gridwise_batchnorm_backward_blockwise_welford.hpp Source File

gridwise_batchnorm_backward_blockwise_welford.hpp Source File#

Composable Kernel: gridwise_batchnorm_backward_blockwise_welford.hpp Source File
// SPDX-License-Identifier: MIT
// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
 
#pragma once
 
#include "ck/utility/data_type.hpp"
#include "ck/utility/math_v2.hpp"
#include "ck/utility/reduction_operator.hpp"
#include "ck/tensor_operation/gpu/block/blockwise_welford.hpp"
#include "ck/tensor_operation/gpu/block/reduction_functions_blockwise.hpp"
#include "ck/tensor_operation/gpu/thread/threadwise_welford.hpp"
#include "ck/tensor_operation/gpu/thread/reduction_functions_threadwise.hpp"
#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
 
namespace ck {
 
template <typename GridwiseBatchrNormBackwardWithBlockwiseWelford_,
          typename XDataType,
          typename DyDataType,
          typename DxDataType,
          typename AccDataType,
          typename ScaleDataType,
          typename DscaleDbiasDataType,
          typename MeanVarDataType,
          typename DyElementwiseOp,
          typename XYGridDesc_M_K,
          typename ScaleBiasGridDesc_M,
          typename MeanVarGridDesc_M,
          typename GetReduceCountPerThreadFunctor>
__global__ void kernel_batchnorm_backward_with_blockwise_welford(
    const XYGridDesc_M_K x_grid_desc_m_k,
    const XYGridDesc_M_K dy_grid_desc_m_k,
    const XYGridDesc_M_K dx_grid_desc_m_k,
    const ScaleBiasGridDesc_M scale_grid_desc_m,
    const ScaleBiasGridDesc_M dscale_dbias_grid_desc_m,
    const MeanVarGridDesc_M mean_var_grid_desc_m,
    const GetReduceCountPerThreadFunctor get_reduce_count_per_thread,
    long_index_t reduce_size,
    index_t num_k_block_tile_iteration,
    AccDataType epsilon,
    const XDataType* const __restrict__ p_x,
    const DyDataType* const __restrict__ p_dy,
    const ScaleDataType* const __restrict__ p_scale,
    bool haveSavedMeanInvVar,
    const MeanVarDataType* const __restrict__ p_savedMean,
    const MeanVarDataType* const __restrict__ p_savedInvVar,
    const DyElementwiseOp dy_elementwise_op,
    DxDataType* const __restrict__ p_dx,
    DscaleDbiasDataType* const __restrict__ p_dscale,
    DscaleDbiasDataType* const __restrict__ p_dbias)
{
    GridwiseBatchrNormBackwardWithBlockwiseWelford_::Run(x_grid_desc_m_k,
                                                         dy_grid_desc_m_k,
                                                         dx_grid_desc_m_k,
                                                         scale_grid_desc_m,
                                                         dscale_dbias_grid_desc_m,
                                                         mean_var_grid_desc_m,
                                                         get_reduce_count_per_thread,
                                                         reduce_size,
                                                         num_k_block_tile_iteration,
                                                         epsilon,
                                                         p_x,
                                                         p_dy,
                                                         p_scale,
                                                         haveSavedMeanInvVar,
                                                         p_savedMean,
                                                         p_savedInvVar,
                                                         dy_elementwise_op,
                                                         p_dx,
                                                         p_dscale,
                                                         p_dbias);
};
 
template <typename XDataType,
          typename DyDataType,
          typename DxDataType,
          typename AccDataType,
          typename ScaleDataType,
          typename DscaleDbiasDataType,
          typename MeanVarDataType,
          typename DyElementwiseOp,
          typename XYGridDesc_M_K,
          typename ScaleBiasGridDesc_M,
          typename MeanVarGridDesc_M,
          typename GetReduceCountPerThreadFunctor,
          index_t BlockSize,
          index_t MThreadClusterSize,
          index_t KThreadClusterSize,
          index_t MThreadSliceSize,
          index_t KThreadSliceSize,
          index_t XDyDxVectorDim,
          index_t XSrcVectorSize,
          index_t DySrcVectorSize,
          index_t DxDstVectorSize,
          index_t ScaleSrcVectorSize,
          index_t DscaleDbiasDstVectorSize,
          index_t MeanVarSrcVectorSize>
struct GridwiseBatchNormBackwardWithBlockwiseWelford
{
    static_assert((XDyDxVectorDim == 0 && MThreadSliceSize % XSrcVectorSize == 0 &&
                   MThreadSliceSize % DySrcVectorSize == 0 &&
                   MThreadSliceSize % DxDstVectorSize == 0) ||
                      (XDyDxVectorDim == 1 && KThreadSliceSize % XSrcVectorSize == 0 &&
                       KThreadSliceSize % DySrcVectorSize == 0 &&
                       KThreadSliceSize % DxDstVectorSize == 0),
                  "Invalid thread slice sizes and/or vector sizes configuration, please check!");
 
    static constexpr bool reorder_thread_cluster = (XDyDxVectorDim == 0);
 
    using ThreadClusterLengths_M_K = Sequence<MThreadClusterSize, KThreadClusterSize>;
 
    using ThreadBufferDimAccessOrder =
        typename conditional<reorder_thread_cluster, Sequence<1, 0>, Sequence<0, 1>>::type;
 
    using ThreadClusterArrangeOrder =
        typename conditional<reorder_thread_cluster, Sequence<1, 0>, Sequence<0, 1>>::type;
 
    static constexpr auto thread_cluster_desc =
        make_cluster_descriptor(ThreadClusterLengths_M_K{}, ThreadClusterArrangeOrder{});
 
    using ThreadReduceSrcDesc_M_K = decltype(make_naive_tensor_descriptor_packed(
        make_tuple(Number<MThreadSliceSize>{}, Number<KThreadSliceSize>{})));
    using ThreadReduceDstDesc_M =
        decltype(make_naive_tensor_descriptor_packed(make_tuple(Number<MThreadSliceSize>{})));
 
    using ThreadwiseWelford =
        ThreadwiseWelford<AccDataType, ThreadReduceSrcDesc_M_K, ThreadReduceDstDesc_M>;
 
    using BlockwiseWelford = BlockwiseWelford<AccDataType,
                                              BlockSize,
                                              ThreadClusterLengths_M_K,
                                              ThreadClusterArrangeOrder>;
 
    using BlockwiseReduce = PartitionedBlockwiseReduction<AccDataType,
                                                          BlockSize,
                                                          ThreadClusterLengths_M_K,
                                                          ThreadClusterArrangeOrder,
                                                          ck::reduce::Add,
                                                          false>;
 
    using ThreadwiseReduce = ThreadwiseReduction<AccDataType,
                                                 ThreadReduceSrcDesc_M_K,
                                                 ThreadReduceDstDesc_M,
                                                 ck::reduce::Add,
                                                 false>;
 
    using PassThroughOp = tensor_operation::element_wise::PassThrough;
 
    static constexpr auto I0 = Number<0>{};
    static constexpr auto I1 = Number<1>{};
 
    static constexpr index_t M_BlockTileSize = MThreadClusterSize * MThreadSliceSize;
    static constexpr index_t K_BlockTileSize = KThreadClusterSize * KThreadSliceSize;
 
    // clang-format off
    // Blockwise BatchNorm Backward
    // Input: x, dy, scale, savedMean and savedInvVar (optional), reduce_size
    // Output: dx, dscale, dbias
    // Step 1: calculating mean and inv-variance using welford method (if savedMean/savedInvVar not available), where inv-variance = 1/sqrt(epsilon+variance)
    // Step 2: reduction: dbias = sum(dy),  dscale = sum(dy *(x-mean) * inv-variance)
    // Step 3: calculating dx = 1/reduce_size * inv-variance * scale * (reduce_size * dy - dbias - dscale * (x - mean) * inv-variance)) elementwise-ly
    // clang-format on
    __device__ static void Run(const XYGridDesc_M_K x_grid_desc_m_k,
                               const XYGridDesc_M_K dy_grid_desc_m_k,
                               const XYGridDesc_M_K dx_grid_desc_m_k,
                               const ScaleBiasGridDesc_M scale_grid_desc_m,
                               const ScaleBiasGridDesc_M dscale_dbias_grid_desc_m,
                               const MeanVarGridDesc_M mean_var_grid_desc_m,
                               const GetReduceCountPerThreadFunctor get_reduce_count_per_thread,
                               long_index_t reduce_size,
                               index_t num_k_block_tile_iteration,
                               AccDataType epsilon,
                               const XDataType* const __restrict__ p_x,
                               const DyDataType* const __restrict__ p_dy,
                               const ScaleDataType* const __restrict__ p_scale,
                               bool haveSavedMeanInvVar,
                               const MeanVarDataType* const __restrict__ p_savedMean,
                               const MeanVarDataType* const __restrict__ p_savedInvVar,
                               const DyElementwiseOp dy_elementwise_op,
                               DxDataType* const __restrict__ p_dx,
                               DscaleDbiasDataType* const __restrict__ p_dscale,
                               DscaleDbiasDataType* const __restrict__ p_dbias)
    {
        using ck::math::sqrt;
 
        __shared__ AccDataType p_reduce_work_buffer[BlockSize];
 
        auto reduce_work_buf =
            make_dynamic_buffer<AddressSpaceEnum::Lds>(p_reduce_work_buffer, BlockSize);
 
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize * KThreadSliceSize, true>
            x_thread_buf;
 
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize * KThreadSliceSize, true>
            dy_thread_buf;
 
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize * KThreadSliceSize, true>
            dx_thread_buf;
 
        // buffer of values of dy * (x-mean) * invVariance, used as input of Blockwise reduction
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize * KThreadSliceSize, true>
            tmp1_thread_buf;
 
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize, true> scale_thread_buf;
 
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize, true> mean_thread_buf;
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize, true> var_thread_buf;
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize, true>&
            inv_var_thread_buf = var_thread_buf;
 
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize, true> dscale_thread_buf;
        StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MThreadSliceSize, true> dbias_thread_buf;
 
        const index_t thread_local_id = get_thread_local_1d_id();
        const index_t block_global_id = get_block_1d_id();
 
        const auto thread_cluster_idx =
            thread_cluster_desc.CalculateBottomIndex(make_multi_index(thread_local_id));
 
        const auto thread_m_cluster_id = thread_cluster_idx[I0];
        const auto thread_k_cluster_id = thread_cluster_idx[I1];
 
        using ThreadBufferLengths_M_K         = Sequence<MThreadSliceSize, KThreadSliceSize>;
        using ThreadBufferLengths_M           = Sequence<MThreadSliceSize>;
        constexpr auto thread_buffer_desc_m_k = make_naive_tensor_descriptor_packed(
            make_tuple(Number<MThreadSliceSize>{}, Number<KThreadSliceSize>{}));
        constexpr auto thread_buffer_desc_m =
            make_naive_tensor_descriptor_packed(make_tuple(Number<MThreadSliceSize>{}));
 
        auto threadwise_x_load = ThreadwiseTensorSliceTransfer_v2<XDataType,
                                                                  AccDataType,
                                                                  XYGridDesc_M_K,
                                                                  decltype(thread_buffer_desc_m_k),
                                                                  ThreadBufferLengths_M_K,
                                                                  ThreadBufferDimAccessOrder,
                                                                  XDyDxVectorDim,
                                                                  XSrcVectorSize,
                                                                  1,
                                                                  true>(
            x_grid_desc_m_k,
            make_multi_index(block_global_id * M_BlockTileSize +
                                 thread_m_cluster_id * MThreadSliceSize,
                             thread_k_cluster_id * KThreadSliceSize));
 
        auto threadwise_dy_load = ThreadwiseTensorSliceTransfer_v2<DyDataType,
                                                                   AccDataType,
                                                                   XYGridDesc_M_K,
                                                                   decltype(thread_buffer_desc_m_k),
                                                                   ThreadBufferLengths_M_K,
                                                                   ThreadBufferDimAccessOrder,
                                                                   XDyDxVectorDim,
                                                                   XSrcVectorSize,
                                                                   1,
                                                                   true>(
            dy_grid_desc_m_k,
            make_multi_index(block_global_id * M_BlockTileSize +
                                 thread_m_cluster_id * MThreadSliceSize,
                             thread_k_cluster_id * KThreadSliceSize));
 
        auto threadwise_dx_store =
            ThreadwiseTensorSliceTransfer_v1r3<AccDataType,
                                               DxDataType,
                                               decltype(thread_buffer_desc_m_k),
                                               XYGridDesc_M_K,
                                               PassThroughOp,
                                               ThreadBufferLengths_M_K,
                                               ThreadBufferDimAccessOrder,
                                               XDyDxVectorDim,
                                               DxDstVectorSize,
                                               InMemoryDataOperationEnum::Set,
                                               1,
                                               true>(
                dx_grid_desc_m_k,
                make_multi_index(block_global_id * M_BlockTileSize +
                                     thread_m_cluster_id * MThreadSliceSize,
                                 thread_k_cluster_id * KThreadSliceSize),
                PassThroughOp{});
 
        auto threadwise_scale_load =
            ThreadwiseTensorSliceTransfer_v2<ScaleDataType,
                                             AccDataType,
                                             ScaleBiasGridDesc_M,
                                             decltype(thread_buffer_desc_m),
                                             ThreadBufferLengths_M,
                                             Sequence<0>,
                                             0,
                                             ScaleSrcVectorSize,
                                             1,
                                             true>(
                scale_grid_desc_m,
                make_multi_index(block_global_id * M_BlockTileSize +
                                 thread_m_cluster_id * MThreadSliceSize));
 
        auto threadwise_dscale_dbias_store =
            ThreadwiseTensorSliceTransfer_v1r3<AccDataType,
                                               DscaleDbiasDataType,
                                               decltype(thread_buffer_desc_m),
                                               ScaleBiasGridDesc_M,
                                               PassThroughOp,
                                               ThreadBufferLengths_M,
                                               Sequence<0>,
                                               0,
                                               DscaleDbiasDstVectorSize,
                                               InMemoryDataOperationEnum::Set,
                                               1,
                                               true>(
                dscale_dbias_grid_desc_m,
                make_multi_index(block_global_id * M_BlockTileSize +
                                 thread_m_cluster_id * MThreadSliceSize),
                PassThroughOp{});
 
        constexpr auto thread_copy_fwd_step_m_k = make_multi_index(0, K_BlockTileSize);
        constexpr auto thread_copy_bwd_step_m_k = make_multi_index(0, -K_BlockTileSize);
 
        const auto x_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_x, x_grid_desc_m_k.GetElementSpaceSize());
 
        const auto dy_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_dy, dy_grid_desc_m_k.GetElementSpaceSize());
 
        auto dx_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_dx, dx_grid_desc_m_k.GetElementSpaceSize());
 
        const auto scale_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_scale, scale_grid_desc_m.GetElementSpaceSize());
 
        auto dscale_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_dscale, dscale_dbias_grid_desc_m.GetElementSpaceSize());
 
        auto dbias_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
            p_dbias, dscale_dbias_grid_desc_m.GetElementSpaceSize());
 
        // clang-format off
        // Step 1: calculating mean and inv-variance using welford method (if savedMean/savedInvVar not available), where inv-variance = 1/sqrt(epsilon+variance)
        // clang-format on
 
        if(haveSavedMeanInvVar)
        {
            const auto mean_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
                p_savedMean, mean_var_grid_desc_m.GetElementSpaceSize());
 
            const auto inv_var_global_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
                p_savedInvVar, mean_var_grid_desc_m.GetElementSpaceSize());
 
            auto threadwise_mean_inv_var_load =
                ThreadwiseTensorSliceTransfer_v2<MeanVarDataType,
                                                 AccDataType,
                                                 MeanVarGridDesc_M,
                                                 decltype(thread_buffer_desc_m),
                                                 ThreadBufferLengths_M,
                                                 Sequence<0>,
                                                 0,
                                                 MeanVarSrcVectorSize,
                                                 1,
                                                 true>(
                    mean_var_grid_desc_m,
                    make_multi_index(block_global_id * M_BlockTileSize +
                                     thread_m_cluster_id * MThreadSliceSize));
 
            threadwise_mean_inv_var_load.Run(mean_var_grid_desc_m,
                                             mean_global_buf,
                                             thread_buffer_desc_m,
                                             make_tuple(I0),
                                             mean_thread_buf);
 
            threadwise_mean_inv_var_load.Run(mean_var_grid_desc_m,
                                             inv_var_global_buf,
                                             thread_buffer_desc_m,
                                             make_tuple(I0),
                                             inv_var_thread_buf);
        }
        else
        {
            auto threadwise_welford       = ThreadwiseWelford();
            threadwise_welford.max_count_ = get_reduce_count_per_thread(thread_k_cluster_id);
 
            static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
                mean_thread_buf(I) = type_convert<AccDataType>(0.0f);
                var_thread_buf(I)  = type_convert<AccDataType>(0.0f);
            });
 
            for(index_t reducedTiles = 0; reducedTiles < num_k_block_tile_iteration; ++reducedTiles)
            {
 
                threadwise_x_load.Run(x_grid_desc_m_k,
                                      x_global_buf,
                                      thread_buffer_desc_m_k,
                                      make_tuple(I0, I0),
                                      x_thread_buf);
 
                threadwise_x_load.MoveSrcSliceWindow(x_grid_desc_m_k, thread_copy_fwd_step_m_k);
                threadwise_welford.Run(x_thread_buf, mean_thread_buf, var_thread_buf);
            }
 
            static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
                if constexpr(I > 0)
                    block_sync_lds();
 
                int count = threadwise_welford.cur_count_;
                BlockwiseWelford::Run(mean_thread_buf(I), var_thread_buf(I), count);
            });
 
            // calculate inv-variance as 1/sqrt(epsilon+variance)
            static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
                inv_var_thread_buf(I) =
                    type_convert<AccDataType>(1.0) / sqrt(var_thread_buf[I] + epsilon);
            });
 
            threadwise_x_load.SetSrcSliceOrigin(
                x_grid_desc_m_k,
                make_multi_index(block_global_id * M_BlockTileSize +
                                     thread_m_cluster_id * MThreadSliceSize,
                                 thread_k_cluster_id * KThreadSliceSize));
        };
 
        // clang-format off
        // Step 2: reduction: dbias = sum(dy),  dscale = sum(dy *(x-mean) * inv-variance)
        // clang-format on
 
        static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
            dscale_thread_buf(I) = type_convert<AccDataType>(0);
            dbias_thread_buf(I)  = type_convert<AccDataType>(0);
        });
 
        for(index_t reducedTiles = 0; reducedTiles < num_k_block_tile_iteration; ++reducedTiles)
        {
            threadwise_x_load.Run(x_grid_desc_m_k,
                                  x_global_buf,
                                  thread_buffer_desc_m_k,
                                  make_tuple(I0, I0),
                                  x_thread_buf);
 
            threadwise_dy_load.Run(dx_grid_desc_m_k,
                                   dy_global_buf,
                                   thread_buffer_desc_m_k,
                                   make_tuple(I0, I0),
                                   dy_thread_buf);
 
            static_for<0, MThreadSliceSize, 1>{}([&](auto iM) {
                static_for<0, KThreadSliceSize, 1>{}([&](auto iK) {
                    constexpr auto offset =
                        thread_buffer_desc_m_k.CalculateOffset(make_tuple(iM, iK));
 
                    dy_elementwise_op(dy_thread_buf(Number<offset>{}),
                                      dy_thread_buf[Number<offset>{}]);
 
                    AccDataType norm_x = (x_thread_buf[Number<offset>{}] - mean_thread_buf[iM]) *
                                         inv_var_thread_buf[iM];
 
                    tmp1_thread_buf(Number<offset>{}) = norm_x * dy_thread_buf[Number<offset>{}];
                });
            });
 
            ThreadwiseReduce::Reduce(tmp1_thread_buf, dscale_thread_buf);
            ThreadwiseReduce::Reduce(dy_thread_buf, dbias_thread_buf);
 
            threadwise_x_load.MoveSrcSliceWindow(x_grid_desc_m_k, thread_copy_fwd_step_m_k);
            threadwise_dy_load.MoveSrcSliceWindow(dy_grid_desc_m_k, thread_copy_fwd_step_m_k);
        };
 
        static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
            if constexpr(I > 0)
                block_sync_lds();
            BlockwiseReduce::Reduce(reduce_work_buf, dscale_thread_buf(I));
            block_sync_lds();
            BlockwiseReduce::Reduce(reduce_work_buf, dbias_thread_buf(I));
        });
 
        if(thread_k_cluster_id == 0)
        {
            threadwise_dscale_dbias_store.Run(thread_buffer_desc_m,
                                              make_tuple(I0),
                                              dscale_thread_buf,
                                              dscale_dbias_grid_desc_m,
                                              dscale_global_buf);
 
            threadwise_dscale_dbias_store.Run(thread_buffer_desc_m,
                                              make_tuple(I0),
                                              dbias_thread_buf,
                                              dscale_dbias_grid_desc_m,
                                              dbias_global_buf);
        };
 
        // clang-format off
        // Step 3: calculating dx = 1/reduce_size * inv-variance * scale * (reduce_size * dy - dbias - dscale * (x - mean) * inv-variance)) elementwise-ly
        // clang-format on
 
        threadwise_scale_load.Run(scale_grid_desc_m,
                                  scale_global_buf,
                                  thread_buffer_desc_m,
                                  make_tuple(I0),
                                  scale_thread_buf);
 
        auto thread_copy_tail_m_k = (num_k_block_tile_iteration - 1) * thread_copy_fwd_step_m_k;
 
        threadwise_x_load.MoveSrcSliceWindow(x_grid_desc_m_k, thread_copy_bwd_step_m_k);
        threadwise_dy_load.MoveSrcSliceWindow(dy_grid_desc_m_k, thread_copy_bwd_step_m_k);
        threadwise_dx_store.MoveDstSliceWindow(dx_grid_desc_m_k, thread_copy_tail_m_k);
 
        AccDataType inv_reduce_size =
            type_convert<AccDataType>(1.0) / type_convert<AccDataType>(reduce_size);
 
        for(index_t reducedTiles = 0; reducedTiles < num_k_block_tile_iteration; ++reducedTiles)
        {
            threadwise_x_load.Run(x_grid_desc_m_k,
                                  x_global_buf,
                                  thread_buffer_desc_m_k,
                                  make_tuple(I0, I0),
                                  x_thread_buf);
 
            threadwise_dy_load.Run(dy_grid_desc_m_k,
                                   dy_global_buf,
                                   thread_buffer_desc_m_k,
                                   make_tuple(I0, I0),
                                   dy_thread_buf);
 
            static_for<0, MThreadSliceSize, 1>{}([&](auto iM) {
                AccDataType multiplier =
                    inv_reduce_size * inv_var_thread_buf[iM] * scale_thread_buf[iM];
 
                static_for<0, KThreadSliceSize, 1>{}([&](auto iK) {
                    constexpr auto offset =
                        thread_buffer_desc_m_k.CalculateOffset(make_tuple(iM, iK));
 
                    dy_elementwise_op(dy_thread_buf(Number<offset>{}),
                                      dy_thread_buf[Number<offset>{}]);
 
                    AccDataType norm_x = (x_thread_buf[Number<offset>{}] - mean_thread_buf[iM]) *
                                         inv_var_thread_buf[iM];
 
                    AccDataType tmpVal = norm_x * dscale_thread_buf[iM];
 
                    dx_thread_buf(Number<offset>{}) =
                        multiplier *
                        (type_convert<AccDataType>(reduce_size) * dy_thread_buf[Number<offset>{}] -
                         dbias_thread_buf[iM] - tmpVal);
                });
            });
 
            threadwise_dx_store.Run(thread_buffer_desc_m_k,
                                    make_tuple(I0, I0),
                                    dx_thread_buf,
                                    dx_grid_desc_m_k,
                                    dx_global_buf);
 
            threadwise_x_load.MoveSrcSliceWindow(x_grid_desc_m_k, thread_copy_bwd_step_m_k);
            threadwise_dy_load.MoveSrcSliceWindow(dy_grid_desc_m_k, thread_copy_bwd_step_m_k);
            threadwise_dx_store.MoveDstSliceWindow(dx_grid_desc_m_k, thread_copy_bwd_step_m_k);
        }
    }
};
 
} // namespace ck