
        FloatC* __restrict__ p_c_grid,
        ReducePtrsGlobal p_reduces_grid,
        const AElementwiseOperation a_element_op,
        const BElementwiseOperation b_element_op,
        const CElementwiseOperation c_element_op,
        const ReduceInElementwiseOperations reduce_in_element_ops,
        const ReduceAccElementwiseOperations reduce_out_element_ops,
        const AGridDesc_AK0_M_AK1 a_grid_desc_ak0_m_ak1,
        const BGridDesc_BK0_N_BK1 b_grid_desc_bk0_n_bk1,
        const CGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
            c_grid_desc_mblock_mperblock_nblock_nperblock,
        const ReduceGridDescriptor_MBlock_MPerBlock reduce_grid_desc_mblock_mperblock,
        const Block2CTileMap block_2_ctile_map)
{
#if defined(__gfx908__) || defined(__gfx90a__) || defined(__gfx94__) || defined(__gfx11__) || \
    defined(__gfx12__)
    if constexpr(GridwiseGemm::template IsValidCompilationParameter<>())
    {
        __shared__ char p_shared[GridwiseGemm::GetSharedMemoryNumberOfByte()];
 
        GridwiseGemm::template Run<HasMainKBlockLoop>(p_a_grid,
                                                      p_b_grid,
                                                      p_c_grid,
                                                      p_reduces_grid,
                                                      p_shared,
                                                      a_element_op,
                                                      b_element_op,
                                                      c_element_op,
                                                      reduce_in_element_ops,
                                                      reduce_out_element_ops,
                                                      a_grid_desc_ak0_m_ak1,
                                                      b_grid_desc_bk0_n_bk1,
                                                      c_grid_desc_mblock_mperblock_nblock_nperblock,
                                                      reduce_grid_desc_mblock_mperblock,
                                                      block_2_ctile_map);
    }
#else
    ignore = p_a_grid;
    ignore = p_b_grid;
    ignore = p_c_grid;
    ignore = p_reduces_grid;
    ignore = a_element_op;
    ignore = b_element_op;
    ignore = c_element_op;
    ignore = reduce_in_element_ops;
    ignore = reduce_out_element_ops;
    ignore = a_grid_desc_ak0_m_ak1;
    ignore = b_grid_desc_bk0_n_bk1;
    ignore = c_grid_desc_mblock_mperblock_nblock_nperblock;
    ignore = reduce_grid_desc_mblock_mperblock;
    ignore = block_2_ctile_map;
#endif // end of if (defined(__gfx908__) || defined(__gfx90a__))
}
 
template <typename FloatAB,
          typename FloatGemmAcc,
          typename FloatCShuffle,
          typename FloatC,
          typename FloatReduceAcc,
          typename ReducePtrsGlobal,
          typename AElementwiseOperation,
          typename BElementwiseOperation,
          typename CElementwiseOperation,
          typename ReduceOperations,
          typename ReduceInElementwiseOperations,
          typename ReduceAccElementwiseOperations,
          InMemoryDataOperationEnum CGlobalMemoryDataOperation,
          typename ReduceGlobalMemoryDataOperation,
          typename AGridDesc_AK0_M_AK1,
          typename BGridDesc_BK0_N_BK1,
          typename CGridDesc_M_N,
          typename ReduceGridDesc_M,
          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_AK0_M_AK1,
          typename ABlockTransferThreadClusterArrangeOrder,
          typename ABlockTransferSrcAccessOrder,
          index_t ABlockTransferSrcVectorDim,
          index_t ABlockTransferSrcScalarPerVector,
          index_t ABlockTransferDstScalarPerVector_AK1,
          bool AThreadTransferSrcResetCoordinateAfterRun,
          index_t ABlockLdsExtraM,
          typename BBlockTransferThreadClusterLengths_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 CShuffleBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
          index_t CShuffleBlockTransferScalarPerVector_NPerBlock,
          typename CReduceThreadClusterLengths_MPerBlock_NPerBlock,
          index_t CReduceThreadLds2VGprCopySrcDstScalarPerVector_NPerBlock,
          index_t CReduceThreadVgpr2GlobalCopySrcDstScalarPerVector_MPerBlock,
          LoopScheduler LoopSched,
          PipelineVersion PipelineVer = PipelineVersion::v1>
struct GridwiseGemmReduce_k0mk1_k0nk1_mn_xdl_cshuffle_v1
{
    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 AK0 = Number<KPerBlock / AK1Value>{};
    static constexpr auto BK0 = Number<KPerBlock / BK1Value>{};
    static constexpr auto AK1 = Number<AK1Value>{};
    static constexpr auto BK1 = Number<BK1Value>{};
 
    using ThisThreadBlock = ThisThreadBlock<BlockSize>;
 
    using GridwiseGemmPipe = remove_cvref_t<
        decltype(GridwiseGemmPipeline_Selector<PipelineVer, NumGemmKPrefetchStage>())>;
 
    __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(AK0, 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(BK0, 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;
    }
 
    __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(FloatAB),
                         c_block_size * sizeof(FloatCShuffle));
    }
 
    template <
        InMemoryDataOperationEnum CGlobalMemoryDataOperation_ = InMemoryDataOperationEnum::Set>
    __device__ static bool constexpr IsValidCompilationParameter()
    {
        return ck::tensor_operation::device::IsValidGemmCompilationParameter<
            BlockSize,
            MPerBlock,
            NPerBlock,
            MPerXdl,
            NPerXdl,
            MXdlPerWave,
            NXdlPerWave,
            FloatC,
            CGlobalMemoryDataOperation>();
    }
 
    // block_id to matrix tile idx (m0, n0) mapping are controlled by {M01, N01}
    template <typename Block2CTileMap>
    __host__ __device__ static constexpr bool
    CheckValidity(const AGridDesc_AK0_M_AK1& a_grid_desc_ak0_m_ak1,
                  const BGridDesc_BK0_N_BK1& b_grid_desc_bk0_n_bk1,
                  const CGridDesc_M_N& c_grid_desc_m_n,
                  const Block2CTileMap& block_2_ctile_map)
    {
        // static_assert(is_known_at_compile_time<remove_cv_t<decltype(AK1)>>::value &&
        //               is_known_at_compile_time<remove_cv_t<decltype(BK1)>>::value,
        //               "wrong! K1 need to be known at compile-time");
 
        static_assert((MPerBlock % (MPerXdl * MXdlPerWave) == 0) &&
                          (NPerBlock % (NXdlPerWave * NPerXdl)) == 0,
                      "Invalid tuning param!");
 
        const auto M = a_grid_desc_ak0_m_ak1.GetLength(I1);
        const auto N = b_grid_desc_bk0_n_bk1.GetLength(I1);
        const auto K = a_grid_desc_ak0_m_ak1.GetLength(I0) * a_grid_desc_ak0_m_ak1.GetLength(I2);
 
        if(!(M == c_grid_desc_m_n.GetLength(I0) && N == c_grid_desc_m_n.GetLength(I1)))
            return false;
 
        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;
        }
 
        if(!block_2_ctile_map.CheckValidity(c_grid_desc_m_n))
        {
            return false;
        }
 
        // TODO: also check validity of all components (blockwise-copy, threadwise-copy, etc)
        return true;
    }
 
    __host__ __device__ static constexpr bool CalculateHasMainKBlockLoop(index_t K)
    {
        const index_t num_loop = K / KPerBlock;
 
        return GridwiseGemmPipe::CalculateHasMainLoop(num_loop);
    }
 
    __host__ __device__ static constexpr auto
    MakeCGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(const CGridDesc_M_N& c_grid_desc_m_n)
    {
        const auto M = c_grid_desc_m_n.GetLength(I0);
        const auto N = c_grid_desc_m_n.GetLength(I1);
 
        const auto MBlock = M / MPerBlock;
        const auto NBlock = N / NPerBlock;
 
        const auto c_grid_desc_mblock_mperblock_nblock_nperblock = transform_tensor_descriptor(
            c_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 c_grid_desc_mblock_mperblock_nblock_nperblock;
    }
 
    __host__ __device__ static constexpr auto
    MakeReduceGridDescriptor_MBlock_MPerBlock(const ReduceGridDesc_M& d_grid_desc_m)
    {
        const auto M      = d_grid_desc_m.GetLength(I0);
        const auto MBlock = M / MPerBlock;
 
        const auto reduce_grid_desc_mblock_mperblock = transform_tensor_descriptor(
            d_grid_desc_m,
            make_tuple(make_unmerge_transform(make_tuple(MBlock, Number<MPerBlock>{}))),
            make_tuple(Sequence<0>{}),
            make_tuple(Sequence<0, 1>{}));
 
        return reduce_grid_desc_mblock_mperblock;
    }
 
    // return block_id to C matrix tile idx (m0, n0) mapping
    __host__ __device__ static constexpr auto
    MakeDefaultBlock2CTileMap(const CGridDesc_M_N& c_grid_desc_m_n)
    {
        return BlockToCTileMap_M00_N0_M01Adapt<MPerBlock, NPerBlock, CGridDesc_M_N>(
            c_grid_desc_m_n);
    }
 
    using CGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock =
        remove_cvref_t<decltype(MakeCGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
            CGridDesc_M_N{}))>;
 
    using ReduceGridDescriptor_MBlock_MPerBlock =
        remove_cvref_t<decltype(MakeReduceGridDescriptor_MBlock_MPerBlock(ReduceGridDesc_M{}))>;
 
    using DefaultBlock2CTileMap =
        remove_cvref_t<decltype(MakeDefaultBlock2CTileMap(CGridDesc_M_N{}))>;
 
    template <bool HasMainKBlockLoop, typename Block2CTileMap>
    __device__ static void
    Run(const FloatAB* __restrict__ p_a_grid,
        const FloatAB* __restrict__ p_b_grid,
        FloatC* __restrict__ p_c_grid,
        ReducePtrsGlobal p_reduces_grid,
        void* __restrict__ p_shared,
        const AElementwiseOperation& a_element_op,
        const BElementwiseOperation& b_element_op,
        const CElementwiseOperation& c_element_op,
        const ReduceInElementwiseOperations& reduce_in_element_ops,
        const ReduceAccElementwiseOperations& reduce_out_element_ops,
        const AGridDesc_AK0_M_AK1& a_grid_desc_ak0_m_ak1,
        const BGridDesc_BK0_N_BK1& b_grid_desc_bk0_n_bk1,
        const CGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock&
            c_grid_desc_mblock_mperblock_nblock_nperblock,
        const ReduceGridDescriptor_MBlock_MPerBlock& reduce_grid_desc_mblock_mperblock,
        const Block2CTileMap& block_2_ctile_map)
    {
        const auto a_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_a_grid, a_grid_desc_ak0_m_ak1.GetElementSpaceSize());
        const auto b_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_b_grid, b_grid_desc_bk0_n_bk1.GetElementSpaceSize());
        auto c_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_c_grid, c_grid_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize());
 
        // divide block work by [M, N]
        const auto block_work_idx =
            block_2_ctile_map.CalculateBottomIndex(make_multi_index(get_block_1d_id()));
 
        if(!block_2_ctile_map.ValidCTileIndex(
               block_work_idx,
               make_tuple(c_grid_desc_mblock_mperblock_nblock_nperblock.GetLength(I0),
                          c_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_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();
 
        // A matrix blockwise copy
        auto a_blockwise_copy =
            ThreadGroupTensorSliceTransfer_v4r1<ThisThreadBlock,
                                                AElementwiseOperation,
                                                ck::tensor_operation::element_wise::PassThrough,
                                                InMemoryDataOperationEnum::Set,
                                                Sequence<AK0, MPerBlock, AK1>,
                                                ABlockTransferThreadClusterLengths_AK0_M_AK1,
                                                ABlockTransferThreadClusterArrangeOrder,
                                                FloatAB,
                                                FloatAB,
                                                decltype(a_grid_desc_ak0_m_ak1),
                                                decltype(a_block_desc_ak0_m_ak1),
                                                ABlockTransferSrcAccessOrder,
                                                Sequence<1, 0, 2>,
                                                ABlockTransferSrcVectorDim,
                                                2,
                                                ABlockTransferSrcScalarPerVector,
                                                ABlockTransferDstScalarPerVector_AK1,
                                                1,
                                                1,
                                                AThreadTransferSrcResetCoordinateAfterRun,
                                                true,
                                                NumGemmKPrefetchStage>(
                a_grid_desc_ak0_m_ak1,
                make_multi_index(0, m_block_data_idx_on_grid, 0),
                a_element_op,
                a_block_desc_ak0_m_ak1,
                make_multi_index(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<BK0, NPerBlock, BK1>,
                                                BBlockTransferThreadClusterLengths_BK0_N_BK1,
                                                BBlockTransferThreadClusterArrangeOrder,
                                                FloatAB,
                                                FloatAB,
                                                decltype(b_grid_desc_bk0_n_bk1),
                                                decltype(b_block_desc_bk0_n_bk1),
                                                BBlockTransferSrcAccessOrder,
                                                Sequence<1, 0, 2>,
                                                BBlockTransferSrcVectorDim,
                                                2,
                                                BBlockTransferSrcScalarPerVector,
                                                BBlockTransferDstScalarPerVector_BK1,
                                                1,
                                                1,
                                                BThreadTransferSrcResetCoordinateAfterRun,
                                                true,
                                                NumGemmKPrefetchStage>(
                b_grid_desc_bk0_n_bk1,
                make_multi_index(0, n_block_data_idx_on_grid, 0),
                b_element_op,
                b_block_desc_bk0_n_bk1,
                make_multi_index(0, 0, 0),
                ck::tensor_operation::element_wise::PassThrough{});
 
        // 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 auto lcm_AK1_BK1 = math::lcm(AK1, BK1);
        constexpr bool is_single_rate_mfma =
            (((is_same<FloatAB, half_t>::value || is_same<FloatAB, bhalf_t>::value) &&
              lcm_AK1_BK1 <= 4) ||
             (is_same<FloatAB, int8_t>::value && lcm_AK1_BK1 <= 8) ||
             ((is_same<FloatAB, f8_t>::value || is_same<FloatAB, bf8_t>::value) &&
              lcm_AK1_BK1 < 32))
                ? true
                : false;
        constexpr auto is_scale_mfma = false;
        constexpr index_t KPack      = math::max(
            lcm_AK1_BK1,
            MfmaSelector<FloatAB, MPerXdl, NPerXdl, FloatAB, is_single_rate_mfma, is_scale_mfma>::
                selected_mfma.k_per_blk);
 
        auto blockwise_gemm = BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_Selector<
            BlockSize,
            FloatAB,
            FloatAB,
            FloatGemmAcc,
            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<FloatAB*>(p_shared), a_block_desc_ak0_m_ak1.GetElementSpaceSize());
 
        auto b_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
            static_cast<FloatAB*>(p_shared) + a_block_space_size_aligned,
            b_block_desc_bk0_n_bk1.GetElementSpaceSize());
 
        constexpr auto a_block_slice_copy_step = make_multi_index(KPerBlock / AK1, 0, 0);
        constexpr auto b_block_slice_copy_step = make_multi_index(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_ak0_m_ak1.GetLength(I0) * a_grid_desc_ak0_m_ak1.GetLength(I2)) /
            KPerBlock);
 
        gridwise_gemm_pipeline.template Run<HasMainKBlockLoop>(a_grid_desc_ak0_m_ak1,
                                                               a_block_desc_ak0_m_ak1,
                                                               a_blockwise_copy,
                                                               a_grid_buf,
                                                               a_block_buf,
                                                               a_block_slice_copy_step,
                                                               b_grid_desc_bk0_n_bk1,
                                                               b_block_desc_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 + reduction + 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<FloatCShuffle*>(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<FloatGemmAcc,
                                                   FloatCShuffle,
                                                   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{}};
 
            // shuffle: blockwise copy C from LDS to global
            auto c_shuffle_block_copy_lds_to_global = ThreadGroupTensorSliceTransfer_v6r1<
                ThisThreadBlock,            // ThreadGroup
                CElementwiseOperation,      // ElementwiseOperation,
                CGlobalMemoryDataOperation, // DstInMemOp,
                Sequence<1,
                         CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl,
                         1,
                         CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>, // BlockSliceLengths,
                CShuffleBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
                Sequence<0, 1, 2, 3>, // typename ThreadClusterArrangeOrder,
                FloatCShuffle,        // typename SrcData,
                FloatC,               // typename DstData,
                decltype(c_shuffle_block_desc_mblock_mperblock_nblock_nperblock),
                decltype(c_grid_desc_mblock_mperblock_nblock_nperblock),
                Sequence<0, 1, 2, 3>,                           // typename DimAccessOrder,
                3,                                              // index_t VectorDim,
                CShuffleBlockTransferScalarPerVector_NPerBlock, // index_t ScalarPerVector,
                true,  // bool ThreadTransferSrcResetCoordinateAfterRun,
                false> // bool ThreadTransferDstResetCoordinateAfterRun>
                {c_shuffle_block_desc_mblock_mperblock_nblock_nperblock,
                 make_multi_index(0, 0, 0, 0),
                 c_grid_desc_mblock_mperblock_nblock_nperblock,
                 make_multi_index(block_work_idx[I0], 0, block_work_idx[I1], 0),
                 c_element_op};
 
            // space filling curve for threadwise C in VGPR
            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 in global mem
            constexpr auto sfc_c_global =
                SpaceFillingCurve<Sequence<1, MPerBlock, 1, NPerBlock>,
                                  Sequence<0, 2, 1, 3>,
                                  Sequence<1,
                                           CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl,
                                           1,
                                           CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>>{};
 
            // TODO: this should be implemented as a blockwise reduction
            // LDS c_reduce_block_desc_mperblock_nperblock
            constexpr auto c_reduce_block_desc_mperblock_nperblock = transform_tensor_descriptor(
                c_shuffle_block_desc_mblock_mperblock_nblock_nperblock,
                make_tuple(
                    make_freeze_transform(I0),
                    make_pass_through_transform(
                        c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetLength(I1)),
                    make_freeze_transform(I0),
                    make_pass_through_transform(
                        c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetLength(I3))),
                make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
                make_tuple(Sequence<>{}, Sequence<0>{}, Sequence<>{}, Sequence<1>{}));
 
            static_assert(CReduceThreadClusterLengths_MPerBlock_NPerBlock::At(I0) *
                                  CReduceThreadClusterLengths_MPerBlock_NPerBlock::At(I1) ==
                              BlockSize,
                          "wrong!");
 
            static_assert((CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl) %
                                      CReduceThreadClusterLengths_MPerBlock_NPerBlock::At(I0) ==
                                  0 &&
                              (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl) %
                                      CReduceThreadClusterLengths_MPerBlock_NPerBlock::At(I1) ==
                                  0,
                          "wrong!");
 
            constexpr index_t mreduce_per_thread =
                (CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl) /
                CReduceThreadClusterLengths_MPerBlock_NPerBlock::At(I0);
 
            constexpr index_t nreduce_per_thread =
                (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl) /
                CReduceThreadClusterLengths_MPerBlock_NPerBlock::At(I1);
 
            constexpr auto c_reduce_thread_lengths_mperblock_nperblock =
                Sequence<mreduce_per_thread, nreduce_per_thread>{};
 
            // VGPR c_reduce_thread_desc_mperblock_nperblock
            constexpr auto c_reduce_thread_desc_mperblock_nperblock =
                make_naive_tensor_descriptor_packed(
                    make_tuple(Number<mreduce_per_thread>{}, Number<nreduce_per_thread>{}));
 
            // VGPR reduce_thread_desc_mperblock
            constexpr auto reduce_thread_desc_mperblock =
                make_naive_tensor_descriptor_packed(make_tuple(Number<mreduce_per_thread>{}));
 
            // VGPR reduce_thread_desc_mblock_mperblock
            constexpr auto reduce_thread_desc_mblock_mperblock =
                make_naive_tensor_descriptor_packed(make_tuple(I1, Number<mreduce_per_thread>{}));
 
            auto c_reduce_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatReduceAcc>(
                c_reduce_thread_desc_mperblock_nperblock.GetElementSpaceSize());
 
            // reduce: threadwise copy from LDS to VGPR
            constexpr auto c_reduce_thread_cluster_desc = make_cluster_descriptor(
                CReduceThreadClusterLengths_MPerBlock_NPerBlock{}, Sequence<1, 0>{});
 
            const auto c_reduce_thread_cluster_idx =
                c_reduce_thread_cluster_desc.CalculateBottomIndex(
                    make_multi_index(get_thread_local_1d_id()));
 
            const auto c_reduce_thread_data_idx_begin =
                c_reduce_thread_cluster_idx * c_reduce_thread_lengths_mperblock_nperblock;
 
            auto c_reduce_thread_copy_lds_to_vgpr = ThreadwiseTensorSliceTransfer_v2<
                FloatCShuffle,
                FloatReduceAcc,
                decltype(c_reduce_block_desc_mperblock_nperblock),
                decltype(c_reduce_thread_desc_mperblock_nperblock),
                decltype(c_reduce_thread_lengths_mperblock_nperblock),
                Sequence<0, 1>,
                1,
                CReduceThreadLds2VGprCopySrcDstScalarPerVector_NPerBlock,
                1,
                true>{c_reduce_block_desc_mperblock_nperblock, c_reduce_thread_data_idx_begin};
 
            auto reduce_tuple_thread_copy_vgpr_to_global = generate_tuple(
                [&](auto I) {
                    auto p_reduce_grid         = p_reduces_grid[I];
                    auto reduce_acc_element_op = reduce_out_element_ops[I];
 
                    return ThreadwiseTensorSliceTransfer_v1r3<
                        FloatReduceAcc,
                        remove_pointer_t<decltype(p_reduce_grid)>,
                        decltype(reduce_thread_desc_mblock_mperblock),
                        decltype(reduce_grid_desc_mblock_mperblock),
                        decltype(reduce_acc_element_op),
                        Sequence<1, mreduce_per_thread>,
                        Sequence<0, 1>,
                        1,
                        CReduceThreadVgpr2GlobalCopySrcDstScalarPerVector_MPerBlock,
                        ReduceGlobalMemoryDataOperation::At(I),
                        1,
                        false>{reduce_grid_desc_mblock_mperblock,
                               make_multi_index(block_work_idx[I0],                  // mblock
                                                c_reduce_thread_data_idx_begin[I0]), // mperblock
                               reduce_acc_element_op};
                },
                Number<p_reduces_grid.Size()>{});
 
            constexpr index_t num_access = sfc_c_vgpr.GetNumOfAccess();
 
            static_assert(num_access == sfc_c_global.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
                c_shuffle_block_copy_lds_to_global.Run(
                    c_shuffle_block_desc_mblock_mperblock_nblock_nperblock,
                    c_shuffle_block_buf,
                    c_grid_desc_mblock_mperblock_nblock_nperblock,
                    c_grid_buf);
 
                // TODO - extract following into reduction_blockwise
                {
                    c_reduce_thread_copy_lds_to_vgpr.Run(c_reduce_block_desc_mperblock_nperblock,
                                                         c_shuffle_block_buf,
                                                         c_reduce_thread_desc_mperblock_nperblock,
                                                         make_tuple(I0, I0),
                                                         c_reduce_thread_buf);
 
                    static_for<0, p_reduces_grid.Size(), 1>{}([&](auto In) {
                        auto& p_reduce_grid = p_reduces_grid[In];
 
                        auto reduce_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
                            p_reduce_grid, reduce_grid_desc_mblock_mperblock.GetElementSpaceSize());
 
                        auto reduce_thread_buf =
                            make_static_buffer<AddressSpaceEnum::Vgpr, FloatReduceAcc>(
                                reduce_thread_desc_mperblock.GetElementSpaceSize());
 
                        auto& reduce_in_element_op = reduce_in_element_ops[In];
 
                        auto& reduce_thread_copy_vgpr_to_global =
                            reduce_tuple_thread_copy_vgpr_to_global(In);
 
                        using ReduceOperation = remove_cvref_t<decltype(ReduceOperations{}[In])>;
                        using ThreadwiseReduce =
                            ThreadwiseReduction<FloatReduceAcc,
                                                decltype(c_reduce_thread_desc_mperblock_nperblock),
                                                decltype(reduce_thread_desc_mperblock),
                                                ReduceOperation,
                                                false>;
 
                        // Global write Gemm shuffle + reduction
                        const auto reduce_identityVal =
                            ReduceOperation::template GetIdentityValue<FloatReduceAcc>();
 
                        static_for<0, mreduce_per_thread, 1>{}(
                            [&](auto I) { reduce_thread_buf(I) = reduce_identityVal; });
 
                        // reduce in VGPR
                        static_for<0, mreduce_per_thread, 1>{}([&](auto im) {
                            static_for<0, nreduce_per_thread, 1>{}([&](auto in) {
                                constexpr auto offset =
                                    Number<c_reduce_thread_desc_mperblock_nperblock.CalculateOffset(
                                        make_tuple(im, in))>{};
 
                                reduce_in_element_op(c_reduce_thread_buf(offset),
                                                     c_reduce_thread_buf(offset));
                            });
                        });
 
                        ThreadwiseReduce::Reduce(c_reduce_thread_buf, reduce_thread_buf);
 
                        // copy from VGPR to Global
                        reduce_thread_copy_vgpr_to_global.Run(reduce_thread_desc_mblock_mperblock,
                                                              make_tuple(I0, I0),
                                                              reduce_thread_buf,
                                                              reduce_grid_desc_mblock_mperblock,
                                                              reduce_grid_buf);
 
                        if constexpr(access_id < num_access - 1)
                        {
                            constexpr auto c_global_step = sfc_c_global.GetForwardStep(access_id);
                            reduce_thread_copy_vgpr_to_global.MoveDstSliceWindow(
                                reduce_grid_desc_mblock_mperblock,
                                make_tuple(c_global_step[I0], c_global_step[I1]));
                        }
                    });
                }
 
                if constexpr(access_id < num_access - 1)
                {
                    constexpr auto c_global_step = sfc_c_global.GetForwardStep(access_id);
 
                    // move on C
                    c_shuffle_block_copy_lds_to_global.MoveDstSliceWindow(
                        c_grid_desc_mblock_mperblock_nblock_nperblock, c_global_step);
                }
            });
 
            // Reduction
        }
    }
};
 
} // namespace ck