Gemm multiple d multiple r (#335)

* Imitate XXX_gemm_multiple_d, add XXX_gemm_multiple_d_multiple_r for gemm + reduction

* Implement run of kernel

* Add example

* Fix parameter of typo

* Rewrite the reduceMax example

* Rewrite the reduceMean + reduceMeanSquare example

* Refine naming

* Refine folder name

* refine naming

* Rewrite the gemm + bias + relu + add + layernorm example

* Rewrite the gemm + layernorm example

* clang-format

* Fix bug if sync lds

* Fix compile error

example/16_gemm_multi_d_multi_reduces/CMakeLists.txt

+add_example_executable(example_gemm_add_add_mean_meansquare_xdl_fp16 gemm_add_add_mean_meansquare_xdl_fp16.cpp)
+add_example_executable(example_gemm_max_xdl_fp16 gemm_max_xdl_fp16.cpp)
+add_example_executable(example_gemm_mean_meansquare_xdl_fp16 gemm_mean_meansquare_xdl_fp16.cpp)

example/16_gemm_multi_d_multi_reduces/gemm_add_add_mean_meansquare_xdl_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/device_gemm_multiple_d_multiple_r_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/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;
+
+// DataType
+using ADataType         = F16;
+using BDataType         = F16;
+using GemmAccDataType   = F32;
+using CShuffleDataType  = F32;
+using D0DataType        = F16;
+using D1DataType        = F16;
+using DsDataType        = ck::Tuple<D0DataType, D1DataType>;
+using EDataType         = F16;
+using ReduceAccDataType = F32;
+using R0DataType        = F32;
+using R1DataType        = F32;
+using RsDataType        = ck::Tuple<R0DataType, R1DataType>;
+
+// Layout
+using ALayout  = Row;
+using BLayout  = Col;
+using D1Layout = Row;
+using ELayout  = D1Layout;
+
+// Elementwise op
+using PassThrough  = ck::tensor_operation::element_wise::PassThrough;
+using AddAdd       = ck::tensor_operation::element_wise::AddAdd;
+using Square       = ck::tensor_operation::element_wise::UnarySquare;
+using Div          = ck::tensor_operation::element_wise::UnaryDivide;
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = AddAdd;
+using QsElementOp  = ck::Tuple<PassThrough, Square>;
+using RsElementOp  = ck::Tuple<Div, Div>;
+
+// ReduceOp
+using R0ThreadReduceOp = ck::reduce::Add;
+using R1ThreadReduceOp = ck::reduce::Add;
+using RsThreadReduceOp = ck::Tuple<R0ThreadReduceOp, R1ThreadReduceOp>;
+
+static constexpr auto R0GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+static constexpr auto R1GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+using RsGlobalReduceOp = ck::InMemoryDataOperationEnumSequence<R0GlobalReduceOp, R1GlobalReduceOp>;
+
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::Default;
+
+// clang-format off
+using DeviceOpInstance = ck::tensor_operation::device::DeviceGemmMultipleDMultipleR_Xdl_CShuffle
+//######| ALayout| BLayout| ELayout|     AData|     BData|     GemmAccData|         CShuffle|     DsData|     EData|     ReduceAccData|     RsData|           A|           B|          CDE|          Qs|          Rs|           Thread|           Global|           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|    CDRThreadTransfer|                  CDE|    RThreadTransfer|
+//######|        |        |        |      Type|      Type|            Type|         DataType|       Type|      Type|              Type|       Type| Elementwise| Elementwise|  Elementwise| Elementwise| Elementwise|           Reduce|           Reduce| 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|       ClusterLengths| ReduceThreadTransfer| DstScalarPerVector|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |   Operation|   Operation|    Operation|   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| _MPerBlock_NPerBlock|      ScalarPerVector|         _MPerBlock|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |            |            |             |            |            |                 |                 |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                     |           _NPerBlock|                   |
+        < ALayout, BLayout, ELayout, ADataType, BDataType, GemmAccDataType, CShuffleDataType, DsDataType, EDataType, ReduceAccDataType, RsDataType,  AElementOp,  BElementOp, CDEElementOp, QsElementOp, RsElementOp, RsThreadReduceOp, RsGlobalReduceOp,    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<64, 4>,                    4,                  1>;
+// clang-format on
+
+using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
+                                                                        BDataType,
+                                                                        EDataType,
+                                                                        GemmAccDataType,
+                                                                        AElementOp,
+                                                                        BElementOp,
+                                                                        PassThrough>;
+
+template <typename ADataType,
+          typename BDataType,
+          typename D0DataType,
+          typename D1DataType,
+          typename EDataType,
+          typename R0DataType,
+          typename R1DataType>
+void DumpPerf(float ave_time, int M, int N, int K)
+{
+    std::size_t flop          = std::size_t(2) * M * N * K + std::size_t(2) * M * N;
+    std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
+                                sizeof(D0DataType) * M * N + sizeof(D1DataType) * M * N +
+                                sizeof(EDataType) * M * N + sizeof(R0DataType) * M +
+                                sizeof(R1DataType) * M;
+
+    float tflops          = static_cast<float>(flop) / 1.E9 / ave_time;
+    float gemm_gb_per_sec = gemm_num_byte / 1.E6 / ave_time;
+
+    std::cout << "Perf: " << ave_time << " ms, " << tflops << " TFlops, " << gemm_gb_per_sec
+              << " GB/s, " << std::endl;
+}
+
+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}));
+        }
+    };
+
+int main()
+{
+    ck::index_t M = 1024;
+    ck::index_t N = 1024;
+    ck::index_t K = 1024;
+
+    ck::index_t StrideA  = 1024;
+    ck::index_t StrideB  = 1024;
+    ck::index_t StrideD0 = 0;
+    ck::index_t StrideD1 = 1024;
+    ck::index_t StrideE  = 1024;
+
+    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<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> r0_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<R1DataType> r1_m(f_host_tensor_descriptor1d(M, 1));
+
+    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});
+
+    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 e_device_buf(sizeof(EDataType) * e_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem r0_device_buf(sizeof(R0DataType) * r0_m.mDesc.GetElementSpaceSize());
+    DeviceMem r1_device_buf(sizeof(R1DataType) * r1_m.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());
+
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{};
+    auto qs_element_op  = QsElementOp{};
+    auto rs_element_op  = RsElementOp{N, N};
+
+    // Prepare GEMM, mean, mean_square
+    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()},
+                               e_device_buf.GetDeviceBuffer(),
+                               {r0_device_buf.GetDeviceBuffer(), r1_device_buf.GetDeviceBuffer()},
+                               M,
+                               N,
+                               K,
+                               StrideA,
+                               StrideB,
+                               {StrideD0, StrideD1},
+                               StrideE,
+                               a_element_op,
+                               b_element_op,
+                               cde_element_op,
+                               qs_element_op,
+                               rs_element_op);
+
+    if(!device_op.IsSupportedArgument(argument))
+    {
+        throw std::runtime_error("wrong! this device_op instance does not support this problem");
+    }
+
+    // init reducetion buffer to 0
+    r0_device_buf.SetZero();
+    r1_device_buf.SetZero();
+
+    invoker.Run(argument, StreamConfig{nullptr, false});
+
+    bool do_verification = true;
+    bool pass            = true;
+
+    if(do_verification)
+    {
+        auto I0 = ck::Number<0>{};
+        auto I1 = ck::Number<1>{};
+
+        Tensor<EDataType> e_m_n_host(e_m_n.mDesc);
+        Tensor<R0DataType> r0_m_host(r0_m.mDesc);
+        Tensor<R1DataType> r1_m_host(r1_m.mDesc);
+
+        auto ref_gemm    = ReferenceGemmInstance{};
+        auto ref_invoker = ref_gemm.MakeInvoker();
+
+        auto ref_argument = ref_gemm.MakeArgument(
+            a_m_k, b_k_n, e_m_n_host, a_element_op, b_element_op, PassThrough{});
+
+        ref_invoker.Run(ref_argument);
+
+        auto reduce0_op = R0ThreadReduceOp{};
+        auto reduce1_op = R1ThreadReduceOp{};
+
+        for(int m = 0; m < M; ++m)
+        {
+            auto reduce0_acc = reduce0_op.GetIdentityValue<ReduceAccDataType>();
+            auto reduce1_acc = reduce1_op.GetIdentityValue<ReduceAccDataType>();
+
+            for(int n = 0; n < N; ++n)
+            {
+                ReduceAccDataType square_e_val;
+
+                auto e_val  = ck::type_convert<GemmAccDataType>(e_m_n_host(m, n));
+                auto d0_val = ck::type_convert<GemmAccDataType>(d0_n(n));
+                auto d1_val = ck::type_convert<GemmAccDataType>(d1_m_n(m, n));
+                cde_element_op(e_val, e_val, d0_val, d1_val);
+                e_m_n_host(m, n) = ck::type_convert<EDataType>(e_val);
+
+                auto e_val_reduce = ck::type_convert<ReduceAccDataType>(e_val);
+                qs_element_op[I1](square_e_val, e_val_reduce);
+
+                reduce0_op(reduce0_acc, e_val_reduce);
+                reduce1_op(reduce1_acc, square_e_val);
+            }
+
+            rs_element_op[I0](reduce0_acc, reduce0_acc);
+            rs_element_op[I1](reduce1_acc, reduce1_acc);
+            r0_m_host(m) = ck::type_convert<R0DataType>(reduce0_acc);
+            r1_m_host(m) = ck::type_convert<R1DataType>(reduce1_acc);
+        }
+
+        e_device_buf.FromDevice(e_m_n.mData.data());
+        r0_device_buf.FromDevice(r0_m.mData.data());
+        r1_device_buf.FromDevice(r1_m.mData.data());
+
+        pass = ck::utils::check_err(
+            e_m_n.mData, e_m_n_host.mData, "Error: Incorrect results c", 1e-2, 1e-2);
+        pass &= ck::utils::check_err(
+            r0_m.mData, r0_m_host.mData, "Error: Incorrect results d0", 1e-2, 1e-2);
+        pass &= ck::utils::check_err(
+            r1_m.mData, r1_m_host.mData, "Error: Incorrect results d1", 1e-2, 1e-2);
+    }
+
+    bool time_kernel = true;
+    if(time_kernel)
+    {
+        float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+        DumpPerf<ADataType, BDataType, D0DataType, D1DataType, EDataType, R0DataType, R1DataType>(
+            ave_time, M, N, K);
+    }
+
+    return pass ? 0 : 1;
+}

example/16_gemm_multi_d_multi_reduces/gemm_max_xdl_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/device_gemm_multiple_d_multiple_r_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/utility/check_err.hpp"
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+using F16 = ck::half_t;
+using F32 = float;
+using F64 = double;
+
+using Row = ck::tensor_layout::gemm::RowMajor;
+using Col = ck::tensor_layout::gemm::ColumnMajor;
+
+// DataType
+using ADataType         = F16;
+using BDataType         = F16;
+using GemmAccDataType   = F32;
+using CShuffleDataType  = F32;
+using DsDataType        = ck::Tuple<>;
+using EDataType         = F16;
+using ReduceAccDataType = F32;
+using R0DataType        = F32;
+using RsDataType        = ck::Tuple<R0DataType>;
+
+// Layout
+using ALayout = Row;
+using BLayout = Col;
+using ELayout = Row;
+
+// Elementwise op
+using PassThrough  = ck::tensor_operation::element_wise::PassThrough;
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = PassThrough;
+using QsElementOp  = ck::Tuple<PassThrough>;
+using RsElementOp  = ck::Tuple<PassThrough>;
+
+// ReduceOp
+using RsThreadReduceOp = ck::Tuple<ck::reduce::Max>;
+
+using RsGlobalReduceOp =
+    ck::InMemoryDataOperationEnumSequence<ck::InMemoryDataOperationEnum::AtomicMax>;
+
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::Default;
+
+// clang-format off
+using DeviceOpInstance = ck::tensor_operation::device::DeviceGemmMultipleDMultipleR_Xdl_CShuffle
+//######| ALayout| BLayout| ELayout|     AData|     BData|     GemmAccData|         CShuffle|     DsData|     EData|     ReduceAccData|     RsData|           A|           B|          CDE|          Qs|          Rs|           Thread|           Global|           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|    CDRThreadTransfer|                  CDE|    RThreadTransfer|
+//######|        |        |        |      Type|      Type|            Type|         DataType|       Type|      Type|              Type|       Type| Elementwise| Elementwise|  Elementwise| Elementwise| Elementwise|           Reduce|           Reduce| 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|       ClusterLengths| ReduceThreadTransfer| DstScalarPerVector|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |   Operation|   Operation|    Operation|   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| _MPerBlock_NPerBlock|      ScalarPerVector|         _MPerBlock|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |            |            |             |            |            |                 |                 |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                     |           _NPerBlock|                   |
+        < ALayout, BLayout, ELayout, ADataType, BDataType, GemmAccDataType, CShuffleDataType, DsDataType, EDataType, ReduceAccDataType, RsDataType,  AElementOp,  BElementOp, CDEElementOp, QsElementOp, RsElementOp, RsThreadReduceOp, RsGlobalReduceOp,    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<64, 4>,                    4,                  1>;
+// clang-format on
+
+using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
+                                                                        BDataType,
+                                                                        EDataType,
+                                                                        GemmAccDataType,
+                                                                        AElementOp,
+                                                                        BElementOp,
+                                                                        CDEElementOp>;
+
+template <typename ADataType, typename BDataType, typename EDataType, typename R0DataType>
+void DumpPerf(float ave_time, int M, int N, int K)
+{
+    std::size_t flop          = std::size_t(2) * M * N * K;
+    std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
+                                sizeof(EDataType) * M * N + sizeof(R0DataType) * M;
+
+    float tflops          = static_cast<float>(flop) / 1.E9 / ave_time;
+    float gemm_gb_per_sec = gemm_num_byte / 1.E6 / ave_time;
+
+    std::cout << "Perf: " << ave_time << " ms, " << tflops << " TFlops, " << gemm_gb_per_sec
+              << " GB/s, " << std::endl;
+}
+
+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}));
+        }
+    };
+
+int main()
+{
+    ck::index_t M = 1024;
+    ck::index_t N = 1024;
+    ck::index_t K = 1024;
+
+    ck::index_t StrideA = 1024;
+    ck::index_t StrideB = 1024;
+    ck::index_t StrideE = 1024;
+
+    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<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> r0_m(f_host_tensor_descriptor1d(M, 1));
+
+    a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{-1, 1});
+    b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-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 e_device_buf(sizeof(EDataType) * e_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem r0_device_buf(sizeof(R0DataType) * r0_m.mDesc.GetElementSpaceSize());
+
+    a_device_buf.ToDevice(a_m_k.mData.data());
+    b_device_buf.ToDevice(b_k_n.mData.data());
+
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{};
+    auto qs_element_op  = QsElementOp{};
+    auto rs_element_op  = RsElementOp{};
+
+    // Prepare GEMM, max
+    auto device_op = DeviceOpInstance{};
+    auto invoker   = device_op.MakeInvoker();
+    auto argument  = device_op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                                           b_device_buf.GetDeviceBuffer(),
+                                           {},
+                                           e_device_buf.GetDeviceBuffer(),
+                                           {r0_device_buf.GetDeviceBuffer()},
+                                           M,
+                                           N,
+                                           K,
+                                           StrideA,
+                                           StrideB,
+                                           {},
+                                           StrideE,
+                                           a_element_op,
+                                           b_element_op,
+                                           cde_element_op,
+                                           qs_element_op,
+                                           rs_element_op);
+
+    if(!device_op.IsSupportedArgument(argument))
+    {
+        throw std::runtime_error("wrong! this device_op instance does not support this problem");
+    }
+
+    // [CAUSION]: launch_and_time_kernel will not initialize D.
+    // If we evaluate kernel multiple time but without initialize D. Verification will fail
+    r0_device_buf.SetValue(ck::NumericLimits<R0DataType>::Lowest());
+
+    invoker.Run(argument, StreamConfig{nullptr, false});
+
+    bool do_verification = true;
+    bool pass            = true;
+
+    if(do_verification)
+    {
+        auto I0 = ck::Number<0>{};
+
+        Tensor<EDataType> e_m_n_host(e_m_n.mDesc);
+        Tensor<R0DataType> r0_m_host(r0_m.mDesc);
+
+        auto ref_gemm    = ReferenceGemmInstance{};
+        auto ref_invoker = ref_gemm.MakeInvoker();
+
+        auto ref_argument = ref_gemm.MakeArgument(
+            a_m_k, b_k_n, e_m_n_host, a_element_op, b_element_op, cde_element_op);
+
+        ref_invoker.Run(ref_argument);
+
+        auto reduce0_op = RsThreadReduceOp{}[I0];
+
+        for(int m = 0; m < M; ++m)
+        {
+            auto reduce0_acc = reduce0_op.GetIdentityValue<ReduceAccDataType>();
+
+            for(int n = 0; n < N; ++n)
+            {
+                auto e_val = ck::type_convert<ReduceAccDataType>(e_m_n_host(m, n));
+                reduce0_op(reduce0_acc, e_val);
+            };
+
+            r0_m_host(m) = ck::type_convert<R0DataType>(reduce0_acc);
+        }
+
+        e_device_buf.FromDevice(e_m_n.mData.data());
+        r0_device_buf.FromDevice(r0_m.mData.data());
+
+        pass = ck::utils::check_err(
+            e_m_n.mData, e_m_n_host.mData, "Error: Incorrect results c", 1e-2, 1e-2);
+        pass &= ck::utils::check_err(
+            r0_m.mData, r0_m_host.mData, "Error: Incorrect results d0", 1e-2, 1e-2);
+    }
+
+    bool time_kernel = true;
+    if(time_kernel)
+    {
+        float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+        DumpPerf<ADataType, BDataType, EDataType, R0DataType>(ave_time, M, N, K);
+    }
+
+    return pass ? 0 : 1;
+}

example/16_gemm_multi_d_multi_reduces/gemm_mean_meansquare_xdl_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/device_gemm_multiple_d_multiple_r_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/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;
+
+// DataType
+using ADataType         = F16;
+using BDataType         = F16;
+using GemmAccDataType   = F32;
+using CShuffleDataType  = F32;
+using DsDataType        = ck::Tuple<>;
+using EDataType         = F16;
+using ReduceAccDataType = F32;
+using R0DataType        = F32;
+using R1DataType        = F32;
+using RsDataType        = ck::Tuple<R0DataType, R1DataType>;
+
+// Layout
+using ALayout = Row;
+using BLayout = Col;
+using ELayout = Row;
+
+// Elementwise op
+using PassThrough  = ck::tensor_operation::element_wise::PassThrough;
+using Square       = ck::tensor_operation::element_wise::UnarySquare;
+using Div          = ck::tensor_operation::element_wise::UnaryDivide;
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = PassThrough;
+using QsElementOp  = ck::Tuple<PassThrough, Square>;
+using RsElementOp  = ck::Tuple<Div, Div>;
+
+// ReduceOp
+using R0ThreadReduceOp = ck::reduce::Add;
+using R1ThreadReduceOp = ck::reduce::Add;
+using RsThreadReduceOp = ck::Tuple<R0ThreadReduceOp, R1ThreadReduceOp>;
+
+static constexpr auto R0GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+static constexpr auto R1GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+using RsGlobalReduceOp = ck::InMemoryDataOperationEnumSequence<R0GlobalReduceOp, R1GlobalReduceOp>;
+
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::Default;
+
+// clang-format off
+using DeviceOpInstance = ck::tensor_operation::device::DeviceGemmMultipleDMultipleR_Xdl_CShuffle
+//######| ALayout| BLayout| ELayout|     AData|     BData|     GemmAccData|         CShuffle|     DsData|     EData|     ReduceAccData|     RsData|           A|           B|          CDE|          Qs|          Rs|           Thread|           Global|           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|    CDRThreadTransfer|                  CDE|    RThreadTransfer|
+//######|        |        |        |      Type|      Type|            Type|         DataType|       Type|      Type|              Type|       Type| Elementwise| Elementwise|  Elementwise| Elementwise| Elementwise|           Reduce|           Reduce| 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|       ClusterLengths| ReduceThreadTransfer| DstScalarPerVector|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |   Operation|   Operation|    Operation|   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| _MPerBlock_NPerBlock|      ScalarPerVector|         _MPerBlock|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |            |            |             |            |            |                 |                 |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                     |           _NPerBlock|                   |
+        < ALayout, BLayout, ELayout, ADataType, BDataType, GemmAccDataType, CShuffleDataType, DsDataType, EDataType, ReduceAccDataType, RsDataType,  AElementOp,  BElementOp, CDEElementOp, QsElementOp, RsElementOp, RsThreadReduceOp, RsGlobalReduceOp,    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<64, 4>,                    4,                  1>;
+// clang-format on
+
+using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
+                                                                        BDataType,
+                                                                        EDataType,
+                                                                        GemmAccDataType,
+                                                                        AElementOp,
+                                                                        BElementOp,
+                                                                        CDEElementOp>;
+
+template <typename ADataType,
+          typename BDataType,
+          typename EDataType,
+          typename R0DataType,
+          typename R1DataType>
+void DumpPerf(float ave_time, int M, int N, int K)
+{
+    std::size_t flop          = std::size_t(2) * M * N * K;
+    std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
+                                sizeof(EDataType) * M * N + sizeof(R0DataType) * M +
+                                sizeof(R1DataType) * M;
+
+    float tflops          = static_cast<float>(flop) / 1.E9 / ave_time;
+    float gemm_gb_per_sec = gemm_num_byte / 1.E6 / ave_time;
+
+    std::cout << "Perf: " << ave_time << " ms, " << tflops << " TFlops, " << gemm_gb_per_sec
+              << " GB/s, " << std::endl;
+}
+
+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}));
+        }
+    };
+
+int main()
+{
+    ck::index_t M = 1024;
+    ck::index_t N = 1024;
+    ck::index_t K = 1024;
+
+    ck::index_t StrideA = 1024;
+    ck::index_t StrideB = 1024;
+    ck::index_t StrideE = 1024;
+
+    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<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> r0_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<R1DataType> r1_m(f_host_tensor_descriptor1d(M, 1));
+
+    a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{-1, 1});
+    b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-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 e_device_buf(sizeof(EDataType) * e_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem r0_device_buf(sizeof(R0DataType) * r0_m.mDesc.GetElementSpaceSize());
+    DeviceMem r1_device_buf(sizeof(R1DataType) * r1_m.mDesc.GetElementSpaceSize());
+
+    a_device_buf.ToDevice(a_m_k.mData.data());
+    b_device_buf.ToDevice(b_k_n.mData.data());
+
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{};
+    auto qs_element_op  = QsElementOp{};
+    auto rs_element_op  = RsElementOp{N, N};
+
+    // Prepare GEMM, mean, mean_square
+    auto device_op = DeviceOpInstance{};
+    auto invoker   = device_op.MakeInvoker();
+    auto argument =
+        device_op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                               b_device_buf.GetDeviceBuffer(),
+                               {},
+                               e_device_buf.GetDeviceBuffer(),
+                               {r0_device_buf.GetDeviceBuffer(), r1_device_buf.GetDeviceBuffer()},
+                               M,
+                               N,
+                               K,
+                               StrideA,
+                               StrideB,
+                               {},
+                               StrideE,
+                               a_element_op,
+                               b_element_op,
+                               cde_element_op,
+                               qs_element_op,
+                               rs_element_op);
+
+    if(!device_op.IsSupportedArgument(argument))
+    {
+        throw std::runtime_error("wrong! this device_op instance does not support this problem");
+    }
+
+    // init reducetion buffer to 0
+    r0_device_buf.SetZero();
+    r1_device_buf.SetZero();
+
+    invoker.Run(argument, StreamConfig{nullptr, false});
+
+    bool do_verification = true;
+    bool pass            = true;
+
+    if(do_verification)
+    {
+        auto I0 = ck::Number<0>{};
+        auto I1 = ck::Number<1>{};
+
+        Tensor<EDataType> e_m_n_host(e_m_n.mDesc);
+        Tensor<R0DataType> r0_m_host(r0_m.mDesc);
+        Tensor<R1DataType> r1_m_host(r1_m.mDesc);
+
+        auto ref_gemm    = ReferenceGemmInstance{};
+        auto ref_invoker = ref_gemm.MakeInvoker();
+
+        auto ref_argument = ref_gemm.MakeArgument(
+            a_m_k, b_k_n, e_m_n_host, a_element_op, b_element_op, PassThrough{});
+
+        ref_invoker.Run(ref_argument);
+
+        auto reduce0_op = R0ThreadReduceOp{};
+        auto reduce1_op = R1ThreadReduceOp{};
+
+        for(int m = 0; m < M; ++m)
+        {
+            auto reduce0_acc = reduce0_op.GetIdentityValue<ReduceAccDataType>();
+            auto reduce1_acc = reduce1_op.GetIdentityValue<ReduceAccDataType>();
+
+            for(int n = 0; n < N; ++n)
+            {
+                ReduceAccDataType square_e_val;
+                auto e_val = ck::type_convert<ReduceAccDataType>(e_m_n_host(m, n));
+                qs_element_op[I1](square_e_val, e_val);
+
+                reduce0_op(reduce0_acc, e_val);
+                reduce1_op(reduce1_acc, square_e_val);
+            }
+
+            rs_element_op[I0](reduce0_acc, reduce0_acc);
+            rs_element_op[I1](reduce1_acc, reduce1_acc);
+            r0_m_host(m) = ck::type_convert<R0DataType>(reduce0_acc);
+            r1_m_host(m) = ck::type_convert<R1DataType>(reduce1_acc);
+        }
+
+        e_device_buf.FromDevice(e_m_n.mData.data());
+        r0_device_buf.FromDevice(r0_m.mData.data());
+        r1_device_buf.FromDevice(r1_m.mData.data());
+
+        pass = ck::utils::check_err(
+            e_m_n.mData, e_m_n_host.mData, "Error: Incorrect results c", 1e-2, 1e-2);
+        pass &= ck::utils::check_err(
+            r0_m.mData, r0_m_host.mData, "Error: Incorrect results d0", 1e-2, 1e-2);
+        pass &= ck::utils::check_err(
+            r1_m.mData, r1_m_host.mData, "Error: Incorrect results d1", 1e-2, 1e-2);
+    }
+
+    bool time_kernel = true;
+    if(time_kernel)
+    {
+        float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+        DumpPerf<ADataType, BDataType, EDataType, R0DataType, R1DataType>(ave_time, M, N, K);
+    }
+
+    return pass ? 0 : 1;
+}

example/16_gemm_reduce/CMakeLists.txt

-add_example_executable(example_gemm_reduce_xdl_max_fp16 gemm_reduce_xdl_max_fp16.cpp)
-add_example_executable(example_gemm_reduce_xdl_mean_squaremean_fp16 gemm_reduce_xdl_mean_squaremean_fp16.cpp)

example/16_gemm_reduce/gemm_reduce_xdl_max_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/device_gemm_reduce_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/utility/check_err.hpp"
-
-template <ck::index_t... Is>
-using S = ck::Sequence<Is...>;
-
-using F16 = ck::half_t;
-using F32 = float;
-using F64 = double;
-
-using Row = ck::tensor_layout::gemm::RowMajor;
-using Col = ck::tensor_layout::gemm::ColumnMajor;
-
-using ADataType         = F16;
-using BDataType         = F16;
-using CDataType         = F16;
-using GemmAccDataType   = F32;
-using ReduceAccDataType = F32;
-using ReduceDataType    = F64;
-using ReducePtrsGlobal  = ck::Tuple<ReduceDataType*>;
-
-using ALayout = ck::tensor_layout::gemm::RowMajor;
-using BLayout = ck::tensor_layout::gemm::ColumnMajor;
-using CLayout = ck::tensor_layout::gemm::RowMajor;
-
-using AElementOp       = ck::tensor_operation::element_wise::PassThrough;
-using BElementOp       = ck::tensor_operation::element_wise::PassThrough;
-using CElementOp       = ck::tensor_operation::element_wise::PassThrough;
-using ReduceOps        = ck::Tuple<ck::reduce::Max>;
-using ReduceElementOps = ck::Tuple<ck::tensor_operation::element_wise::PassThrough>;
-using ReduceGlobalMemOps =
-    ck::InMemoryDataOperationEnumSequence<ck::InMemoryDataOperationEnum::AtomicMax>;
-
-static constexpr auto GemmSpecialization =
-    ck::tensor_operation::device::GemmSpecialization::Default;
-
-// clang-format off
-using DeviceGemmReduceInstance = ck::tensor_operation::device::DeviceGemmReduce_Xdl_CShuffle
-//######| ALayout| BLayout| CLayout|AData| BData| CData|  GemmAcc| CShuffle|         ReduceAcc|       ReduceData|           A|           B|           C|      Reduce|    ReduceInEleOp|   ReduceAccEleOp|             Reduce|               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| CBlockTransferClusterLengths|  CBlockTransfer|              CReduce| CReduceThreadLds2VGprCopy| CReduceThreadVgpr2GlobalCopy|
-//######|        |        |        | Type|  Type|  Type| DataType| DataType|          DataType|       Type Tuple| Elementwise| Elementwise| Elementwise|   Operation|                 |                 |         MemoryData|     Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar|    ExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar|    ExtraN| MXdlPerWave| NXdlPerWave|            _MBlock_MPerBlock| ScalarPerVector| ThreadClusterLengths|     SrcDstScalarPerVector|        SrcDstScalarPerVector|
-//######|        |        |        |     |      |      |         |         |                  |                 |   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|            _NBlock_NPerBlock|      _NPerBlock| _MPerBlock_NPerBlock|                _NPerBlock|                   _MPerBlock|
-//######|        |        |        |     |      |      |         |         |                  |                 |            |            |            |            |                 |                 |                   |                   |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                     |                          |                             |
-        <     Row,     Col,     Row,  F16,   F16,   F16,      F32,      F32, ReduceAccDataType, ReducePtrsGlobal,  AElementOp,  BElementOp,  CElementOp,   ReduceOps, ReduceElementOps, ReduceElementOps, ReduceGlobalMemOps, GemmSpecialization,        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<1, 32, 1, 8>,               8,             S<64, 4>,                         4,                            1>;
-// clang-format on
-
-using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
-                                                                        BDataType,
-                                                                        CDataType,
-                                                                        GemmAccDataType,
-                                                                        AElementOp,
-                                                                        BElementOp,
-                                                                        CElementOp>;
-
-template <typename ADataType, typename BDataType, typename CDataType, typename ReduceDataType>
-void DumpGemmLayerNormPerf(float gemm_reduce_time, int M, int N, int K)
-{
-    std::size_t gemm_flop     = std::size_t(2) * M * N * K;
-    std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
-                                sizeof(CDataType) * M * N + sizeof(ReduceDataType) * M;
-
-    float tflops          = static_cast<float>(gemm_flop) / 1.E9 / gemm_reduce_time;
-    float gemm_gb_per_sec = gemm_num_byte / 1.E6 / gemm_reduce_time;
-
-    std::cout << "gemm + reduceMax Perf: " << gemm_reduce_time << " ms, " << tflops << " TFlops, "
-              << gemm_gb_per_sec << " GB/s, " << std::endl;
-}
-
-int main(int argc, char* argv[])
-{
-    bool do_verification = true;
-    int init_method      = 1;
-    bool time_kernel     = false;
-
-    // GEMM shape
-    ck::index_t M = 3840;
-    ck::index_t N = 4096;
-    ck::index_t K = 4096;
-
-    ck::index_t StrideA = 4096;
-    ck::index_t StrideB = 4096;
-    ck::index_t StrideC = 4096;
-
-    if(argc == 1)
-    {
-        // do nothing
-    }
-    else if(argc == 4)
-    {
-        do_verification = std::stoi(argv[1]);
-        init_method     = std::stoi(argv[2]);
-        time_kernel     = std::stoi(argv[3]);
-    }
-    else if(argc == 10)
-    {
-        do_verification = std::stoi(argv[1]);
-        init_method     = std::stoi(argv[2]);
-        time_kernel     = std::stoi(argv[3]);
-
-        M = std::stoi(argv[4]);
-        N = std::stoi(argv[5]);
-        K = std::stoi(argv[6]);
-
-        StrideA = std::stoi(argv[7]);
-        StrideB = std::stoi(argv[8]);
-        StrideC = std::stoi(argv[9]);
-    }
-    else
-    {
-        printf("arg1: verification (0=no, 1=yes)\n");
-        printf("arg2: initialization (0=no init, 1=integer value, 2=decimal value)\n");
-        printf("arg3: run kernel # of times (>1)\n");
-        printf("arg4 to 9: M (256x), N(128x), K(32x), StrideA, StrideB, StrideC\n");
-        exit(0);
-    }
-
-    auto f_host_tensor_descriptor =
-        [](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}));
-            }
-        };
-
-    Tensor<ADataType> a_m_k(f_host_tensor_descriptor(M, K, StrideA, ALayout{}));
-    Tensor<BDataType> b_k_n(f_host_tensor_descriptor(K, N, StrideB, BLayout{}));
-
-    Tensor<CDataType> c_m_n_host_result(f_host_tensor_descriptor(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> reduce_m_host_result(
-        HostTensorDescriptor(std::vector<std::size_t>({static_cast<std::size_t>(M)})));
-
-    Tensor<CDataType> c_m_n_device_result(f_host_tensor_descriptor(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> reduce_m_device_result(
-        HostTensorDescriptor(std::vector<std::size_t>({static_cast<std::size_t>(M)})));
-
-    std::cout << "a_m_k: " << a_m_k.mDesc << std::endl;
-    std::cout << "b_k_n: " << b_k_n.mDesc << std::endl;
-    std::cout << "c_m_n: " << c_m_n_host_result.mDesc << std::endl;
-    std::cout << "reduce_m: " << reduce_m_host_result.mDesc << std::endl;
-
-    switch(init_method)
-    {
-    case 0: break;
-    case 1:
-        a_m_k.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
-        b_k_n.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
-        break;
-    default:
-        a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
-        b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
-        break;
-    }
-
-    DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpaceSize());
-    DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpaceSize());
-    DeviceMem c_device_buf(sizeof(CDataType) * c_m_n_device_result.mDesc.GetElementSpaceSize());
-    DeviceMem reduce_device_buf(sizeof(ReduceDataType) *
-                                reduce_m_device_result.mDesc.GetElementSpaceSize());
-
-    a_device_buf.ToDevice(a_m_k.mData.data());
-    b_device_buf.ToDevice(b_k_n.mData.data());
-
-    auto a_element_op                       = AElementOp{};
-    auto b_element_op                       = BElementOp{};
-    auto c_element_op                       = CElementOp{};
-    auto reduce_element_op                  = ReduceElementOps{}[ck::Number<0>{}];
-    std::array<void*, 3> gemm_element_ops   = {&a_element_op, &b_element_op, &c_element_op};
-    std::array<void*, 1> reduce_element_ops = {&reduce_element_op};
-    std::array<void*, 1> p_reduces          = {reduce_device_buf.GetDeviceBuffer()};
-
-    // do GEMM
-    auto gemm     = DeviceGemmReduceInstance{};
-    auto invoker  = gemm.MakeInvoker();
-    auto argument = gemm.MakeArgument(a_device_buf.GetDeviceBuffer(),
-                                      b_device_buf.GetDeviceBuffer(),
-                                      nullptr,
-                                      {},
-                                      c_device_buf.GetDeviceBuffer(),
-                                      p_reduces,
-                                      M,
-                                      N,
-                                      K,
-                                      StrideA,
-                                      StrideB,
-                                      StrideC,
-                                      {},
-                                      gemm_element_ops,
-                                      {},
-                                      reduce_element_ops,
-                                      reduce_element_ops);
-
-    if(!gemm.IsSupportedArgument(argument))
-    {
-        throw std::runtime_error(
-            "wrong! device_gemm with the specified compilation parameters does "
-            "not support this GEMM problem");
-    }
-
-    // [CAUSION]: launch_and_time_kernel will not initialize D.
-    // If we evaluate kernel multiple time but without initialize D. Verification will fail
-    reduce_device_buf.SetValue(ck::NumericLimits<ReduceDataType>::Lowest());
-    invoker.Run(argument, StreamConfig{nullptr, false});
-
-    bool pass = true;
-
-    if(do_verification)
-    {
-        c_device_buf.FromDevice(c_m_n_device_result.mData.data());
-        reduce_device_buf.FromDevice(reduce_m_device_result.mData.data());
-
-        auto ref_gemm    = ReferenceGemmInstance{};
-        auto ref_invoker = ref_gemm.MakeInvoker();
-
-        auto ref_argument = ref_gemm.MakeArgument(
-            a_m_k, b_k_n, c_m_n_host_result, a_element_op, b_element_op, c_element_op);
-
-        ref_invoker.Run(ref_argument);
-
-        auto reduce_op = ReduceOps{}[ck::Number<0>{}];
-
-        for(int m = 0; m < M; ++m)
-        {
-            ReduceAccDataType reduce_acc = reduce_op.GetIdentityValue<ReduceAccDataType>();
-
-            for(int n = 0; n < N; ++n)
-            {
-                ReduceAccDataType curr_val =
-                    ck::type_convert<ReduceAccDataType>(c_m_n_host_result(m, n));
-                reduce_op(reduce_acc, curr_val);
-            };
-
-            reduce_m_host_result(m) = reduce_acc;
-        }
-
-        pass = ck::utils::check_err(c_m_n_device_result.mData,
-                                    c_m_n_host_result.mData,
-                                    "Error: Incorrect results c") &&
-               ck::utils::check_err(reduce_m_device_result.mData,
-                                    reduce_m_host_result.mData,
-                                    "Error: Incorrect results d",
-                                    1e-3,
-                                    1e-3);
-    }
-
-    if(time_kernel)
-    {
-        float gemm_reduceMax_ave_time = invoker.Run(argument, StreamConfig{nullptr, true});
-
-        DumpGemmLayerNormPerf<ADataType, BDataType, CDataType, ReduceDataType>(
-            gemm_reduceMax_ave_time, M, N, K);
-    }
-
-    return pass ? 0 : 1;
-}

example/16_gemm_reduce/gemm_reduce_xdl_mean_squaremean_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/device_gemm_reduce_xdl_cshuffle.hpp"
-#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
-#include "ck/utility/reduction_operator.hpp"
-
-#include "ck/library/utility/check_err.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"
-
-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 ADataType         = F16;
-using BDataType         = F16;
-using CDataType         = F16;
-using GemmAccDataType   = F32;
-using ReduceAccDataType = F32;
-using ReduceDataType    = F32;
-using ReducePtrsGlobal  = ck::Tuple<ReduceDataType*, ReduceDataType*>;
-
-using ALayout = ck::tensor_layout::gemm::RowMajor;
-using BLayout = ck::tensor_layout::gemm::ColumnMajor;
-using CLayout = ck::tensor_layout::gemm::RowMajor;
-
-using AElementOp = ck::tensor_operation::element_wise::PassThrough;
-using BElementOp = ck::tensor_operation::element_wise::PassThrough;
-using CElementOp = ck::tensor_operation::element_wise::PassThrough;
-using ReduceOp0  = ck::reduce::Add;
-using ReduceOp1  = ck::reduce::Add;
-using ReduceOps  = ck::Tuple<ReduceOp0, ReduceOp1>;
-
-using UnaryIdenticElementOp = ck::tensor_operation::element_wise::PassThrough;
-using UnaryDivElementOp     = ck::tensor_operation::element_wise::UnaryDivide;
-using UnarySquareElementOp  = ck::tensor_operation::element_wise::UnarySquare;
-using ReduceInElementOps    = ck::Tuple<UnaryIdenticElementOp, UnarySquareElementOp>;
-using ReduceOutElementOps   = ck::Tuple<UnaryDivElementOp, UnaryDivElementOp>;
-
-using ReduceGlobalMemOps =
-    ck::InMemoryDataOperationEnumSequence<ck::InMemoryDataOperationEnum::AtomicAdd,
-                                          ck::InMemoryDataOperationEnum::AtomicAdd>;
-
-static constexpr auto GemmSpecialization =
-    ck::tensor_operation::device::GemmSpecialization::Default;
-
-// clang-format off
-using DeviceGemmReduceInstance = ck::tensor_operation::device::DeviceGemmReduce_Xdl_CShuffle
-//######| ALayout| BLayout| CLayout|AData| BData| CData|  GemmAcc| CShuffle| ReduceAcc|      ReduceDData|           A|           B|           C|      Reduce|      ReduceInEleOp|      ReduceOutEleOp|              Reduce|               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| CBlockTransferClusterLengths|  CBlockTransfer|              CReduce| CReduceThreadLds2VGprCopy| CReduceThreadVgpr2GlobalCopy|
-//######|        |        |        | Type|  Type|  Type| DataType| DataType|  DataType|       Type Tuple| Elementwise| Elementwise| Elementwise|   Operation|                   |                    |          MemoryData|     Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar|    ExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar|    ExtraN| MXdlPerWave| NXdlPerWave|            _MBlock_MPerBlock| ScalarPerVector| ThreadClusterLengths|     SrcDstScalarPerVector|        SrcDstScalarPerVector|
-//######|        |        |        |     |      |      |         |         |          |                 |   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|            _NBlock_NPerBlock|      _NPerBlock| _MPerBlock_NPerBlock|                _NPerBlock|                   _MPerBlock|
-//######|        |        |        |     |      |      |         |         |          |                 |            |            |            |            |                   |                    |                    |                   |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                     |                          |                             |
-        <     Row,     Col,     Row,  F16,   F16,   F16,      F32,      F32,       F32, ReducePtrsGlobal,  AElementOp,  BElementOp,  CElementOp,   ReduceOps, ReduceInElementOps, ReduceOutElementOps,  ReduceGlobalMemOps, GemmSpecialization,        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<1, 32, 1, 8>,               8,             S<64, 4>,                         4,                            1>;
-// clang-format on
-
-using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
-                                                                        BDataType,
-                                                                        CDataType,
-                                                                        GemmAccDataType,
-                                                                        AElementOp,
-                                                                        BElementOp,
-                                                                        CElementOp>;
-
-template <typename ADataType, typename BDataType, typename CDataType, typename ReduceDataType>
-void DumpGemmLayerNormPerf(float gemm_reduce_time, int M, int N, int K)
-{
-    std::size_t gemm_flop     = std::size_t(2) * M * N * K;
-    std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
-                                sizeof(CDataType) * M * N + sizeof(ReduceDataType) * M +
-                                sizeof(ReduceDataType) * M;
-
-    float tflops          = static_cast<float>(gemm_flop) / 1.E9 / gemm_reduce_time;
-    float gemm_gb_per_sec = gemm_num_byte / 1.E6 / gemm_reduce_time;
-
-    std::cout << "gemm + reduce_mean + reduce_mean_square Perf: " << gemm_reduce_time << " ms, "
-              << tflops << " TFlops, " << gemm_gb_per_sec << " GB/s, " << std::endl;
-}
-
-int main(int argc, char* argv[])
-{
-    bool do_verification = true;
-    int init_method      = 1;
-    bool time_kernel     = false;
-
-    // GEMM shape
-    ck::index_t M = 3840;
-    ck::index_t N = 4096;
-    ck::index_t K = 4096;
-
-    ck::index_t StrideA = 4096;
-    ck::index_t StrideB = 4096;
-    ck::index_t StrideC = 4096;
-
-    if(argc == 1)
-    {
-        // do nothing
-    }
-    else if(argc == 4)
-    {
-        do_verification = std::stoi(argv[1]);
-        init_method     = std::stoi(argv[2]);
-        time_kernel     = std::stoi(argv[3]);
-    }
-    else if(argc == 10)
-    {
-        do_verification = std::stoi(argv[1]);
-        init_method     = std::stoi(argv[2]);
-        time_kernel     = std::stoi(argv[3]);
-
-        M = std::stoi(argv[4]);
-        N = std::stoi(argv[5]);
-        K = std::stoi(argv[6]);
-
-        StrideA = std::stoi(argv[7]);
-        StrideB = std::stoi(argv[8]);
-        StrideC = std::stoi(argv[9]);
-    }
-    else
-    {
-        printf("arg1: verification (0=no, 1=yes)\n");
-        printf("arg2: initialization (0=no init, 1=integer value, 2=decimal value)\n");
-        printf("arg3: time kernel (0=n0, 1=yes)\n");
-        printf("arg4 to 9: M (256x), N(128x), K(32x), StrideA, StrideB, StrideC\n");
-        exit(0);
-    }
-
-    auto f_host_tensor_descriptor =
-        [](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}));
-            }
-        };
-
-    Tensor<ADataType> a_m_k(f_host_tensor_descriptor(M, K, StrideA, ALayout{}));
-    Tensor<BDataType> b_k_n(f_host_tensor_descriptor(K, N, StrideB, BLayout{}));
-
-    Tensor<CDataType> c_m_n_host_result(f_host_tensor_descriptor(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> reduce0_m_host_result(
-        HostTensorDescriptor(std::vector<std::size_t>({static_cast<std::size_t>(M)})));
-    Tensor<ReduceDataType> reduce1_m_host_result(
-        HostTensorDescriptor(std::vector<std::size_t>({static_cast<std::size_t>(M)})));
-
-    Tensor<CDataType> c_m_n_device_result(f_host_tensor_descriptor(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> reduce0_m_device_result(
-        HostTensorDescriptor(std::vector<std::size_t>({static_cast<std::size_t>(M)})));
-    Tensor<ReduceDataType> reduce1_m_device_result(
-        HostTensorDescriptor(std::vector<std::size_t>({static_cast<std::size_t>(M)})));
-
-    std::cout << "a_m_k: " << a_m_k.mDesc << std::endl;
-    std::cout << "b_k_n: " << b_k_n.mDesc << std::endl;
-    std::cout << "c_m_n: " << c_m_n_host_result.mDesc << std::endl;
-    std::cout << "reduce0_m: " << reduce0_m_host_result.mDesc << std::endl;
-    std::cout << "reduce1_m: " << reduce1_m_host_result.mDesc << std::endl;
-
-    switch(init_method)
-    {
-    case 0: break;
-    case 1:
-        a_m_k.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
-        b_k_n.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
-        break;
-    default:
-        a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
-        b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
-        break;
-    }
-
-    DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpaceSize());
-    DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpaceSize());
-    DeviceMem c_device_buf(sizeof(CDataType) * c_m_n_device_result.mDesc.GetElementSpaceSize());
-    DeviceMem reduce0_device_buf(sizeof(ReduceDataType) *
-                                 reduce0_m_device_result.mDesc.GetElementSpaceSize());
-    DeviceMem reduce1_device_buf(sizeof(ReduceDataType) *
-                                 reduce1_m_device_result.mDesc.GetElementSpaceSize());
-
-    a_device_buf.ToDevice(a_m_k.mData.data());
-    b_device_buf.ToDevice(b_k_n.mData.data());
-
-    auto a_element_op                     = AElementOp{};
-    auto b_element_op                     = BElementOp{};
-    auto c_element_op                     = CElementOp{};
-    std::array<void*, 3> gemm_element_ops = {&a_element_op, &b_element_op, &c_element_op};
-
-    auto passthrough                            = UnaryIdenticElementOp{};
-    auto square                                 = UnarySquareElementOp{};
-    auto div                                    = UnaryDivElementOp{N};
-    std::array<void*, 2> reduce_in_element_ops  = {&passthrough, &square};
-    std::array<void*, 2> reduce_out_element_ops = {&div, &div};
-
-    std::array<void*, 2> p_reduces = {reduce0_device_buf.GetDeviceBuffer(),
-                                      reduce1_device_buf.GetDeviceBuffer()};
-
-    // do GEMM
-    auto gemm     = DeviceGemmReduceInstance{};
-    auto invoker  = gemm.MakeInvoker();
-    auto argument = gemm.MakeArgument(a_device_buf.GetDeviceBuffer(),
-                                      b_device_buf.GetDeviceBuffer(),
-                                      nullptr,
-                                      {},
-                                      c_device_buf.GetDeviceBuffer(),
-                                      p_reduces,
-                                      M,
-                                      N,
-                                      K,
-                                      StrideA,
-                                      StrideB,
-                                      StrideC,
-                                      {},
-                                      gemm_element_ops,
-                                      {},
-                                      reduce_in_element_ops,
-                                      reduce_out_element_ops);
-
-    if(!gemm.IsSupportedArgument(argument))
-    {
-        throw std::runtime_error(
-            "wrong! device_gemm with the specified compilation parameters does "
-            "not support this GEMM problem");
-    }
-
-    // init reducetion buffer to 0
-    reduce0_device_buf.SetZero();
-    reduce1_device_buf.SetZero();
-
-    // if time_kernel == true, kernel will run multiple times. This kernel use atomic-add so result
-    // will not be correct. need to set time_kernel = false for correctness test
-    invoker.Run(argument, StreamConfig{nullptr, false});
-    bool pass = true;
-
-    if(do_verification)
-    {
-        c_device_buf.FromDevice(c_m_n_device_result.mData.data());
-        reduce0_device_buf.FromDevice(reduce0_m_device_result.mData.data());
-        reduce1_device_buf.FromDevice(reduce1_m_device_result.mData.data());
-
-        auto ref_gemm    = ReferenceGemmInstance{};
-        auto ref_invoker = ref_gemm.MakeInvoker();
-
-        auto ref_argument = ref_gemm.MakeArgument(
-            a_m_k, b_k_n, c_m_n_host_result, a_element_op, b_element_op, c_element_op);
-
-        ref_invoker.Run(ref_argument);
-
-        auto reduce0_op = ReduceOp0{};
-        auto reduce1_op = ReduceOp1{};
-
-        for(int m = 0; m < M; ++m)
-        {
-            auto reduce0_acc = reduce0_op.GetIdentityValue<ReduceAccDataType>();
-            auto reduce1_acc = reduce1_op.GetIdentityValue<ReduceAccDataType>();
-
-            for(int n = 0; n < N; ++n)
-            {
-                auto c_val = ck::type_convert<ReduceAccDataType>(c_m_n_host_result(m, n));
-                ReduceAccDataType square_c_val;
-                square(square_c_val, c_val);
-
-                reduce0_op(reduce0_acc, c_val);
-                reduce1_op(reduce1_acc, square_c_val);
-            }
-
-            div(reduce0_acc, reduce0_acc);
-            div(reduce1_acc, reduce1_acc);
-            reduce0_m_host_result(m) = ck::type_convert<ReduceDataType>(reduce0_acc);
-            reduce1_m_host_result(m) = ck::type_convert<ReduceDataType>(reduce1_acc);
-        }
-
-        pass = ck::utils::check_err(c_m_n_device_result.mData,
-                                    c_m_n_host_result.mData,
-                                    "Error: Incorrect results c") &&
-               ck::utils::check_err(reduce0_m_device_result.mData,
-                                    reduce0_m_host_result.mData,
-                                    "Error: Incorrect results d0",
-                                    1e-4,
-                                    1e-5) &&
-               ck::utils::check_err(reduce1_m_device_result.mData,
-                                    reduce1_m_host_result.mData,
-                                    "Error: Incorrect results d1",
-                                    1e-3,
-                                    1e-5);
-    }
-
-    if(time_kernel)
-    {
-        float ave_time = invoker.Run(argument, StreamConfig{nullptr, true});
-
-        DumpGemmLayerNormPerf<ADataType, BDataType, CDataType, ReduceDataType>(ave_time, M, N, K);
-    }
-
-    return pass ? 0 : 1;
-}

example/21_gemm_layernorm/gemm_bias_relu_add_layernorm_xdl_fp16.cpp

@@ -9,7 +9,7 @@
 #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/device_gemm_bias_add_reduce_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/device/device_gemm_multiple_d_multiple_r_xdl_cshuffle.hpp"
 #include "ck/tensor_operation/gpu/device/device_5ary_elementwise.hpp"
 #include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
 
@@ -28,57 +28,64 @@ using F32 = float;
 using Row = ck::tensor_layout::gemm::RowMajor;
 using Col = ck::tensor_layout::gemm::ColumnMajor;
 
+// DataType
 using ADataType                = F16;
 using BDataType                = F16;
-using CDataType                = F16;
-using BiasDataType             = F32;
-using D0DataType               = F16;
 using GemmAccDataType          = F32;
+using CShuffleDataType         = F32;
+using D0DataType               = F16;
+using D1DataType               = F16;
+using DsDataType               = ck::Tuple<D0DataType, D1DataType>;
+using EDataType                = F16;
 using ReduceAccDataType        = F32;
-using ReduceDataType           = F32;
-using ReducePtrsGlobal         = ck::Tuple<ReduceDataType*, ReduceDataType*>;
+using R0DataType               = F32;
+using R1DataType               = F32;
+using RsDataType               = ck::Tuple<R0DataType, R1DataType>;
 using GammaDataType            = F16;
 using BetaDataType             = F16;
 using LayerNormOutDataType     = F16;
 using NormalizeComputeDataType = F32;
 
-using ALayout = ck::tensor_layout::gemm::RowMajor;
-using BLayout = ck::tensor_layout::gemm::ColumnMajor;
-using CLayout = ck::tensor_layout::gemm::RowMajor;
+// Layout
+using ALayout  = Row;
+using BLayout  = Col;
+using D1Layout = Row;
+using ELayout  = D1Layout;
 
+// Elementwise op
 using PassThrough  = ck::tensor_operation::element_wise::PassThrough;
+using AddReluAdd   = ck::tensor_operation::element_wise::AddReluAdd;
+using Square       = ck::tensor_operation::element_wise::UnarySquare;
+using Div          = ck::tensor_operation::element_wise::UnaryDivide;
 using AElementOp   = PassThrough;
 using BElementOp   = PassThrough;
-using CElementOp  = ck::tensor_operation::element_wise::Relu;
-using D0ElementOp = PassThrough;
-using ReduceSumOp = ck::reduce::Add;
-using ReduceOps   = ck::Tuple<ReduceSumOp, ReduceSumOp>;
+using CDEElementOp = AddReluAdd;
+using QsElementOp  = ck::Tuple<PassThrough, Square>;
+using RsElementOp  = ck::Tuple<Div, Div>;
 
-using UnaryIdenticElementOp = ck::tensor_operation::element_wise::PassThrough;
-using UnaryDivElementOp     = ck::tensor_operation::element_wise::UnaryDivide;
-using UnarySquareElementOp  = ck::tensor_operation::element_wise::UnarySquare;
-using ReduceInElementOps    = ck::Tuple<UnaryIdenticElementOp, UnarySquareElementOp>;
-using ReduceOutElementOps   = ck::Tuple<UnaryDivElementOp, UnaryDivElementOp>;
+// ReduceOp
+using R0ThreadReduceOp = ck::reduce::Add;
+using R1ThreadReduceOp = ck::reduce::Add;
+using RsThreadReduceOp = ck::Tuple<R0ThreadReduceOp, R1ThreadReduceOp>;
 
-using ReduceGlobalMemOps =
-    ck::InMemoryDataOperationEnumSequence<ck::InMemoryDataOperationEnum::AtomicAdd,
-                                          ck::InMemoryDataOperationEnum::AtomicAdd>;
+static constexpr auto R0GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+static constexpr auto R1GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+using RsGlobalReduceOp = ck::InMemoryDataOperationEnumSequence<R0GlobalReduceOp, R1GlobalReduceOp>;
 
-static constexpr auto GemmSpecialization =
-    ck::tensor_operation::device::GemmSpecialization::Default;
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::Default;
 
 // clang-format off
-using DeviceGemmBiasAddReduceInstance = ck::tensor_operation::device::DeviceGemmBiasAddReduce_Xdl_CShuffle
-//######| ALayout| BLayout| CLayout|AData| BData| CData|C0Data|C1Data|  GemmAcc| CShuffle| ReduceAcc|       ReduceData|           A|           B|           C|          C1|    Reduce|     ReduceInEleOp|      ReduceAccEleOp|              Reduce|               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| CBlockTransferClusterLengths|  CBlockTransfer|              CReduce| CReduceThreadLds2VGprCopy| CReduceThreadVgpr2GlobalCopy|
-//######|        |        |        | Type|  Type|  Type|  Type|  Type| DataType| DataType|  DataType|       Type Tuple| Elementwise| Elementwise| Elementwise| Elementwise| Operation|                  |                    |          MemoryData|     Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar|    ExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar|    ExtraN| MXdlPerWave| NXdlPerWave|            _MBlock_MPerBlock| ScalarPerVector| ThreadClusterLengths|     SrcDstScalarPerVector|        SrcDstScalarPerVector|
-//######|        |        |        |     |      |      |      |      |         |         |          |                 |   Operation|   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|            _NBlock_NPerBlock|      _NPerBlock| _MPerBlock_NPerBlock|                _NPerBlock|                   _MPerBlock|
-//######|        |        |        |     |      |      |      |      |         |         |          |                 |            |            |            |            |          |                  |                    |                    |                   |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                     |                          |                             |
-        <     Row,     Col,     Row,  F16,   F16,   F16,   F32,   F16,      F32,      F32,       F32, ReducePtrsGlobal,  AElementOp,  BElementOp,  CElementOp, D0ElementOp, ReduceOps,ReduceInElementOps, ReduceOutElementOps,  ReduceGlobalMemOps, GemmSpecialization,        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<1, 32, 1, 8>,               8,             S<64, 4>,                         4,                            1>;
+using DeviceOpInstance = ck::tensor_operation::device::DeviceGemmMultipleDMultipleR_Xdl_CShuffle
+//######| ALayout| BLayout| ELayout|     AData|     BData|     GemmAccData|         CShuffle|     DsData|     EData|     ReduceAccData|     RsData|           A|           B|          CDE|          Qs|          Rs|           Thread|           Global|           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|    CDRThreadTransfer|                  CDE|    RThreadTransfer|
+//######|        |        |        |      Type|      Type|            Type|         DataType|       Type|      Type|              Type|       Type| Elementwise| Elementwise|  Elementwise| Elementwise| Elementwise|           Reduce|           Reduce| 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|       ClusterLengths| ReduceThreadTransfer| DstScalarPerVector|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |   Operation|   Operation|    Operation|   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| _MPerBlock_NPerBlock|      ScalarPerVector|         _MPerBlock|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |            |            |             |            |            |                 |                 |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                     |           _NPerBlock|                   |
+        < ALayout, BLayout, ELayout, ADataType, BDataType, GemmAccDataType, CShuffleDataType, DsDataType, EDataType, ReduceAccDataType, RsDataType,  AElementOp,  BElementOp, CDEElementOp, QsElementOp, RsElementOp, RsThreadReduceOp, RsGlobalReduceOp,    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<64, 4>,                    4,                  1>;
 // clang-format on
 
 using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
                                                                         BDataType,
-                                                                        CDataType,
+                                                                        EDataType,
                                                                         GemmAccDataType,
                                                                         AElementOp,
                                                                         BElementOp,
@@ -88,9 +95,9 @@ using NormalizeFunctor = ck::tensor_operation::element_wise::Normalize;
 
 // A:x, B:E[x], C:E[x^2], D:Gamma, E:Beta , F:y
 using DeviceNormalizeInstance =
-    ck::tensor_operation::device::Device5AryElementwise<CDataType,
-                                                        ReduceDataType,
-                                                        ReduceDataType,
+    ck::tensor_operation::device::Device5AryElementwise<EDataType,
+                                                        R0DataType,
+                                                        R1DataType,
                                                         GammaDataType,
                                                         BetaDataType,
                                                         LayerNormOutDataType,
@@ -124,41 +131,31 @@ auto f_host_tensor_descriptor2d =
         }
     };
 
-template <typename CDataType,
-          typename ReduceDataType,
-          typename AccDataType,
-          typename BiasDataType,
-          typename D0DataType,
-          typename A_functor,
-          typename B_functor,
-          typename C_functor,
-          typename C1_functor>
 void host_gemm_layernorm(Tensor<LayerNormOutDataType>& out_m_n,
                          const Tensor<ADataType>& a_m_k,
-                         const Tensor<ADataType>& b_k_n,
-                         const Tensor<BiasDataType>& bias_n,
-                         const Tensor<D0DataType>& c1_m_n,
+                         const Tensor<BDataType>& b_k_n,
+                         const Tensor<D0DataType>& bias_n,
+                         const Tensor<D1DataType>& d1_m_n,
                          const Tensor<GammaDataType>& gamma_n,
-                         const Tensor<GammaDataType>& beta_n,
-                         A_functor a_element_op,
-                         B_functor b_element_op,
-                         C_functor c_element_op,
-                         C1_functor c1_element_op,
+                         const Tensor<BetaDataType>& beta_n,
+                         AElementOp a_element_op,
+                         BElementOp b_element_op,
+                         CDEElementOp cde_element_op,
                          int M,
                          int N)
 {
 
-    int StrideC = N;
-    Tensor<CDataType> c_m_n(f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> mean_m(f_host_tensor_descriptor1d(M, 1));
-    Tensor<ReduceDataType> meanSquare_m(f_host_tensor_descriptor1d(M, 1));
-    auto averageOpInst = UnaryDivElementOp{N};
+    int StrideE = N;
+    Tensor<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> mean_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<R1DataType> meanSquare_m(f_host_tensor_descriptor1d(M, 1));
+    auto averageOpInst = Div{N};
 
     auto ref_gemm    = ReferenceGemmInstance{};
     auto ref_invoker = ref_gemm.MakeInvoker();
 
     auto ref_argument =
-        ref_gemm.MakeArgument(a_m_k, b_k_n, c_m_n, a_element_op, b_element_op, PassThrough{});
+        ref_gemm.MakeArgument(a_m_k, b_k_n, e_m_n, a_element_op, b_element_op, PassThrough{});
 
     ref_invoker.Run(ref_argument);
 
@@ -166,38 +163,32 @@ void host_gemm_layernorm(Tensor<LayerNormOutDataType>& out_m_n,
     for(int m = 0; m < M; ++m)
         for(int n = 0; n < N; ++n)
         {
-            AccDataType acc = ck::type_convert<AccDataType>(c_m_n(m, n)) +
-                              ck::type_convert<AccDataType>(bias_n(n));
-
-            AccDataType c1 = ck::type_convert<AccDataType>(c1_m_n(m, n));
-
-            c_element_op(acc, acc);
-            c1_element_op(c1, c1);
-            acc += c1;
-            c_m_n(m, n) = ck::type_convert<CDataType>(acc);
+            auto acc = ck::type_convert<GemmAccDataType>(e_m_n(m, n));
+            cde_element_op(e_m_n(m, n), acc, bias_n(n), d1_m_n(m, n));
         }
 
     // reduce_mean and reduce_square_mean
-    auto reduceSumOpInst = ReduceSumOp{};
+    auto r0Op = R0ThreadReduceOp{};
+    auto r1Op = R1ThreadReduceOp{};
     for(int m = 0; m < M; ++m)
     {
-        auto mean_acc        = reduceSumOpInst.GetIdentityValue<AccDataType>();
-        auto square_mean_acc = reduceSumOpInst.GetIdentityValue<AccDataType>();
+        auto mean_acc        = r0Op.GetIdentityValue<ReduceAccDataType>();
+        auto mean_square_acc = r1Op.GetIdentityValue<ReduceAccDataType>();
 
         for(int n = 0; n < N; ++n)
         {
-            AccDataType c_val        = ck::type_convert<AccDataType>(c_m_n(m, n));
-            AccDataType square_c_val = 0;
-            UnarySquareElementOp{}(square_c_val, c_val);
+            auto e_val                     = ck::type_convert<ReduceAccDataType>(e_m_n(m, n));
+            ReduceAccDataType square_e_val = 0;
+            Square{}(square_e_val, e_val);
 
-            reduceSumOpInst(mean_acc, c_val);
-            reduceSumOpInst(square_mean_acc, square_c_val);
+            r0Op(mean_acc, e_val);
+            r1Op(mean_square_acc, square_e_val);
         }
 
         averageOpInst(mean_acc, mean_acc);
-        averageOpInst(square_mean_acc, square_mean_acc);
-        mean_m(m)       = ck::type_convert<ReduceDataType>(mean_acc);
-        meanSquare_m(m) = ck::type_convert<ReduceDataType>(square_mean_acc);
+        averageOpInst(mean_square_acc, mean_square_acc);
+        mean_m(m)       = ck::type_convert<R0DataType>(mean_acc);
+        meanSquare_m(m) = ck::type_convert<R1DataType>(mean_square_acc);
     }
 
     // LayerNorm
@@ -206,24 +197,25 @@ void host_gemm_layernorm(Tensor<LayerNormOutDataType>& out_m_n,
     {
         for(int n = 0; n < N; ++n)
         {
-            AccDataType out_acc = 0;
+            NormalizeComputeDataType out_acc = 0;
             layerNormInst(out_acc,
-                          ck::type_convert<AccDataType>(c_m_n(m, n)),
-                          ck::type_convert<AccDataType>(mean_m(m)),
-                          ck::type_convert<AccDataType>(meanSquare_m(m)),
-                          ck::type_convert<AccDataType>(gamma_n(n)),
-                          ck::type_convert<AccDataType>(beta_n(n)));
-            out_m_n(m, n) = ck::type_convert<ReduceDataType>(out_acc);
+                          ck::type_convert<NormalizeComputeDataType>(e_m_n(m, n)),
+                          ck::type_convert<NormalizeComputeDataType>(mean_m(m)),
+                          ck::type_convert<NormalizeComputeDataType>(meanSquare_m(m)),
+                          ck::type_convert<NormalizeComputeDataType>(gamma_n(n)),
+                          ck::type_convert<NormalizeComputeDataType>(beta_n(n)));
+            out_m_n(m, n) = ck::type_convert<LayerNormOutDataType>(out_acc);
         }
     }
 }
 
 template <typename ADataType,
           typename BDataType,
-          typename CDataType,
-          typename BiasDataType,
+          typename EDataType,
           typename D0DataType,
-          typename ReduceDataType,
+          typename D1DataType,
+          typename R0DataType,
+          typename R1DataType,
           typename GammaDataType,
           typename BetaDataType,
           typename NormalizeDataType>
@@ -231,12 +223,12 @@ void DumpGemmLayerNormPerf(float gemm_reduce_time, float normalize_time, int M,
 {
     std::size_t gemm_flop     = std::size_t(2) * M * N * K + std::size_t(2) * M * N;
     std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
-                                sizeof(CDataType) * M * N + sizeof(BiasDataType) * M * N +
-                                sizeof(D0DataType) * M * N + sizeof(ReduceDataType) * M +
-                                sizeof(ReduceDataType) * M;
+                                sizeof(EDataType) * M * N + sizeof(D0DataType) * M * N +
+                                sizeof(D0DataType) * M * N + sizeof(R0DataType) * M +
+                                sizeof(R1DataType) * M;
 
-    std::size_t normalize_num_byte = sizeof(CDataType) * M * N + sizeof(ReduceDataType) * M +
-                                     sizeof(ReduceDataType) * M + sizeof(GammaDataType) * N +
+    std::size_t normalize_num_byte = sizeof(EDataType) * M * N + sizeof(R0DataType) * M +
+                                     sizeof(R1DataType) * M + sizeof(GammaDataType) * N +
                                      sizeof(BetaDataType) * N + sizeof(NormalizeDataType) * M * N;
 
     float tflops               = static_cast<float>(gemm_flop) / 1.E9 / gemm_reduce_time;
@@ -259,37 +251,37 @@ int main()
 
     ck::index_t StrideA  = 1024;
     ck::index_t StrideB  = 1024;
-    ck::index_t StrideC  = 1024;
-    ck::index_t StrideD0 = 1024;
+    ck::index_t StrideD0 = 0;
+    ck::index_t StrideD1 = 1024;
+    ck::index_t StrideE  = 1024;
 
     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<CDataType> c_m_n(f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
-    Tensor<BiasDataType> bias_n(f_host_tensor_descriptor1d(N, 1));
-    Tensor<D0DataType> c1_m_n(f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> reduceMean_m(f_host_tensor_descriptor1d(M, 1));
-    Tensor<ReduceDataType> reduceMeanSquare_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<D0DataType> bias_n(f_host_tensor_descriptor1d(N, 1));
+    Tensor<D1DataType> d1_m_n(f_host_tensor_descriptor2d(M, N, StrideD1, ELayout{}));
+    Tensor<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> r0_Mean_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<R1DataType> r1_MeanSquare_m(f_host_tensor_descriptor1d(M, 1));
     Tensor<GammaDataType> gamma_n(f_host_tensor_descriptor1d(N, 1));
     Tensor<BetaDataType> beta_n(f_host_tensor_descriptor1d(N, 1));
     Tensor<LayerNormOutDataType> layerNorm_m_n(
-        f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
+        f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
 
     a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{-1, 1});
     b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-1, 1});
-    bias_n.GenerateTensorValue(GeneratorTensor_3<BiasDataType>{-1, 1});
-    c1_m_n.GenerateTensorValue(GeneratorTensor_3<D0DataType>{-5, 5});
+    bias_n.GenerateTensorValue(GeneratorTensor_3<D0DataType>{-1, 1});
+    d1_m_n.GenerateTensorValue(GeneratorTensor_3<D1DataType>{-5, 5});
     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 c_device_buf(sizeof(CDataType) * c_m_n.mDesc.GetElementSpaceSize());
-    DeviceMem bias_device_buf(sizeof(BiasDataType) * bias_n.mDesc.GetElementSpaceSize());
-    DeviceMem d0_device_buf(sizeof(D0DataType) * c1_m_n.mDesc.GetElementSpaceSize());
-    DeviceMem reduceMean_device_buf(sizeof(ReduceDataType) *
-                                    reduceMean_m.mDesc.GetElementSpaceSize());
-    DeviceMem reduceMeanSquare_device_buf(sizeof(ReduceDataType) *
-                                          reduceMeanSquare_m.mDesc.GetElementSpaceSize());
+    DeviceMem bias_device_buf(sizeof(D0DataType) * bias_n.mDesc.GetElementSpaceSize());
+    DeviceMem d1_device_buf(sizeof(D1DataType) * d1_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem r0_Mean_device_buf(sizeof(R0DataType) * r0_Mean_m.mDesc.GetElementSpaceSize());
+    DeviceMem r1_MeanSquare_device_buf(sizeof(R1DataType) *
+                                       r1_MeanSquare_m.mDesc.GetElementSpaceSize());
     DeviceMem gamma_device_buf(sizeof(GammaDataType) * gamma_n.mDesc.GetElementSpaceSize());
     DeviceMem beta_device_buf(sizeof(BetaDataType) * beta_n.mDesc.GetElementSpaceSize());
     DeviceMem layerNorm_device_buf(sizeof(LayerNormOutDataType) *
@@ -298,60 +290,51 @@ int main()
     a_device_buf.ToDevice(a_m_k.mData.data());
     b_device_buf.ToDevice(b_k_n.mData.data());
     bias_device_buf.ToDevice(bias_n.mData.data());
-    d0_device_buf.ToDevice(c1_m_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 c_element_op                     = CElementOp{};
-    auto d_element_op                     = D0ElementOp{};
-    std::array<void*, 3> gemm_element_ops = {&a_element_op, &b_element_op, &c_element_op};
+    auto cde_element_op = CDEElementOp{};
+    auto qs_element_op  = QsElementOp{};
+    auto rs_element_op  = RsElementOp{N, N};
 
-    auto passthrough                            = UnaryIdenticElementOp{};
-    auto square                                 = UnarySquareElementOp{};
-    auto div                                    = UnaryDivElementOp{N};
-    std::array<void*, 2> reduce_in_element_ops  = {&passthrough, &square};
-    std::array<void*, 2> reduce_out_element_ops = {&div, &div};
-
-    std::array<void*, 2> p_reduces = {reduceMean_device_buf.GetDeviceBuffer(),
-                                      reduceMeanSquare_device_buf.GetDeviceBuffer()};
-
-    // Prepare GEMM, reduce_mean, reduce_mean_square
-    auto gemmReduce          = DeviceGemmBiasAddReduceInstance{};
+    // Prepare GEMM, mean, mean_square
+    auto gemmReduce          = DeviceOpInstance{};
     auto gemmReduce_invoker  = gemmReduce.MakeInvoker();
-    auto gemmReduce_argument = gemmReduce.MakeArgument(a_device_buf.GetDeviceBuffer(),
+    auto gemmReduce_argument = gemmReduce.MakeArgument(
+        a_device_buf.GetDeviceBuffer(),
         b_device_buf.GetDeviceBuffer(),
-                                                       bias_device_buf.GetDeviceBuffer(),
-                                                       {d0_device_buf.GetDeviceBuffer()},
-                                                       c_device_buf.GetDeviceBuffer(),
-                                                       p_reduces,
+        {bias_device_buf.GetDeviceBuffer(), d1_device_buf.GetDeviceBuffer()},
+        e_device_buf.GetDeviceBuffer(),
+        {r0_Mean_device_buf.GetDeviceBuffer(), r1_MeanSquare_device_buf.GetDeviceBuffer()},
         M,
         N,
         K,
         StrideA,
         StrideB,
-                                                       StrideC,
-                                                       {StrideD0},
-                                                       gemm_element_ops,
-                                                       {&d_element_op},
-                                                       reduce_in_element_ops,
-                                                       reduce_out_element_ops);
+        {StrideD0, StrideD1},
+        StrideE,
+        a_element_op,
+        b_element_op,
+        cde_element_op,
+        qs_element_op,
+        rs_element_op);
 
     if(!gemmReduce.IsSupportedArgument(gemmReduce_argument))
     {
-        throw std::runtime_error(
-            "wrong! device_gemm with the specified compilation parameters does "
-            "not support this GEMM problem");
+        throw std::runtime_error("wrong! this device_op instance does not support this problem");
     }
 
-    reduceMean_device_buf.SetZero();
-    reduceMeanSquare_device_buf.SetZero();
+    // init reducetion buffer to 0
+    r0_Mean_device_buf.SetZero();
+    r1_MeanSquare_device_buf.SetZero();
 
     // Prepare LayerNorm
-    std::array<const void*, 5> input = {c_device_buf.GetDeviceBuffer(),
-                                        reduceMean_device_buf.GetDeviceBuffer(),
-                                        reduceMeanSquare_device_buf.GetDeviceBuffer(),
+    std::array<const void*, 5> input = {e_device_buf.GetDeviceBuffer(),
+                                        r0_Mean_device_buf.GetDeviceBuffer(),
+                                        r1_MeanSquare_device_buf.GetDeviceBuffer(),
                                         gamma_device_buf.GetDeviceBuffer(),
                                         beta_device_buf.GetDeviceBuffer()};
     std::array<void*, 1> output      = {layerNorm_device_buf.GetDeviceBuffer()};
@@ -361,12 +344,12 @@ int main()
     auto normalize_argument = normalize.MakeArgument(input,
                                                      output,
                                                      {M, N},
-                                                     {StrideC, 1},
+                                                     {StrideE, 1},
                                                      {1, 0},
                                                      {1, 0},
                                                      {0, 1},
                                                      {0, 1},
-                                                     {StrideC, 1},
+                                                     {StrideE, 1},
                                                      NormalizeFunctor{});
 
     if(!normalize.IsSupportedArgument(normalize_argument))
@@ -383,19 +366,18 @@ int main()
     {
         // verification
         Tensor<LayerNormOutDataType> host_layerNorm_m_n(
-            f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
+            f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
 
-        host_gemm_layernorm<CDataType, ReduceDataType, ReduceAccDataType>(host_layerNorm_m_n,
+        host_gemm_layernorm(host_layerNorm_m_n,
                             a_m_k,
                             b_k_n,
                             bias_n,
-                                                                          c1_m_n,
+                            d1_m_n,
                             gamma_n,
                             beta_n,
                             a_element_op,
                             b_element_op,
-                                                                          c_element_op,
-                                                                          d_element_op,
+                            cde_element_op,
                             M,
                             N);
 
@@ -419,10 +401,11 @@ int main()
         if(time_kernel)
             DumpGemmLayerNormPerf<ADataType,
                                   BDataType,
-                                  CDataType,
-                                  BiasDataType,
+                                  EDataType,
                                   D0DataType,
-                                  ReduceDataType,
+                                  D1DataType,
+                                  R0DataType,
+                                  R1DataType,
                                   GammaDataType,
                                   BetaDataType,
                                   LayerNormOutDataType>(

example/21_gemm_layernorm/gemm_layernorm_xdl_fp16.cpp

@@ -9,7 +9,7 @@
 #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/device_gemm_reduce_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/device/device_gemm_multiple_d_multiple_r_xdl_cshuffle.hpp"
 #include "ck/tensor_operation/gpu/device/device_5ary_elementwise.hpp"
 #include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
 
@@ -28,65 +28,73 @@ using F32 = float;
 using Row = ck::tensor_layout::gemm::RowMajor;
 using Col = ck::tensor_layout::gemm::ColumnMajor;
 
+// DataType
 using ADataType                = F16;
 using BDataType                = F16;
-using CDataType                = F16;
 using GemmAccDataType          = F32;
+using CShuffleDataType         = F32;
+using DsDataType               = ck::Tuple<>;
+using EDataType                = F16;
 using ReduceAccDataType        = F32;
-using ReduceDataType           = F32;
-using ReducePtrsGlobal         = ck::Tuple<ReduceDataType*, ReduceDataType*>;
+using R0DataType               = F32;
+using R1DataType               = F32;
+using RsDataType               = ck::Tuple<R0DataType, R1DataType>;
 using GammaDataType            = F16;
 using BetaDataType             = F16;
 using LayerNormOutDataType     = F16;
 using NormalizeComputeDataType = F32;
 
-using ALayout = ck::tensor_layout::gemm::RowMajor;
-using BLayout = ck::tensor_layout::gemm::ColumnMajor;
-using CLayout = ck::tensor_layout::gemm::RowMajor;
-
-using AElementOp  = ck::tensor_operation::element_wise::PassThrough;
-using BElementOp  = ck::tensor_operation::element_wise::PassThrough;
-using CElementOp  = ck::tensor_operation::element_wise::PassThrough;
-using ReduceSumOp = ck::reduce::Add;
-using ReduceOps   = ck::Tuple<ReduceSumOp, ReduceSumOp>;
-
-using UnaryIdenticElementOp = ck::tensor_operation::element_wise::PassThrough;
-using UnaryDivElementOp     = ck::tensor_operation::element_wise::UnaryDivide;
-using UnarySquareElementOp  = ck::tensor_operation::element_wise::UnarySquare;
-using ReduceInElementOps    = ck::Tuple<UnaryIdenticElementOp, UnarySquareElementOp>;
-using ReduceOutElementOps   = ck::Tuple<UnaryDivElementOp, UnaryDivElementOp>;
-
-using ReduceGlobalMemOps =
-    ck::InMemoryDataOperationEnumSequence<ck::InMemoryDataOperationEnum::AtomicAdd,
-                                          ck::InMemoryDataOperationEnum::AtomicAdd>;
-
-static constexpr auto GemmSpecialization =
-    ck::tensor_operation::device::GemmSpecialization::Default;
+// Layout
+using ALayout  = Row;
+using BLayout  = Col;
+using D1Layout = Row;
+using ELayout  = D1Layout;
+
+// Elementwise op
+using PassThrough  = ck::tensor_operation::element_wise::PassThrough;
+using Square       = ck::tensor_operation::element_wise::UnarySquare;
+using Div          = ck::tensor_operation::element_wise::UnaryDivide;
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = PassThrough;
+using QsElementOp  = ck::Tuple<PassThrough, Square>;
+using RsElementOp  = ck::Tuple<Div, Div>;
+
+// ReduceOp
+using R0ThreadReduceOp = ck::reduce::Add;
+using R1ThreadReduceOp = ck::reduce::Add;
+using RsThreadReduceOp = ck::Tuple<R0ThreadReduceOp, R1ThreadReduceOp>;
+
+static constexpr auto R0GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+static constexpr auto R1GlobalReduceOp = ck::InMemoryDataOperationEnum::AtomicAdd;
+using RsGlobalReduceOp = ck::InMemoryDataOperationEnumSequence<R0GlobalReduceOp, R1GlobalReduceOp>;
+
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::Default;
 
 // clang-format off
-using DeviceGemmReduceInstance = ck::tensor_operation::device::DeviceGemmReduce_Xdl_CShuffle
-//######| ALayout| BLayout| CLayout|AData| BData| CData|  GemmAcc| CShuffle| ReduceAcc|        ReduceData|           A|           B|           C|    Reduce|     ReduceInEleOp|      ReduceAccEleOp|             Reduce|               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| CBlockTransferClusterLengths|  CBlockTransfer|              CReduce| CReduceThreadLds2VGprCopy| CReduceThreadVgpr2GlobalCopy|
-//######|        |        |        | Type|  Type|  Type| DataType| DataType|  DataType|        Type Tuple| Elementwise| Elementwise| Elementwise| Operation|                  |                    |         MemoryData|     Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar|    ExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar|    ExtraN| MXdlPerWave| NXdlPerWave|            _MBlock_MPerBlock| ScalarPerVector| ThreadClusterLengths|     SrcDstScalarPerVector|        SrcDstScalarPerVector|
-//######|        |        |        |     |      |      |         |         |          |                  |   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|            _NBlock_NPerBlock|      _NPerBlock| _MPerBlock_NPerBlock|                _NPerBlock|                   _MPerBlock|
-//######|        |        |        |     |      |      |         |         |          |                  |            |            |            |          |                  |                    |                   |                   |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                     |                          |                             |
-        <     Row,     Col,     Row,  F16,   F16,   F16,      F32,      F32,       F32,  ReducePtrsGlobal,  AElementOp,  BElementOp,  CElementOp, ReduceOps,ReduceInElementOps, ReduceOutElementOps, ReduceGlobalMemOps, GemmSpecialization,        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<1, 32, 1, 8>,               8,             S<64, 4>,                         4,                            1>;
+using DeviceOpInstance = ck::tensor_operation::device::DeviceGemmMultipleDMultipleR_Xdl_CShuffle
+//######| ALayout| BLayout| ELayout|     AData|     BData|     GemmAccData|         CShuffle|     DsData|     EData|     ReduceAccData|     RsData|           A|           B|          CDE|          Qs|          Rs|           Thread|           Global|           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|    CDRThreadTransfer|                  CDE|    RThreadTransfer|
+//######|        |        |        |      Type|      Type|            Type|         DataType|       Type|      Type|              Type|       Type| Elementwise| Elementwise|  Elementwise| Elementwise| Elementwise|           Reduce|           Reduce| 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|       ClusterLengths| ReduceThreadTransfer| DstScalarPerVector|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |   Operation|   Operation|    Operation|   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| _MPerBlock_NPerBlock|      ScalarPerVector|         _MPerBlock|
+//######|        |        |        |          |          |                |                 |           |          |                  |           |            |            |             |            |            |                 |                 |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                     |           _NPerBlock|                   |
+        < ALayout, BLayout, ELayout, ADataType, BDataType, GemmAccDataType, CShuffleDataType, DsDataType, EDataType, ReduceAccDataType, RsDataType,  AElementOp,  BElementOp, CDEElementOp, QsElementOp, RsElementOp, RsThreadReduceOp, RsGlobalReduceOp,    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<64, 4>,                    4,                  1>;
 // clang-format on
 
 using ReferenceGemmInstance = ck::tensor_operation::host::ReferenceGemm<ADataType,
                                                                         BDataType,
-                                                                        CDataType,
+                                                                        EDataType,
                                                                         GemmAccDataType,
                                                                         AElementOp,
                                                                         BElementOp,
-                                                                        CElementOp>;
+                                                                        PassThrough>;
 
 using NormalizeFunctor = ck::tensor_operation::element_wise::Normalize;
 
 // A:x, B:E[x], C:E[x^2], D:Gamma, E:Beta , F:y
 using DeviceNormalizeInstance =
-    ck::tensor_operation::device::Device5AryElementwise<CDataType,
-                                                        ReduceDataType,
-                                                        ReduceDataType,
+    ck::tensor_operation::device::Device5AryElementwise<EDataType,
+                                                        R0DataType,
+                                                        R1DataType,
                                                         GammaDataType,
                                                         BetaDataType,
                                                         LayerNormOutDataType,
@@ -120,60 +128,54 @@ auto f_host_tensor_descriptor2d =
         }
     };
 
-template <typename CDataType,
-          typename ReduceDataType,
-          typename A_functor,
-          typename B_functor,
-          typename C_functor>
 void host_gemm_layernorm(Tensor<LayerNormOutDataType>& out_m_n,
                          const Tensor<ADataType>& a_m_k,
-                         const Tensor<ADataType>& b_k_n,
+                         const Tensor<BDataType>& b_k_n,
                          const Tensor<GammaDataType>& gamma_n,
                          const Tensor<BetaDataType>& beta_n,
-                         A_functor a_element_op,
-                         B_functor b_element_op,
-                         C_functor c_element_op,
+                         AElementOp a_element_op,
+                         BElementOp b_element_op,
+                         CDEElementOp c_element_op,
                          int M,
                          int N)
 {
-    using out_type = ck::remove_reference_t<decltype(out_m_n(0, 0))>;
 
-    int StrideC = N;
-    Tensor<CDataType> c_m_n(f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> mean_m(f_host_tensor_descriptor1d(M, 1));
-    Tensor<ReduceDataType> meanSquare_m(f_host_tensor_descriptor1d(M, 1));
-    auto averageOpInst = UnaryDivElementOp{N};
+    int StrideE = N;
+    Tensor<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> mean_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<R1DataType> meanSquare_m(f_host_tensor_descriptor1d(M, 1));
+    auto averageOpInst = Div{N};
 
     auto ref_gemm    = ReferenceGemmInstance{};
     auto ref_invoker = ref_gemm.MakeInvoker();
 
     auto ref_argument =
-        ref_gemm.MakeArgument(a_m_k, b_k_n, c_m_n, a_element_op, b_element_op, c_element_op);
+        ref_gemm.MakeArgument(a_m_k, b_k_n, e_m_n, a_element_op, b_element_op, c_element_op);
 
     ref_invoker.Run(ref_argument);
 
     // reduce_mean and reduce_square_mean
-    auto reduceSumOpInst = ReduceSumOp{};
+    auto r0Op = R0ThreadReduceOp{};
+    auto r1Op = R1ThreadReduceOp{};
     for(int m = 0; m < M; ++m)
     {
-        auto mean_acc        = reduceSumOpInst.GetIdentityValue<ReduceAccDataType>();
-        auto square_mean_acc = reduceSumOpInst.GetIdentityValue<ReduceAccDataType>();
+        auto mean_acc        = r0Op.GetIdentityValue<ReduceAccDataType>();
+        auto mean_square_acc = r1Op.GetIdentityValue<ReduceAccDataType>();
 
         for(int n = 0; n < N; ++n)
         {
-            auto c_val        = ck::type_convert<ReduceAccDataType>(c_m_n(m, n));
-            auto square_c_val = reduceSumOpInst.GetIdentityValue<ReduceAccDataType>();
-
-            UnarySquareElementOp{}(square_c_val, c_val);
+            auto e_val                     = ck::type_convert<ReduceAccDataType>(e_m_n(m, n));
+            ReduceAccDataType square_e_val = 0;
+            Square{}(square_e_val, e_val);
 
-            reduceSumOpInst(mean_acc, c_val);
-            reduceSumOpInst(square_mean_acc, square_c_val);
+            r0Op(mean_acc, e_val);
+            r1Op(mean_square_acc, square_e_val);
         }
 
         averageOpInst(mean_acc, mean_acc);
-        averageOpInst(square_mean_acc, square_mean_acc);
-        mean_m(m)       = ck::type_convert<ReduceDataType>(mean_acc);
-        meanSquare_m(m) = ck::type_convert<ReduceDataType>(square_mean_acc);
+        averageOpInst(mean_square_acc, mean_square_acc);
+        mean_m(m)       = ck::type_convert<R0DataType>(mean_acc);
+        meanSquare_m(m) = ck::type_convert<R1DataType>(mean_square_acc);
     }
 
     // LayerNorm
@@ -182,22 +184,23 @@ void host_gemm_layernorm(Tensor<LayerNormOutDataType>& out_m_n,
     {
         for(int n = 0; n < N; ++n)
         {
-            float out_f32 = 0;
-            layerNormInst(out_f32,
-                          static_cast<float>(c_m_n(m, n)),
-                          static_cast<float>(mean_m(m)),
-                          static_cast<float>(meanSquare_m(m)),
-                          static_cast<float>(gamma_n(n)),
-                          static_cast<float>(beta_n(n)));
-            out_m_n(m, n) = static_cast<out_type>(out_f32);
+            NormalizeComputeDataType out_acc = 0;
+            layerNormInst(out_acc,
+                          ck::type_convert<NormalizeComputeDataType>(e_m_n(m, n)),
+                          ck::type_convert<NormalizeComputeDataType>(mean_m(m)),
+                          ck::type_convert<NormalizeComputeDataType>(meanSquare_m(m)),
+                          ck::type_convert<NormalizeComputeDataType>(gamma_n(n)),
+                          ck::type_convert<NormalizeComputeDataType>(beta_n(n)));
+            out_m_n(m, n) = ck::type_convert<LayerNormOutDataType>(out_acc);
         }
     }
 }
 
 template <typename ADataType,
           typename BDataType,
-          typename CDataType,
-          typename ReduceDataType,
+          typename EDataType,
+          typename R0DataType,
+          typename R1DataType,
           typename GammaDataType,
           typename BetaDataType,
           typename NormalizeDataType>
@@ -205,11 +208,11 @@ void DumpGemmLayerNormPerf(float gemm_reduce_time, float normalize_time, int M,
 {
     std::size_t gemm_flop     = std::size_t(2) * M * N * K;
     std::size_t gemm_num_byte = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
-                                sizeof(CDataType) * M * N + sizeof(ReduceDataType) * M +
-                                sizeof(ReduceDataType) * M;
+                                sizeof(EDataType) * M * N + sizeof(R0DataType) * M +
+                                sizeof(R1DataType) * M;
 
-    std::size_t normalize_num_btye = sizeof(CDataType) * M * N + sizeof(ReduceDataType) * M +
-                                     sizeof(ReduceDataType) * M + sizeof(GammaDataType) * N +
+    std::size_t normalize_num_btye = sizeof(EDataType) * M * N + sizeof(R0DataType) * M +
+                                     sizeof(R1DataType) * M + sizeof(GammaDataType) * N +
                                      sizeof(BetaDataType) * N + sizeof(NormalizeDataType) * M * N;
 
     float tflops               = static_cast<float>(gemm_flop) / 1.E9 / gemm_reduce_time;
@@ -232,17 +235,17 @@ int main()
 
     ck::index_t StrideA = 1024;
     ck::index_t StrideB = 1024;
-    ck::index_t StrideC = 1024;
+    ck::index_t StrideE = 1024;
 
     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<CDataType> c_m_n(f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
-    Tensor<ReduceDataType> reduceMean_m(f_host_tensor_descriptor1d(M, 1));
-    Tensor<ReduceDataType> reduceMeanSquare_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<EDataType> e_m_n(f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
+    Tensor<R0DataType> r0_Mean_m(f_host_tensor_descriptor1d(M, 1));
+    Tensor<R1DataType> r1_MeanSquare_m(f_host_tensor_descriptor1d(M, 1));
     Tensor<GammaDataType> gamma_n(f_host_tensor_descriptor1d(N, 1));
     Tensor<BetaDataType> beta_n(f_host_tensor_descriptor1d(N, 1));
     Tensor<LayerNormOutDataType> layerNorm_m_n(
-        f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
+        f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
 
     a_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{-1, 1});
     b_k_n.GenerateTensorValue(GeneratorTensor_3<BDataType>{-1, 1});
@@ -251,11 +254,10 @@ int main()
 
     DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpaceSize());
     DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpaceSize());
-    DeviceMem c_device_buf(sizeof(CDataType) * c_m_n.mDesc.GetElementSpaceSize());
-    DeviceMem reduceMean_device_buf(sizeof(ReduceDataType) *
-                                    reduceMean_m.mDesc.GetElementSpaceSize());
-    DeviceMem reduceMeanSquare_device_buf(sizeof(ReduceDataType) *
-                                          reduceMeanSquare_m.mDesc.GetElementSpaceSize());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_m_n.mDesc.GetElementSpaceSize());
+    DeviceMem r0_Mean_device_buf(sizeof(R0DataType) * r0_Mean_m.mDesc.GetElementSpaceSize());
+    DeviceMem r1_MeanSquare_device_buf(sizeof(R1DataType) *
+                                       r1_MeanSquare_m.mDesc.GetElementSpaceSize());
     DeviceMem gamma_device_buf(sizeof(GammaDataType) * gamma_n.mDesc.GetElementSpaceSize());
     DeviceMem beta_device_buf(sizeof(BetaDataType) * beta_n.mDesc.GetElementSpaceSize());
     DeviceMem layerNorm_device_buf(sizeof(LayerNormOutDataType) *
@@ -268,38 +270,31 @@ int main()
 
     auto a_element_op   = AElementOp{};
     auto b_element_op   = BElementOp{};
-    auto c_element_op                     = CElementOp{};
-    std::array<void*, 3> gemm_element_ops = {&a_element_op, &b_element_op, &c_element_op};
+    auto cde_element_op = CDEElementOp{};
+    auto qs_element_op  = QsElementOp{};
+    auto rs_element_op  = RsElementOp{N, N};
 
-    auto passthrough                            = UnaryIdenticElementOp{};
-    auto square                                 = UnarySquareElementOp{};
-    auto div                                    = UnaryDivElementOp{N};
-    std::array<void*, 2> reduce_in_element_ops  = {&passthrough, &square};
-    std::array<void*, 2> reduce_out_element_ops = {&div, &div};
-
-    std::array<void*, 2> p_reduces = {reduceMean_device_buf.GetDeviceBuffer(),
-                                      reduceMeanSquare_device_buf.GetDeviceBuffer()};
-
-    // Prepare GEMM, reduce_mean, reduce_mean_square
-    auto gemmReduce          = DeviceGemmReduceInstance{};
+    // Prepare GEMM, mean, mean_square
+    auto gemmReduce          = DeviceOpInstance{};
     auto gemmReduce_invoker  = gemmReduce.MakeInvoker();
-    auto gemmReduce_argument = gemmReduce.MakeArgument(a_device_buf.GetDeviceBuffer(),
+    auto gemmReduce_argument = gemmReduce.MakeArgument(
+        a_device_buf.GetDeviceBuffer(),
         b_device_buf.GetDeviceBuffer(),
-                                                       nullptr,
         {},
-                                                       c_device_buf.GetDeviceBuffer(),
-                                                       p_reduces,
+        e_device_buf.GetDeviceBuffer(),
+        {r0_Mean_device_buf.GetDeviceBuffer(), r1_MeanSquare_device_buf.GetDeviceBuffer()},
         M,
         N,
         K,
         StrideA,
         StrideB,
-                                                       StrideC,
-                                                       {},
-                                                       gemm_element_ops,
         {},
-                                                       reduce_in_element_ops,
-                                                       reduce_out_element_ops);
+        StrideE,
+        a_element_op,
+        b_element_op,
+        cde_element_op,
+        qs_element_op,
+        rs_element_op);
 
     if(!gemmReduce.IsSupportedArgument(gemmReduce_argument))
     {
@@ -308,13 +303,13 @@ int main()
             "not support this GEMM problem");
     }
 
-    reduceMean_device_buf.SetZero();
-    reduceMeanSquare_device_buf.SetZero();
+    r0_Mean_device_buf.SetZero();
+    r1_MeanSquare_device_buf.SetZero();
 
     // Prepare LayerNorm
-    std::array<const void*, 5> input = {c_device_buf.GetDeviceBuffer(),
-                                        reduceMean_device_buf.GetDeviceBuffer(),
-                                        reduceMeanSquare_device_buf.GetDeviceBuffer(),
+    std::array<const void*, 5> input = {e_device_buf.GetDeviceBuffer(),
+                                        r0_Mean_device_buf.GetDeviceBuffer(),
+                                        r1_MeanSquare_device_buf.GetDeviceBuffer(),
                                         gamma_device_buf.GetDeviceBuffer(),
                                         beta_device_buf.GetDeviceBuffer()};
     std::array<void*, 1> output      = {layerNorm_device_buf.GetDeviceBuffer()};
@@ -324,12 +319,12 @@ int main()
     auto normalize_argument = normalize.MakeArgument(input,
                                                      output,
                                                      {M, N},
-                                                     {StrideC, 1},
+                                                     {StrideE, 1},
                                                      {1, 0},
                                                      {1, 0},
                                                      {0, 1},
                                                      {0, 1},
-                                                     {StrideC, 1},
+                                                     {StrideE, 1},
                                                      NormalizeFunctor{});
 
     if(!normalize.IsSupportedArgument(normalize_argument))
@@ -346,16 +341,16 @@ int main()
     {
         // verification
         Tensor<LayerNormOutDataType> host_layerNorm_m_n(
-            f_host_tensor_descriptor2d(M, N, StrideC, CLayout{}));
+            f_host_tensor_descriptor2d(M, N, StrideE, ELayout{}));
 
-        host_gemm_layernorm<CDataType, ReduceDataType>(host_layerNorm_m_n,
+        host_gemm_layernorm(host_layerNorm_m_n,
                             a_m_k,
                             b_k_n,
                             gamma_n,
                             beta_n,
                             a_element_op,
                             b_element_op,
-                                                       c_element_op,
+                            cde_element_op,
                             M,
                             N);
 
@@ -379,8 +374,9 @@ int main()
         if(time_kernel)
             DumpGemmLayerNormPerf<ADataType,
                                   BDataType,
-                                  CDataType,
-                                  ReduceDataType,
+                                  EDataType,
+                                  R0DataType,
+                                  R1DataType,
                                   GammaDataType,
                                   BetaDataType,
                                   LayerNormOutDataType>(

example/CMakeLists.txt

@@ -30,7 +30,7 @@ add_subdirectory(12_reduce)
 add_subdirectory(13_pool2d_fwd)
 add_subdirectory(14_gemm_xdl_requant_relu_requant)
 add_subdirectory(15_grouped_gemm)
-add_subdirectory(16_gemm_reduce)
+add_subdirectory(16_gemm_multi_d_multi_reduces)
 add_subdirectory(17_convnd_bwd_data)
 add_subdirectory(18_batched_gemm_reduce)
 add_subdirectory(19_binary_elementwise)

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

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+
+#include "device_base.hpp"
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+// FIXME: DeviceGemmReduce type need to well define the problem
+template <typename ALayout,
+          typename BLayout,
+          typename DELayout,
+          typename ADataType,
+          typename BDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename RsDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename QsElementwiseOperation,
+          typename RsElementwiseOperation>
+struct DeviceGemmMultipleDMultipleR : public BaseOperator
+{
+    static constexpr index_t NumDTensor = DsDataType::Size();
+    static constexpr index_t NumRTensor = RsDataType::Size();
+
+    virtual std::unique_ptr<BaseArgument>
+    MakeArgumentPointer(const void* p_a,
+                        const void* p_b,
+                        std::array<const void*, NumDTensor> p_ds,
+                        void* p_e,
+                        std::array<void*, NumRTensor> p_rs,
+                        ck::index_t M,
+                        ck::index_t N,
+                        ck::index_t K,
+                        ck::index_t StrideA,
+                        ck::index_t StrideB,
+                        std::array<ck::index_t, NumDTensor> StrideDs,
+                        ck::index_t StrideE,
+                        AElementwiseOperation a_element_op,
+                        BElementwiseOperation b_element_op,
+                        CDEElementwiseOperation cde_element_op,
+                        QsElementwiseOperation qs_element_op,
+                        RsElementwiseOperation rs_element_op) = 0;
+
+    virtual std::unique_ptr<BaseInvoker> MakeInvokerPointer() = 0;
+};
+
+template <typename ALayout,
+          typename BLayout,
+          typename DELayout,
+          typename ADataType,
+          typename BDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename RsDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename QsElementwiseOperation,
+          typename RsElementwiseOperation>
+using DeviceGemmMultipleDMultipleRPtr =
+    std::unique_ptr<DeviceGemmMultipleDMultipleR<ALayout,
+                                                 BLayout,
+                                                 DELayout,
+                                                 ADataType,
+                                                 BDataType,
+                                                 DsDataType,
+                                                 EDataType,
+                                                 RsDataType,
+                                                 AElementwiseOperation,
+                                                 BElementwiseOperation,
+                                                 CDEElementwiseOperation,
+                                                 QsElementwiseOperation,
+                                                 RsElementwiseOperation>>;
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

include/ck/tensor_operation/gpu/device/device_gemm_multiple_d_multiple_r_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_multiple_r.hpp"
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/grid/gridwise_gemm_multiple_d_multiple_r_xdl_cshuffle.hpp"
+#include "ck/host_utility/device_prop.hpp"
+#include "ck/host_utility/kernel_launch.hpp"
+
+namespace ck {
+
+template <typename GridwiseGemm,
+          typename FloatAB,
+          typename FloatDsPointer,
+          typename FloatE,
+          typename FloatRsPointer,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename QsElementwiseOperation,
+          typename RsElementwiseOperation,
+          typename AGridDesc_AK0_M_AK1,
+          typename BGridDesc_BK0_N_BK1,
+          typename DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+          typename EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+          typename RsGridDescriptor_MBlock_MPerBlock,
+          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_multiple_r_xdl_cshuffle(
+            const FloatAB* __restrict__ p_a_grid,
+            const FloatAB* __restrict__ p_b_grid,
+            FloatDsPointer p_ds_grid,
+            FloatE* __restrict__ p_e_grid,
+            FloatRsPointer p_rs_grid,
+            const AElementwiseOperation a_element_op,
+            const BElementwiseOperation b_element_op,
+            const CDEElementwiseOperation cde_element_op,
+            const QsElementwiseOperation qs_element_op,
+            const RsElementwiseOperation rs_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 RsGridDescriptor_MBlock_MPerBlock rs_grid_desc_mblock_mperblock,
+            const Block2ETileMap block_2_etile_map)
+{
+#if(!defined(__HIP_DEVICE_COMPILE__) || defined(__gfx908__) || defined(__gfx90a__))
+    __shared__ char p_shared[GridwiseGemm::GetSharedMemoryNumberOfByte()];
+
+    GridwiseGemm::template Run<HasMainKBlockLoop>(p_a_grid,
+                                                  p_b_grid,
+                                                  p_ds_grid,
+                                                  p_e_grid,
+                                                  p_rs_grid,
+                                                  p_shared,
+                                                  a_element_op,
+                                                  b_element_op,
+                                                  cde_element_op,
+                                                  qs_element_op,
+                                                  rs_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,
+                                                  rs_grid_desc_mblock_mperblock,
+                                                  block_2_etile_map);
+#else
+    ignore = p_a_grid;
+    ignore = p_b_grid;
+    ignore = p_ds_grid;
+    ignore = p_e_grid;
+    ignore = p_rs_grid;
+    ignore = a_element_op;
+    ignore = b_element_op;
+    ignore = cde_element_op;
+    ignore = qs_element_op;
+    ignore = rs_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 = rs_grid_desc_mblock_mperblock;
+    ignore = block_2_etile_map;
+#endif
+}
+
+} // namespace ck
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+// GEMM:
+//   input : A[AK0, M, AK1]
+//   input : B[AK0, N, AK1]
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   output : R0[M], R1[M], ...
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+//   Q0 = reduce0(q_op0(E)), Q1 = reduce1(q_op0(E)), ...
+//   R0 = r_op0(Q0), R1 = r_op1(Q1), ...
+// Assume:
+//   D0, D1, ... and E have the same layout
+template <typename ALayout,
+          typename BLayout,
+          typename DELayout,
+          typename ADataType,
+          typename BDataType,
+          typename GemmAccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ReduceAccDataType,
+          typename RsDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename QsElementwiseOperation,
+          typename RsElementwiseOperation,
+          typename ThreadReduceOperations,
+          typename RsGlobalMemoryDataOperation,
+          GemmSpecialization GemmSpec,
+          index_t NumGemmKPrefetchStage,
+          index_t BlockSize,
+          index_t MPerBlock,
+          index_t NPerBlock,
+          index_t KPerBlock,
+          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 CDRThreadTransferClusterLengths_MPerBlock_NPerBlock,
+          index_t CDEReduceThreadTransferScalarPerVector_NPerBlock,
+          index_t RThreadTransferDstScalarPerVector_MPerBlock,
+          LoopScheduler LoopSched = make_default_loop_scheduler()>
+struct DeviceGemmMultipleDMultipleR_Xdl_CShuffle
+    : public DeviceGemmMultipleDMultipleR<ALayout,
+                                          BLayout,
+                                          DELayout,
+                                          ADataType,
+                                          BDataType,
+                                          DsDataType,
+                                          EDataType,
+                                          RsDataType,
+                                          AElementwiseOperation,
+                                          BElementwiseOperation,
+                                          CDEElementwiseOperation,
+                                          QsElementwiseOperation,
+                                          RsElementwiseOperation>
+{
+    using DeviceOp = DeviceGemmMultipleDMultipleR_Xdl_CShuffle;
+
+    static constexpr index_t NumDTensor = DsDataType::Size();
+    static constexpr index_t NumRTensor = RsDataType::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 auto MakeAGridDescriptor_AK0_M_AK1(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));
+            }
+        }();
+
+        const auto M = math::integer_divide_ceil(MRaw, MPerBlock) * MPerBlock;
+        const auto K = math::integer_divide_ceil(KRaw, KPerBlock) * KPerBlock;
+
+        const auto MPad = M - MRaw;
+        const auto KPad = K - KRaw;
+
+        if constexpr(GemmSpec == GemmSpecialization::MKPadding ||
+                     GemmSpec == GemmSpecialization::MNKPadding)
+        {
+            // pad both M and K
+            assert(K % AK1 == 0);
+
+            const auto AK0 = K / AK1;
+
+            const auto a_grid_desc_m_k =
+                transform_tensor_descriptor(a_grid_desc_mraw_kraw,
+                                            make_tuple(make_right_pad_transform(MRaw, MPad),
+                                                       make_right_pad_transform(KRaw, KPad)),
+                                            make_tuple(Sequence<0>{}, Sequence<1>{}),
+                                            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+            const auto a_grid_desc_ak0_m_ak1 =
+                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>{}));
+
+            return a_grid_desc_ak0_m_ak1;
+        }
+        else if constexpr(GemmSpec == GemmSpecialization::MPadding ||
+                          GemmSpec == GemmSpecialization::MNPadding)
+        {
+            // pad M, but not K
+            assert(KRaw % AK1 == 0);
+
+            const auto AK0 = KRaw / AK1;
+
+            const auto a_grid_desc_ak0_m_ak1 =
+                transform_tensor_descriptor(a_grid_desc_mraw_kraw,
+                                            make_tuple(make_unmerge_transform(make_tuple(AK0, AK1)),
+                                                       make_right_pad_transform(MRaw, MPad)),
+                                            make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                            make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+
+            return a_grid_desc_ak0_m_ak1;
+        }
+        else if constexpr(GemmSpec == GemmSpecialization::KPadding ||
+                          GemmSpec == GemmSpecialization::NKPadding)
+        {
+            // pad K, but not M
+            assert(K % AK1 == 0);
+
+            const auto AK0 = K / AK1;
+
+            const auto a_grid_desc_m_k = transform_tensor_descriptor(
+                a_grid_desc_mraw_kraw,
+                make_tuple(make_pass_through_transform(MRaw), make_right_pad_transform(KRaw, KPad)),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+            const auto a_grid_desc_ak0_m_ak1 =
+                transform_tensor_descriptor(a_grid_desc_m_k,
+                                            make_tuple(make_unmerge_transform(make_tuple(AK0, AK1)),
+                                                       make_pass_through_transform(MRaw)),
+                                            make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                            make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+
+            return a_grid_desc_ak0_m_ak1;
+        }
+        else
+        {
+            // not pad M or K
+            assert(KRaw % AK1 == 0);
+
+            const auto AK0 = KRaw / AK1;
+
+            const auto a_grid_desc_ak0_m_ak1 =
+                transform_tensor_descriptor(a_grid_desc_mraw_kraw,
+                                            make_tuple(make_unmerge_transform(make_tuple(AK0, AK1)),
+                                                       make_pass_through_transform(MRaw)),
+                                            make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                            make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+
+            return a_grid_desc_ak0_m_ak1;
+        }
+    }
+
+    static auto MakeBGridDescriptor_BK0_N_BK1(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));
+            }
+        }();
+
+        const auto N = math::integer_divide_ceil(NRaw, NPerBlock) * NPerBlock;
+        const auto K = math::integer_divide_ceil(KRaw, KPerBlock) * KPerBlock;
+
+        const auto NPad = N - NRaw;
+        const auto KPad = K - KRaw;
+
+        if constexpr(GemmSpec == GemmSpecialization::NKPadding ||
+                     GemmSpec == GemmSpecialization::MNKPadding)
+        {
+            // pad both N and K
+            assert(K % BK1 == 0);
+
+            const auto BK0 = K / BK1;
+
+            const auto b_grid_desc_n_k =
+                transform_tensor_descriptor(b_grid_desc_nraw_kraw,
+                                            make_tuple(make_right_pad_transform(NRaw, NPad),
+                                                       make_right_pad_transform(KRaw, KPad)),
+                                            make_tuple(Sequence<0>{}, Sequence<1>{}),
+                                            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+            const auto b_grid_desc_bk0_n_bk1 =
+                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>{}));
+
+            return b_grid_desc_bk0_n_bk1;
+        }
+        else if constexpr(GemmSpec == GemmSpecialization::NPadding ||
+                          GemmSpec == GemmSpecialization::MNPadding)
+        {
+            // pad N, but not K
+            assert(KRaw % BK1 == 0);
+
+            const auto BK0 = KRaw / BK1;
+
+            const auto b_grid_desc_bk0_n_bk1 =
+                transform_tensor_descriptor(b_grid_desc_nraw_kraw,
+                                            make_tuple(make_unmerge_transform(make_tuple(BK0, BK1)),
+                                                       make_right_pad_transform(NRaw, NPad)),
+                                            make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                            make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+
+            return b_grid_desc_bk0_n_bk1;
+        }
+        else if constexpr(GemmSpec == GemmSpecialization::KPadding ||
+                          GemmSpec == GemmSpecialization::MKPadding)
+        {
+            // pad K, but not N
+            assert(K % BK1 == 0);
+
+            const auto BK0 = K / BK1;
+
+            const auto b_grid_desc_n_k = transform_tensor_descriptor(
+                b_grid_desc_nraw_kraw,
+                make_tuple(make_pass_through_transform(NRaw), make_right_pad_transform(KRaw, KPad)),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+            const auto b_grid_desc_bk0_n_bk1 =
+                transform_tensor_descriptor(b_grid_desc_n_k,
+                                            make_tuple(make_unmerge_transform(make_tuple(BK0, BK1)),
+                                                       make_pass_through_transform(NRaw)),
+                                            make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                            make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+
+            return b_grid_desc_bk0_n_bk1;
+        }
+        else
+        {
+            // not pad N or K
+            assert(KRaw % BK1 == 0);
+
+            const auto BK0 = KRaw / BK1;
+
+            const auto b_grid_desc_bk0_n_bk1 =
+                transform_tensor_descriptor(b_grid_desc_nraw_kraw,
+                                            make_tuple(make_unmerge_transform(make_tuple(BK0, BK1)),
+                                                       make_pass_through_transform(NRaw)),
+                                            make_tuple(Sequence<1>{}, Sequence<0>{}),
+                                            make_tuple(Sequence<0, 2>{}, Sequence<1>{}));
+
+            return b_grid_desc_bk0_n_bk1;
+        }
+    }
+
+    static auto MakeEGridDescriptor_M_N(index_t MRaw, index_t NRaw, index_t StrideE)
+    {
+        const auto e_grid_desc_mraw_nraw = [&]() {
+            if constexpr(is_same<tensor_layout::gemm::RowMajor, DELayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(MRaw, NRaw),
+                                                    make_tuple(StrideE, I1));
+            }
+            else if constexpr(is_same<tensor_layout::gemm::ColumnMajor, DELayout>::value)
+            {
+                return make_naive_tensor_descriptor(make_tuple(MRaw, NRaw),
+                                                    make_tuple(I1, StrideE));
+            }
+        }();
+
+        const auto M = math::integer_divide_ceil(MRaw, MPerBlock) * MPerBlock;
+        const auto N = math::integer_divide_ceil(NRaw, NPerBlock) * NPerBlock;
+
+        const auto MPad = M - MRaw;
+        const auto NPad = N - NRaw;
+
+        if constexpr(GemmSpec == GemmSpecialization::MNPadding ||
+                     GemmSpec == GemmSpecialization::MNKPadding)
+        {
+            // pad M and N
+            return transform_tensor_descriptor(e_grid_desc_mraw_nraw,
+                                               make_tuple(make_right_pad_transform(MRaw, MPad),
+                                                          make_right_pad_transform(NRaw, NPad)),
+                                               make_tuple(Sequence<0>{}, Sequence<1>{}),
+                                               make_tuple(Sequence<0>{}, Sequence<1>{}));
+        }
+        else if constexpr(GemmSpec == GemmSpecialization::MPadding ||
+                          GemmSpec == GemmSpecialization::MKPadding)
+        {
+            // pad M, but not N
+            return transform_tensor_descriptor(
+                e_grid_desc_mraw_nraw,
+                make_tuple(make_right_pad_transform(MRaw, MPad), make_pass_through_transform(NRaw)),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0>{}, Sequence<1>{}));
+        }
+        else if constexpr(GemmSpec == GemmSpecialization::NPadding ||
+                          GemmSpec == GemmSpecialization::NKPadding)
+        {
+            // pad N, but not M
+            return transform_tensor_descriptor(
+                e_grid_desc_mraw_nraw,
+                make_tuple(make_pass_through_transform(MRaw), make_right_pad_transform(NRaw, NPad)),
+                make_tuple(Sequence<0>{}, Sequence<1>{}),
+                make_tuple(Sequence<0>{}, Sequence<1>{}));
+        }
+        else
+        {
+            // not pad M or N
+            return e_grid_desc_mraw_nraw;
+        }
+    }
+
+    // assume D is packed tensor
+    static auto MakeRGridDescriptor_M(index_t MRaw)
+    {
+        const auto r_grid_desc_mraw = make_naive_tensor_descriptor_packed(make_tuple(MRaw));
+
+        const auto M    = math::integer_divide_ceil(MRaw, MPerBlock) * MPerBlock;
+        const auto MPad = M - MRaw;
+
+        if constexpr(GemmSpec == GemmSpecialization::MPadding ||
+                     GemmSpec == GemmSpecialization::MNPadding ||
+                     GemmSpec == GemmSpecialization::MKPadding ||
+                     GemmSpec == GemmSpecialization::MNKPadding)
+        {
+            // pad M
+            return transform_tensor_descriptor(r_grid_desc_mraw,
+                                               make_tuple(make_right_pad_transform(MRaw, MPad)),
+                                               make_tuple(Sequence<0>{}),
+                                               make_tuple(Sequence<0>{}));
+        }
+        else
+        {
+            // not pad M
+            return r_grid_desc_mraw;
+        }
+    }
+
+    using AGridDesc_AK0_M_AK1 = decltype(MakeAGridDescriptor_AK0_M_AK1(1, 1, 1));
+    using BGridDesc_BK0_N_BK1 = decltype(MakeBGridDescriptor_BK0_N_BK1(1, 1, 1));
+    using EGridDesc_M_N       = decltype(MakeEGridDescriptor_M_N(1, 1, 1));
+    using RGridDesc_M         = decltype(MakeRGridDescriptor_M(1));
+
+    // GridwiseGemm
+    using GridwiseGemm = GridwiseGemmMultipleDMultipleR_k0mk1_k0nk1_mn_xdl_cshuffle_v1<
+        ADataType, // TODO: distinguish A/B datatype
+        GemmAccDataType,
+        CShuffleDataType,
+        DsDataType,
+        EDataType,
+        ReduceAccDataType,
+        RsDataType,
+        AElementwiseOperation,
+        BElementwiseOperation,
+        CDEElementwiseOperation,
+        QsElementwiseOperation,
+        RsElementwiseOperation,
+        ThreadReduceOperations,
+        InMemoryDataOperationEnum::Set,
+        RsGlobalMemoryDataOperation,
+        AGridDesc_AK0_M_AK1,
+        BGridDesc_BK0_N_BK1,
+        EGridDesc_M_N,
+        RGridDesc_M,
+        NumGemmKPrefetchStage,
+        BlockSize,
+        MPerBlock,
+        NPerBlock,
+        KPerBlock,
+        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,
+        CDRThreadTransferClusterLengths_MPerBlock_NPerBlock,
+        CDEReduceThreadTransferScalarPerVector_NPerBlock,
+        RThreadTransferDstScalarPerVector_MPerBlock,
+        LoopSched>;
+
+    // Argument
+    struct Argument : public BaseArgument
+    {
+        Argument(const void* p_a_grid,
+                 const void* p_b_grid,
+                 std::array<const void*, NumDTensor> p_ds_grid,
+                 void* p_e_grid,
+                 std::array<void*, NumRTensor> p_rs_grid,
+                 index_t MRaw,
+                 index_t NRaw,
+                 index_t KRaw,
+                 index_t StrideA,
+                 index_t StrideB,
+                 std::array<index_t, NumDTensor> StrideDs,
+                 index_t StrideE,
+                 AElementwiseOperation a_element_op,
+                 BElementwiseOperation b_element_op,
+                 CDEElementwiseOperation cde_element_op,
+                 QsElementwiseOperation qs_element_op,
+                 RsElementwiseOperation rs_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_{}, // FIXME
+              p_e_grid_{static_cast<EDataType*>(p_e_grid)},
+              p_rs_grid_{}, // FIXME
+              a_grid_desc_ak0_m_ak1_{DeviceOp::MakeAGridDescriptor_AK0_M_AK1(MRaw, KRaw, StrideA)},
+              b_grid_desc_bk0_n_bk1_{DeviceOp::MakeBGridDescriptor_BK0_N_BK1(KRaw, NRaw, StrideB)},
+              ds_grid_desc_mblock_mperblock_nblock_nperblock_{},
+              e_grid_desc_m_n_{DeviceOp::MakeEGridDescriptor_M_N(MRaw, NRaw, StrideE)},
+              e_grid_desc_mblock_mperblock_nblock_nperblock_{},
+              r_grid_desc_m_{DeviceOp::MakeRGridDescriptor_M(MRaw)},
+              rs_grid_desc_mblock_mperblock_{},
+              block_2_etile_map_{GridwiseGemm::MakeDefaultBlock2ETileMap(e_grid_desc_m_n_)},
+              a_element_op_{a_element_op},
+              b_element_op_{b_element_op},
+              cde_element_op_{cde_element_op},
+              qs_element_op_{qs_element_op},
+              rs_element_op_{rs_element_op}
+        {
+            if(GridwiseGemm::CheckValidity(a_grid_desc_ak0_m_ak1_,
+                                           b_grid_desc_bk0_n_bk1_,
+                                           e_grid_desc_m_n_,
+                                           r_grid_desc_m_,
+                                           block_2_etile_map_))
+            {
+                e_grid_desc_mblock_mperblock_nblock_nperblock_ =
+                    GridwiseGemm::MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+                        e_grid_desc_m_n_);
+
+                static_for<0, NumDTensor, 1>{}([&](auto i) {
+                    using DDataType = remove_cvref_t<tuple_element_t<i.value, DsDataType>>;
+
+                    p_ds_grid_(i) = static_cast<const DDataType*>(p_ds_grid[i]);
+
+                    const auto d_grid_desc_m_n =
+                        DeviceOp::MakeEGridDescriptor_M_N(MRaw, NRaw, StrideDs[i]);
+
+                    ds_grid_desc_mblock_mperblock_nblock_nperblock_(i) =
+                        GridwiseGemm::MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+                            d_grid_desc_m_n);
+                });
+
+                static_for<0, NumRTensor, 1>{}([&](auto i) {
+                    using RDataType = remove_cvref_t<tuple_element_t<i.value, RsDataType>>;
+
+                    p_rs_grid_(i) = static_cast<RDataType*>(p_rs_grid[i]);
+
+                    rs_grid_desc_mblock_mperblock_(i) =
+                        GridwiseGemm::MakeRGridDescriptor_MBlock_MPerBlock(r_grid_desc_m_);
+                });
+            }
+        }
+
+        //  private:
+        // pointers
+        const ADataType* p_a_grid_;
+        const BDataType* p_b_grid_;
+        typename GridwiseGemm::DsGridPointer p_ds_grid_;
+        EDataType* p_e_grid_;
+        typename GridwiseGemm::RsGridPointer p_rs_grid_;
+
+        // tensor descriptors
+        AGridDesc_AK0_M_AK1 a_grid_desc_ak0_m_ak1_;
+        BGridDesc_BK0_N_BK1 b_grid_desc_bk0_n_bk1_;
+        StaticallyIndexedArray<
+            typename GridwiseGemm::EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+            NumDTensor>
+            ds_grid_desc_mblock_mperblock_nblock_nperblock_; // FIXME: Ds desc may be of different
+                                                             // type from E
+        EGridDesc_M_N e_grid_desc_m_n_;
+        typename GridwiseGemm::EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+            e_grid_desc_mblock_mperblock_nblock_nperblock_;
+
+        RGridDesc_M r_grid_desc_m_;
+        StaticallyIndexedArray<typename GridwiseGemm::RGridDescriptor_MBlock_MPerBlock, NumRTensor>
+            rs_grid_desc_mblock_mperblock_;
+
+        // block-to-e-tile map
+        typename GridwiseGemm::DefaultBlock2ETileMap block_2_etile_map_;
+
+        // element-wise op
+        AElementwiseOperation a_element_op_;
+        BElementwiseOperation b_element_op_;
+        CDEElementwiseOperation cde_element_op_;
+        QsElementwiseOperation qs_element_op_;
+        RsElementwiseOperation rs_element_op_;
+    };
+
+    // Invoker
+    struct Invoker : public BaseInvoker
+    {
+        using Argument = DeviceOp::Argument;
+
+        float Run(const Argument& arg, const StreamConfig& stream_config = StreamConfig{})
+        {
+            if(!GridwiseGemm::CheckValidity(arg.a_grid_desc_ak0_m_ak1_,
+                                            arg.b_grid_desc_bk0_n_bk1_,
+                                            arg.e_grid_desc_m_n_,
+                                            arg.r_grid_desc_m_,
+                                            arg.block_2_etile_map_))
+            {
+                throw std::runtime_error("wrong! GridwiseGemm has invalid setting");
+            }
+
+            const index_t grid_size =
+                arg.block_2_etile_map_.CalculateGridSize(arg.e_grid_desc_m_n_);
+
+            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 = kernel_gemm_multiple_d_multiple_r_xdl_cshuffle<
+                    GridwiseGemm,
+                    ADataType, // TODO: distiguish A/B datatype
+                    typename GridwiseGemm::DsGridPointer,
+                    EDataType,
+                    typename GridwiseGemm::RsGridPointer,
+                    AElementwiseOperation,
+                    BElementwiseOperation,
+                    CDEElementwiseOperation,
+                    QsElementwiseOperation,
+                    RsElementwiseOperation,
+                    DeviceOp::AGridDesc_AK0_M_AK1,
+                    DeviceOp::BGridDesc_BK0_N_BK1,
+                    ck::StaticallyIndexedArray<
+                        typename GridwiseGemm::EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+                        NumDTensor>,
+                    typename GridwiseGemm::EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+                    ck::StaticallyIndexedArray<
+                        typename GridwiseGemm::RGridDescriptor_MBlock_MPerBlock,
+                        NumRTensor>,
+                    typename GridwiseGemm::DefaultBlock2ETileMap,
+                    has_main_loop>;
+
+                return launch_and_time_kernel(stream_config,
+                                              kernel,
+                                              dim3(grid_size),
+                                              dim3(BlockSize),
+                                              0,
+                                              arg.p_a_grid_,
+                                              arg.p_b_grid_,
+                                              arg.p_ds_grid_,
+                                              arg.p_e_grid_,
+                                              arg.p_rs_grid_,
+                                              arg.a_element_op_,
+                                              arg.b_element_op_,
+                                              arg.cde_element_op_,
+                                              arg.qs_element_op_,
+                                              arg.rs_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.rs_grid_desc_mblock_mperblock_,
+                                              arg.block_2_etile_map_);
+            };
+
+            float ave_time = 0;
+
+            if(GridwiseGemm::CalculateHasMainKBlockLoop(K))
+            {
+                ave_time = launch_kernel(integral_constant<bool, true>{});
+            }
+            else
+            {
+                ave_time = launch_kernel(integral_constant<bool, false>{});
+            }
+
+            return ave_time;
+        }
+
+        // polymorphic
+        float Run(const BaseArgument* p_arg,
+                  const StreamConfig& stream_config = StreamConfig{}) override
+        {
+            return Run(*dynamic_cast<const Argument*>(p_arg), stream_config);
+        }
+    };
+
+    static bool IsSupportedArgument(const Argument& arg)
+    {
+        if(!(ck::get_device_name() == "gfx908" || ck::get_device_name() == "gfx90a"))
+        {
+            return false;
+        }
+
+        return GridwiseGemm::CheckValidity(arg.a_grid_desc_ak0_m_ak1_,
+                                           arg.b_grid_desc_bk0_n_bk1_,
+                                           arg.e_grid_desc_m_n_,
+                                           arg.r_grid_desc_m_,
+                                           arg.block_2_etile_map_);
+    }
+
+    // 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,
+                             void* p_e,
+                             std::array<void*, NumRTensor> p_rs,
+                             index_t MRaw,
+                             index_t NRaw,
+                             index_t KRaw,
+                             index_t StrideA,
+                             index_t StrideB,
+                             std::array<index_t, NumDTensor> StrideDs,
+                             index_t StrideE,
+                             AElementwiseOperation a_element_op,
+                             BElementwiseOperation b_element_op,
+                             CDEElementwiseOperation cde_element_op,
+                             QsElementwiseOperation qs_element_op,
+                             RsElementwiseOperation rs_element_op)
+    {
+        return Argument{p_a,
+                        p_b,
+                        p_ds,
+                        p_e,
+                        p_rs,
+                        MRaw,
+                        NRaw,
+                        KRaw,
+                        StrideA,
+                        StrideB,
+                        StrideDs,
+                        StrideE,
+                        a_element_op,
+                        b_element_op,
+                        cde_element_op,
+                        qs_element_op,
+                        rs_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,
+                                                      void* p_e,
+                                                      std::array<void*, NumRTensor> p_rs,
+                                                      index_t MRaw,
+                                                      index_t NRaw,
+                                                      index_t KRaw,
+                                                      index_t StrideA,
+                                                      index_t StrideB,
+                                                      std::array<index_t, NumDTensor> StrideDs,
+                                                      index_t StrideE,
+                                                      AElementwiseOperation a_element_op,
+                                                      BElementwiseOperation b_element_op,
+                                                      CDEElementwiseOperation cde_element_op,
+                                                      QsElementwiseOperation qs_element_op,
+                                                      RsElementwiseOperation rs_element_op) override
+    {
+        return std::make_unique<Argument>(p_a,
+                                          p_b,
+                                          p_ds,
+                                          p_e,
+                                          p_rs,
+                                          MRaw,
+                                          NRaw,
+                                          KRaw,
+                                          StrideA,
+                                          StrideB,
+                                          StrideDs,
+                                          StrideE,
+                                          a_element_op,
+                                          b_element_op,
+                                          cde_element_op,
+                                          qs_element_op,
+                                          rs_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();
+
+        // clang-format off
+        str << "DeviceGemmMultipleDMultipleR_Xdl_CShuffle"
+            << "<"
+            << BlockSize << ", "
+            << MPerBlock << ", "
+            << NPerBlock << ", "
+            << KPerBlock << ", "
+            << AK1 << ", "
+            << BK1 << ", "
+            << getGemmSpecializationString(GemmSpec)
+            << ">";
+        // clang-format on
+
+        return str.str();
+    }
+};
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

include/ck/tensor_operation/gpu/element/element_wise_operation.hpp

@@ -130,6 +130,35 @@ struct AddHardswishAdd
     }
 };
 
+// C = A * B
+// E = C + D0 + D1
+struct AddAdd
+{
+    template <typename E, typename C, typename D0, typename D1>
+    __host__ __device__ void operator()(E& e, const C& c, const D0& d0, const D1& d1) const
+    {
+        // Only support floating so far
+        static_assert(is_same<E, half_t>::value || is_same<E, float>::value ||
+                          is_same<E, double>::value,
+                      "Data type is not supported by this operation!");
+
+        static_assert(is_same<C, half_t>::value || is_same<C, float>::value ||
+                          is_same<C, double>::value,
+                      "Data type is not supported by this operation!");
+
+        static_assert(is_same<D0, half_t>::value || is_same<D0, float>::value ||
+                          is_same<D0, double>::value,
+                      "Data type is not supported by this operation!");
+
+        static_assert(is_same<D1, half_t>::value || is_same<D1, float>::value ||
+                          is_same<D1, double>::value,
+                      "Data type is not supported by this operation!");
+
+        const C y = c + type_convert<C>(d0) + type_convert<C>(d1);
+        e         = type_convert<E>(y);
+    }
+};
+
 // C = A * B
 // E = FastGelu(C + D0 + D1)
 struct AddAddFastGelu

include/ck/tensor_operation/gpu/grid/gridwise_gemm_multiple_d_multiple_r_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_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_v6r1.hpp"
+#include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
+#include "ck/tensor_operation/gpu/thread/reduction_functions_threadwise.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+namespace ck {
+template <typename FloatAB,
+          typename FloatGemmAcc,
+          typename FloatCShuffle,
+          typename DsDataType,
+          typename FloatE,
+          typename FloatReduceAcc,
+          typename RsDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename QsElementwiseOperation,
+          typename RsElementwiseOperation,
+          typename ThreadReduceOperations,
+          InMemoryDataOperationEnum EGlobalMemoryDataOperation,
+          typename RsGlobalMemoryDataOperation,
+          typename AGridDesc_AK0_M_AK1,
+          typename BGridDesc_BK0_N_BK1,
+          typename EGridDesc_M_N,
+          typename RGridDesc_M,
+          index_t NumGemmKPrefetchStage,
+          index_t BlockSize,
+          index_t MPerBlock,
+          index_t NPerBlock,
+          index_t KPerBlock,
+          index_t AK1Value,
+          index_t BK1Value,
+          index_t MPerXdl,
+          index_t NPerXdl,
+          index_t MXdlPerWave,
+          index_t NXdlPerWave,
+          typename ABlockTransferThreadClusterLengths_AK0_M_AK1,
+          typename ABlockTransferThreadClusterArrangeOrder,
+          typename ABlockTransferSrcAccessOrder,
+          index_t ABlockTransferSrcVectorDim,
+          index_t ABlockTransferSrcScalarPerVector,
+          index_t ABlockTransferDstScalarPerVector_AK1,
+          bool AThreadTransferSrcResetCoordinateAfterRun,
+          index_t ABlockLdsExtraM,
+          typename BBlockTransferThreadClusterLengths_BK0_N_BK1,
+          typename BBlockTransferThreadClusterArrangeOrder,
+          typename BBlockTransferSrcAccessOrder,
+          index_t BBlockTransferSrcVectorDim,
+          index_t BBlockTransferSrcScalarPerVector,
+          index_t BBlockTransferDstScalarPerVector_BK1,
+          bool BThreadTransferSrcResetCoordinateAfterRun,
+          index_t BBlockLdsExtraN,
+          index_t CShuffleMXdlPerWavePerShuffle,
+          index_t CShuffleNXdlPerWavePerShuffle,
+          typename CDRThreadTransferClusterLengths_MPerBlock_NPerBlock,
+          index_t CDEReduceThreadTransferScalarPerVector_NPerBlock,
+          index_t RThreadTransferDstScalarPerVector_MPerBlock,
+          LoopScheduler LoopSched>
+struct GridwiseGemmMultipleDMultipleR_k0mk1_k0nk1_mn_xdl_cshuffle_v1
+{
+    static constexpr index_t NumDTensor = DsDataType::Size();
+    static constexpr index_t NumRTensor = RsDataType::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 AK0 = Number<KPerBlock / AK1Value>{};
+    static constexpr auto BK0 = Number<KPerBlock / BK1Value>{};
+    static constexpr auto AK1 = Number<AK1Value>{};
+    static constexpr auto BK1 = Number<BK1Value>{};
+
+    using ThisThreadBlock = ThisThreadBlock<BlockSize>;
+
+    using GridwiseGemmPipe = GridwiseGemmPipeline_v1<NumGemmKPrefetchStage>;
+
+    __host__ __device__ static constexpr auto GetABlockDescriptor_AK0PerBlock_MPerBlock_AK1()
+    {
+        // A matrix in LDS memory, dst of blockwise copy
+        return make_naive_tensor_descriptor(
+            make_tuple(AK0, Number<MPerBlock>{}, AK1),
+            make_tuple(Number<MPerBlock + ABlockLdsExtraM>{} * AK1, AK1, I1));
+    }
+
+    __host__ __device__ static constexpr auto GetBBlockDescriptor_BK0PerBlock_NPerBlock_BK1()
+    {
+        // B matrix in LDS memory, dst of blockwise copy
+        return make_naive_tensor_descriptor(
+            make_tuple(BK0, Number<NPerBlock>{}, BK1),
+            make_tuple(Number<NPerBlock + BBlockLdsExtraN>{} * BK1, BK1, I1));
+    }
+
+    __host__ __device__ static constexpr auto
+    GetCShuffleBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock()
+    {
+        constexpr index_t MWave = MPerBlock / (MXdlPerWave * MPerXdl);
+        constexpr index_t NWave = NPerBlock / (NXdlPerWave * NPerXdl);
+
+        constexpr auto c_shuffle_block_desc_mblock_mperblock_nblock_nperblock =
+            make_naive_tensor_descriptor_packed(
+                make_tuple(I1,
+                           Number<CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl>{},
+                           I1,
+                           Number<CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>{}));
+
+        return c_shuffle_block_desc_mblock_mperblock_nblock_nperblock;
+    }
+
+    // ck::Tuple<const T0DataType*, const T1DataType*, ...>
+    template <typename Ts, bool isConst = true>
+    static constexpr auto MakeTsGridPointer()
+    {
+        return generate_tuple(
+            [&](auto i) {
+                using T = remove_cvref_t<tuple_element_t<i.value, Ts>>;
+                if constexpr(isConst)
+                    return static_cast<const T*>(nullptr);
+                else
+                    return static_cast<T*>(nullptr);
+            },
+            Number<Ts::Size()>{});
+    }
+
+    __host__ __device__ static constexpr index_t GetSharedMemoryNumberOfByte()
+    {
+        // LDS allocation for A and B: be careful of alignment
+        constexpr auto a_block_desc_ak0_m_ak1 = GetABlockDescriptor_AK0PerBlock_MPerBlock_AK1();
+        constexpr auto b_block_desc_bk0_n_bk1 = GetBBlockDescriptor_BK0PerBlock_NPerBlock_BK1();
+
+        // lds max alignment
+        constexpr auto max_lds_align = math::lcm(AK1, BK1);
+
+        constexpr auto a_block_space_size_aligned = math::integer_least_multiple(
+            a_block_desc_ak0_m_ak1.GetElementSpaceSize(), max_lds_align);
+
+        constexpr auto b_block_space_size_aligned = math::integer_least_multiple(
+            b_block_desc_bk0_n_bk1.GetElementSpaceSize(), max_lds_align);
+
+        // LDS allocation for C shuffle in LDS
+        constexpr auto c_shuffle_block_desc_mblock_mperblock_nblock_nperblock =
+            GetCShuffleBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock();
+
+        constexpr auto c_block_size =
+            c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize();
+
+        return math::max((a_block_space_size_aligned + b_block_space_size_aligned) *
+                             sizeof(FloatAB),
+                         c_block_size * sizeof(FloatCShuffle));
+    }
+
+    // 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_AK0_M_AK1& a_grid_desc_ak0_m_ak1,
+                  const BGridDesc_BK0_N_BK1& b_grid_desc_bk0_n_bk1,
+                  const EGridDesc_M_N& e_grid_desc_m_n,
+                  const RGridDesc_M& r_grid_desc_m,
+                  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_ak0_m_ak1.GetLength(I1);
+        const auto N = b_grid_desc_bk0_n_bk1.GetLength(I1);
+        const auto K = a_grid_desc_ak0_m_ak1.GetLength(I0) * a_grid_desc_ak0_m_ak1.GetLength(I2);
+
+        if(!(M == e_grid_desc_m_n.GetLength(I0) && N == e_grid_desc_m_n.GetLength(I1)))
+            return false;
+
+        if(!(M % MPerBlock == 0 && N % NPerBlock == 0 && K % KPerBlock == 0))
+            return false;
+
+        if(M != r_grid_desc_m.GetLength(I0))
+            return false;
+
+        // check gridwise gemm pipeline
+        const auto num_k_loop = K / KPerBlock;
+
+        if(!GridwiseGemmPipe::IsSupported(num_k_loop))
+        {
+            return false;
+        }
+
+        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)
+        return true;
+    }
+
+    __host__ __device__ static constexpr bool CalculateHasMainKBlockLoop(index_t K)
+    {
+        const index_t num_loop = K / KPerBlock;
+
+        return GridwiseGemmPipe::CalculateHasMainLoop(num_loop);
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(const EGridDesc_M_N& e_grid_desc_m_n)
+    {
+        const auto M = e_grid_desc_m_n.GetLength(I0);
+        const auto N = e_grid_desc_m_n.GetLength(I1);
+
+        const auto MBlock = M / MPerBlock;
+        const auto NBlock = N / NPerBlock;
+
+        const auto e_grid_desc_mblock_mperblock_nblock_nperblock = transform_tensor_descriptor(
+            e_grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(MBlock, Number<MPerBlock>{})),
+                       make_unmerge_transform(make_tuple(NBlock, Number<NPerBlock>{}))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 1>{}, Sequence<2, 3>{}));
+
+        return e_grid_desc_mblock_mperblock_nblock_nperblock;
+    }
+
+    __host__ __device__ static constexpr auto
+    MakeRGridDescriptor_MBlock_MPerBlock(const RGridDesc_M& r_grid_desc_m)
+    {
+        const auto M      = r_grid_desc_m.GetLength(I0);
+        const auto MBlock = M / MPerBlock;
+
+        const auto r_grid_desc_mblock_mperblock = transform_tensor_descriptor(
+            r_grid_desc_m,
+            make_tuple(make_unmerge_transform(make_tuple(MBlock, Number<MPerBlock>{}))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1>{}));
+
+        return r_grid_desc_mblock_mperblock;
+    }
+
+    // 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);
+    }
+
+    using EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock = remove_cvref_t<decltype(
+        MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(EGridDesc_M_N{}))>;
+
+    // Support 2 dimension in the future. Not only M
+    using RGridDescriptor_MBlock_MPerBlock =
+        remove_cvref_t<decltype(MakeRGridDescriptor_MBlock_MPerBlock(RGridDesc_M{}))>;
+
+    using DefaultBlock2ETileMap =
+        remove_cvref_t<decltype(MakeDefaultBlock2ETileMap(EGridDesc_M_N{}))>;
+
+    using DsGridPointer = decltype(MakeTsGridPointer<DsDataType, true>());
+    using RsGridPointer = decltype(MakeTsGridPointer<RsDataType, false>());
+
+    template <bool HasMainKBlockLoop, typename Block2ETileMap>
+    __device__ static void
+    Run(const FloatAB* __restrict__ p_a_grid,
+        const FloatAB* __restrict__ p_b_grid,
+        DsGridPointer p_ds_grid,
+        FloatE* __restrict__ p_e_grid,
+        RsGridPointer p_rs_grid,
+        void* __restrict__ p_shared,
+        const AElementwiseOperation& a_element_op,
+        const BElementwiseOperation& b_element_op,
+        const CDEElementwiseOperation& cde_element_op,
+        const QsElementwiseOperation& qs_element_op,
+        const RsElementwiseOperation& rs_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 StaticallyIndexedArray<EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+                                     NumDTensor>&
+            ds_grid_desc_mblock_mperblock_nblock_nperblock, // FIXME: Ds desc may be of different
+        const EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock&
+            e_grid_desc_mblock_mperblock_nblock_nperblock,
+        const StaticallyIndexedArray<RGridDescriptor_MBlock_MPerBlock,
+                                     NumRTensor>&
+            rs_grid_desc_mblock_mperblock, // FIXME: Rs desc may be of different
+        const Block2ETileMap& block_2_etile_map)
+    {
+        // FIXME - Share code with other gemm kernel
+        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 rs_grid_buf = generate_tuple(
+            [&](auto i) {
+                return make_dynamic_buffer<AddressSpaceEnum::Global>(
+                    p_rs_grid(i), rs_grid_desc_mblock_mperblock[i].GetElementSpaceSize());
+            },
+            Number<NumRTensor>{});
+
+        // 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<AK0, MPerBlock, AK1>,
+                                                ABlockTransferThreadClusterLengths_AK0_M_AK1,
+                                                ABlockTransferThreadClusterArrangeOrder,
+                                                FloatAB,
+                                                FloatAB,
+                                                decltype(a_grid_desc_ak0_m_ak1),
+                                                decltype(a_block_desc_ak0_m_ak1),
+                                                ABlockTransferSrcAccessOrder,
+                                                Sequence<1, 0, 2>,
+                                                ABlockTransferSrcVectorDim,
+                                                2,
+                                                ABlockTransferSrcScalarPerVector,
+                                                ABlockTransferDstScalarPerVector_AK1,
+                                                1,
+                                                1,
+                                                AThreadTransferSrcResetCoordinateAfterRun,
+                                                true,
+                                                NumGemmKPrefetchStage>(
+                a_grid_desc_ak0_m_ak1,
+                make_multi_index(0, m_block_data_idx_on_grid, 0),
+                a_element_op,
+                a_block_desc_ak0_m_ak1,
+                make_multi_index(0, 0, 0),
+                ck::tensor_operation::element_wise::PassThrough{});
+
+        // B matrix blockwise copy
+        auto b_blockwise_copy =
+            ThreadGroupTensorSliceTransfer_v4r1<ThisThreadBlock,
+                                                BElementwiseOperation,
+                                                ck::tensor_operation::element_wise::PassThrough,
+                                                InMemoryDataOperationEnum::Set,
+                                                Sequence<BK0, NPerBlock, BK1>,
+                                                BBlockTransferThreadClusterLengths_BK0_N_BK1,
+                                                BBlockTransferThreadClusterArrangeOrder,
+                                                FloatAB,
+                                                FloatAB,
+                                                decltype(b_grid_desc_bk0_n_bk1),
+                                                decltype(b_block_desc_bk0_n_bk1),
+                                                BBlockTransferSrcAccessOrder,
+                                                Sequence<1, 0, 2>,
+                                                BBlockTransferSrcVectorDim,
+                                                2,
+                                                BBlockTransferSrcScalarPerVector,
+                                                BBlockTransferDstScalarPerVector_BK1,
+                                                1,
+                                                1,
+                                                BThreadTransferSrcResetCoordinateAfterRun,
+                                                true,
+                                                NumGemmKPrefetchStage>(
+                b_grid_desc_bk0_n_bk1,
+                make_multi_index(0, n_block_data_idx_on_grid, 0),
+                b_element_op,
+                b_block_desc_bk0_n_bk1,
+                make_multi_index(0, 0, 0),
+                ck::tensor_operation::element_wise::PassThrough{});
+
+        // GEMM definition
+        //   c_mtx += transpose(a_mtx) * b_mtx
+        //     a_mtx[K0PerBlock, MPerBlock] is in LDS
+        //     b_mtx[K0PerBlock, NPerBlock] is in LDS
+        //     c_mtx[MPerBlock, NPerBlock] is distributed among threads, and saved in
+        //       register
+        // sanity check
+        constexpr index_t KPack = math::max(
+            math::lcm(AK1, BK1), MfmaSelector<FloatAB, MPerXdl, NPerXdl>::selected_mfma.k_per_blk);
+
+        auto blockwise_gemm = BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_Selector<
+            BlockSize,
+            FloatAB,
+            FloatGemmAcc,
+            decltype(a_block_desc_ak0_m_ak1),
+            decltype(b_block_desc_bk0_n_bk1),
+            MPerXdl,
+            NPerXdl,
+            MXdlPerWave,
+            NXdlPerWave,
+            KPack,
+            LoopSched>();
+
+        auto c_thread_buf = blockwise_gemm.GetCThreadBuffer();
+
+        // LDS allocation for A and B: be careful of alignment
+        constexpr auto a_block_space_size_aligned = math::integer_least_multiple(
+            a_block_desc_ak0_m_ak1.GetElementSpaceSize(), max_lds_align);
+
+        auto a_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+            static_cast<FloatAB*>(p_shared), a_block_desc_ak0_m_ak1.GetElementSpaceSize());
+
+        auto b_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+            static_cast<FloatAB*>(p_shared) + a_block_space_size_aligned,
+            b_block_desc_bk0_n_bk1.GetElementSpaceSize());
+
+        constexpr auto a_block_slice_copy_step = make_multi_index(KPerBlock / AK1, 0, 0);
+        constexpr auto b_block_slice_copy_step = make_multi_index(KPerBlock / BK1, 0, 0);
+
+        // gridwise GEMM pipeline
+        const auto gridwise_gemm_pipeline =
+            GridwiseGemmPipeline_v1_Selector<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 + Ds + reduction + write out
+        {
+            static_assert(MXdlPerWave % CShuffleMXdlPerWavePerShuffle == 0 &&
+                              NXdlPerWave % CShuffleNXdlPerWavePerShuffle == 0,
+                          "wrong!");
+
+            constexpr index_t MWave = MPerBlock / (MXdlPerWave * MPerXdl);
+            constexpr index_t NWave = NPerBlock / (NXdlPerWave * NPerXdl);
+
+            // TODO: hacky, fix it!
+            constexpr auto c_thread_desc_m0_n0_m1_n1_m2_m3_m4_n2 =
+                blockwise_gemm.GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2();
+
+            // TODO: hacky, fix it!
+            // c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp is only used to get lengths
+            constexpr auto c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp =
+                blockwise_gemm.GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2();
+
+            constexpr auto M0 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I0);
+            constexpr auto N0 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I1);
+            constexpr auto M1 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I2);
+            constexpr auto N1 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I3);
+            constexpr auto M2 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I4);
+            constexpr auto M3 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I5);
+            constexpr auto M4 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I6);
+            constexpr auto N2 = c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2_tmp.GetLength(I7);
+
+            constexpr auto c_shuffle_block_desc_mblock_mperblock_nblock_nperblock =
+                GetCShuffleBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock();
+
+            auto c_shuffle_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
+                static_cast<FloatCShuffle*>(p_shared),
+                c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize());
+
+            constexpr auto c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2 = transform_tensor_descriptor(
+                c_shuffle_block_desc_mblock_mperblock_nblock_nperblock,
+                make_tuple(
+                    make_freeze_transform(I0),
+                    make_unmerge_transform(make_tuple(
+                        Number<CShuffleMXdlPerWavePerShuffle>{}, // M0 (MXdlPerWave) per shuffle
+                        M1,                                      // M1 = MWave
+                        M2,                                      // M2 * M3 * M4 = MPerXdl
+                        M3,
+                        M4)),
+                    make_freeze_transform(I0),
+                    make_unmerge_transform(make_tuple(
+                        Number<CShuffleNXdlPerWavePerShuffle>{}, // N0 (NXdlPerWave) per shuffle
+                        N1,                                      // N1 = NWave
+                        N2))),                                   // N2 = NPerXdl
+                make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
+                make_tuple(
+                    Sequence<>{}, Sequence<0, 2, 4, 5, 6>{}, Sequence<>{}, Sequence<1, 3, 7>{}));
+
+            // calculate origin of thread output tensor on global memory
+            //     blockwise GEMM c matrix starting index
+            const auto c_thread_mtx_on_block =
+                blockwise_gemm.CalculateCThreadOriginDataIndex(I0, I0, I0, I0);
+
+            const index_t m_thread_data_on_block = c_thread_mtx_on_block[I0];
+            const index_t n_thread_data_on_block = c_thread_mtx_on_block[I1];
+
+            const auto m_thread_data_on_block_to_m0_m1_m2_m3_m4_adaptor =
+                make_single_stage_tensor_adaptor(
+                    make_tuple(make_merge_transform(make_tuple(M0, M1, M2, M3, M4))),
+                    make_tuple(Sequence<0, 1, 2, 3, 4>{}),
+                    make_tuple(Sequence<0>{}));
+
+            const auto m_thread_data_on_block_idx =
+                m_thread_data_on_block_to_m0_m1_m2_m3_m4_adaptor.CalculateBottomIndex(
+                    make_multi_index(m_thread_data_on_block));
+
+            const auto n_thread_data_on_block_to_n0_n1_n2_adaptor =
+                make_single_stage_tensor_adaptor(
+                    make_tuple(make_merge_transform(make_tuple(N0, N1, N2))),
+                    make_tuple(Sequence<0, 1, 2>{}),
+                    make_tuple(Sequence<0>{}));
+
+            const auto n_thread_data_on_block_idx =
+                n_thread_data_on_block_to_n0_n1_n2_adaptor.CalculateBottomIndex(
+                    make_multi_index(n_thread_data_on_block));
+
+            // shuffle: threadwise copy C from VGPR to LDS
+            auto c_thread_copy_vgpr_to_lds =
+                ThreadwiseTensorSliceTransfer_v1r3<FloatGemmAcc,
+                                                   FloatCShuffle,
+                                                   decltype(c_thread_desc_m0_n0_m1_n1_m2_m3_m4_n2),
+                                                   decltype(c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2),
+                                                   ck::tensor_operation::element_wise::PassThrough,
+                                                   Sequence<CShuffleMXdlPerWavePerShuffle,
+                                                            CShuffleNXdlPerWavePerShuffle,
+                                                            I1,
+                                                            I1,
+                                                            M2,
+                                                            I1,
+                                                            M4,
+                                                            I1>,
+                                                   Sequence<0, 1, 2, 3, 4, 5, 6, 7>,
+                                                   7,
+                                                   1,
+                                                   InMemoryDataOperationEnum::Set,
+                                                   1,
+                                                   true>{
+                    c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2,
+                    make_multi_index(0,
+                                     0,
+                                     m_thread_data_on_block_idx[I1],
+                                     n_thread_data_on_block_idx[I1],
+                                     m_thread_data_on_block_idx[I2],
+                                     m_thread_data_on_block_idx[I3],
+                                     m_thread_data_on_block_idx[I4],
+                                     n_thread_data_on_block_idx[I2]),
+                    ck::tensor_operation::element_wise::PassThrough{}};
+
+            // space filling curve for threadwise C in VGPR
+            constexpr auto sfc_c_vgpr =
+                SpaceFillingCurve<Sequence<MXdlPerWave, NXdlPerWave, 1, 1, M2, 1, M4, 1>,
+                                  Sequence<0, 1, 2, 3, 4, 5, 6, 7>,
+                                  Sequence<CShuffleMXdlPerWavePerShuffle,
+                                           CShuffleNXdlPerWavePerShuffle,
+                                           1,
+                                           1,
+                                           M2,
+                                           1,
+                                           M4,
+                                           1>>{};
+
+            // space filling curve for shuffled blockwise C in global mem
+            constexpr auto sfc_der_global =
+                SpaceFillingCurve<Sequence<1, MPerBlock, 1, NPerBlock>,
+                                  Sequence<0, 2, 1, 3>,
+                                  Sequence<1,
+                                           CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl,
+                                           1,
+                                           CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl>>{};
+
+            // TODO: this should be implemented as a blockwise reduction
+            // LDS c_reduce_block_desc_mperblock_nperblock
+            constexpr auto c_reduce_block_desc_mperblock_nperblock = transform_tensor_descriptor(
+                c_shuffle_block_desc_mblock_mperblock_nblock_nperblock,
+                make_tuple(
+                    make_freeze_transform(I0),
+                    make_pass_through_transform(
+                        c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetLength(I1)),
+                    make_freeze_transform(I0),
+                    make_pass_through_transform(
+                        c_shuffle_block_desc_mblock_mperblock_nblock_nperblock.GetLength(I3))),
+                make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
+                make_tuple(Sequence<>{}, Sequence<0>{}, Sequence<>{}, Sequence<1>{}));
+
+            static_assert(CDRThreadTransferClusterLengths_MPerBlock_NPerBlock::At(I0) *
+                                  CDRThreadTransferClusterLengths_MPerBlock_NPerBlock::At(I1) ==
+                              BlockSize,
+                          "wrong!");
+
+            static_assert((CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl) %
+                                      CDRThreadTransferClusterLengths_MPerBlock_NPerBlock::At(I0) ==
+                                  0 &&
+                              (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl) %
+                                      CDRThreadTransferClusterLengths_MPerBlock_NPerBlock::At(I1) ==
+                                  0,
+                          "wrong!");
+
+            constexpr index_t mreduce_per_thread =
+                (CShuffleMXdlPerWavePerShuffle * MWave * MPerXdl) /
+                CDRThreadTransferClusterLengths_MPerBlock_NPerBlock::At(I0);
+
+            constexpr index_t nreduce_per_thread =
+                (CShuffleNXdlPerWavePerShuffle * NWave * NPerXdl) /
+                CDRThreadTransferClusterLengths_MPerBlock_NPerBlock::At(I1);
+
+            constexpr auto c_reduce_thread_lengths_mperblock_nperblock =
+                Sequence<mreduce_per_thread, nreduce_per_thread>{};
+
+            // VGPR cde_reduce_thread_desc_mperblock_nperblock
+            constexpr auto cde_reduce_thread_desc_mperblock_nperblock =
+                make_naive_tensor_descriptor_packed(
+                    make_tuple(Number<mreduce_per_thread>{}, Number<nreduce_per_thread>{}));
+
+            constexpr auto r_thread_desc_mperblock =
+                make_naive_tensor_descriptor_packed(make_tuple(Number<mreduce_per_thread>{}));
+
+            constexpr auto r_thread_desc_mblock_mperblock =
+                make_naive_tensor_descriptor_packed(make_tuple(I1, Number<mreduce_per_thread>{}));
+
+            auto e_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatReduceAcc>(
+                cde_reduce_thread_desc_mperblock_nperblock.GetElementSpaceSize());
+
+            // reduce: threadwise copy from LDS to VGPR
+            constexpr auto c_reduce_thread_cluster_desc = make_cluster_descriptor(
+                CDRThreadTransferClusterLengths_MPerBlock_NPerBlock{}, Sequence<1, 0>{});
+
+            const auto c_reduce_thread_cluster_idx =
+                c_reduce_thread_cluster_desc.CalculateBottomIndex(
+                    make_multi_index(get_thread_local_1d_id()));
+
+            const auto c_reduce_thread_data_idx_begin =
+                c_reduce_thread_cluster_idx * c_reduce_thread_lengths_mperblock_nperblock;
+
+            // To apply D0, D1, ... and reduction.
+            // Copy c shuffle from LDS back to VGPR
+            auto c_reduce_thread_copy_lds_to_vgpr = ThreadwiseTensorSliceTransfer_v2<
+                FloatCShuffle,
+                FloatReduceAcc,
+                decltype(c_reduce_block_desc_mperblock_nperblock),
+                decltype(cde_reduce_thread_desc_mperblock_nperblock),
+                decltype(c_reduce_thread_lengths_mperblock_nperblock),
+                Sequence<0, 1>,
+                1,
+                CDEReduceThreadTransferScalarPerVector_NPerBlock,
+                1,
+                true>{c_reduce_block_desc_mperblock_nperblock, c_reduce_thread_data_idx_begin};
+
+            // Copy result of reduction back from VGPR to global
+            auto reduce_tuple_thread_copy_vgpr_to_global = generate_tuple(
+                [&](auto I) {
+                    auto p_r_grid                     = p_rs_grid[I];
+                    auto r_element_op                 = rs_element_op[I];
+                    auto r_grid_desc_mblock_mperblock = rs_grid_desc_mblock_mperblock[I];
+
+                    return ThreadwiseTensorSliceTransfer_v1r3<
+                        FloatReduceAcc,
+                        remove_pointer_t<decltype(p_r_grid)>,
+                        decltype(r_thread_desc_mblock_mperblock),
+                        decltype(r_grid_desc_mblock_mperblock),
+                        decltype(r_element_op),
+                        Sequence<1, mreduce_per_thread>,
+                        Sequence<0, 1>,
+                        1,
+                        RThreadTransferDstScalarPerVector_MPerBlock,
+                        RsGlobalMemoryDataOperation::At(I),
+                        1,
+                        false>{r_grid_desc_mblock_mperblock,
+                               make_multi_index(block_work_idx[I0],                  // mblock
+                                                c_reduce_thread_data_idx_begin[I0]), // mperblock
+                               r_element_op};
+                },
+                Number<NumRTensor>{});
+
+            // D0, D1, ..., Dn
+            constexpr auto cde_reduce_thread_desc_I1_mperblock_I1_nperblock =
+                make_naive_tensor_descriptor_packed(
+                    make_tuple(I1, Number<mreduce_per_thread>{}, I1, Number<nreduce_per_thread>{}));
+
+            // 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, FloatReduceAcc>(
+                        cde_reduce_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,
+                        FloatReduceAcc,
+                        decltype(ds_grid_desc_mblock_mperblock_nblock_nperblock[I]),
+                        decltype(cde_reduce_thread_desc_I1_mperblock_I1_nperblock),
+                        Sequence<I1, mreduce_per_thread, I1, nreduce_per_thread>,
+                        Sequence<0, 1, 2, 3>,
+                        3,
+                        CDEReduceThreadTransferScalarPerVector_NPerBlock,
+                        1,
+                        true>(ds_grid_desc_mblock_mperblock_nblock_nperblock[I],
+                              make_multi_index(
+                                  I0,
+                                  m_block_data_idx_on_grid + c_reduce_thread_data_idx_begin[I0],
+                                  I0,
+                                  n_block_data_idx_on_grid + c_reduce_thread_data_idx_begin[I1]));
+                },
+                Number<NumDTensor>{});
+
+            auto e_thread_copy_vgpr_to_global = ThreadwiseTensorSliceTransfer_v1r3<
+                FloatReduceAcc,
+                FloatE,
+                decltype(cde_reduce_thread_desc_I1_mperblock_I1_nperblock),
+                decltype(e_grid_desc_mblock_mperblock_nblock_nperblock),
+                tensor_operation::element_wise::PassThrough,
+                Sequence<I1, mreduce_per_thread, I1, nreduce_per_thread>, // SliceLengths
+                Sequence<0, 1, 2, 3>,                                     // DimAccessOrder
+                3,                                                        // DstVectorDim
+                CDEReduceThreadTransferScalarPerVector_NPerBlock,
+                InMemoryDataOperationEnum::Set,
+                1,
+                true>{
+                e_grid_desc_mblock_mperblock_nblock_nperblock,
+                make_multi_index(I0,
+                                 m_block_data_idx_on_grid + c_reduce_thread_data_idx_begin[I0],
+                                 I0,
+                                 n_block_data_idx_on_grid + c_reduce_thread_data_idx_begin[I1]),
+                tensor_operation::element_wise::PassThrough{}};
+
+            constexpr index_t num_access = sfc_c_vgpr.GetNumOfAccess();
+
+            static_assert(num_access == sfc_der_global.GetNumOfAccess(), "wrong!");
+
+            static_for<0, num_access, 1>{}([&](auto access_id) {
+                // make sure it's safe to read from LDS
+                if constexpr(access_id > 0)
+                    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
+                c_reduce_thread_copy_lds_to_vgpr.Run(c_reduce_block_desc_mperblock_nperblock,
+                                                     c_shuffle_block_buf,
+                                                     cde_reduce_thread_desc_mperblock_nperblock,
+                                                     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],
+                        cde_reduce_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, cde_reduce_thread_desc_mperblock_nperblock.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(cde_reduce_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);
+                }
+
+                // reduction
+                static_for<0, NumRTensor, 1>{}([&](auto Ir) {
+                    auto r_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatReduceAcc>(
+                        r_thread_desc_mperblock.GetElementSpaceSize());
+
+                    auto& reduce_thread_copy_vgpr_to_global =
+                        reduce_tuple_thread_copy_vgpr_to_global(Ir);
+
+                    using ThreadReduceOperation =
+                        remove_cvref_t<decltype(ThreadReduceOperations{}[Ir])>;
+
+                    using ThreadwiseReduce =
+                        ThreadwiseReduction<FloatReduceAcc,
+                                            decltype(cde_reduce_thread_desc_mperblock_nperblock),
+                                            decltype(r_thread_desc_mperblock),
+                                            ThreadReduceOperation,
+                                            false>;
+
+                    // threadwise reduction
+                    const auto reduce_identityVal =
+                        ThreadReduceOperation::template GetIdentityValue<FloatReduceAcc>();
+                    static_for<0, mreduce_per_thread, 1>{}(
+                        [&](auto I) { r_thread_buf(I) = reduce_identityVal; });
+                    static_for<0, mreduce_per_thread, 1>{}([&](auto im) {
+                        static_for<0, nreduce_per_thread, 1>{}([&](auto in) {
+                            constexpr auto offset =
+                                Number<cde_reduce_thread_desc_mperblock_nperblock.CalculateOffset(
+                                    make_tuple(im, in))>{};
+
+                            qs_element_op[Ir](e_thread_buf(offset), e_thread_buf(offset));
+                        });
+                    });
+                    ThreadwiseReduce::Reduce(e_thread_buf, r_thread_buf);
+
+                    // gridwise reduction
+                    reduce_thread_copy_vgpr_to_global.Run(r_thread_desc_mblock_mperblock,
+                                                          make_tuple(I0, I0),
+                                                          r_thread_buf,
+                                                          rs_grid_desc_mblock_mperblock[Ir],
+                                                          rs_grid_buf(Ir));
+
+                    if constexpr(access_id < num_access - 1)
+                    {
+                        // move on R0, R1, ...
+                        constexpr auto de_global_step = sfc_der_global.GetForwardStep(access_id);
+                        reduce_thread_copy_vgpr_to_global.MoveDstSliceWindow(
+                            rs_grid_desc_mblock_mperblock[Ir],
+                            make_tuple(de_global_step[I0], de_global_step[I1]));
+                    }
+                });
+            }); // copy c, d, e + reduction
+
+        } // shuffle C + Ds + reduction + write out
+    }     // Run
+};
+
+} // namespace ck