Gemm layernorm welford (#413)

* Add device op of gemm layernorm

* [What] Rename F to H
[Why] F and G prepare for welford tensor

* Add gridwise gemm + welford

* Extract template parameter

* Rename kernel. Prepare to add second half kernel

* Extract var

* Add second kernel for gemm+layernorm

* Move to the gemm_layernorm folder

* Rename F and G to mean and var

* Do not use snakeCurved, it makes determination of padding  for welford difficult

* Rewrite the device interface and rename some var

* Add welford count

* Update interface

* Sync code, prepare to test on MI200

* Clean the code

* Implement layernorm

* Add comment to mension hipFree

* Wrtie out the e for debug.
This could be remove and use h for instead

* 1. Allocate mean, var and count into by SetWorkSpacePointer.
2. Add GetWorkSpaceSize to calculate the space size

* Add gemm layernorm host code

* use reference layernorm

* Fix bug of blockwise welford for first kernel

* Fix bug of mean var padding for layernorm

* Use sgpr for shuffleM_index

* padding for GemmMeanVarCountGridDescriptor_M_NBlock

* Add layout parameter

* Check argument for gemm

* calculate max count for tail block

* Share E and H memory in device op

* Hard code the vector dim

* Refine the MakeDescriptor

* 1. Remove E parameter, because E is inside of device op
2. Check vector size

* [What] Rename MakeMeanVarDescriptor_M_N
[Why] Prepare to add count version of make descriptor

* Use 1D global memory for count

* Prevent redundant IO

* Update parameter

* Add pipeline v1/v2 selector

* Rename the example name

* Add base class for gemm layernorm

* Refine naming to distinguish naive and welford

* Add comment to explan in detail

* We don't need to pad in N dimension in gemm for mean/var/count. Set NPerTile 1

* Rewrite the 2st kernel, use multiple block along N dimension in layernorm kernel

* Share the vector size

* Refine var name

* [What] Force LayernormThreadSliceSize_N = vector size.
[Why] Memory coalesce

* Add comment

* Extract divisor out of the loop in reference layernorm

* Pad different size for E and H in layernorm kernel according to different block tile

* Refine naming

* Refine naming

* Prevent implicit cast

* [What] use ck::math::sqrt instead of __builtin_amdgcn_sqrtf
[Why] __builtin_amdgcn_sqrtf is only support float, double will cause casting

* Cast only constant

* Change of post shuffle thread descriptor

* Add EMeanVarDataType parameter.

* Merge the mean and var threadwise copy

* Add missing index

* Fix Typo

* Sync the variable with previous if

* 1. Declare e inside the host_gemm_layernorm()
2. Prevent implicit cast in reference code
Co-authored-by: Po Yen Chen <PoYen.Chen@amd.com>

example/21_gemm_layernorm/CMakeLists.txt

-add_example_executable(example_gemm_bias_relu_add_layernorm_xdl_fp16 gemm_bias_relu_add_layernorm_xdl_fp16.cpp)
-add_example_executable(example_gemm_layernorm_xdl_fp16 gemm_layernorm_xdl_fp16.cpp)
-add_example_executable(example_gemm_xdl_layernorm_single_kernel_fp16 gemm_xdl_layernorm_single_kernel_fp16.cpp)
+add_example_executable(example_gemm_bias_relu_add_layernorm_xdl_welford_fp16 gemm_bias_relu_add_layernorm_xdl_welford_fp16.cpp)
+add_example_executable(example_gemm_bias_relu_add_layernorm_xdl_naive_fp16 gemm_bias_relu_add_layernorm_xdl_naive_fp16.cpp)
+add_example_executable(example_gemm_layernorm_xdl_naive_fp16 gemm_layernorm_xdl_naive_fp16.cpp)
+add_example_executable(example_gemm_xdl_layernorm_naive_single_kernel_fp16 gemm_xdl_layernorm_naive_single_kernel_fp16.cpp)

example/21_gemm_layernorm/gemm_bias_relu_add_layernorm_xdl_welford_fp16.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#include <iostream>
+#include <numeric>
+#include <initializer_list>
+#include <cstdlib>
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/device/tensor_layout.hpp"
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/impl/device_gemm_multiple_d_layernorm_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/utility/device_memory.hpp"
+#include "ck/library/utility/host_tensor.hpp"
+#include "ck/library/utility/host_tensor_generator.hpp"
+#include "ck/library/reference_tensor_operation/cpu/reference_gemm.hpp"
+#include "ck/library/reference_tensor_operation/cpu/reference_layernorm.hpp"
+#include "ck/library/utility/check_err.hpp"
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+using F16 = ck::half_t;
+using F32 = float;
+
+using Row = ck::tensor_layout::gemm::RowMajor;
+using Col = ck::tensor_layout::gemm::ColumnMajor;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+using AddReluAdd  = ck::tensor_operation::element_wise::AddReluAdd;
+
+// DataType
+using ADataType        = F16;
+using BDataType        = F16;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using D0DataType       = F16;
+using D1DataType       = F16;
+using DsDataType       = ck::Tuple<D0DataType, D1DataType>;
+using EMeanVarDataType = F16;
+using GammaDataType    = F16;
+using BetaDataType     = F16;
+using HDataType        = F16;
+
+// Layout
+using ALayout  = Row;
+using BLayout  = Col;
+using D0Layout = Row;
+using D1Layout = Row;
+using DsLayout = ck::Tuple<D0Layout, D1Layout>;
+using HLayout  = Row;
+
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = AddReluAdd;
+using HElementOp   = PassThrough;
+
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::MNKPadding;
+
+// clang-format off
+using DeviceOpInstance = ck::tensor_operation::device::DeviceGemmMultipleDLayernorm_Xdl_CShuffle
+//######| ALayout| BLayout| DsLayout| HLayout|     AData|     BData|     AccData|         CShuffle|     DsData|     EMeanVarData|     GammaData|     BetaData|     HData|           A|           B|          CDE|            H|           GEMM| NumGemmK| Block|  MPer|  NPer|  KPer| AK1| BK1| MPer| NPer| MXdl| NXdl|  ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockLds|  BBlockTransfer| BBlockTransfer| BBlockTransfer| BlockTransfer| BBlockTransfer| BBlockTransfer| BBlockLds|    CShuffle|    CShuffle|           PostShuffle|     PostShuffle|            Layernorm|       Layernorm|
+//######|        |        |         |        |      Type|      Type|        Type|         DataType|       Type|             Type|          Type|         Type|      Type| Elementwise| Elementwise|  Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|  ThreadClusterLengths| ScalarPerVector| ThreadClusterLengths| ThreadSliceSize|
+//######|        |        |         |        |          |          |            |                 |           |                 |              |             |          |   Operation|   Operation|    Operation|    Operation|               |    Stage|      |      |      |      |    |    |     |     | Wave| Wave| Lengths_K0_M_K1|   ArrangeOrder|               |               |      PerVector|   PerVector_K1|          | Lengths_K0_N_K1|   ArrangeOrder|               |              |      PerVector|   PerVector_K1|          |  PerShuffle|  PerShuffle|                  _M_N|            _M_N|                 _M_N|              _M|
+//######|        |        |         |        |          |          |            |                 |           |                 |              |             |          |            |            |             |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                      |                |                     |                |
+        < ALayout, BLayout, DsLayout, HLayout, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EMeanVarDataType, GammaDataType, BetaDataType, HDataType,  AElementOp,  BElementOp, CDEElementOp,   HElementOp,    GemmDefault,        1,   256,   256,   128,    32,   8,   8,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,         1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              8,              8,         1,           1,           1,              S<32, 8>,               8,             S<8, 32>,               8>;
+// clang-format on
+
+auto f_host_tensor_descriptor1d = [](std::size_t len, std::size_t stride) {
+    return HostTensorDescriptor(std::vector<std::size_t>({len}),
+                                std::vector<std::size_t>({stride}));
+};
+
+auto f_host_tensor_descriptor2d =
+    [](std::size_t row, std::size_t col, std::size_t stride, auto layout) {
+        if(std::is_same<decltype(layout), ck::tensor_layout::gemm::RowMajor>::value)
+        {
+            return HostTensorDescriptor(std::vector<std::size_t>({row, col}),
+                                        std::vector<std::size_t>({stride, 1}));
+        }
+        else
+        {
+            return HostTensorDescriptor(std::vector<std::size_t>({row, col}),
+                                        std::vector<std::size_t>({1, stride}));
+        }
+    };
+
+void host_gemm_layernorm(Tensor<HDataType>& h_m_n,
+                         const Tensor<ADataType>& a_m_k,
+                         const Tensor<BDataType>& b_k_n,
+                         const Tensor<D0DataType>& bias_n,
+                         const Tensor<D1DataType>& d1_m_n,
+                         const Tensor<GammaDataType>& gamma_n,
+                         const Tensor<BetaDataType>& beta_n,
+                         AElementOp a_element_op,
+                         BElementOp b_element_op,
+                         CDEElementOp cde_element_op,
+                         int M,
+                         int N,
+                         AccDataType epsilon = 1e-5)
+{
+    using ReferenceGemm = ck::tensor_operation::host::ReferenceGemm<ADataType,
+                                                                    BDataType,
+                                                                    AccDataType,
+                                                                    AccDataType,
+                                                                    AElementOp,
+                                                                    BElementOp,
+                                                                    PassThrough>;
+
+    using ReferenceLayernorm = ck::tensor_operation::host::ReferenceLayernorm<EMeanVarDataType,
+                                                                              GammaDataType,
+                                                                              BetaDataType,
+                                                                              HDataType,
+                                                                              AccDataType,
+                                                                              HElementOp,
+                                                                              2,
+                                                                              1>;
+
+    Tensor<EMeanVarDataType> e_m_n(HostTensorDescriptor{M, N});
+    Tensor<AccDataType> c_m_n(HostTensorDescriptor{M, N});
+
+    auto ref_gemm         = ReferenceGemm{};
+    auto ref_gemm_invoker = ref_gemm.MakeInvoker();
+
+    auto ref_gemm_argument =
+        ref_gemm.MakeArgument(a_m_k, b_k_n, c_m_n, a_element_op, b_element_op, PassThrough{});
+
+    ref_gemm_invoker.Run(ref_gemm_argument);
+
+    for(int n = 0; n < N; ++n)
+    {
+        AccDataType bias = static_cast<AccDataType>(bias_n(n));
+        for(int m = 0; m < M; ++m)
+        {
+            AccDataType e  = static_cast<AccDataType>(e_m_n(m, n));
+            AccDataType d1 = static_cast<AccDataType>(d1_m_n(m, n));
+            cde_element_op(e, c_m_n(m, n), bias, d1);
+            e_m_n(m, n) = static_cast<EMeanVarDataType>(e);
+        }
+    }
+
+    ReferenceLayernorm ref_layernorm;
+    auto ref_layernorm_invoker = ref_layernorm.MakeInvoker();
+
+    auto ref_layernorm_argument = ref_layernorm.MakeArgument(
+        e_m_n, gamma_n, beta_n, h_m_n, HElementOp{}, {M, N}, {1}, epsilon);
+    ref_layernorm_invoker.Run(ref_layernorm_argument);
+}
+
+int main()
+{
+    bool do_verification = true;
+
+    // GEMM shape
+    ck::index_t M = 1024;
+    ck::index_t N = 1024;
+    ck::index_t K = 1024;
+
+    ck::index_t StrideA  = K;
+    ck::index_t StrideB  = K;
+    ck::index_t StrideD0 = 0;
+    ck::index_t StrideD1 = N;
+    ck::index_t StrideH  = N;
+
+    float epsilon = 1e-5;
+
+    Tensor<ADataType> a_m_k(f_host_tensor_descriptor2d(M, K, StrideA, ALayout{}));
+    Tensor<BDataType> b_k_n(f_host_tensor_descriptor2d(K, N, StrideB, BLayout{}));
+    Tensor<D0DataType> d0_n(f_host_tensor_descriptor1d(N, 1));
+    Tensor<D1DataType> d1_m_n(f_host_tensor_descriptor2d(M, N, StrideD1, D1Layout{}));
+    Tensor<GammaDataType> gamma_n(f_host_tensor_descriptor1d(N, 1));
+    Tensor<BetaDataType> beta_n(f_host_tensor_descriptor1d(N, 1));
+    Tensor<HDataType> h_m_n(f_host_tensor_descriptor2d(M, N, StrideH, HLayout{}));
+
+    a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{-1, 1});
+    b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-1, 1});
+    d0_n.GenerateTensorValue(GeneratorTensor_3<D0DataType>{-1, 1});
+    d1_m_n.GenerateTensorValue(GeneratorTensor_3<D1DataType>{-1, 1});
+    gamma_n.GenerateTensorValue(GeneratorTensor_3<GammaDataType>{-1, 1});
+    beta_n.GenerateTensorValue(GeneratorTensor_3<BetaDataType>{-1, 1});
+
+    DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpaceSize());
+    DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpaceSize());
+    DeviceMem d0_device_buf(sizeof(D0DataType) * d0_n.mDesc.GetElementSpaceSize());
+    DeviceMem d1_device_buf(sizeof(D1DataType) * d1_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem gamma_device_buf(sizeof(GammaDataType) * gamma_n.mDesc.GetElementSpaceSize());
+    DeviceMem beta_device_buf(sizeof(BetaDataType) * beta_n.mDesc.GetElementSpaceSize());
+    DeviceMem h_device_buf(sizeof(HDataType) * h_m_n.mDesc.GetElementSpaceSize());
+
+    a_device_buf.ToDevice(a_m_k.mData.data());
+    b_device_buf.ToDevice(b_k_n.mData.data());
+    d0_device_buf.ToDevice(d0_n.mData.data());
+    d1_device_buf.ToDevice(d1_m_n.mData.data());
+    gamma_device_buf.ToDevice(gamma_n.mData.data());
+    beta_device_buf.ToDevice(beta_n.mData.data());
+
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{};
+    auto h_element_op   = HElementOp{};
+
+    auto device_op = DeviceOpInstance{};
+    auto invoker   = device_op.MakeInvoker();
+    auto argument =
+        device_op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                               b_device_buf.GetDeviceBuffer(),
+                               {d0_device_buf.GetDeviceBuffer(), d1_device_buf.GetDeviceBuffer()},
+                               gamma_device_buf.GetDeviceBuffer(),
+                               beta_device_buf.GetDeviceBuffer(),
+                               h_device_buf.GetDeviceBuffer(),
+                               M,
+                               N,
+                               K,
+                               StrideA,
+                               StrideB,
+                               {StrideD0, StrideD1},
+                               StrideH,
+                               epsilon,
+                               a_element_op,
+                               b_element_op,
+                               cde_element_op,
+                               h_element_op);
+
+    if(!device_op.IsSupportedArgument(argument))
+    {
+        throw std::runtime_error("wrong! this device_op instance does not support this problem");
+    }
+
+    size_t workspace_sz = device_op.GetWorkSpaceSize(&argument);
+    DeviceMem workspace_dev(workspace_sz);
+    device_op.SetWorkSpacePointer(&argument, workspace_dev.GetDeviceBuffer());
+
+    invoker.Run(argument, StreamConfig{nullptr, false});
+
+    bool pass = true;
+
+    if(do_verification)
+    {
+        Tensor<HDataType> h_m_n_host(HostTensorDescriptor{M, N});
+        host_gemm_layernorm(h_m_n_host,
+                            a_m_k,
+                            b_k_n,
+                            d0_n,
+                            d1_m_n,
+                            gamma_n,
+                            beta_n,
+                            a_element_op,
+                            b_element_op,
+                            cde_element_op,
+                            M,
+                            N,
+                            epsilon);
+
+        h_device_buf.FromDevice(h_m_n.mData.data());
+        pass &=
+            ck::utils::check_err(h_m_n, h_m_n_host, "Error: Incorrect results h_m_n", 1e-2, 1e-2);
+    }
+
+    return pass ? 0 : 1;
+}

include/ck/tensor_operation/gpu/device/device_gemm_multiple_d_layernorm.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <array>
+#include "device_base.hpp"
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+// GEMM:
+//   input : A[M, K]
+//   input : B[N, K]
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   output : H[M, N]
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+//   H = layernorm(E)
+// Assume:
+//   D0, D1, ... and E have the same layout
+//   Calculate mean & variance along N dimension in layernorm(E)
+template <typename ALayout,
+          typename BLayout,
+          typename DsLayout,
+          typename HLayout,
+          typename ADataType,
+          typename BDataType,
+          typename DsDataType,
+          typename GammaDataType,
+          typename BetaDataType,
+          typename HDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename HElementwiseOperation>
+struct DeviceGemmMultipleDLayernorm : public BaseOperator
+{
+    static constexpr index_t NumDTensor = DsDataType::Size();
+    virtual std::unique_ptr<BaseArgument>
+    MakeArgumentPointer(const void* p_a,
+                        const void* p_b,
+                        std::array<const void*, NumDTensor> p_ds,
+                        const void* p_gamma,
+                        const void* p_beta,
+                        void* p_h,
+                        index_t MRaw,
+                        index_t NRaw,
+                        index_t KRaw,
+                        index_t StrideA,
+                        index_t StrideB,
+                        std::array<index_t, NumDTensor> StrideDs,
+                        index_t StrideH,
+                        double epsilon,
+                        AElementwiseOperation a_element_op,
+                        BElementwiseOperation b_element_op,
+                        CDEElementwiseOperation cde_element_op,
+                        HElementwiseOperation h_element_op) = 0;
+
+    virtual std::unique_ptr<BaseInvoker> MakeInvokerPointer() = 0;
+}; // namespace device
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

include/ck/tensor_operation/gpu/device/impl/device_gemm_multiple_d_layernorm_xdl_cshuffle.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <sstream>
+
+#include "ck/utility/common_header.hpp"
+#include "ck/tensor_description/tensor_descriptor.hpp"
+#include "ck/tensor_description/tensor_descriptor_helper.hpp"
+#include "ck/tensor_operation/gpu/device/tensor_layout.hpp"
+#include "ck/tensor_operation/gpu/device/device_gemm_multiple_d_layernorm.hpp"
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/matrix_padder.hpp"
+#include "ck/tensor_operation/gpu/grid/gemm_layernorm/gridwise_gemm_multiple_d_welford_first_half_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/grid/gemm_layernorm/gridwise_welford_second_half_layernorm2d.hpp"
+#include "ck/host_utility/device_prop.hpp"
+#include "ck/host_utility/kernel_launch.hpp"
+
+namespace ck {
+
+template <typename GridwiseGemmWelford,
+          typename ABDataType,
+          typename DsPointer,
+          typename EMeanVarDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename AGridDesc_AK0_M_AK1,
+          typename BGridDesc_BK0_N_BK1,
+          typename DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+          typename EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+          typename MeanVarGridDescriptor_MBlock_MPerBlock_NBlock,
+          typename CountGridDescriptor_MBlock_MPerBlock_NBlock,
+          typename Block2ETileMap,
+          bool HasMainKBlockLoop>
+__global__ void
+#if CK_USE_LAUNCH_BOUNDS
+    __launch_bounds__(CK_MAX_THREAD_PER_BLOCK, CK_MIN_BLOCK_PER_CU)
+#endif
+        kernel_gemm_multiple_d_welford_first_half_xdl_cshuffle(
+            const ABDataType* __restrict__ p_a_grid,
+            const ABDataType* __restrict__ p_b_grid,
+            DsPointer p_ds_grid,
+            EMeanVarDataType* __restrict__ p_e_grid,
+            EMeanVarDataType* __restrict__ p_welford_mean_grid,
+            EMeanVarDataType* __restrict__ p_welford_var_grid,
+            int32_t* __restrict__ p_welford_count_grid,
+            const AElementwiseOperation a_element_op,
+            const BElementwiseOperation b_element_op,
+            const CDEElementwiseOperation cde_element_op,
+            const AGridDesc_AK0_M_AK1 a_grid_desc_ak0_m_ak1,
+            const BGridDesc_BK0_N_BK1 b_grid_desc_bk0_n_bk1,
+            const DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+                ds_grid_desc_mblock_mperblock_nblock_nperblock,
+            const EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+                e_grid_desc_mblock_mperblock_nblock_nperblock,
+            const MeanVarGridDescriptor_MBlock_MPerBlock_NBlock
+                mean_var_grid_desc_mblock_mperblock_nblock,
+            const CountGridDescriptor_MBlock_MPerBlock_NBlock
+                count_grid_desc_mblock_mperblock_nblock,
+            const Block2ETileMap block_2_etile_map,
+            index_t NRaw)
+{
+#if(!defined(__HIP_DEVICE_COMPILE__) || defined(__gfx908__) || defined(__gfx90a__))
+    __shared__ char p_shared[GridwiseGemmWelford::GetSharedMemoryNumberOfByte()];
+
+    GridwiseGemmWelford::template Run<HasMainKBlockLoop>(
+        p_a_grid,
+        p_b_grid,
+        p_ds_grid,
+        p_e_grid,
+        p_welford_mean_grid,
+        p_welford_var_grid,
+        p_welford_count_grid,
+        p_shared,
+        a_element_op,
+        b_element_op,
+        cde_element_op,
+        a_grid_desc_ak0_m_ak1,
+        b_grid_desc_bk0_n_bk1,
+        ds_grid_desc_mblock_mperblock_nblock_nperblock,
+        e_grid_desc_mblock_mperblock_nblock_nperblock,
+        mean_var_grid_desc_mblock_mperblock_nblock,
+        count_grid_desc_mblock_mperblock_nblock,
+        block_2_etile_map,
+        NRaw);
+#else
+    ignore = p_a_grid;
+    ignore = p_b_grid;
+    ignore = p_ds_grid;
+    ignore = p_e_grid;
+    ignore = p_welford_mean_grid;
+    ignore = p_welford_var_grid;
+    ignore = p_welford_count_grid;
+    ignore = a_element_op;
+    ignore = b_element_op;
+    ignore = cde_element_op;
+    ignore = a_grid_desc_ak0_m_ak1;
+    ignore = b_grid_desc_bk0_n_bk1;
+    ignore = ds_grid_desc_mblock_mperblock_nblock_nperblock;
+    ignore = e_grid_desc_mblock_mperblock_nblock_nperblock;
+    ignore = mean_var_grid_desc_mblock_mperblock_nblock;
+    ignore = count_grid_desc_mblock_mperblock_nblock;
+    ignore = block_2_etile_map;
+    ignore = NRaw;
+#endif
+}
+
+template <typename GridwiseWelfordLayernorm,
+          typename EMeanVarDataType,
+          typename HDataType,
+          typename GammaDataType,
+          typename BetaDataType,
+          typename ComputeDataType,
+          typename EHGridDesc_M_N,
+          typename LayernormMeanVarGridDesc_M_NBlock,
+          typename LayernormCountGridDesc_M_NBlock,
+          typename GammaBetaGridDesc_N,
+          typename HElementwiseOperation>
+__global__ void
+#if CK_USE_LAUNCH_BOUNDS
+    __launch_bounds__(CK_MAX_THREAD_PER_BLOCK, CK_MIN_BLOCK_PER_CU)
+#endif
+        kernel_welford_layernorm2d_second_half(
+            const EMeanVarDataType* __restrict__ p_e_grid,
+            const EMeanVarDataType* __restrict__ p_in_welford_mean_grid,
+            const EMeanVarDataType* __restrict__ p_in_welford_var_grid,
+            const int32_t* __restrict__ p_in_welford_count_grid,
+            const GammaDataType* __restrict__ p_gamma_grid,
+            const BetaDataType* __restrict__ p_beta_grid,
+            HDataType* __restrict__ p_h_grid,
+            const EHGridDesc_M_N e_grid_desc_m_n,
+            const EHGridDesc_M_N h_grid_desc_m_n,
+            const LayernormMeanVarGridDesc_M_NBlock mean_var_grid_desc_m_nblock,
+            const LayernormCountGridDesc_M_NBlock count_grid_desc_m_nblock,
+            const GammaBetaGridDesc_N gamma_grid_desc_n,
+            const GammaBetaGridDesc_N beta_grid_desc_n,
+            index_t numMeanVarCountBlockTileIteration_N,
+            index_t NBlockClusterLength,
+            ComputeDataType epsilon,
+            HElementwiseOperation h_element_op)
+{
+    GridwiseWelfordLayernorm::Run(p_e_grid,
+                                  p_in_welford_mean_grid,
+                                  p_in_welford_var_grid,
+                                  p_in_welford_count_grid,
+                                  p_gamma_grid,
+                                  p_beta_grid,
+                                  p_h_grid,
+                                  e_grid_desc_m_n,
+                                  h_grid_desc_m_n,
+                                  mean_var_grid_desc_m_nblock,
+                                  count_grid_desc_m_nblock,
+                                  gamma_grid_desc_n,
+                                  beta_grid_desc_n,
+                                  numMeanVarCountBlockTileIteration_N,
+                                  NBlockClusterLength,
+                                  epsilon,
+                                  h_element_op);
+}
+
+} // namespace ck
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+// GEMM:
+//   input : A[M, K]
+//   input : B[N, K]
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   output : H[M, N]
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+//   H = layernorm(E)
+// Assume:
+//   D0, D1, ... and E have the same layout
+//   Calculate mean & variance along N dimension in layernorm(E)
+template <typename ALayout,
+          typename BLayout,
+          typename DsLayout,
+          typename HLayout,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EMeanVarDataType,
+          typename GammaDataType,
+          typename BetaDataType,
+          typename HDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename HElementwiseOperation,
+          GemmSpecialization GemmSpec,
+          index_t NumGemmKPrefetchStage,
+          index_t BlockSize,
+          index_t GemmMPerBlock,
+          index_t GemmNPerBlock,
+          index_t GemmKPerBlock,
+          index_t AK1,
+          index_t BK1,
+          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 ABlockLdsExtraM,
+          typename BBlockTransferThreadClusterLengths_BK0_N_BK1,
+          typename BBlockTransferThreadClusterArrangeOrder,
+          typename BBlockTransferSrcAccessOrder,
+          index_t BBlockTransferSrcVectorDim,
+          index_t BBlockTransferSrcScalarPerVector,
+          index_t BBlockTransferDstScalarPerVector_BK1,
+          bool BBlockLdsExtraN,
+          index_t CShuffleMXdlPerWavePerShuffle,
+          index_t CShuffleNXdlPerWavePerShuffle,
+          typename PostShuffleThreadClusterSize_M_N,
+          index_t PostShuffleScalarPerVector,
+          typename LayernormThreadClusterSize_M_N,
+          index_t LayernormThreadSliceSize_M,
+          LoopScheduler LoopSched     = make_default_loop_scheduler(),
+          PipelineVersion PipelineVer = PipelineVersion::v1>
+struct DeviceGemmMultipleDLayernorm_Xdl_CShuffle
+    : public DeviceGemmMultipleDLayernorm<ALayout,
+                                          BLayout,
+                                          DsLayout,
+                                          HLayout,
+                                          ADataType,
+                                          BDataType,
+                                          DsDataType,
+                                          GammaDataType,
+                                          BetaDataType,
+                                          HDataType,
+                                          AElementwiseOperation,
+                                          BElementwiseOperation,
+                                          CDEElementwiseOperation,
+                                          HElementwiseOperation>
+{
+    // EDataType, MeanDataType and VarDataType must be the same.
+    // eg. M, N, K = [1, 1, 1],
+    // in case of layernorm, divisor = 1 / sqrt(var + 1e-5) = 316.227783
+    // if (x - mean) != 0, (x - mean) * divisor * gamma might be too large
+    // However, (x - mean) * divisor * gamma should be 0 in this case
+
+    using DeviceOp = DeviceGemmMultipleDLayernorm_Xdl_CShuffle;
+    using ELayout  = HLayout;
+
+    static constexpr index_t NumDTensor                  = DsDataType::Size();
+    static constexpr index_t LayernormHDstVectorSize     = PostShuffleScalarPerVector;
+    static constexpr index_t LayernormGammaSrcVectorSize = PostShuffleScalarPerVector;
+    static constexpr index_t LayernormBetaSrcVectorSize  = PostShuffleScalarPerVector;
+    static constexpr index_t LayernormESrcVectorSize     = PostShuffleScalarPerVector;
+    static constexpr index_t LayernormThreadSliceSize_N  = PostShuffleScalarPerVector;
+    using LayernormBlockTileSize_M_N =
+        Sequence<LayernormThreadClusterSize_M_N::At(0) * LayernormThreadSliceSize_M,
+                 LayernormThreadClusterSize_M_N::At(1) * LayernormThreadSliceSize_N>;
+
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+
+    static constexpr auto matrix_padder = MatrixPadder<GemmSpec, index_t, index_t, index_t>{
+        GemmMPerBlock, GemmNPerBlock, GemmKPerBlock};
+
+    static auto MakeAGridDescriptor_M_K(index_t MRaw, index_t KRaw, index_t StrideA)
+    {
+        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);
+    }
+
+    static auto MakeBGridDescriptor_N_K(index_t KRaw, index_t NRaw, index_t StrideB)
+    {
+        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);
+    }
+
+    template <typename DoPads, index_t MPerTile, index_t NPerTile>
+    static auto MakeEHGridDescriptor_M_N(index_t M, index_t N, index_t Stride)
+    {
+        // Only support row major for E and H
+        const auto grid_desc_m_n =
+            make_naive_tensor_descriptor(make_tuple(M, N), make_tuple(Stride, I1));
+        return PadTensorDescriptor(grid_desc_m_n, make_tuple(MPerTile, NPerTile), DoPads{});
+    }
+
+    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>>;
+                static_assert(is_same<tensor_layout::gemm::RowMajor, DLayout>::value);
+
+                return DeviceOp::
+                    MakeEHGridDescriptor_M_N<Sequence<true, true>, GemmMPerBlock, GemmNPerBlock>(
+                        MRaws[i], NRaws[i], DsStride[i]);
+            },
+            Number<NumDTensor>{});
+    }
+
+    template <typename DoPads, index_t MPerTile, index_t NPerTile>
+    static auto MakeMeanVarDescriptor_M_N(index_t M, index_t N)
+    {
+        const auto grid_desc_m_n =
+            make_naive_tensor_descriptor(make_tuple(M, N), make_tuple(N, I1));
+        return PadTensorDescriptor(grid_desc_m_n, make_tuple(MPerTile, NPerTile), DoPads{});
+    }
+
+    template <typename DoPads, index_t MPerTile, index_t NPerTile>
+    static auto MakeCountDescriptor_M_N(index_t M, index_t N)
+    {
+        // We will broadcast [N] to [M, N] in this descriptor
+        // Hence, 1st stride is 0
+        const auto grid_desc_m_n =
+            make_naive_tensor_descriptor(make_tuple(M, N), make_tuple(I0, I1));
+        return PadTensorDescriptor(grid_desc_m_n, make_tuple(MPerTile, NPerTile), DoPads{});
+    }
+
+    template <index_t XPerTile>
+    static auto MakeDescriptor_X(index_t X)
+    {
+        const auto grid_desc_x = make_naive_tensor_descriptor_packed(make_tuple(X));
+        return PadTensorDescriptor(grid_desc_x, make_tuple(XPerTile), Sequence<true>{});
+    }
+
+    using AGridDesc_M_K  = decltype(MakeAGridDescriptor_M_K(1, 1, 1));
+    using BGridDesc_N_K  = decltype(MakeBGridDescriptor_N_K(1, 1, 1));
+    using DsGridDesc_M_N = remove_cvref_t<decltype(MakeDsGridDescriptor_M_N({}, {}, {}))>;
+    // We have to separate mean var descriptor for gemm and layernorm bacause of different grid
+    // layout(different padding)
+    using GemmMeanVarGridDesc_M_NBlock = decltype(
+        MakeMeanVarDescriptor_M_N<Sequence<true, false>, GemmMPerBlock, GemmNPerBlock>(1, 1));
+
+    using GemmCountGridDesc_M_NBlock = decltype(
+        MakeCountDescriptor_M_N<Sequence<true, false>, GemmMPerBlock, GemmNPerBlock>(1, 1));
+
+    using LayernormMeanVarGridDesc_M_NBlock =
+        decltype(MakeMeanVarDescriptor_M_N<Sequence<true, true>,
+                                           LayernormBlockTileSize_M_N::At(0),
+                                           LayernormBlockTileSize_M_N::At(1)>(1, 1));
+
+    using LayernormCountGridDesc_M_NBlock =
+        decltype(MakeCountDescriptor_M_N<Sequence<true, true>,
+                                         LayernormBlockTileSize_M_N::At(0),
+                                         LayernormBlockTileSize_M_N::At(1)>(1, 1));
+
+    using GammaBetaGridDesc_N = decltype(MakeDescriptor_X<LayernormBlockTileSize_M_N::At(1)>(1));
+    using EHGridDesc_M_N = decltype(MakeEHGridDescriptor_M_N<Sequence<true, true>, 1, 1>(1, 1, 1));
+
+    using GridwiseGemmWelford = GridwiseGemmMultipleDWelfordFirstHalf_xdl_cshuffle<
+        ADataType, // TODO: distinguish A/B datatype
+        AccDataType,
+        CShuffleDataType,
+        DsDataType,
+        EMeanVarDataType,
+        AElementwiseOperation,
+        BElementwiseOperation,
+        CDEElementwiseOperation,
+        InMemoryDataOperationEnum::Set,
+        AGridDesc_M_K,
+        BGridDesc_N_K,
+        DsGridDesc_M_N,
+        EHGridDesc_M_N,
+        GemmMeanVarGridDesc_M_NBlock,
+        GemmCountGridDesc_M_NBlock,
+        NumGemmKPrefetchStage,
+        BlockSize,
+        GemmMPerBlock,
+        GemmNPerBlock,
+        GemmKPerBlock,
+        AK1,
+        BK1,
+        MPerXDL,
+        NPerXDL,
+        MXdlPerWave,
+        NXdlPerWave,
+        ABlockTransferThreadClusterLengths_AK0_M_AK1,
+        ABlockTransferThreadClusterArrangeOrder,
+        ABlockTransferSrcAccessOrder,
+        ABlockTransferSrcVectorDim,
+        ABlockTransferSrcScalarPerVector,
+        ABlockTransferDstScalarPerVector_AK1,
+        false,
+        ABlockLdsExtraM,
+        BBlockTransferThreadClusterLengths_BK0_N_BK1,
+        BBlockTransferThreadClusterArrangeOrder,
+        BBlockTransferSrcAccessOrder,
+        BBlockTransferSrcVectorDim,
+        BBlockTransferSrcScalarPerVector,
+        BBlockTransferDstScalarPerVector_BK1,
+        false,
+        BBlockLdsExtraN,
+        CShuffleMXdlPerWavePerShuffle,
+        CShuffleNXdlPerWavePerShuffle,
+        PostShuffleThreadClusterSize_M_N,
+        PostShuffleScalarPerVector,
+        LoopSched,
+        PipelineVer>;
+
+    using Block2ETileMap = typename GridwiseGemmWelford::DefaultBlock2ETileMap;
+
+    using GridwiseWelfordLayernorm =
+        GridwiseWelfordSecondHalfLayernorm2d<EMeanVarDataType,
+                                             HDataType,
+                                             GammaDataType,
+                                             BetaDataType,
+                                             AccDataType,
+                                             EHGridDesc_M_N,
+                                             LayernormMeanVarGridDesc_M_NBlock,
+                                             LayernormCountGridDesc_M_NBlock,
+                                             GammaBetaGridDesc_N,
+                                             HElementwiseOperation,
+                                             BlockSize,
+                                             LayernormThreadClusterSize_M_N::At(I0),
+                                             LayernormThreadClusterSize_M_N::At(I1),
+                                             LayernormThreadSliceSize_M,
+                                             LayernormThreadSliceSize_N,
+                                             LayernormESrcVectorSize,
+                                             LayernormHDstVectorSize,
+                                             LayernormGammaSrcVectorSize,
+                                             LayernormBetaSrcVectorSize>;
+
+    // Argument
+    struct Argument : public BaseArgument
+    {
+        Argument(const void* p_a_grid,
+                 const void* p_b_grid,
+                 std::array<const void*, NumDTensor> p_ds_grid,
+                 const void* p_gamma_grid,
+                 const void* p_beta_grid,
+                 void* p_h_grid,
+                 index_t MRaw,
+                 index_t NRaw,
+                 index_t KRaw,
+                 index_t StrideA,
+                 index_t StrideB,
+                 std::array<index_t, NumDTensor> StrideDs,
+                 index_t StrideH,
+                 double epsilon,
+                 AElementwiseOperation a_element_op,
+                 BElementwiseOperation b_element_op,
+                 CDEElementwiseOperation cde_element_op,
+                 HElementwiseOperation h_element_op)
+            : p_a_grid_{static_cast<const ADataType*>(p_a_grid)},
+              p_b_grid_{static_cast<const BDataType*>(p_b_grid)},
+              p_ds_grid_{},
+              p_workspace_e_grid_{nullptr},
+              p_workspace_mean_{nullptr},
+              p_workspace_var_{nullptr},
+              p_workspace_count_{nullptr},
+              p_gamma_grid_{static_cast<const GammaDataType*>(p_gamma_grid)},
+              p_beta_grid_{static_cast<const BetaDataType*>(p_beta_grid)},
+              p_h_grid_{static_cast<HDataType*>(p_h_grid)},
+              a_grid_desc_m_k_{DeviceOp::MakeAGridDescriptor_M_K(MRaw, KRaw, StrideA)},
+              b_grid_desc_n_k_{DeviceOp::MakeBGridDescriptor_N_K(KRaw, NRaw, StrideB)},
+              ds_grid_desc_m_n_{},
+              gemm_e_grid_desc_m_n_{
+                  DeviceOp::MakeEHGridDescriptor_M_N<Sequence<true, true>,
+                                                     GemmMPerBlock,
+                                                     GemmNPerBlock>(MRaw, NRaw, StrideH)},
+              layernorm_e_grid_desc_m_n_{
+                  DeviceOp::MakeEHGridDescriptor_M_N<Sequence<true, true>,
+                                                     LayernormBlockTileSize_M_N::At(0),
+                                                     LayernormBlockTileSize_M_N::At(1)>(
+                      MRaw, NRaw, StrideH)},
+              gemm_mean_var_grid_desc_m_nblock_{},
+              gemm_count_grid_desc_m_nblock_{},
+              layernorm_mean_var_grid_desc_m_nblock_{},
+              layernorm_count_grid_desc_m_nblock_{},
+              gamma_grid_desc_n_{
+                  DeviceOp::MakeDescriptor_X<LayernormBlockTileSize_M_N::At(1)>(NRaw)},
+              beta_grid_desc_n_{
+                  DeviceOp::MakeDescriptor_X<LayernormBlockTileSize_M_N::At(1)>(NRaw)},
+              h_grid_desc_m_n_{
+                  DeviceOp::MakeEHGridDescriptor_M_N<Sequence<true, true>,
+                                                     LayernormBlockTileSize_M_N::At(0),
+                                                     LayernormBlockTileSize_M_N::At(1)>(
+                      MRaw, NRaw, StrideH)},
+              a_grid_desc_ak0_m_ak1_{
+                  GridwiseGemmWelford::MakeDefaultAGridDescriptor_AK0_M_AK1(a_grid_desc_m_k_)},
+              b_grid_desc_bk0_n_bk1_{
+                  GridwiseGemmWelford::MakeDefaultBGridDescriptor_BK0_N_BK1(b_grid_desc_n_k_)},
+              block_2_etile_map_{
+                  GridwiseGemmWelford::MakeDefaultBlock2ETileMap(gemm_e_grid_desc_m_n_)},
+              a_element_op_{a_element_op},
+              b_element_op_{b_element_op},
+              cde_element_op_{cde_element_op},
+              h_element_op_{h_element_op},
+              MRaw_{MRaw},
+              NRaw_{NRaw},
+              KRaw_{KRaw},
+              gemm_nblock_{math::integer_divide_ceil(NRaw, GemmNPerBlock)},
+              epsilon_{static_cast<AccDataType>(epsilon)}
+        {
+            // We don't need to pad in N dimension in gemm for mean/var/count. Set NPerTile 1.
+            gemm_mean_var_grid_desc_m_nblock_ =
+                DeviceOp::MakeMeanVarDescriptor_M_N<Sequence<true, false>, GemmMPerBlock, 1>(
+                    MRaw, gemm_nblock_);
+
+            gemm_count_grid_desc_m_nblock_ =
+                DeviceOp::MakeCountDescriptor_M_N<Sequence<true, false>, GemmMPerBlock, 1>(
+                    MRaw, gemm_nblock_);
+
+            layernorm_mean_var_grid_desc_m_nblock_ =
+                DeviceOp::MakeMeanVarDescriptor_M_N<Sequence<true, true>,
+                                                    LayernormBlockTileSize_M_N::At(0),
+                                                    LayernormBlockTileSize_M_N::At(1)>(
+                    MRaw, gemm_nblock_);
+
+            layernorm_count_grid_desc_m_nblock_ =
+                DeviceOp::MakeCountDescriptor_M_N<Sequence<true, true>,
+                                                  LayernormBlockTileSize_M_N::At(0),
+                                                  LayernormBlockTileSize_M_N::At(1)>(MRaw,
+                                                                                     gemm_nblock_);
+
+            // populate pointer, desc for Ds
+            static_for<0, NumDTensor, 1>{}([&](auto i) {
+                using DDataType = remove_cvref_t<tuple_element_t<i.value, DsDataType>>;
+
+                // D pointer
+                p_ds_grid_(i) = static_cast<const DDataType*>(p_ds_grid[i]);
+
+                // D desc
+                ds_grid_desc_m_n_(i) =
+                    DeviceOp::MakeEHGridDescriptor_M_N<Sequence<true, true>,
+                                                       GemmMPerBlock,
+                                                       GemmNPerBlock>(MRaw, NRaw, StrideDs[i]);
+            });
+
+            // populate desc for Ds/E/mean/var/count
+            if(GridwiseGemmWelford::CheckValidity(a_grid_desc_m_k_,
+                                                  b_grid_desc_n_k_,
+                                                  ds_grid_desc_m_n_,
+                                                  gemm_e_grid_desc_m_n_,
+                                                  block_2_etile_map_))
+            {
+                ds_grid_desc_mblock_mperblock_nblock_nperblock_ =
+                    GridwiseGemmWelford::MakeDsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+                        ds_grid_desc_m_n_);
+
+                e_grid_desc_mblock_mperblock_nblock_nperblock_ =
+                    GridwiseGemmWelford::MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+                        gemm_e_grid_desc_m_n_);
+
+                gemm_mean_var_grid_desc_mblock_mperblock_nblock_ =
+                    GridwiseGemmWelford::MakeMeanVarCountGridDescriptor_MBlock_MPerBlock_NBlock(
+                        gemm_mean_var_grid_desc_m_nblock_);
+
+                gemm_count_grid_desc_mblock_mperblock_nblock_ =
+                    GridwiseGemmWelford::MakeMeanVarCountGridDescriptor_MBlock_MPerBlock_NBlock(
+                        gemm_count_grid_desc_m_nblock_);
+            }
+        }
+
+        void Print() const
+        {
+            std::cout << "A[M, K]: " << a_grid_desc_m_k_ << std::endl;
+            std::cout << "B[N, K]: " << b_grid_desc_n_k_ << std::endl;
+            static_for<0, NumDTensor, 1>{}(
+                [&](auto i) { std::cout << "Ds[M, N]: " << ds_grid_desc_m_n_[i] << std::endl; });
+            std::cout << "E[M, N]: " << gemm_e_grid_desc_m_n_ << std::endl;
+            std::cout << "H[M, N]: " << h_grid_desc_m_n_ << std::endl;
+        }
+
+        //  private:
+        // pointers
+        const ADataType* p_a_grid_;
+        const BDataType* p_b_grid_;
+        typename GridwiseGemmWelford::DsGridPointer p_ds_grid_;
+        void* p_workspace_e_grid_;
+        void* p_workspace_mean_;
+        void* p_workspace_var_;
+        void* p_workspace_count_;
+        const GammaDataType* p_gamma_grid_;
+        const BetaDataType* p_beta_grid_;
+        HDataType* p_h_grid_;
+
+        // tensor descriptors for problem definiton
+        AGridDesc_M_K a_grid_desc_m_k_;
+        BGridDesc_N_K b_grid_desc_n_k_;
+        DsGridDesc_M_N ds_grid_desc_m_n_;
+        EHGridDesc_M_N gemm_e_grid_desc_m_n_;
+        EHGridDesc_M_N layernorm_e_grid_desc_m_n_;
+        GemmMeanVarGridDesc_M_NBlock gemm_mean_var_grid_desc_m_nblock_;
+        GemmCountGridDesc_M_NBlock gemm_count_grid_desc_m_nblock_;
+        LayernormMeanVarGridDesc_M_NBlock layernorm_mean_var_grid_desc_m_nblock_;
+        LayernormCountGridDesc_M_NBlock layernorm_count_grid_desc_m_nblock_;
+        GammaBetaGridDesc_N gamma_grid_desc_n_;
+        GammaBetaGridDesc_N beta_grid_desc_n_;
+        EHGridDesc_M_N h_grid_desc_m_n_;
+
+        // tensor descriptors for block/thread-wise copy
+        typename GridwiseGemmWelford::DefaultAGridDesc_AK0_M_AK1 a_grid_desc_ak0_m_ak1_;
+        typename GridwiseGemmWelford::DefaultBGridDesc_BK0_N_BK1 b_grid_desc_bk0_n_bk1_;
+        typename GridwiseGemmWelford::DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+            ds_grid_desc_mblock_mperblock_nblock_nperblock_;
+        typename GridwiseGemmWelford::EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+            e_grid_desc_mblock_mperblock_nblock_nperblock_;
+        typename GridwiseGemmWelford::MeanVarGridDescriptor_MBlock_MPerBlock_NBlock
+            gemm_mean_var_grid_desc_mblock_mperblock_nblock_;
+        typename GridwiseGemmWelford::CountGridDescriptor_MBlock_MPerBlock_NBlock
+            gemm_count_grid_desc_mblock_mperblock_nblock_;
+
+        // block-to-e-tile map
+        Block2ETileMap block_2_etile_map_;
+
+        // element-wise op
+        AElementwiseOperation a_element_op_;
+        BElementwiseOperation b_element_op_;
+        CDEElementwiseOperation cde_element_op_;
+        HElementwiseOperation h_element_op_;
+
+        index_t MRaw_;
+        index_t NRaw_;
+        index_t KRaw_;
+        index_t gemm_nblock_;
+        AccDataType epsilon_;
+    };
+
+    // Invoker
+    struct Invoker : public BaseInvoker
+    {
+        using Argument = DeviceOp::Argument;
+
+        float Run(const Argument& arg, const StreamConfig& stream_config = StreamConfig{})
+        {
+            float avg_time = 0;
+
+            if(!GridwiseGemmWelford::CheckValidity(arg.a_grid_desc_m_k_,
+                                                   arg.b_grid_desc_n_k_,
+                                                   arg.ds_grid_desc_m_n_,
+                                                   arg.gemm_e_grid_desc_m_n_,
+                                                   arg.block_2_etile_map_))
+            {
+                throw std::runtime_error("wrong! GridwiseGemmWelford has invalid setting");
+            }
+
+            index_t grid_size = arg.block_2_etile_map_.CalculateGridSize(arg.gemm_e_grid_desc_m_n_);
+
+            const auto M = arg.h_grid_desc_m_n_.GetLength(I0);
+            const auto N = arg.h_grid_desc_m_n_.GetLength(I1);
+            const auto K =
+                arg.a_grid_desc_ak0_m_ak1_.GetLength(I0) * arg.a_grid_desc_ak0_m_ak1_.GetLength(I2);
+
+            auto launch_kernel = [&](auto has_main_k_block_loop) {
+                constexpr bool has_main_loop = has_main_k_block_loop.value;
+
+                const auto kernel_gemm_welford =
+                    kernel_gemm_multiple_d_welford_first_half_xdl_cshuffle<
+                        GridwiseGemmWelford,
+                        ADataType, // TODO: distiguish A/B datatype
+                        typename GridwiseGemmWelford::DsGridPointer,
+                        EMeanVarDataType,
+                        AElementwiseOperation,
+                        BElementwiseOperation,
+                        CDEElementwiseOperation,
+                        typename GridwiseGemmWelford::DefaultAGridDesc_AK0_M_AK1,
+                        typename GridwiseGemmWelford::DefaultBGridDesc_BK0_N_BK1,
+                        typename GridwiseGemmWelford::
+                            DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+                        typename GridwiseGemmWelford::
+                            EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+                        typename GridwiseGemmWelford::MeanVarGridDescriptor_MBlock_MPerBlock_NBlock,
+                        typename GridwiseGemmWelford::CountGridDescriptor_MBlock_MPerBlock_NBlock,
+                        typename GridwiseGemmWelford::DefaultBlock2ETileMap,
+                        has_main_loop>;
+
+                const auto kernel_welford_layernorm =
+                    kernel_welford_layernorm2d_second_half<GridwiseWelfordLayernorm,
+                                                           EMeanVarDataType,
+                                                           HDataType,
+                                                           GammaDataType,
+                                                           BetaDataType,
+                                                           AccDataType,
+                                                           EHGridDesc_M_N,
+                                                           LayernormMeanVarGridDesc_M_NBlock,
+                                                           LayernormCountGridDesc_M_NBlock,
+                                                           GammaBetaGridDesc_N,
+                                                           HElementwiseOperation>;
+
+                avg_time +=
+                    launch_and_time_kernel(stream_config,
+                                           kernel_gemm_welford,
+                                           dim3(grid_size),
+                                           dim3(BlockSize),
+                                           0,
+                                           arg.p_a_grid_,
+                                           arg.p_b_grid_,
+                                           arg.p_ds_grid_,
+                                           static_cast<EMeanVarDataType*>(arg.p_workspace_e_grid_),
+                                           static_cast<EMeanVarDataType*>(arg.p_workspace_mean_),
+                                           static_cast<EMeanVarDataType*>(arg.p_workspace_var_),
+                                           static_cast<int32_t*>(arg.p_workspace_count_),
+                                           arg.a_element_op_,
+                                           arg.b_element_op_,
+                                           arg.cde_element_op_,
+                                           arg.a_grid_desc_ak0_m_ak1_,
+                                           arg.b_grid_desc_bk0_n_bk1_,
+                                           arg.ds_grid_desc_mblock_mperblock_nblock_nperblock_,
+                                           arg.e_grid_desc_mblock_mperblock_nblock_nperblock_,
+                                           arg.gemm_mean_var_grid_desc_mblock_mperblock_nblock_,
+                                           arg.gemm_count_grid_desc_mblock_mperblock_nblock_,
+                                           arg.block_2_etile_map_,
+                                           arg.NRaw_);
+
+                index_t MBlockClusterLength =
+                    math::integer_divide_ceil(M, LayernormBlockTileSize_M_N::At(0));
+                index_t NBlockClusterLength =
+                    math::integer_divide_ceil(N, LayernormBlockTileSize_M_N::At(1));
+                grid_size = MBlockClusterLength * NBlockClusterLength;
+
+                index_t numMeanVarCountBlockTileIteration_N = math::integer_divide_ceil(
+                    arg.gemm_nblock_, LayernormThreadClusterSize_M_N::At(I1));
+
+                avg_time += launch_and_time_kernel(
+                    stream_config,
+                    kernel_welford_layernorm,
+                    dim3(grid_size),
+                    dim3(BlockSize),
+                    0,
+                    static_cast<EMeanVarDataType*>(arg.p_workspace_e_grid_),
+                    static_cast<const EMeanVarDataType*>(arg.p_workspace_mean_),
+                    static_cast<const EMeanVarDataType*>(arg.p_workspace_var_),
+                    static_cast<const int32_t*>(arg.p_workspace_count_),
+                    arg.p_gamma_grid_,
+                    arg.p_beta_grid_,
+                    arg.p_h_grid_,
+                    arg.layernorm_e_grid_desc_m_n_,
+                    arg.h_grid_desc_m_n_,
+                    arg.layernorm_mean_var_grid_desc_m_nblock_,
+                    arg.layernorm_count_grid_desc_m_nblock_,
+                    arg.gamma_grid_desc_n_,
+                    arg.beta_grid_desc_n_,
+                    numMeanVarCountBlockTileIteration_N,
+                    NBlockClusterLength,
+                    arg.epsilon_,
+                    arg.h_element_op_);
+
+                return avg_time;
+            };
+
+            if(GridwiseGemmWelford::CalculateHasMainKBlockLoop(K))
+            {
+                return launch_kernel(integral_constant<bool, true>{});
+            }
+            else
+            {
+                return launch_kernel(integral_constant<bool, false>{});
+            }
+        }
+
+        // polymorphic
+        float Run(const BaseArgument* p_arg,
+                  const StreamConfig& stream_config = StreamConfig{}) override
+        {
+            return Run(*dynamic_cast<const Argument*>(p_arg), stream_config);
+        }
+    };
+
+    size_t GetWorkSpaceSize(const BaseArgument* pArg) const override
+    {
+        const Argument* pArg_ = dynamic_cast<const Argument*>(pArg);
+
+        size_t workspace_size = 0;
+
+        int gemm_welford_size = pArg_->MRaw_ * pArg_->gemm_nblock_;
+
+        // workspace for welford intermediate mean
+        workspace_size += gemm_welford_size * sizeof(EMeanVarDataType) + 64;
+
+        // workspace for welford intermediate mean
+        workspace_size += gemm_welford_size * sizeof(EMeanVarDataType) + 64;
+
+        // workspace for welford intermediate count
+        workspace_size += pArg_->gemm_nblock_ * sizeof(int32_t) + 64;
+
+        if constexpr(!is_same_v<EMeanVarDataType, HDataType>)
+            workspace_size += pArg_->MRaw_ * pArg_->NRaw_ * sizeof(EMeanVarDataType);
+
+        return (workspace_size);
+    };
+
+    void SetWorkSpacePointer(BaseArgument* pArg, void* p_workspace) const override
+    {
+        Argument* pArg_ = dynamic_cast<Argument*>(pArg);
+
+        pArg_->p_workspace_ = p_workspace;
+
+        int gemm_welford_size = pArg_->MRaw_ * pArg_->gemm_nblock_;
+
+        // setup buffer used for intermediate welford mean
+        pArg_->p_workspace_mean_ = static_cast<char*>(pArg_->p_workspace_);
+
+        index_t mean_space_sz = gemm_welford_size * sizeof(EMeanVarDataType);
+        mean_space_sz         = math::integer_least_multiple(mean_space_sz, 64);
+
+        // setup buffer used for intermediate welford varirance
+        pArg_->p_workspace_var_ = reinterpret_cast<char*>(pArg_->p_workspace_mean_) + mean_space_sz;
+
+        index_t variance_space_sz = gemm_welford_size * sizeof(EMeanVarDataType);
+        variance_space_sz         = math::integer_least_multiple(variance_space_sz, 64);
+
+        // setup buffer used for intermediate welford count
+        pArg_->p_workspace_count_ =
+            reinterpret_cast<char*>(pArg_->p_workspace_var_) + variance_space_sz;
+
+        index_t count_space_sz = gemm_welford_size * sizeof(int32_t);
+        count_space_sz         = math::integer_least_multiple(count_space_sz, 64);
+
+        if constexpr(!is_same_v<EMeanVarDataType, HDataType>)
+            pArg_->p_workspace_e_grid_ =
+                reinterpret_cast<char*>(pArg_->p_workspace_count_) + count_space_sz;
+        else
+            pArg_->p_workspace_e_grid_ = static_cast<void*>(pArg_->p_h_grid_);
+    };
+
+    static bool IsSupportedArgument(const Argument& arg)
+    {
+        if(!(ck::get_device_name() == "gfx908" || ck::get_device_name() == "gfx90a"))
+        {
+            return false;
+        }
+
+        // check vector load/store
+        {
+            using Row = ck::tensor_layout::gemm::RowMajor;
+            using Col = ck::tensor_layout::gemm::ColumnMajor;
+
+            // check vector load of A
+            if constexpr(is_same_v<ALayout, Row> && ABlockTransferSrcVectorDim == 2)
+            {
+                if(arg.KRaw_ % ABlockTransferSrcScalarPerVector != 0)
+                {
+                    return false;
+                }
+            }
+            else if constexpr(is_same_v<ALayout, Col> && ABlockTransferSrcVectorDim == 1)
+            {
+                // FIXME: not rigorous
+                if(arg.MRaw_ % ABlockTransferSrcScalarPerVector != 0)
+                {
+                    return false;
+                }
+            }
+            else
+            {
+                return false;
+            }
+
+            // check vector laod of B
+            if constexpr(is_same_v<BLayout, Col> && BBlockTransferSrcVectorDim == 2)
+            {
+                if(arg.KRaw_ % BBlockTransferSrcScalarPerVector != 0)
+                {
+                    return false;
+                }
+            }
+            else if constexpr(is_same_v<BLayout, Row> && BBlockTransferSrcVectorDim == 1)
+            {
+                // FIXME: not rigorous
+                if(arg.NRaw_ % BBlockTransferSrcScalarPerVector != 0)
+                {
+                    return false;
+                }
+            }
+            else
+            {
+                return false;
+            }
+
+            // check vector load of Ds
+            // only support RowMajor for now
+            bool all_valid = true;
+
+            static_for<0, NumDTensor, 1>{}([&](auto i) {
+                using DLayout = remove_cvref_t<tuple_element_t<i.value, DsLayout>>;
+
+                if constexpr(!is_same_v<DLayout, Row>)
+                {
+                    all_valid = false;
+                }
+            });
+
+            if(!all_valid)
+            {
+                return false;
+            }
+
+            // check vector store of E
+            // E and H only support RowMajor for now
+            if constexpr(is_same_v<ELayout, Row> && is_same_v<HLayout, Row>)
+            {
+                if(arg.NRaw_ % PostShuffleScalarPerVector != 0 ||
+                   arg.NRaw_ % LayernormGammaSrcVectorSize != 0 ||
+                   arg.NRaw_ % LayernormBetaSrcVectorSize != 0 ||
+                   arg.NRaw_ % LayernormHDstVectorSize != 0)
+                {
+                    return false;
+                }
+            }
+            else
+            {
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    // polymorphic
+    bool IsSupportedArgument(const BaseArgument* p_arg) override
+    {
+        return IsSupportedArgument(*dynamic_cast<const Argument*>(p_arg));
+    }
+
+    static auto MakeArgument(const void* p_a,
+                             const void* p_b,
+                             std::array<const void*, NumDTensor> p_ds,
+                             const void* p_gamma,
+                             const void* p_beta,
+                             void* p_h,
+                             index_t MRaw,
+                             index_t NRaw,
+                             index_t KRaw,
+                             index_t StrideA,
+                             index_t StrideB,
+                             std::array<index_t, NumDTensor> StrideDs,
+                             index_t StrideH,
+                             double epsilon,
+                             AElementwiseOperation a_element_op,
+                             BElementwiseOperation b_element_op,
+                             CDEElementwiseOperation cde_element_op,
+                             HElementwiseOperation h_element_op)
+    {
+        return Argument{p_a,
+                        p_b,
+                        p_ds,
+                        p_gamma,
+                        p_beta,
+                        p_h,
+                        MRaw,
+                        NRaw,
+                        KRaw,
+                        StrideA,
+                        StrideB,
+                        StrideDs,
+                        StrideH,
+                        epsilon,
+                        a_element_op,
+                        b_element_op,
+                        cde_element_op,
+                        h_element_op};
+    }
+
+    static auto MakeInvoker() { return Invoker{}; }
+
+    // polymorphic
+    std::unique_ptr<BaseArgument> MakeArgumentPointer(const void* p_a,
+                                                      const void* p_b,
+                                                      std::array<const void*, NumDTensor> p_ds,
+                                                      const void* p_gamma,
+                                                      const void* p_beta,
+                                                      void* p_h,
+                                                      index_t MRaw,
+                                                      index_t NRaw,
+                                                      index_t KRaw,
+                                                      index_t StrideA,
+                                                      index_t StrideB,
+                                                      std::array<index_t, NumDTensor> StrideDs,
+                                                      index_t StrideH,
+                                                      double epsilon,
+                                                      AElementwiseOperation a_element_op,
+                                                      BElementwiseOperation b_element_op,
+                                                      CDEElementwiseOperation cde_element_op,
+                                                      HElementwiseOperation h_element_op) override
+    {
+        return std::make_unique<Argument>(p_a,
+                                          p_b,
+                                          p_ds,
+                                          p_gamma,
+                                          p_beta,
+                                          p_h,
+                                          MRaw,
+                                          NRaw,
+                                          KRaw,
+                                          StrideA,
+                                          StrideB,
+                                          StrideDs,
+                                          StrideH,
+                                          epsilon,
+                                          a_element_op,
+                                          b_element_op,
+                                          cde_element_op,
+                                          h_element_op);
+    }
+
+    // polymorphic
+    std::unique_ptr<BaseInvoker> MakeInvokerPointer() override
+    {
+        return std::make_unique<Invoker>(Invoker{});
+    }
+
+    // polymorphic
+    std::string GetTypeString() const override
+    {
+        auto str = std::stringstream();
+
+        std::map<LoopScheduler, std::string> LoopSchedToString{
+            {LoopScheduler::Default, "Default"}, {LoopScheduler::Interwave, "Interwave"}};
+
+        std::map<PipelineVersion, std::string> PipelineVersionToString{{PipelineVersion::v1, "v1"},
+                                                                       {PipelineVersion::v2, "v2"}};
+
+        // clang-format off
+        str << "DeviceGemmMultipleDLayernorm_Xdl_CShuffle"
+            << "<"
+            << BlockSize << ", "
+            << GemmMPerBlock << ", "
+            << GemmNPerBlock << ", "
+            << GemmKPerBlock << ", "
+            << AK1 << ", "
+            << BK1 << ", "
+            << getGemmSpecializationString(GemmSpec)
+            << ">"
+            << " LoopScheduler: "
+            << LoopSchedToString[LoopSched] << ", "
+            << "PipelineVersion: "
+            << PipelineVersionToString[PipelineVer];
+        // clang-format on
+
+        return str.str();
+    }
+}; // namespace device
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

include/ck/tensor_operation/gpu/grid/gemm_layernorm/gridwise_gemm_multiple_d_welford_first_half_xdl_cshuffle.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, 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/block/blockwise_welford.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_welford.hpp"
+
+namespace ck {
+
+// GEMM:
+//   input : A[M, K]
+//   input : B[N, K]
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   output : F[M, N0], where N0 is number of blocks along N dimension
+//   output : G[M, N0], where N0 is number of blocks along N dimension
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+//   F, G = welford(E)
+// Assume:
+//   D0, D1, ... and E have the same layout
+//   Calculate mean & variance along N dimension for E
+template <typename ABDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EMeanVarDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          InMemoryDataOperationEnum EGlobalMemoryDataOperation,
+          typename AGridDesc_M_K,
+          typename BGridDesc_N_K,
+          typename DsGridDesc_M_N,
+          typename EGridDesc_M_N,
+          typename MeanVarGridDesc_M_NBlock,
+          typename CountGridDesc_M_NBlock,
+          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 PostShuffleThreadClusterSize_M_N,
+          index_t PostShuffleScalarPerVector,
+          LoopScheduler LoopSched,
+          PipelineVersion PipelineVer = PipelineVersion::v1>
+struct GridwiseGemmMultipleDWelfordFirstHalf_xdl_cshuffle
+{
+    static constexpr index_t NumDTensor = DsDataType::Size();
+
+    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>())>;
+
+    __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
+    __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
+    __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>{}));
+    }
+
+    // E desc for destination in blockwise copy
+    template <typename EGridDescriptor_M_N>
+    __host__ __device__ static constexpr auto MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+        const EGridDescriptor_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 DsGridDescriptor_M_N>
+    __host__ __device__ static constexpr auto
+    MakeDsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+        const DsGridDescriptor_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>{});
+    }
+
+    template <typename GridDescriptor_M_N>
+    __host__ __device__ static constexpr auto
+    MakeMeanVarCountGridDescriptor_MBlock_MPerBlock_NBlock(const GridDescriptor_M_N& grid_desc_m_n)
+    {
+        const auto M      = grid_desc_m_n.GetLength(I0);
+        const auto NBlock = grid_desc_m_n.GetLength(I1);
+        const auto MBlock = M / MPerBlock;
+
+        const auto grid_desc_mblock_mperblock_nblock = transform_tensor_descriptor(
+            grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(MBlock, Number<MPerBlock>{})),
+                       make_pass_through_transform(NBlock)),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 1>{}, Sequence<2>{}));
+
+        return grid_desc_mblock_mperblock_nblock;
+    }
+
+    // return block_id to E matrix tile idx (m0, n0) mapping
+    __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 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(EMeanVarDataType) <= 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 DefaultAGridDesc_AK0_M_AK1 =
+        remove_cvref_t<decltype(MakeDefaultAGridDescriptor_AK0_M_AK1(AGridDesc_M_K{}))>;
+    using DefaultBGridDesc_BK0_N_BK1 =
+        remove_cvref_t<decltype(MakeDefaultBGridDescriptor_BK0_N_BK1(BGridDesc_N_K{}))>;
+    using EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock  = remove_cvref_t<decltype(
+        MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(EGridDesc_M_N{}))>;
+    using MeanVarGridDescriptor_MBlock_MPerBlock_NBlock      = remove_cvref_t<decltype(
+        MakeMeanVarCountGridDescriptor_MBlock_MPerBlock_NBlock(MeanVarGridDesc_M_NBlock{}))>;
+    using CountGridDescriptor_MBlock_MPerBlock_NBlock        = remove_cvref_t<decltype(
+        MakeMeanVarCountGridDescriptor_MBlock_MPerBlock_NBlock(CountGridDesc_M_NBlock{}))>;
+    using DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock = remove_cvref_t<decltype(
+        MakeDsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(DsGridDesc_M_N{}))>;
+
+    using DefaultBlock2ETileMap =
+        remove_cvref_t<decltype(MakeDefaultBlock2ETileMap(EGridDesc_M_N{}))>;
+
+    using DsGridPointer = decltype(MakeDsGridPointer());
+
+    template <bool HasMainKBlockLoop,
+              typename AGridDesc_AK0_M_AK1,
+              typename BGridDesc_BK0_N_BK1,
+              typename Block2ETileMap>
+    __device__ static void
+    Run(const ABDataType* __restrict__ p_a_grid,
+        const ABDataType* __restrict__ p_b_grid,
+        DsGridPointer p_ds_grid,
+        EMeanVarDataType* __restrict__ p_e_grid,
+        EMeanVarDataType* __restrict__ p_welford_mean_grid,
+        EMeanVarDataType* __restrict__ p_welford_var_grid,
+        int32_t* __restrict__ p_welford_count,
+        void* __restrict__ p_shared,
+        const AElementwiseOperation& a_element_op,
+        const BElementwiseOperation& b_element_op,
+        const CDEElementwiseOperation& cde_element_op,
+        const AGridDesc_AK0_M_AK1& a_grid_desc_ak0_m_ak1,
+        const BGridDesc_BK0_N_BK1& b_grid_desc_bk0_n_bk1,
+        const DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock&
+            ds_grid_desc_mblock_mperblock_nblock_nperblock,
+        const EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock&
+            e_grid_desc_mblock_mperblock_nblock_nperblock,
+        const MeanVarGridDescriptor_MBlock_MPerBlock_NBlock&
+            mean_var_grid_desc_mblock_mperblock_nblock,
+        const CountGridDescriptor_MBlock_MPerBlock_NBlock& count_grid_desc_mblock_mperblock_nblock,
+        const Block2ETileMap& block_2_etile_map,
+        index_t NRaw)
+    {
+        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());
+
+        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());
+
+        auto mean_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_welford_mean_grid, mean_var_grid_desc_mblock_mperblock_nblock.GetElementSpaceSize());
+
+        auto var_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_welford_var_grid, mean_var_grid_desc_mblock_mperblock_nblock.GetElementSpaceSize());
+
+        auto welford_count_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_welford_count, count_grid_desc_mblock_mperblock_nblock.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_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<AK0PerBlock, MPerBlock, AK1>,
+                                                ABlockTransferThreadClusterLengths_AK0_M_AK1,
+                                                ABlockTransferThreadClusterArrangeOrder,
+                                                ABDataType,
+                                                ABDataType,
+                                                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<BK0PerBlock, NPerBlock, BK1>,
+                                                BBlockTransferThreadClusterLengths_BK0_N_BK1,
+                                                BBlockTransferThreadClusterArrangeOrder,
+                                                ABDataType,
+                                                ABDataType,
+                                                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 index_t KPack =
+            math::max(math::lcm(AK1, BK1),
+                      MfmaSelector<ABDataType, MPerXdl, NPerXdl>::selected_mfma.k_per_blk);
+
+        auto blockwise_gemm = BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_Selector<
+            BlockSize,
+            ABDataType,
+            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<ABDataType*>(p_shared), a_block_desc_ak0_m_ak1.GetElementSpaceSize());
+
+        auto b_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+            static_cast<ABDataType*>(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, Welford 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{}};
+
+            // 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>,
+                                  false>{};
+
+            // space filling curve for shuffled blockwise C in global mem
+            constexpr auto sfc_der_global =
+                SpaceFillingCurve<Sequence<1, MPerBlock, 1, NPerBlock>,
+                                  Sequence<0, 2, 1, 3>,
+                                  Sequence<1,
+                                           CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl,
+                                           1,
+                                           CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>,
+                                  false>{};
+
+            // LDS c_shuffle_block_desc_mperblock_nperblock
+            constexpr auto c_shuffle_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(PostShuffleThreadClusterSize_M_N::At(I0) *
+                                  PostShuffleThreadClusterSize_M_N::At(I1) ==
+                              BlockSize,
+                          "wrong!");
+
+            static_assert((CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl) %
+                                      PostShuffleThreadClusterSize_M_N::At(I0) ==
+                                  0 &&
+                              (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl) %
+                                      PostShuffleThreadClusterSize_M_N::At(I1) ==
+                                  0,
+                          "wrong!");
+
+            constexpr index_t PostShuffleThreadSliceSize_M =
+                (CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl) /
+                PostShuffleThreadClusterSize_M_N::At(I0);
+
+            constexpr index_t PostShuffleThreadSliceSize_N =
+                (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl) /
+                PostShuffleThreadClusterSize_M_N::At(I1);
+
+            constexpr auto PostShuffleThreadSliceSize_M_N =
+                Sequence<PostShuffleThreadSliceSize_M, PostShuffleThreadSliceSize_N>{};
+
+            // VGPR post_shuffle_thread_desc_m_n
+            constexpr auto post_shuffle_thread_desc_m_n = make_naive_tensor_descriptor_packed(
+                make_tuple(Number<PostShuffleThreadSliceSize_M>{},
+                           Number<PostShuffleThreadSliceSize_N>{}));
+
+            auto e_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, AccDataType>(
+                post_shuffle_thread_desc_m_n.GetElementSpaceSize());
+
+            // To apply D0, D1, ... and Welford.
+            // threadwise copy from LDS to VGPR
+            constexpr auto post_shuffle_thread_cluster_desc =
+                make_cluster_descriptor(PostShuffleThreadClusterSize_M_N{}, Sequence<0, 1>{});
+
+            const auto post_shuffle_thread_cluster_idx =
+                post_shuffle_thread_cluster_desc.CalculateBottomIndex(
+                    make_multi_index(get_thread_local_1d_id()));
+
+            const auto post_shuffle_thread_data_idx_begin =
+                post_shuffle_thread_cluster_idx * PostShuffleThreadSliceSize_M_N;
+
+            // To apply D0, D1, ... and Welford.
+            // Copy c shuffle from LDS back to VGPR
+            auto post_shuffle_thread_copy_lds_to_vgpr =
+                ThreadwiseTensorSliceTransfer_v2<CShuffleDataType,
+                                                 AccDataType,
+                                                 decltype(c_shuffle_block_desc_mperblock_nperblock),
+                                                 decltype(post_shuffle_thread_desc_m_n),
+                                                 decltype(PostShuffleThreadSliceSize_M_N),
+                                                 Sequence<0, 1>,
+                                                 1,
+                                                 PostShuffleScalarPerVector,
+                                                 1,
+                                                 true>{c_shuffle_block_desc_mperblock_nperblock,
+                                                       post_shuffle_thread_data_idx_begin};
+
+            // D0, D1, ..., Dn
+            constexpr auto post_shuffle_thread_desc_I1_mperblock_I1_nperblock =
+                make_naive_tensor_descriptor_packed(
+                    make_tuple(I1,
+                               Number<PostShuffleThreadSliceSize_M>{},
+                               I1,
+                               Number<PostShuffleThreadSliceSize_N>{}));
+
+            // FIXME: Decrease usage of VGPR
+            // Apply pointwise lambda function from multi-source (Global and LDS) into VGPR
+            auto ds_thread_buf = generate_tuple(
+                [&](auto) {
+                    return make_static_buffer<AddressSpaceEnum::Vgpr, CShuffleDataType>(
+                        post_shuffle_thread_desc_I1_mperblock_I1_nperblock.GetElementSpaceSize());
+                },
+                Number<NumDTensor>{});
+
+            // Copy D0, D1, ..., Dn from global to VGPR
+            auto ds_thread_copy_global_to_vgpr = generate_tuple(
+                [&](auto I) {
+                    using DDataType = remove_cvref_t<tuple_element_t<I.value, DsDataType>>;
+                    return ThreadwiseTensorSliceTransfer_v2<
+                        DDataType,
+                        AccDataType,
+                        decltype(ds_grid_desc_mblock_mperblock_nblock_nperblock[I]),
+                        decltype(post_shuffle_thread_desc_I1_mperblock_I1_nperblock),
+                        Sequence<I1,
+                                 PostShuffleThreadSliceSize_M,
+                                 I1,
+                                 PostShuffleThreadSliceSize_N>,
+                        Sequence<0, 1, 2, 3>,
+                        3,
+                        PostShuffleScalarPerVector,
+                        1,
+                        true>(
+                        ds_grid_desc_mblock_mperblock_nblock_nperblock[I],
+                        make_multi_index(
+                            I0,
+                            m_block_data_idx_on_grid + post_shuffle_thread_data_idx_begin[I0],
+                            I0,
+                            n_block_data_idx_on_grid + post_shuffle_thread_data_idx_begin[I1]));
+                },
+                Number<NumDTensor>{});
+
+            auto e_thread_copy_vgpr_to_global = ThreadwiseTensorSliceTransfer_v1r3<
+                AccDataType,
+                EMeanVarDataType,
+                decltype(post_shuffle_thread_desc_I1_mperblock_I1_nperblock),
+                decltype(e_grid_desc_mblock_mperblock_nblock_nperblock),
+                tensor_operation::element_wise::PassThrough,
+                Sequence<I1,
+                         PostShuffleThreadSliceSize_M,
+                         I1,
+                         PostShuffleThreadSliceSize_N>, // SliceLengths
+                Sequence<0, 1, 2, 3>,                   // DimAccessOrder
+                3,                                      // DstVectorDim
+                PostShuffleScalarPerVector,
+                InMemoryDataOperationEnum::Set,
+                1,
+                true>{
+                e_grid_desc_mblock_mperblock_nblock_nperblock,
+                make_multi_index(I0,
+                                 m_block_data_idx_on_grid + post_shuffle_thread_data_idx_begin[I0],
+                                 I0,
+                                 n_block_data_idx_on_grid + post_shuffle_thread_data_idx_begin[I1]),
+                tensor_operation::element_wise::PassThrough{}};
+
+            // Welford
+            constexpr auto thread_welford_src_desc_m_k = make_naive_tensor_descriptor_packed(
+                make_tuple(Number<PostShuffleThreadSliceSize_M>{},
+                           Number<PostShuffleThreadSliceSize_N>{}));
+
+            constexpr auto thread_welford_dst_desc_m = make_naive_tensor_descriptor_packed(
+                make_tuple(Number<PostShuffleThreadSliceSize_M>{}));
+
+            using ThreadwiseWelford = ThreadwiseWelford<AccDataType,
+                                                        decltype(thread_welford_src_desc_m_k),
+                                                        decltype(thread_welford_dst_desc_m)>;
+
+            using BlockwiseWelford = BlockwiseWelford<AccDataType,
+                                                      BlockSize,
+                                                      PostShuffleThreadClusterSize_M_N,
+                                                      Sequence<0, 1>,
+                                                      false>;
+
+            constexpr int num_shuffleM =
+                MPerBlock / (CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl);
+
+            constexpr int num_shuffleN =
+                NPerBlock / (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl);
+
+            using mean_var_vgpr_type =
+                decltype(make_static_buffer<AddressSpaceEnum::Vgpr, AccDataType>(
+                    thread_welford_dst_desc_m.GetElementSpaceSize()));
+
+            using welford_count_vgpr_type =
+                decltype(make_static_buffer<AddressSpaceEnum::Vgpr, int32_t>(
+                    thread_welford_dst_desc_m.GetElementSpaceSize()));
+
+            Array<ThreadwiseWelford, num_shuffleM> threadwise_welfords;
+            Array<mean_var_vgpr_type, num_shuffleM> mean_thread_bufs;
+            Array<mean_var_vgpr_type, num_shuffleM> var_thread_bufs;
+            Array<welford_count_vgpr_type, num_shuffleM> welford_count_thread_bufs;
+
+            int max_count     = PostShuffleThreadSliceSize_N * num_shuffleN;
+            const auto nblock = mean_var_grid_desc_mblock_mperblock_nblock.GetLength(I2);
+
+            // tail block
+            if(block_work_idx[I1] % nblock == nblock - 1)
+            {
+                constexpr index_t NPerShuffleBlock =
+                    CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl;
+
+                int NPerBlockTail = NRaw - NPerBlock * (nblock - 1);
+                int thread_max_len =
+                    PostShuffleThreadSliceSize_N * (post_shuffle_thread_cluster_idx[I1] + 1);
+                int shuffle_step = 0;
+                while(thread_max_len <= NPerBlockTail && shuffle_step < num_shuffleN)
+                {
+                    ++shuffle_step;
+                    thread_max_len += NPerShuffleBlock;
+                }
+
+                int delta = 0;
+                if(thread_max_len - NPerBlockTail > PostShuffleThreadSliceSize_N)
+                    delta = 0;
+                else if(NPerBlockTail > thread_max_len)
+                    delta = PostShuffleThreadSliceSize_N;
+                else
+                    delta = PostShuffleThreadSliceSize_N - thread_max_len + NPerBlockTail;
+
+                max_count = shuffle_step * PostShuffleThreadSliceSize_N + delta;
+            }
+
+            static_for<0, num_shuffleM, 1>{}([&](auto i) {
+                threadwise_welfords(i).max_count_ = max_count;
+                mean_thread_bufs(i) = make_static_buffer<AddressSpaceEnum::Vgpr, AccDataType>(
+                    thread_welford_dst_desc_m.GetElementSpaceSize());
+
+                var_thread_bufs(i) = make_static_buffer<AddressSpaceEnum::Vgpr, AccDataType>(
+                    thread_welford_dst_desc_m.GetElementSpaceSize());
+
+                welford_count_thread_bufs(i) = make_static_buffer<AddressSpaceEnum::Vgpr, int32_t>(
+                    thread_welford_dst_desc_m.GetElementSpaceSize());
+
+                static_for<0, PostShuffleThreadSliceSize_M, 1>{}([&](auto j) {
+                    mean_thread_bufs(i)(j)          = type_convert<AccDataType>(0.0f);
+                    var_thread_bufs(i)(j)           = type_convert<AccDataType>(0.0f);
+                    welford_count_thread_bufs(i)(j) = 0;
+                });
+            });
+
+            constexpr index_t num_access = sfc_c_vgpr.GetNumOfAccess();
+
+            static_assert(num_access == sfc_der_global.GetNumOfAccess(), "wrong!");
+
+            int shuffleM_index = __builtin_amdgcn_readfirstlane(0);
+            static_for<0, num_access, 1>{}([&](auto access_id) {
+                // make sure it's safe to read from LDS
+                block_sync_lds();
+
+                // each thread shuffle 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 write to LDS
+                block_sync_lds();
+
+                // Get shuffle data from LDS to VGPR
+                post_shuffle_thread_copy_lds_to_vgpr.Run(c_shuffle_block_desc_mperblock_nperblock,
+                                                         c_shuffle_block_buf,
+                                                         post_shuffle_thread_desc_m_n,
+                                                         make_tuple(I0, I0),
+                                                         e_thread_buf);
+
+                // Global read D0, D1, ...
+                static_for<0, NumDTensor, 1>{}([&](auto Id) {
+                    auto& d_thread_copy_global_to_vgpr = ds_thread_copy_global_to_vgpr(Id);
+                    d_thread_copy_global_to_vgpr.Run(
+                        ds_grid_desc_mblock_mperblock_nblock_nperblock[Id],
+                        ds_grid_buf[Id],
+                        post_shuffle_thread_desc_I1_mperblock_I1_nperblock,
+                        make_tuple(I0, I0, I0, I0),
+                        ds_thread_buf(Id));
+
+                    if constexpr(access_id < num_access - 1)
+                    {
+                        // move on D0, D1, ...
+                        constexpr auto de_global_step = sfc_der_global.GetForwardStep(access_id);
+                        d_thread_copy_global_to_vgpr.MoveSrcSliceWindow(
+                            ds_grid_desc_mblock_mperblock_nblock_nperblock[Id], de_global_step);
+                    }
+                });
+
+                // cde_element_op(e, c, d0, d1, ...);
+                static_for<0, post_shuffle_thread_desc_m_n.GetElementSize(), 1>{}([&](auto i) {
+                    const auto c_ds_src_data_refs = concat_tuple_of_reference(
+                        tie(e_thread_buf[i]),
+                        generate_tie(
+                            [&](auto Id) -> const auto& { return ds_thread_buf[Id][i]; },
+                            Number<NumDTensor>{}));
+                    auto e_dst_data_refs = tie(e_thread_buf(i));
+                    unpack2(cde_element_op, e_dst_data_refs, c_ds_src_data_refs);
+                });
+
+                // Global write E
+                e_thread_copy_vgpr_to_global.Run(post_shuffle_thread_desc_I1_mperblock_I1_nperblock,
+                                                 make_tuple(I0, I0, I0, I0),
+                                                 e_thread_buf,
+                                                 e_grid_desc_mblock_mperblock_nblock_nperblock,
+                                                 e_grid_buf);
+
+                if constexpr(access_id < num_access - 1)
+                {
+                    // move on E
+                    constexpr auto de_global_step = sfc_der_global.GetForwardStep(access_id);
+                    e_thread_copy_vgpr_to_global.MoveDstSliceWindow(
+                        e_grid_desc_mblock_mperblock_nblock_nperblock, de_global_step);
+                }
+
+                // Threadwise welford
+                auto& threadwise_welford = threadwise_welfords(shuffleM_index);
+                auto& mean_thread_buf    = mean_thread_bufs(shuffleM_index);
+                auto& var_thread_buf     = var_thread_bufs(shuffleM_index);
+
+                threadwise_welford.Run(e_thread_buf, mean_thread_buf, var_thread_buf);
+
+                if constexpr(access_id < num_access - 1)
+                {
+                    constexpr auto de_global_step = sfc_der_global.GetForwardStep(access_id);
+                    constexpr int shuffleMInc =
+                        de_global_step[I1] /
+                        c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetLength(I1);
+                    shuffleM_index = __builtin_amdgcn_readfirstlane(shuffleM_index + shuffleMInc);
+                }
+            }); // copy c, d, e + welford
+
+            // Blockwise welford and write out
+            static_for<0, num_shuffleM, 1>{}([&](auto i) {
+                auto& mean_thread_buf  = mean_thread_bufs(i);
+                auto& var_thread_buf   = var_thread_bufs(i);
+                auto& count_thread_buf = welford_count_thread_bufs(i);
+
+                static_for<0, PostShuffleThreadSliceSize_M, 1>{}([&](auto j) {
+                    block_sync_lds();
+                    count_thread_buf(j) = threadwise_welfords(i).cur_count_;
+                    BlockwiseWelford::Run(
+                        mean_thread_buf(j), var_thread_buf(j), count_thread_buf(j));
+                });
+
+                if(post_shuffle_thread_cluster_idx[I1] == 0)
+                {
+                    constexpr auto thread_welford_desc_I_m_I = make_naive_tensor_descriptor_packed(
+                        make_tuple(I1, Number<PostShuffleThreadSliceSize_M>{}, I1));
+
+                    constexpr int shuffleMPerBlock =
+                        c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetLength(I1);
+
+                    auto mean_var_count_thread_copy_index = make_multi_index(
+                        block_work_idx[I0],                                            // mblock
+                        shuffleMPerBlock * i + post_shuffle_thread_data_idx_begin[I0], // mperblock
+                        block_work_idx[I1]);                                           // nblock
+
+                    auto mean_var_thread_copy_vgpr_to_global = ThreadwiseTensorSliceTransfer_v1r3<
+                        AccDataType,
+                        EMeanVarDataType,
+                        decltype(thread_welford_desc_I_m_I),
+                        decltype(mean_var_grid_desc_mblock_mperblock_nblock),
+                        tensor_operation::element_wise::PassThrough,
+                        Sequence<1, PostShuffleThreadSliceSize_M, 1>,
+                        Sequence<0, 1, 2>,
+                        1,
+                        1,
+                        InMemoryDataOperationEnum::Set,
+                        1,
+                        true>{mean_var_grid_desc_mblock_mperblock_nblock,
+                              mean_var_count_thread_copy_index,
+                              tensor_operation::element_wise::PassThrough{}};
+
+                    mean_var_thread_copy_vgpr_to_global.Run(
+                        thread_welford_desc_I_m_I,
+                        make_tuple(I0, I0, I0),
+                        mean_thread_buf,
+                        mean_var_grid_desc_mblock_mperblock_nblock,
+                        mean_grid_buf); // write mean
+
+                    mean_var_thread_copy_vgpr_to_global.Run(
+                        thread_welford_desc_I_m_I,
+                        make_tuple(I0, I0, I0),
+                        var_thread_buf,
+                        mean_var_grid_desc_mblock_mperblock_nblock,
+                        var_grid_buf); // write variance
+
+                    // Stride of count is [0, 1]. Only the first row in count[0, 0:nblock] need
+                    // to be written.
+                    if(i == 0 && block_work_idx[I0] == 0 &&
+                       post_shuffle_thread_cluster_idx[I0] == 0)
+                    {
+                        auto count_thread_copy_vgpr_to_global = ThreadwiseTensorSliceTransfer_v1r3<
+                            int32_t,
+                            int32_t,
+                            decltype(thread_welford_desc_I_m_I),
+                            decltype(count_grid_desc_mblock_mperblock_nblock),
+                            tensor_operation::element_wise::PassThrough,
+                            Sequence<1, PostShuffleThreadSliceSize_M, 1>,
+                            Sequence<0, 1, 2>,
+                            1,
+                            1,
+                            InMemoryDataOperationEnum::Set,
+                            1,
+                            false>{count_grid_desc_mblock_mperblock_nblock,
+                                   mean_var_count_thread_copy_index,
+                                   tensor_operation::element_wise::PassThrough{}};
+
+                        count_thread_copy_vgpr_to_global.Run(
+                            thread_welford_desc_I_m_I,
+                            make_tuple(I0, I0, I0),
+                            count_thread_buf,
+                            count_grid_desc_mblock_mperblock_nblock,
+                            welford_count_grid_buf); // write count
+                    }
+                }
+            });
+
+        } // shuffle C + Ds + welford + write out
+    }     // run
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/grid/gemm_layernorm/gridwise_welford_second_half_layernorm2d.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, 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_v1.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/block/blockwise_welford.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_welford.hpp"
+
+namespace ck {
+
+template <typename EMeanVarDataType,
+          typename HDataType,
+          typename GammaDataType,
+          typename BetaDataType,
+          typename ComputeDataType,
+          typename EHGridDesc_M_N,
+          typename MeanVarGridDesc_M_NBlock,
+          typename CountGridDesc_M_NBlock,
+          typename GammaBetaGridDesc_N,
+          typename HElementwiseOperation,
+          index_t BlockSize,
+          index_t MThreadClusterSize,
+          index_t NThreadClusterSize,
+          index_t MThreadSliceSize,
+          index_t NThreadSliceSize,
+          index_t ESrcVectorSize,
+          index_t HDstVectorSize,
+          index_t GammaSrcVectorSize,
+          index_t BetaSrcVectorSize>
+struct GridwiseWelfordSecondHalfLayernorm2d
+{
+    static_assert(NThreadSliceSize % ESrcVectorSize == 0 &&
+                      NThreadSliceSize % GammaSrcVectorSize == 0 &&
+                      NThreadSliceSize % BetaSrcVectorSize == 0,
+                  "Invalid thread slice sizes and/or vector sizes configuration, please check!");
+
+    static_assert(NThreadSliceSize % HDstVectorSize == 0,
+                  "Invalid thread slice sizes and/or vector sizes configuration, please check!");
+
+    using ThreadClusterLengths_M_N   = Sequence<MThreadClusterSize, NThreadClusterSize>;
+    using ThreadBufferDimAccessOrder = Sequence<0, 1>;
+    using ThreadClusterArrangeOrder  = Sequence<0, 1>;
+
+    static constexpr auto thread_cluster_desc_m_n =
+        make_cluster_descriptor(ThreadClusterLengths_M_N{}, ThreadClusterArrangeOrder{});
+
+    using ThreadBufferLengths_M_N                = Sequence<MThreadSliceSize, NThreadSliceSize>;
+    static constexpr auto thread_buffer_desc_m_n = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<MThreadSliceSize>{}, Number<NThreadSliceSize>{}));
+
+    using ThreadBufferLengths_M_1 = Sequence<MThreadSliceSize, 1>;
+    static constexpr auto thread_buffer_desc_m_1 =
+        make_naive_tensor_descriptor_packed(make_tuple(Number<MThreadSliceSize>{}, Number<1>{}));
+
+    using ThreadBufferLengths_N = Sequence<NThreadSliceSize>;
+    static constexpr auto thread_buffer_desc_n =
+        make_naive_tensor_descriptor_packed(make_tuple(Number<NThreadSliceSize>{}));
+
+    using ThreadWelfordSrcDesc_M_1 = decltype(thread_buffer_desc_m_1);
+    using ThreadWelfordDstDesc_M =
+        decltype(make_naive_tensor_descriptor_packed(make_tuple(Number<MThreadSliceSize>{})));
+
+    using ThreadwiseWelford =
+        ThreadwiseWelfordMerge<ComputeDataType, ThreadWelfordSrcDesc_M_1, ThreadWelfordDstDesc_M>;
+
+    using BlockwiseWelford = BlockwiseWelford<ComputeDataType,
+                                              BlockSize,
+                                              ThreadClusterLengths_M_N,
+                                              ThreadClusterArrangeOrder>;
+
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+
+    static constexpr index_t M_BlockTileSize = MThreadClusterSize * MThreadSliceSize;
+    static constexpr index_t N_BlockTileSize = NThreadClusterSize * NThreadSliceSize;
+
+    __device__ static void Run(const EMeanVarDataType* __restrict__ p_e_grid,
+                               const EMeanVarDataType* __restrict__ p_in_welford_mean_grid,
+                               const EMeanVarDataType* __restrict__ p_in_welford_var_grid,
+                               const int32_t* __restrict__ p_in_welford_count_grid,
+                               const GammaDataType* __restrict__ p_gamma_grid,
+                               const BetaDataType* __restrict__ p_beta_grid,
+                               HDataType* __restrict__ p_h_grid,
+                               const EHGridDesc_M_N& e_grid_desc_m_n,
+                               const EHGridDesc_M_N& h_grid_desc_m_n,
+                               const MeanVarGridDesc_M_NBlock& mean_var_grid_desc_m_nblock,
+                               const CountGridDesc_M_NBlock& count_grid_desc_m_nblock,
+                               const GammaBetaGridDesc_N& gamma_grid_desc_n,
+                               const GammaBetaGridDesc_N& beta_grid_desc_n,
+                               index_t numMeanVarCountBlockTileIteration_N,
+                               index_t NBlockClusterLength,
+                               ComputeDataType epsilon,
+                               HElementwiseOperation h_element_op)
+    {
+        // Thread/Block id
+        const index_t thread_local_id = get_thread_local_1d_id();
+        const index_t block_global_id = get_block_1d_id();
+        const auto block_work_idx     = make_tuple(block_global_id / NBlockClusterLength,
+                                               block_global_id % NBlockClusterLength);
+
+        const auto thread_cluster_idx =
+            thread_cluster_desc_m_n.CalculateBottomIndex(make_multi_index(thread_local_id));
+        const auto thread_m_cluster_id = thread_cluster_idx[I0];
+        const auto thread_n_cluster_id = thread_cluster_idx[I1];
+
+        // Global Memory
+        const auto e_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_e_grid, e_grid_desc_m_n.GetElementSpaceSize());
+
+        const auto welford_mean_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_in_welford_mean_grid, mean_var_grid_desc_m_nblock.GetElementSpaceSize());
+
+        const auto welford_var_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_in_welford_var_grid, mean_var_grid_desc_m_nblock.GetElementSpaceSize());
+
+        const auto welford_count_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_in_welford_count_grid, count_grid_desc_m_nblock.GetElementSpaceSize());
+
+        const auto gamma_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_gamma_grid, gamma_grid_desc_n.GetElementSpaceSize());
+
+        const auto beta_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_beta_grid, beta_grid_desc_n.GetElementSpaceSize());
+
+        auto h_global_val_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
+            p_h_grid, h_grid_desc_m_n.GetElementSpaceSize());
+
+        // VGPR
+        StaticBuffer<AddressSpaceEnum::Vgpr, ComputeDataType, MThreadSliceSize, true>
+            in_welford_mean_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr, ComputeDataType, MThreadSliceSize, true>
+            in_welford_var_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr, int32_t, MThreadSliceSize, true>
+            in_welford_count_thread_buf;
+
+        StaticBuffer<AddressSpaceEnum::Vgpr, ComputeDataType, MThreadSliceSize, true>
+            welford_mean_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr, ComputeDataType, MThreadSliceSize, true>
+            welford_var_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr, int32_t, MThreadSliceSize, true>
+            welford_count_thread_buf;
+
+        StaticBuffer<AddressSpaceEnum::Vgpr,
+                     ComputeDataType,
+                     MThreadSliceSize * NThreadSliceSize,
+                     true>
+            e_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr,
+                     ComputeDataType,
+                     MThreadSliceSize * NThreadSliceSize,
+                     true>
+            gamma_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr,
+                     ComputeDataType,
+                     MThreadSliceSize * NThreadSliceSize,
+                     true>
+            beta_thread_buf;
+        StaticBuffer<AddressSpaceEnum::Vgpr,
+                     ComputeDataType,
+                     MThreadSliceSize * NThreadSliceSize,
+                     true>
+            h_thread_buf;
+
+        // IO
+        auto threadwise_mean_load_m_nblock =
+            ThreadwiseTensorSliceTransfer_v2<EMeanVarDataType,
+                                             ComputeDataType,
+                                             MeanVarGridDesc_M_NBlock,
+                                             decltype(thread_buffer_desc_m_1),
+                                             ThreadBufferLengths_M_1,
+                                             ThreadBufferDimAccessOrder,
+                                             1,
+                                             1,
+                                             1,
+                                             true>(
+                mean_var_grid_desc_m_nblock,
+                make_multi_index(block_work_idx[I0] * M_BlockTileSize +
+                                     thread_m_cluster_id * MThreadSliceSize,
+                                 thread_n_cluster_id));
+
+        auto threadwise_var_load_m_nblock =
+            ThreadwiseTensorSliceTransfer_v2<EMeanVarDataType,
+                                             ComputeDataType,
+                                             MeanVarGridDesc_M_NBlock,
+                                             decltype(thread_buffer_desc_m_1),
+                                             ThreadBufferLengths_M_1,
+                                             ThreadBufferDimAccessOrder,
+                                             1,
+                                             1,
+                                             1,
+                                             true>(
+                mean_var_grid_desc_m_nblock,
+                make_multi_index(block_work_idx[I0] * M_BlockTileSize +
+                                     thread_m_cluster_id * MThreadSliceSize,
+                                 thread_n_cluster_id));
+
+        auto threadwise_count_load_m_nblock =
+            ThreadwiseTensorSliceTransfer_v2<int32_t,
+                                             int32_t,
+                                             CountGridDesc_M_NBlock,
+                                             decltype(thread_buffer_desc_m_1),
+                                             ThreadBufferLengths_M_1,
+                                             ThreadBufferDimAccessOrder,
+                                             1,
+                                             1,
+                                             1,
+                                             true>(
+                count_grid_desc_m_nblock,
+                make_multi_index(block_work_idx[I0] * M_BlockTileSize +
+                                     thread_m_cluster_id * MThreadSliceSize,
+                                 thread_n_cluster_id));
+
+        auto threadwise_e_load_m_n =
+            ThreadwiseTensorSliceTransfer_v2<EMeanVarDataType,
+                                             ComputeDataType,
+                                             decltype(e_grid_desc_m_n),
+                                             decltype(thread_buffer_desc_m_n),
+                                             ThreadBufferLengths_M_N,
+                                             ThreadBufferDimAccessOrder,
+                                             1, // SrcVectorDim
+                                             ESrcVectorSize,
+                                             1,
+                                             true>(
+                e_grid_desc_m_n,
+                make_multi_index(
+                    block_work_idx[I0] * M_BlockTileSize + thread_m_cluster_id * MThreadSliceSize,
+                    block_work_idx[I1] * N_BlockTileSize + thread_n_cluster_id * NThreadSliceSize));
+
+        auto threadwise_gamma_load_n =
+            ThreadwiseTensorSliceTransfer_v2<GammaDataType,
+                                             ComputeDataType,
+                                             decltype(gamma_grid_desc_n),
+                                             decltype(thread_buffer_desc_n),
+                                             ThreadBufferLengths_N,
+                                             Sequence<0>, // DimAccessOrder,
+                                             0,           // SrcVectorDim,
+                                             GammaSrcVectorSize,
+                                             1,
+                                             true>(
+                gamma_grid_desc_n,
+                make_multi_index(block_work_idx[I1] * N_BlockTileSize +
+                                 thread_n_cluster_id * NThreadSliceSize));
+
+        auto threadwise_beta_load_n =
+            ThreadwiseTensorSliceTransfer_v2<BetaDataType,
+                                             ComputeDataType,
+                                             decltype(beta_grid_desc_n),
+                                             decltype(thread_buffer_desc_n),
+                                             ThreadBufferLengths_N,
+                                             Sequence<0>, // DimAccessOrder,
+                                             0,           // SrcVectorDim,
+                                             BetaSrcVectorSize,
+                                             1,
+                                             true>(
+                beta_grid_desc_n,
+                make_multi_index(block_work_idx[I1] * N_BlockTileSize +
+                                 thread_n_cluster_id * NThreadSliceSize));
+
+        auto threadwise_h_store_m_n =
+            ThreadwiseTensorSliceTransfer_v1r3<ComputeDataType,
+                                               HDataType,
+                                               decltype(thread_buffer_desc_m_n),
+                                               decltype(h_grid_desc_m_n),
+                                               HElementwiseOperation,
+                                               ThreadBufferLengths_M_N,
+                                               ThreadBufferDimAccessOrder,
+                                               1, // DstVectorDim
+                                               HDstVectorSize,
+                                               InMemoryDataOperationEnum::Set,
+                                               1,
+                                               true>(
+                h_grid_desc_m_n,
+                make_multi_index(
+                    block_work_idx[I0] * M_BlockTileSize + thread_m_cluster_id * MThreadSliceSize,
+                    block_work_idx[I1] * N_BlockTileSize + thread_n_cluster_id * NThreadSliceSize),
+                h_element_op);
+
+        // step1: Merge mean and variance
+        constexpr auto mean_var_count_thread_copy_step_I0_n =
+            make_multi_index(I0, NThreadClusterSize);
+
+        static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
+            welford_mean_thread_buf(I)  = type_convert<ComputeDataType>(0.0f);
+            welford_var_thread_buf(I)   = type_convert<ComputeDataType>(0.0f);
+            welford_count_thread_buf(I) = 0;
+        });
+
+        for(index_t n = 0; n < numMeanVarCountBlockTileIteration_N; ++n)
+        {
+            threadwise_mean_load_m_nblock.Run(mean_var_grid_desc_m_nblock,
+                                              welford_mean_global_val_buf,
+                                              thread_buffer_desc_m_1,
+                                              make_tuple(I0, I0),
+                                              in_welford_mean_thread_buf);
+
+            threadwise_var_load_m_nblock.Run(mean_var_grid_desc_m_nblock,
+                                             welford_var_global_val_buf,
+                                             thread_buffer_desc_m_1,
+                                             make_tuple(I0, I0),
+                                             in_welford_var_thread_buf);
+
+            threadwise_count_load_m_nblock.Run(count_grid_desc_m_nblock,
+                                               welford_count_global_val_buf,
+                                               thread_buffer_desc_m_1,
+                                               make_tuple(I0, I0),
+                                               in_welford_count_thread_buf);
+
+            ThreadwiseWelford::Run(in_welford_mean_thread_buf,
+                                   in_welford_var_thread_buf,
+                                   in_welford_count_thread_buf,
+                                   welford_mean_thread_buf,
+                                   welford_var_thread_buf,
+                                   welford_count_thread_buf);
+
+            threadwise_mean_load_m_nblock.MoveSrcSliceWindow(mean_var_grid_desc_m_nblock,
+                                                             mean_var_count_thread_copy_step_I0_n);
+            threadwise_var_load_m_nblock.MoveSrcSliceWindow(mean_var_grid_desc_m_nblock,
+                                                            mean_var_count_thread_copy_step_I0_n);
+            threadwise_count_load_m_nblock.MoveSrcSliceWindow(count_grid_desc_m_nblock,
+                                                              mean_var_count_thread_copy_step_I0_n);
+        }
+
+        static_for<0, MThreadSliceSize, 1>{}([&](auto I) {
+            if constexpr(I > 0)
+                block_sync_lds();
+
+            BlockwiseWelford::Run(
+                welford_mean_thread_buf(I), welford_var_thread_buf(I), welford_count_thread_buf(I));
+        });
+
+        // step2: normalization
+        // h[m, n] = [(e[m, n] - mean[m]) / sqrt(var[m] + eps)] * gamma[n] + beta[n]
+        threadwise_e_load_m_n.Run(e_grid_desc_m_n,
+                                  e_global_val_buf,
+                                  thread_buffer_desc_m_n,
+                                  make_tuple(I0, I0),
+                                  e_thread_buf);
+
+        static_for<0, MThreadSliceSize, 1>{}([&](auto m) {
+            auto divisor = 1 / ck::math::sqrt(welford_var_thread_buf(m) + epsilon);
+            static_for<0, NThreadSliceSize, 1>{}([&](auto n) {
+                constexpr auto m_n = thread_buffer_desc_m_n.CalculateOffset(make_tuple(m, n));
+                h_thread_buf(Number<m_n>{}) =
+                    (e_thread_buf(Number<m_n>{}) - welford_mean_thread_buf(m)) * divisor;
+            });
+        });
+
+        threadwise_gamma_load_n.Run(gamma_grid_desc_n,
+                                    gamma_global_val_buf,
+                                    thread_buffer_desc_n,
+                                    make_tuple(I0),
+                                    gamma_thread_buf);
+
+        static_for<0, MThreadSliceSize, 1>{}([&](auto m) {
+            static_for<0, NThreadSliceSize, 1>{}([&](auto n) {
+                constexpr auto m_n = thread_buffer_desc_m_n.CalculateOffset(make_tuple(m, n));
+                h_thread_buf(Number<m_n>{}) = h_thread_buf(Number<m_n>{}) * gamma_thread_buf(n);
+            });
+        });
+
+        threadwise_beta_load_n.Run(beta_grid_desc_n,
+                                   beta_global_val_buf,
+                                   thread_buffer_desc_n,
+                                   make_tuple(I0),
+                                   beta_thread_buf);
+
+        static_for<0, MThreadSliceSize, 1>{}([&](auto m) {
+            static_for<0, NThreadSliceSize, 1>{}([&](auto n) {
+                constexpr auto m_n = thread_buffer_desc_m_n.CalculateOffset(make_tuple(m, n));
+                h_thread_buf(Number<m_n>{}) = h_thread_buf(Number<m_n>{}) + beta_thread_buf(n);
+            });
+        });
+
+        threadwise_h_store_m_n.Run(thread_buffer_desc_m_n,
+                                   make_tuple(I0, I0),
+                                   h_thread_buf,
+                                   h_grid_desc_m_n,
+                                   h_global_val_buf);
+
+    } // run
+};
+
+} // namespace ck

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

@@ -434,7 +434,7 @@ struct GridwiseElementwiseLayernormWelfordVariance_mk_to_mk
             });
 
             static_for<0, MThreadSliceSize, 1>{}([&](auto iM) {
-                auto divisor = 1 / __builtin_amdgcn_sqrtf(var_thread_buf(iM) + epsilon);
+                auto divisor = 1 / ck::math::sqrt(var_thread_buf(iM) + epsilon);
                 static_for<0, XThreadBufferNumber, 1>{}([&](auto iK0) {
                     static_for<0, XSrcVectorSize, 1>{}([&](auto iK1) {
                         constexpr auto offset_m_k =

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

@@ -319,7 +319,7 @@ struct GridwiseNormalizationWelfordVariance_mk_to_mk
             });
 
             static_for<0, MThreadSliceSize, 1>{}([&](auto iM) {
-                auto divisor = 1 / __builtin_amdgcn_sqrtf(var_thread_buf(iM) + epsilon);
+                auto divisor = 1 / ck::math::sqrt(var_thread_buf(iM) + epsilon);
                 static_for<0, XThreadBufferNumber, 1>{}([&](auto iK0) {
                     static_for<0, XSrcVectorSize, 1>{}([&](auto iK1) {
                         constexpr auto offset_m_k =

library/include/ck/library/reference_tensor_operation/cpu/reference_layernorm.hpp

@@ -90,10 +90,13 @@ struct ReferenceLayernorm : public device::BaseOperator
 
             for(int m = 0; m < M; ++m)
             {
+                AccDataType divisor =
+                    static_cast<AccDataType>(1) / ck::math::sqrt(var(m) + arg.epsilon_);
+
                 for(int n = 0; n < N; ++n)
                 {
                     auto x_val = ck::type_convert<AccDataType>(arg.x_m_n_(m, n));
-                    auto y_val = (x_val - mean(m)) / sqrt(var(m) + arg.epsilon_);
+                    auto y_val = (x_val - mean(m)) * divisor;
                     y_val      = (y_val * arg.gamma_n_(n)) + arg.beta_n_(n);
                     arg.acc_elementwise_op_(y_val, y_val);
                     arg.y_m_n_(m, n) = ck::type_convert<YDataType>(y_val);