N-D Tensor Contraction example, instance, and client example (#270)

* adding contraction

* add contraction example

* update examle

* update example

* format

* update readme

* clean header

* clean header

* contraction with multiple D

* rename

* fix naming issue; add instances for contraction+bilinear

* change assumed virtual layout of contraction; add client example

* update example

* update

* contraction+scale

* use type_convert

* rename

client_example/04_contraction/CMakeLists.txt

+add_executable(client_contraction_scale contraction_scale.cpp)
+target_link_libraries(client_contraction_scale PRIVATE composable_kernel::device_operations)
+
+add_executable(client_contraction_bilinear contraction_bilinear.cpp)
+target_link_libraries(client_contraction_bilinear PRIVATE composable_kernel::device_operations)
+

client_example/04_contraction/contraction_bilinear.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#include <iomanip>
+#include <numeric>
+#include <vector>
+#include <iostream>
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/device/tensor_layout.hpp"
+#include "ck/tensor_operation/gpu/device/device_contraction_multiple_d.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/tensor_operation_instance/gpu/contraction_bilinear.hpp"
+
+using F32 = float;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+using Bilinear    = ck::tensor_operation::element_wise::Bilinear;
+
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = Bilinear;
+
+using ADataType        = F32;
+using BDataType        = F32;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using DDataType        = F32;
+using DsDataType       = ck::Tuple<DDataType>;
+using EDataType        = F32;
+
+static constexpr ck::index_t NumDimM = 2;
+static constexpr ck::index_t NumDimN = 2;
+static constexpr ck::index_t NumDimK = 2;
+
+struct SimpleDeviceMem
+{
+    SimpleDeviceMem() = delete;
+
+    SimpleDeviceMem(std::size_t mem_size) : p_mem_{}
+    {
+        (void)hipMalloc(static_cast<void**>(&p_mem_), mem_size);
+    }
+
+    void* GetDeviceBuffer() { return p_mem_; }
+
+    ~SimpleDeviceMem() { (void)hipFree(p_mem_); }
+
+    void* p_mem_;
+};
+
+int main(int argc, char* argv[])
+{
+    // A[M0, M1, K0, K1]
+    std::vector<ck::index_t> a_ms_ks_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> a_ms_ks_strides{524288, 4096, 128, 1};
+    // B[N0, N1, K0, K1]
+    std::vector<ck::index_t> b_ns_ks_lengths{32, 64, 32, 64};
+    std::vector<ck::index_t> b_ns_ks_strides{524288, 4096, 128, 1};
+    // D[M0, M1, N0, N1]
+    std::vector<ck::index_t> d_ms_ns_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> d_ms_ns_strides{524288, 4096, 128, 1};
+    // E[M0, M1, N0, N1]
+    std::vector<ck::index_t> e_ms_ns_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> e_ms_ns_strides{524288, 4096, 128, 1};
+
+    float alpha = 1.f;
+    float beta  = 1.f;
+
+    if(argc == 1)
+    {
+        // use default case
+    }
+    else if(argc == 25)
+    {
+        const ck::index_t M0 = std::stoi(argv[1]);
+        const ck::index_t M1 = std::stoi(argv[2]);
+
+        const ck::index_t N0 = std::stoi(argv[3]);
+        const ck::index_t N1 = std::stoi(argv[4]);
+
+        const ck::index_t K0 = std::stoi(argv[5]);
+        const ck::index_t K1 = std::stoi(argv[6]);
+
+        a_ms_ks_lengths = {M0, M1, K0, K1};
+        a_ms_ks_strides = {
+            std::stoi(argv[7]), std::stoi(argv[8]), std::stoi(argv[9]), std::stoi(argv[10])};
+
+        b_ns_ks_lengths = {N0, N1, K0, K1};
+        b_ns_ks_strides = {
+            std::stoi(argv[11]), std::stoi(argv[12]), std::stoi(argv[13]), std::stoi(argv[14])};
+
+        d_ms_ns_lengths = {M0, M1, N0, N1};
+        d_ms_ns_strides = {
+            std::stoi(argv[15]), std::stoi(argv[16]), std::stoi(argv[17]), std::stoi(argv[18])};
+
+        e_ms_ns_lengths = {M0, M1, N0, N1};
+        e_ms_ns_strides = {
+            std::stoi(argv[19]), std::stoi(argv[20]), std::stoi(argv[21]), std::stoi(argv[22])};
+
+        alpha = std::stof(argv[23]);
+        beta  = std::stof(argv[24]);
+    }
+    else
+    {
+        printf("arg1 to 6: M0, M1, N0, N1, K0, K1\n");
+        printf("arg7 to 10: Stride_A_M0, Stride_A_M1, Stride_A_K0, Stride_A_K1\n");
+        printf("arg11 to 14: Stride_B_N0, Stride_B_N1, Stride_B_K0, Stride_B_K1\n");
+        printf("arg15 to 18: Stride_D_M0, Stride_D_M1, Stride_D_N0, Stride_D_N1\n");
+        printf("arg19 to 22: Stride_E_M0, Stride_E_M1, Stride_E_N0, Stride_E_N1\n");
+        printf("arg23 to 24: alpha, beta\n");
+        exit(0);
+    }
+
+    auto f_tensor_space_size = [](auto lengths, auto strides) {
+        std::size_t space_size = 1;
+        for(std::size_t i = 0; i < lengths.size(); ++i)
+        {
+            space_size += (lengths[i] - 1) * strides[i];
+        }
+        return space_size;
+    };
+
+    SimpleDeviceMem a_device_buf(sizeof(ADataType) *
+                                 f_tensor_space_size(a_ms_ks_lengths, a_ms_ks_strides));
+    SimpleDeviceMem b_device_buf(sizeof(BDataType) *
+                                 f_tensor_space_size(b_ns_ks_lengths, b_ns_ks_strides));
+    SimpleDeviceMem d_device_buf(sizeof(DDataType) *
+                                 f_tensor_space_size(d_ms_ns_lengths, d_ms_ns_strides));
+    SimpleDeviceMem e_device_buf(sizeof(EDataType) *
+                                 f_tensor_space_size(e_ms_ns_lengths, e_ms_ns_strides));
+
+    using DeviceOp = ck::tensor_operation::device::DeviceContractionMultipleD<
+        NumDimM,
+        NumDimN,
+        NumDimK,
+        ADataType,
+        BDataType,
+        ck::Tuple<DDataType>,
+        EDataType,
+        ck::tensor_operation::element_wise::PassThrough,
+        ck::tensor_operation::element_wise::PassThrough,
+        ck::tensor_operation::element_wise::Bilinear>;
+
+    // get device op instances
+    const auto op_ptrs = ck::tensor_operation::device::instance::DeviceOperationInstanceFactory<
+        DeviceOp>::GetInstances();
+
+    std::cout << "found " << op_ptrs.size() << " instances" << std::endl;
+
+    const auto a_element_op   = AElementOp{};
+    const auto b_element_op   = BElementOp{};
+    const auto cde_element_op = CDEElementOp{alpha, beta};
+
+    std::string best_op_name;
+    bool found            = false;
+    int best_op_id        = -1;
+    float best_ave_time   = 0;
+    float best_tflops     = 0;
+    float best_gb_per_sec = 0;
+
+    // profile device operation instances
+    std::cout << "Run all instances and do timing" << std::endl;
+
+    for(int i = 0; i < op_ptrs.size(); ++i)
+    {
+        auto& op_ptr = op_ptrs[i];
+
+        auto argument_ptr =
+            op_ptr->MakeArgumentPointer(a_device_buf.GetDeviceBuffer(),
+                                        b_device_buf.GetDeviceBuffer(),
+                                        std::array<const void*, 1>{d_device_buf.GetDeviceBuffer()},
+                                        e_device_buf.GetDeviceBuffer(),
+                                        a_ms_ks_lengths,
+                                        a_ms_ks_strides,
+                                        b_ns_ks_lengths,
+                                        b_ns_ks_strides,
+                                        std::array<std::vector<ck::index_t>, 1>{d_ms_ns_lengths},
+                                        std::array<std::vector<ck::index_t>, 1>{d_ms_ns_strides},
+                                        e_ms_ns_lengths,
+                                        e_ms_ns_strides,
+                                        a_element_op,
+                                        b_element_op,
+                                        cde_element_op);
+
+        auto invoker_ptr = op_ptr->MakeInvokerPointer();
+
+        std::string op_name = op_ptr->GetTypeString();
+
+        if(op_ptr->IsSupportedArgument(argument_ptr.get()))
+        {
+            float ave_time = invoker_ptr->Run(argument_ptr.get(), StreamConfig{nullptr, true});
+
+            ck::index_t M = std::accumulate(e_ms_ns_lengths.begin(),
+                                            e_ms_ns_lengths.begin() + NumDimM,
+                                            ck::index_t{1},
+                                            std::multiplies<ck::index_t>{});
+
+            ck::index_t N = std::accumulate(e_ms_ns_lengths.begin() + NumDimM,
+                                            e_ms_ns_lengths.begin() + NumDimM + NumDimN,
+                                            ck::index_t{1},
+                                            std::multiplies<ck::index_t>{});
+
+            ck::index_t K = std::accumulate(a_ms_ks_lengths.begin() + NumDimM,
+                                            a_ms_ks_lengths.begin() + NumDimM + NumDimK,
+                                            ck::index_t{1},
+                                            std::multiplies<ck::index_t>{});
+
+            std::size_t flop      = std::size_t(2) * M * N * K;
+            std::size_t num_btype = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
+                                    sizeof(DDataType) * M * N + sizeof(EDataType) * M * N;
+
+            float tflops = static_cast<float>(flop) / 1.E9 / ave_time;
+
+            float gb_per_sec = num_btype / 1.E6 / ave_time;
+
+            std::cout << "Perf: " << std::setw(10) << ave_time << " ms, " << tflops << " TFlops, "
+                      << gb_per_sec << " GB/s, " << op_name << std::endl;
+
+            if(tflops > best_tflops)
+            {
+                found           = true;
+                best_op_id      = i;
+                best_op_name    = op_name;
+                best_tflops     = tflops;
+                best_ave_time   = ave_time;
+                best_gb_per_sec = gb_per_sec;
+            }
+        }
+        else
+        {
+            std::cout << op_name << " does not support this problem" << std::endl;
+        }
+    }
+
+    std::cout << "Best Perf: " << best_ave_time << " ms, " << best_tflops << " TFlops, "
+              << best_gb_per_sec << " GB/s, " << best_op_name << std::endl;
+
+    return 0;
+}

client_example/04_contraction/contraction_scale.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#include <iomanip>
+#include <numeric>
+#include <vector>
+#include <iostream>
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/device/tensor_layout.hpp"
+#include "ck/tensor_operation/gpu/device/device_contraction_multiple_d.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/tensor_operation_instance/gpu/contraction_scale.hpp"
+
+using F32 = float;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+using Scale       = ck::tensor_operation::element_wise::Scale;
+
+using AElementOp   = PassThrough;
+using BElementOp   = PassThrough;
+using CDEElementOp = Scale;
+
+using ADataType        = F32;
+using BDataType        = F32;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using DsDataType       = ck::Tuple<>;
+using EDataType        = F32;
+
+static constexpr ck::index_t NumDimM = 2;
+static constexpr ck::index_t NumDimN = 2;
+static constexpr ck::index_t NumDimK = 2;
+
+struct SimpleDeviceMem
+{
+    SimpleDeviceMem() = delete;
+
+    SimpleDeviceMem(std::size_t mem_size) : p_mem_{}
+    {
+        (void)hipMalloc(static_cast<void**>(&p_mem_), mem_size);
+    }
+
+    void* GetDeviceBuffer() { return p_mem_; }
+
+    ~SimpleDeviceMem() { (void)hipFree(p_mem_); }
+
+    void* p_mem_;
+};
+
+int main(int argc, char* argv[])
+{
+    // A[M0, M1, K0, K1]
+    std::vector<ck::index_t> a_ms_ks_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> a_ms_ks_strides{524288, 4096, 128, 1};
+    // B[N0, N1, K0, K1]
+    std::vector<ck::index_t> b_ns_ks_lengths{32, 64, 32, 64};
+    std::vector<ck::index_t> b_ns_ks_strides{524288, 4096, 128, 1};
+    // E[M0, M1, N0, N1]
+    std::vector<ck::index_t> e_ms_ns_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> e_ms_ns_strides{524288, 4096, 128, 1};
+
+    float scale = 1.f;
+
+    if(argc == 1)
+    {
+        // use default case
+    }
+    else if(argc == 20)
+    {
+        const ck::index_t M0 = std::stoi(argv[1]);
+        const ck::index_t M1 = std::stoi(argv[2]);
+
+        const ck::index_t N0 = std::stoi(argv[3]);
+        const ck::index_t N1 = std::stoi(argv[4]);
+
+        const ck::index_t K0 = std::stoi(argv[5]);
+        const ck::index_t K1 = std::stoi(argv[6]);
+
+        a_ms_ks_lengths = {M0, M1, K0, K1};
+        a_ms_ks_strides = {
+            std::stoi(argv[7]), std::stoi(argv[8]), std::stoi(argv[9]), std::stoi(argv[10])};
+
+        b_ns_ks_lengths = {N0, N1, K0, K1};
+        b_ns_ks_strides = {
+            std::stoi(argv[11]), std::stoi(argv[12]), std::stoi(argv[13]), std::stoi(argv[14])};
+
+        e_ms_ns_lengths = {M0, M1, N0, N1};
+        e_ms_ns_strides = {
+            std::stoi(argv[15]), std::stoi(argv[16]), std::stoi(argv[17]), std::stoi(argv[18])};
+
+        scale = std::stof(argv[19]);
+    }
+    else
+    {
+        printf("arg1 to 6: M0, M1, N0, N1, K0, K1\n");
+        printf("arg7 to 10: Stride_A_M0, Stride_A_M1, Stride_A_K0, Stride_A_K1\n");
+        printf("arg11 to 14: Stride_B_N0, Stride_B_N1, Stride_B_K0, Stride_B_K1\n");
+        printf("arg15 to 18: Stride_E_M0, Stride_E_M1, Stride_E_N0, Stride_E_N1\n");
+        printf("arg19: scale\n");
+        exit(0);
+    }
+
+    auto f_tensor_space_size = [](auto lengths, auto strides) {
+        std::size_t space_size = 1;
+        for(std::size_t i = 0; i < lengths.size(); ++i)
+        {
+            space_size += (lengths[i] - 1) * strides[i];
+        }
+        return space_size;
+    };
+
+    SimpleDeviceMem a_device_buf(sizeof(ADataType) *
+                                 f_tensor_space_size(a_ms_ks_lengths, a_ms_ks_strides));
+    SimpleDeviceMem b_device_buf(sizeof(BDataType) *
+                                 f_tensor_space_size(b_ns_ks_lengths, b_ns_ks_strides));
+    SimpleDeviceMem e_device_buf(sizeof(EDataType) *
+                                 f_tensor_space_size(e_ms_ns_lengths, e_ms_ns_strides));
+
+    using DeviceOp = ck::tensor_operation::device::DeviceContractionMultipleD<
+        NumDimM,
+        NumDimN,
+        NumDimK,
+        ADataType,
+        BDataType,
+        ck::Tuple<>,
+        EDataType,
+        ck::tensor_operation::element_wise::PassThrough,
+        ck::tensor_operation::element_wise::PassThrough,
+        ck::tensor_operation::element_wise::Scale>;
+
+    // get device op instances
+    const auto op_ptrs = ck::tensor_operation::device::instance::DeviceOperationInstanceFactory<
+        DeviceOp>::GetInstances();
+
+    std::cout << "found " << op_ptrs.size() << " instances" << std::endl;
+
+    const auto a_element_op   = AElementOp{};
+    const auto b_element_op   = BElementOp{};
+    const auto cde_element_op = CDEElementOp{scale};
+
+    std::string best_op_name;
+    bool found            = false;
+    int best_op_id        = -1;
+    float best_ave_time   = 0;
+    float best_tflops     = 0;
+    float best_gb_per_sec = 0;
+
+    // profile device operation instances
+    std::cout << "Run all instances and do timing" << std::endl;
+
+    for(int i = 0; i < op_ptrs.size(); ++i)
+    {
+        auto& op_ptr = op_ptrs[i];
+
+        auto argument_ptr = op_ptr->MakeArgumentPointer(a_device_buf.GetDeviceBuffer(),
+                                                        b_device_buf.GetDeviceBuffer(),
+                                                        std::array<const void*, 0>{},
+                                                        e_device_buf.GetDeviceBuffer(),
+                                                        a_ms_ks_lengths,
+                                                        a_ms_ks_strides,
+                                                        b_ns_ks_lengths,
+                                                        b_ns_ks_strides,
+                                                        std::array<std::vector<ck::index_t>, 0>{},
+                                                        std::array<std::vector<ck::index_t>, 0>{},
+                                                        e_ms_ns_lengths,
+                                                        e_ms_ns_strides,
+                                                        a_element_op,
+                                                        b_element_op,
+                                                        cde_element_op);
+
+        auto invoker_ptr = op_ptr->MakeInvokerPointer();
+
+        std::string op_name = op_ptr->GetTypeString();
+
+        if(op_ptr->IsSupportedArgument(argument_ptr.get()))
+        {
+            float ave_time = invoker_ptr->Run(argument_ptr.get(), StreamConfig{nullptr, true});
+
+            ck::index_t M = std::accumulate(e_ms_ns_lengths.begin(),
+                                            e_ms_ns_lengths.begin() + NumDimM,
+                                            ck::index_t{1},
+                                            std::multiplies<ck::index_t>{});
+
+            ck::index_t N = std::accumulate(e_ms_ns_lengths.begin() + NumDimM,
+                                            e_ms_ns_lengths.begin() + NumDimM + NumDimN,
+                                            ck::index_t{1},
+                                            std::multiplies<ck::index_t>{});
+
+            ck::index_t K = std::accumulate(a_ms_ks_lengths.begin() + NumDimM,
+                                            a_ms_ks_lengths.begin() + NumDimM + NumDimK,
+                                            ck::index_t{1},
+                                            std::multiplies<ck::index_t>{});
+
+            std::size_t flop = std::size_t(2) * M * N * K;
+            std::size_t num_btype =
+                sizeof(ADataType) * M * K + sizeof(BDataType) * K * N + sizeof(EDataType) * M * N;
+
+            float tflops = static_cast<float>(flop) / 1.E9 / ave_time;
+
+            float gb_per_sec = num_btype / 1.E6 / ave_time;
+
+            std::cout << "Perf: " << std::setw(10) << ave_time << " ms, " << tflops << " TFlops, "
+                      << gb_per_sec << " GB/s, " << op_name << std::endl;
+
+            if(tflops > best_tflops)
+            {
+                found           = true;
+                best_op_id      = i;
+                best_op_name    = op_name;
+                best_tflops     = tflops;
+                best_ave_time   = ave_time;
+                best_gb_per_sec = gb_per_sec;
+            }
+        }
+        else
+        {
+            std::cout << op_name << " does not support this problem" << std::endl;
+        }
+    }
+
+    std::cout << "Best Perf: " << best_ave_time << " ms, " << best_tflops << " TFlops, "
+              << best_gb_per_sec << " GB/s, " << best_op_name << std::endl;
+
+    return 0;
+}

client_example/CMakeLists.txt

@@ -9,3 +9,4 @@ message(STATUS "Build with HIP ${hip_VERSION}")
 add_subdirectory(01_gemm)
 add_subdirectory(02_gemm_add_add_fastgelu)
 add_subdirectory(03_gemm_layernorm)
+add_subdirectory(04_contraction)

example/02_gemm_bilinear/gemm_bilinear_xdl_fp16.cpp

@@ -213,15 +213,15 @@ int main(int argc, char* argv[])
         d_m_n.GenerateTensorValue(GeneratorTensor_3<DDataType>{-0.5, 0.5});
     }
 
-    DeviceMem a_m_k_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpace());
-    DeviceMem b_k_n_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpace());
-    DeviceMem d_m_n_device_buf(sizeof(DDataType) * d_m_n.mDesc.GetElementSpace());
-    DeviceMem e_m_n_device_buf(sizeof(EDataType) * e_m_n_device_result.mDesc.GetElementSpace());
+    DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpace());
+    DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpace());
+    DeviceMem d_device_buf(sizeof(DDataType) * d_m_n.mDesc.GetElementSpace());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_m_n_device_result.mDesc.GetElementSpace());
 
-    a_m_k_device_buf.ToDevice(a_m_k.mData.data());
-    b_k_n_device_buf.ToDevice(b_k_n.mData.data());
-    d_m_n_device_buf.ToDevice(d_m_n.mData.data());
-    e_m_n_device_buf.ToDevice(e_m_n_device_result.mData.data());
+    a_device_buf.ToDevice(a_m_k.mData.data());
+    b_device_buf.ToDevice(b_k_n.mData.data());
+    d_device_buf.ToDevice(d_m_n.mData.data());
+    e_device_buf.ToDevice(e_m_n_device_result.mData.data());
 
     auto a_element_op   = AElementOp{};
     auto b_element_op   = BElementOp{};
@@ -231,10 +231,10 @@ int main(int argc, char* argv[])
     auto device_op = DeviceOpInstance{};
     auto invoker   = device_op.MakeInvoker();
     auto argument =
-        device_op.MakeArgument(a_m_k_device_buf.GetDeviceBuffer(),
-                               b_k_n_device_buf.GetDeviceBuffer(),
-                               std::array<const void*, 1>{d_m_n_device_buf.GetDeviceBuffer()},
-                               e_m_n_device_buf.GetDeviceBuffer(),
+        device_op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                               b_device_buf.GetDeviceBuffer(),
+                               std::array<const void*, 1>{d_device_buf.GetDeviceBuffer()},
+                               e_device_buf.GetDeviceBuffer(),
                                M,
                                N,
                                K,
@@ -266,7 +266,7 @@ int main(int argc, char* argv[])
     std::cout << "Perf: " << ave_time << " ms, " << tflops << " TFlops, " << gb_per_sec << " GB/s"
               << std::endl;
 
-    e_m_n_device_buf.FromDevice(e_m_n_device_result.mData.data());
+    e_device_buf.FromDevice(e_m_n_device_result.mData.data());
 
     if(do_verification)
     {
@@ -296,7 +296,7 @@ int main(int argc, char* argv[])
             }
         }
 
-        e_m_n_device_buf.FromDevice(e_m_n_device_result.mData.data());
+        e_device_buf.FromDevice(e_m_n_device_result.mData.data());
 
         return ck::utils::check_err(e_m_n_device_result.mData, e_m_n_host_result.mData) ? 0 : 1;
     }

example/03_gemm_bias_relu/gemm_bias_relu_xdl_fp16.cpp

@@ -191,14 +191,14 @@ int main(int argc, char* argv[])
         d_m_n.GenerateTensorValue(GeneratorTensor_3<DDataType>{0.0, 1.0});
     }
 
-    DeviceMem a_m_k_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpace());
-    DeviceMem b_k_n_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpace());
-    DeviceMem d_m_n_device_buf(sizeof(DDataType) * d_m_n.mDesc.GetElementSpace());
-    DeviceMem e_m_n_device_buf(sizeof(EDataType) * e_m_n_device_result.mDesc.GetElementSpace());
+    DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpace());
+    DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpace());
+    DeviceMem d_device_buf(sizeof(DDataType) * d_m_n.mDesc.GetElementSpace());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_m_n_device_result.mDesc.GetElementSpace());
 
-    a_m_k_device_buf.ToDevice(a_m_k.mData.data());
-    b_k_n_device_buf.ToDevice(b_k_n.mData.data());
-    d_m_n_device_buf.ToDevice(d_m_n.mData.data());
+    a_device_buf.ToDevice(a_m_k.mData.data());
+    b_device_buf.ToDevice(b_k_n.mData.data());
+    d_device_buf.ToDevice(d_m_n.mData.data());
 
     auto a_element_op   = AElementOp{};
     auto b_element_op   = BElementOp{};
@@ -210,10 +210,10 @@ int main(int argc, char* argv[])
     auto invoker = device_op.MakeInvoker();
 
     auto argument =
-        device_op.MakeArgument(a_m_k_device_buf.GetDeviceBuffer(),
-                               b_k_n_device_buf.GetDeviceBuffer(),
-                               std::array<const void*, 1>{d_m_n_device_buf.GetDeviceBuffer()},
-                               e_m_n_device_buf.GetDeviceBuffer(),
+        device_op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                               b_device_buf.GetDeviceBuffer(),
+                               std::array<const void*, 1>{d_device_buf.GetDeviceBuffer()},
+                               e_device_buf.GetDeviceBuffer(),
                                M,
                                N,
                                K,
@@ -246,7 +246,7 @@ int main(int argc, char* argv[])
 
     if(do_verification)
     {
-        e_m_n_device_buf.FromDevice(e_m_n_device_result.mData.data());
+        e_device_buf.FromDevice(e_m_n_device_result.mData.data());
 
         Tensor<AccDataType> c_m_n(f_host_tensor_descriptor(M, N, StrideE, ELayout{}));
 

example/04_gemm_add_add_fastgelu/gemm_add_add_fastgelu_xdl_fp16.cpp

@@ -156,16 +156,16 @@ int main(int argc, char* argv[])
         d1_m_n.GenerateTensorValue(GeneratorTensor_3<D1DataType>{0.0, 1.0});
     }
 
-    DeviceMem a_m_k_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpace());
-    DeviceMem b_k_n_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpace());
-    DeviceMem d0_m_n_device_buf(sizeof(D0DataType) * d0_m_n.mDesc.GetElementSpace());
-    DeviceMem d1_m_n_device_buf(sizeof(D1DataType) * d1_m_n.mDesc.GetElementSpace());
-    DeviceMem e_m_n_device_buf(sizeof(EDataType) * e_m_n_device_result.mDesc.GetElementSpace());
+    DeviceMem a_device_buf(sizeof(ADataType) * a_m_k.mDesc.GetElementSpace());
+    DeviceMem b_device_buf(sizeof(BDataType) * b_k_n.mDesc.GetElementSpace());
+    DeviceMem d0_device_buf(sizeof(D0DataType) * d0_m_n.mDesc.GetElementSpace());
+    DeviceMem d1_device_buf(sizeof(D1DataType) * d1_m_n.mDesc.GetElementSpace());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_m_n_device_result.mDesc.GetElementSpace());
 
-    a_m_k_device_buf.ToDevice(a_m_k.mData.data());
-    b_k_n_device_buf.ToDevice(b_k_n.mData.data());
-    d0_m_n_device_buf.ToDevice(d0_m_n.mData.data());
-    d1_m_n_device_buf.ToDevice(d1_m_n.mData.data());
+    a_device_buf.ToDevice(a_m_k.mData.data());
+    b_device_buf.ToDevice(b_k_n.mData.data());
+    d0_device_buf.ToDevice(d0_m_n.mData.data());
+    d1_device_buf.ToDevice(d1_m_n.mData.data());
 
     auto a_element_op   = AElementOp{};
     auto b_element_op   = BElementOp{};
@@ -175,11 +175,11 @@ int main(int argc, char* argv[])
     auto device_op = DeviceOpInstance{};
     auto invoker   = device_op.MakeInvoker();
     auto argument =
-        device_op.MakeArgument(a_m_k_device_buf.GetDeviceBuffer(),
-                               b_k_n_device_buf.GetDeviceBuffer(),
-                               std::array<const void*, 2>{d0_m_n_device_buf.GetDeviceBuffer(),
-                                                          d1_m_n_device_buf.GetDeviceBuffer()},
-                               e_m_n_device_buf.GetDeviceBuffer(),
+        device_op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                               b_device_buf.GetDeviceBuffer(),
+                               std::array<const void*, 2>{d0_device_buf.GetDeviceBuffer(),
+                                                          d1_device_buf.GetDeviceBuffer()},
+                               e_device_buf.GetDeviceBuffer(),
                                M,
                                N,
                                K,
@@ -239,7 +239,7 @@ int main(int argc, char* argv[])
             }
         }
 
-        e_m_n_device_buf.FromDevice(e_m_n_device_result.mData.data());
+        e_device_buf.FromDevice(e_m_n_device_result.mData.data());
 
         return ck::utils::check_err(e_m_n_device_result.mData, e_m_n_host_result.mData) ? 0 : 1;
     }

example/21_gemm_layernorm/gemm_bias_relu_add_layernorm_xdl_fp16.cpp

@@ -166,15 +166,15 @@ 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 =
-                static_cast<AccDataType>(c_m_n(m, n)) + static_cast<AccDataType>(bias_n(n));
+            AccDataType acc = ck::type_convert<AccDataType>(c_m_n(m, n)) +
+                              ck::type_convert<AccDataType>(bias_n(n));
 
-            AccDataType c1 = static_cast<AccDataType>(c1_m_n(m, 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) = static_cast<CDataType>(acc);
+            c_m_n(m, n) = ck::type_convert<CDataType>(acc);
         }
 
     // reduce_mean and reduce_square_mean
@@ -208,12 +208,12 @@ void host_gemm_layernorm(Tensor<LayerNormOutDataType>& out_m_n,
         {
             AccDataType out_acc = 0;
             layerNormInst(out_acc,
-                          static_cast<AccDataType>(c_m_n(m, n)),
-                          static_cast<AccDataType>(mean_m(m)),
-                          static_cast<AccDataType>(meanSquare_m(m)),
-                          static_cast<AccDataType>(gamma_n(n)),
-                          static_cast<AccDataType>(beta_n(n)));
-            out_m_n(m, n) = static_cast<ReduceDataType>(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);
         }
     }
 }

example/26_contraction/CMakeLists.txt

+add_example_executable(example_contraction_bilinear_xdl_fp32 contraction_bilinear_xdl_fp32.cpp)
+add_example_executable(example_contraction_scale_xdl_fp32 contraction_scale_xdl_fp32.cpp)

example/26_contraction/README.md

+# Instructions for ```example_contraction_bilinear_xdl_fp32```
+
+## Run
+```bash
+#arg1: verification (0=no, 1=yes)
+#arg2: initialization (0=no init, 1=integer value, 2=decimal value)
+#arg3: time kernel (0=no, 1=yes)
+./bin/example_contraction_bilinear_xdl_fp32 1 1 1
+```
+
+Result (MI100 @ dynammic freq, 46TFlops peak FP32)
+```
+a_ms_ks: dim 4, lengths {30, 128, 32, 64}, strides {524288, 4096, 128, 1}
+b_ks_ns: dim 4, lengths {32, 64, 32, 64}, strides {128, 1, 524288, 4096}
+c_ms_ns: dim 4, lengths {30, 128, 32, 64}, strides {524288, 4096, 128, 1}
+launch_and_time_kernel: grid_dim {240, 1, 1}, block_dim {256, 1, 1}
+Warm up 1 time
+Start running 10 times...
+Perf: 0.843286 ms, 38.1985 TFlops, 94.5014 GB/s, DeviceContractionMultipleD_Xdl_CShuffle<256, 256, 128, 16, 4, 4>
+```

example/26_contraction/contraction_bilinear_xdl_fp32.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/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/device_contraction_multiple_d_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/utility/check_err.hpp"
+#include "ck/library/host_tensor/device_memory.hpp"
+#include "ck/library/host_tensor/host_tensor.hpp"
+#include "ck/library/host_tensor/host_tensor_generator.hpp"
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+using F32 = float;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+
+using ADataType        = F32;
+using BDataType        = F32;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using DDataType        = F32;
+using DsDataType       = ck::Tuple<DDataType>;
+using EDataType        = F32;
+
+static constexpr ck::index_t NumDimM = 2;
+static constexpr ck::index_t NumDimN = 2;
+static constexpr ck::index_t NumDimK = 2;
+
+using AElementOp   = ck::tensor_operation::element_wise::PassThrough;
+using BElementOp   = ck::tensor_operation::element_wise::PassThrough;
+using CDEElementOp = ck::tensor_operation::element_wise::Bilinear;
+
+static constexpr auto GemmSpec = ck::tensor_operation::device::GemmSpecialization::MNKPadding;
+
+// clang-format off
+using DeviceOpInstanceKKNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   4,   4,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              4,              4,         1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              4,              4,         1,           1,           1,              S<1, 16, 1, 16>,               4>;
+
+using DeviceOpInstanceKNNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   4,   1,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              4,              4,         1,     S<8, 32, 1>,     S<0, 2, 1>,     S<0, 2, 1>,             1,              4,              1,         0,           1,           1,              S<1, 16, 1, 16>,               4>;
+
+using DeviceOpInstanceMKNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   1,   4,   32,   32,    4,    2,     S<4, 64, 1>,     S<0, 2, 1>,     S<0, 2, 1>,              1,              4,              1,         0,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              4,              4,         1,           1,           1,              S<1, 16, 1, 16>,               4>;
+
+using DeviceOpInstanceMNNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   1,   1,   32,   32,    4,    2,     S<4, 64, 1>,     S<0, 2, 1>,     S<0, 2, 1>,              1,              4,              1,         0,     S<8, 32, 1>,     S<0, 2, 1>,     S<0, 2, 1>,             1,              4,              1,         0,           1,           1,              S<1, 16, 1, 16>,               4>;
+// clang-format on
+
+using DeviceOpInstance = DeviceOpInstanceKKNN;
+
+// hardcoded for NumDimM == NumDimN == NumDimK == 2
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename EDataType,
+          typename AccDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          ck::enable_if_t<NumDimM == 2 && NumDimN == 2 && NumDimK == 2, bool> = false>
+struct ReferenceContraction_M2_N2_K2 : public ck::tensor_operation::device::BaseOperator
+{
+    // Argument
+    struct Argument : public ck::tensor_operation::device::BaseArgument
+    {
+        Argument(const Tensor<ADataType>& a_ms_ks,
+                 const Tensor<BDataType>& b_ns_ks,
+                 Tensor<EDataType>& e_ms_ns,
+                 AElementwiseOperation a_element_op,
+                 BElementwiseOperation b_element_op,
+                 CDEElementwiseOperation cde_element_op)
+            : a_ms_ks_{a_ms_ks},
+              b_ns_ks_{b_ns_ks},
+              e_ms_ns_{e_ms_ns},
+              a_element_op_{a_element_op},
+              b_element_op_{b_element_op},
+              cde_element_op_{cde_element_op}
+        {
+        }
+
+        const Tensor<ADataType>& a_ms_ks_;
+        const Tensor<BDataType>& b_ns_ks_;
+        Tensor<EDataType>& e_ms_ns_;
+
+        AElementwiseOperation a_element_op_;
+        BElementwiseOperation b_element_op_;
+        CDEElementwiseOperation cde_element_op_;
+    };
+
+    // Invoker
+    struct Invoker : public ck::tensor_operation::device::BaseInvoker
+    {
+        using Argument = ReferenceContraction_M2_N2_K2::Argument;
+
+        float Run(const Argument& arg)
+        {
+            auto f_ms_ns = [&](auto m0, auto m1, auto n0, auto n1) {
+                const int K0 = arg.a_ms_ks_.mDesc.GetLengths()[2];
+                const int K1 = arg.a_ms_ks_.mDesc.GetLengths()[3];
+
+                AccDataType v_acc = 0;
+
+                for(int k0 = 0; k0 < K0; ++k0)
+                {
+                    for(int k1 = 0; k1 < K1; ++k1)
+                    {
+                        AccDataType v_a;
+                        AccDataType v_b;
+
+                        arg.a_element_op_(
+                            v_a, ck::type_convert<const AccDataType>(arg.a_ms_ks_(m0, m1, k0, k1)));
+                        arg.b_element_op_(
+                            v_b, ck::type_convert<const AccDataType>(arg.b_ns_ks_(n0, n1, k0, k1)));
+
+                        v_acc += v_a * v_b;
+                    }
+                }
+
+                AccDataType v_c;
+
+                arg.cde_element_op_(v_c, v_acc);
+
+                arg.e_ms_ns_(m0, m1, n0, n1) = v_c;
+            };
+
+            make_ParallelTensorFunctor(f_ms_ns,
+                                       arg.e_ms_ns_.mDesc.GetLengths()[0],
+                                       arg.e_ms_ns_.mDesc.GetLengths()[1],
+                                       arg.e_ms_ns_.mDesc.GetLengths()[2],
+                                       arg.e_ms_ns_.mDesc.GetLengths()[3])(
+                std::thread::hardware_concurrency());
+
+            return 0;
+        }
+
+        float Run(const ck::tensor_operation::device::BaseArgument* p_arg,
+                  const StreamConfig& /* stream_config */ = StreamConfig{}) override
+        {
+            return Run(*dynamic_cast<const Argument*>(p_arg));
+        }
+    };
+
+    static constexpr bool IsValidCompilationParameter()
+    {
+        // TODO: properly implement this check
+        return true;
+    }
+
+    bool IsSupportedArgument(const ck::tensor_operation::device::BaseArgument*) override
+    {
+        return true;
+    }
+
+    static auto MakeArgument(const Tensor<ADataType>& a_ms_ks,
+                             const Tensor<BDataType>& b_ns_ks,
+                             Tensor<EDataType>& e_ms_ns,
+                             AElementwiseOperation a_element_op,
+                             BElementwiseOperation b_element_op,
+                             CDEElementwiseOperation cde_element_op)
+    {
+        return Argument{a_ms_ks, b_ns_ks, e_ms_ns, a_element_op, b_element_op, cde_element_op};
+    }
+
+    static auto MakeInvoker() { return Invoker{}; }
+
+    virtual std::unique_ptr<ck::tensor_operation::device::BaseInvoker> MakeInvokerPointer()
+    {
+        return std::make_unique<Invoker>(Invoker{});
+    }
+
+    std::string GetTypeString() const override
+    {
+        auto str = std::stringstream();
+
+        // clang-format off
+        str << "ReferenceContraction_M2_N2_K2"
+            << std::endl;
+        // clang-format on
+
+        return str.str();
+    }
+};
+
+int main(int argc, char* argv[])
+{
+    bool do_verification = true;
+    int init_method      = 1;
+    bool time_kernel     = false;
+
+    // A[M0, M1, K0, K1]
+    std::vector<ck::index_t> a_ms_ks_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> a_ms_ks_strides{524288, 4096, 128, 1};
+    // B[N0, N1, K0, K1]
+    std::vector<ck::index_t> b_ns_ks_lengths{32, 64, 32, 64};
+    std::vector<ck::index_t> b_ns_ks_strides{524288, 4096, 128, 1};
+    // D[M0, M1, N0, N1]
+    std::vector<ck::index_t> d_ms_ns_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> d_ms_ns_strides{524288, 4096, 128, 1};
+    // E[M0, M1, N0, N1]
+    std::vector<ck::index_t> e_ms_ns_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> e_ms_ns_strides{524288, 4096, 128, 1};
+
+    float alpha = 1.f;
+    float beta  = 1.f;
+
+    if(argc == 1)
+    {
+        // use default case
+    }
+    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 == 28)
+    {
+        do_verification = std::stoi(argv[1]);
+        init_method     = std::stoi(argv[2]);
+        time_kernel     = std::stoi(argv[3]);
+
+        const ck::index_t M0 = std::stoi(argv[4]);
+        const ck::index_t M1 = std::stoi(argv[5]);
+
+        const ck::index_t N0 = std::stoi(argv[6]);
+        const ck::index_t N1 = std::stoi(argv[7]);
+
+        const ck::index_t K0 = std::stoi(argv[8]);
+        const ck::index_t K1 = std::stoi(argv[9]);
+
+        a_ms_ks_lengths = {M0, M1, K0, K1};
+        a_ms_ks_strides = {
+            std::stoi(argv[10]), std::stoi(argv[11]), std::stoi(argv[12]), std::stoi(argv[13])};
+
+        b_ns_ks_lengths = {N0, N1, K0, K1};
+        b_ns_ks_strides = {
+            std::stoi(argv[14]), std::stoi(argv[15]), std::stoi(argv[16]), std::stoi(argv[17])};
+
+        d_ms_ns_lengths = {M0, M1, N0, N1};
+        d_ms_ns_strides = {
+            std::stoi(argv[18]), std::stoi(argv[19]), std::stoi(argv[20]), std::stoi(argv[21])};
+
+        e_ms_ns_lengths = {M0, M1, N0, N1};
+        e_ms_ns_strides = {
+            std::stoi(argv[22]), std::stoi(argv[23]), std::stoi(argv[24]), std::stoi(argv[25])};
+
+        alpha = std::stof(argv[26]);
+        beta  = std::stof(argv[27]);
+    }
+    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=no, 1=yes)\n");
+        printf("arg4 to 7: M0, M1, N0, N1, K0, K1\n");
+        printf("arg10 to 13: Stride_A_M0, Stride_A_M1, Stride_A_K0, Stride_A_K1\n");
+        printf("arg14 to 17: Stride_B_N0, Stride_B_N1, Stride_B_K0, Stride_B_K1\n");
+        printf("arg18 to 21: Stride_D_M0, Stride_D_M1, Stride_D_N0, Stride_D_N1\n");
+        printf("arg22 to 25: Stride_E_M0, Stride_E_M1, Stride_E_N0, Stride_E_N1\n");
+        printf("arg26 to 27: alpha, beta\n");
+        exit(0);
+    }
+
+    Tensor<ADataType> a_ms_ks(
+        std::vector<std::size_t>(a_ms_ks_lengths.begin(), a_ms_ks_lengths.end()),
+        std::vector<std::size_t>(a_ms_ks_strides.begin(), a_ms_ks_strides.end()));
+    Tensor<BDataType> b_ns_ks(
+        std::vector<std::size_t>(b_ns_ks_lengths.begin(), b_ns_ks_lengths.end()),
+        std::vector<std::size_t>(b_ns_ks_strides.begin(), b_ns_ks_strides.end()));
+    Tensor<EDataType> d_ms_ns(
+        std::vector<std::size_t>(d_ms_ns_lengths.begin(), d_ms_ns_lengths.end()),
+        std::vector<std::size_t>(d_ms_ns_strides.begin(), d_ms_ns_strides.end()));
+    Tensor<EDataType> e_ms_ns_host_result(
+        std::vector<std::size_t>(e_ms_ns_lengths.begin(), e_ms_ns_lengths.end()),
+        std::vector<std::size_t>(e_ms_ns_strides.begin(), e_ms_ns_strides.end()));
+    Tensor<EDataType> e_ms_ns_device_result(
+        std::vector<std::size_t>(e_ms_ns_lengths.begin(), e_ms_ns_lengths.end()),
+        std::vector<std::size_t>(e_ms_ns_strides.begin(), e_ms_ns_strides.end()));
+
+    std::cout << "a_ms_ks: " << a_ms_ks.mDesc << std::endl;
+    std::cout << "b_ns_ks: " << b_ns_ks.mDesc << std::endl;
+    std::cout << "d_ms_ns: " << d_ms_ns.mDesc << std::endl;
+    std::cout << "e_ms_ns: " << e_ms_ns_host_result.mDesc << std::endl;
+
+    switch(init_method)
+    {
+    case 0: break;
+    case 1:
+        a_ms_ks.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
+        b_ns_ks.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+        d_ms_ns.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+        break;
+    default:
+        a_ms_ks.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
+        b_ns_ks.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+        d_ms_ns.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+        break;
+    }
+
+    DeviceMem a_device_buf(sizeof(ADataType) * a_ms_ks.mDesc.GetElementSpace());
+    DeviceMem b_device_buf(sizeof(BDataType) * b_ns_ks.mDesc.GetElementSpace());
+    DeviceMem d_device_buf(sizeof(DDataType) * d_ms_ns.mDesc.GetElementSpace());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_ms_ns_device_result.mDesc.GetElementSpace());
+
+    a_device_buf.ToDevice(a_ms_ks.mData.data());
+    b_device_buf.ToDevice(b_ns_ks.mData.data());
+    d_device_buf.ToDevice(d_ms_ns.mData.data());
+
+    // set zero
+    e_device_buf.SetZero();
+
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{alpha, beta};
+
+    // device operation
+    auto op       = DeviceOpInstance{};
+    auto invoker  = op.MakeInvoker();
+    auto argument = op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                                    b_device_buf.GetDeviceBuffer(),
+                                    std::array<const void*, 1>{d_device_buf.GetDeviceBuffer()},
+                                    e_device_buf.GetDeviceBuffer(),
+                                    a_ms_ks_lengths,
+                                    a_ms_ks_strides,
+                                    b_ns_ks_lengths,
+                                    b_ns_ks_strides,
+                                    std::array<std::vector<ck::index_t>, 1>{d_ms_ns_lengths},
+                                    std::array<std::vector<ck::index_t>, 1>{d_ms_ns_strides},
+                                    e_ms_ns_lengths,
+                                    e_ms_ns_strides,
+                                    a_element_op,
+                                    b_element_op,
+                                    cde_element_op);
+
+    if(!op.IsSupportedArgument(argument))
+    {
+        std::cout << op.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+
+    ck::index_t M = std::accumulate(e_ms_ns_lengths.begin(),
+                                    e_ms_ns_lengths.begin() + NumDimM,
+                                    ck::index_t{1},
+                                    std::multiplies<ck::index_t>{});
+
+    ck::index_t N = std::accumulate(e_ms_ns_lengths.begin() + NumDimM,
+                                    e_ms_ns_lengths.begin() + NumDimM + NumDimN,
+                                    ck::index_t{1},
+                                    std::multiplies<ck::index_t>{});
+
+    ck::index_t K = std::accumulate(a_ms_ks_lengths.begin() + NumDimM,
+                                    a_ms_ks_lengths.begin() + NumDimM + NumDimK,
+                                    ck::index_t{1},
+                                    std::multiplies<ck::index_t>{});
+
+    std::size_t flop      = std::size_t(2) * M * N * K;
+    std::size_t num_btype = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
+                            sizeof(DDataType) * M * N + sizeof(EDataType) * M * N;
+
+    float tflops = static_cast<float>(flop) / 1.E9 / ave_time;
+
+    float gb_per_sec = num_btype / 1.E6 / ave_time;
+
+    std::cout << "Perf: " << ave_time << " ms, " << tflops << " TFlops, " << gb_per_sec << " GB/s, "
+              << op.GetTypeString() << std::endl;
+
+    e_device_buf.FromDevice(e_ms_ns_device_result.mData.data());
+
+    if(do_verification)
+    {
+        Tensor<CShuffleDataType> c_ms_ns_host_result(
+            std::vector<std::size_t>(e_ms_ns_lengths.begin(), e_ms_ns_lengths.end()),
+            std::vector<std::size_t>(e_ms_ns_strides.begin(), e_ms_ns_strides.end()));
+
+        using ReferenceOpInstance = ReferenceContraction_M2_N2_K2<NumDimM,
+                                                                  NumDimN,
+                                                                  NumDimK,
+                                                                  ADataType,
+                                                                  BDataType,
+                                                                  CShuffleDataType,
+                                                                  AccDataType,
+                                                                  AElementOp,
+                                                                  BElementOp,
+                                                                  PassThrough>;
+
+        auto ref_gemm    = ReferenceOpInstance{};
+        auto ref_invoker = ref_gemm.MakeInvoker();
+
+        auto ref_argument = ref_gemm.MakeArgument(
+            a_ms_ks, b_ns_ks, c_ms_ns_host_result, a_element_op, b_element_op, PassThrough{});
+
+        ref_invoker.Run(ref_argument);
+
+        for(size_t m0 = 0; m0 < e_ms_ns_host_result.mDesc.GetLengths()[0]; ++m0)
+        {
+            for(size_t m1 = 0; m1 < e_ms_ns_host_result.mDesc.GetLengths()[1]; ++m1)
+            {
+                for(size_t n0 = 0; n0 < e_ms_ns_host_result.mDesc.GetLengths()[2]; ++n0)
+                {
+                    for(size_t n1 = 0; n1 < e_ms_ns_host_result.mDesc.GetLengths()[3]; ++n1)
+                    {
+                        cde_element_op(e_ms_ns_host_result(m0, m1, n0, n1),
+                                       c_ms_ns_host_result(m0, m1, n0, n1),
+                                       d_ms_ns(m0, m1, n0, n1));
+                    }
+                }
+            }
+        }
+
+        return ck::utils::check_err(e_ms_ns_device_result.mData, e_ms_ns_host_result.mData) ? 0 : 1;
+    }
+
+    return 0;
+}

example/26_contraction/contraction_scale_xdl_fp32.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/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/device_contraction_multiple_d_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/utility/check_err.hpp"
+#include "ck/library/host_tensor/device_memory.hpp"
+#include "ck/library/host_tensor/host_tensor.hpp"
+#include "ck/library/host_tensor/host_tensor_generator.hpp"
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+using F32 = float;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+
+using ADataType        = F32;
+using BDataType        = F32;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using DsDataType       = ck::Tuple<>;
+using EDataType        = F32;
+
+static constexpr ck::index_t NumDimM = 2;
+static constexpr ck::index_t NumDimN = 2;
+static constexpr ck::index_t NumDimK = 2;
+
+using AElementOp   = ck::tensor_operation::element_wise::PassThrough;
+using BElementOp   = ck::tensor_operation::element_wise::PassThrough;
+using CDEElementOp = ck::tensor_operation::element_wise::Scale;
+
+static constexpr auto GemmSpec = ck::tensor_operation::device::GemmSpecialization::MNKPadding;
+
+// clang-format off
+using DeviceOpInstanceKKNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   4,   4,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              4,              4,         1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              4,              4,         1,           1,           1,              S<1, 16, 1, 16>,               4>;
+
+using DeviceOpInstanceKNNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   4,   1,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              4,              4,         1,     S<8, 32, 1>,     S<0, 2, 1>,     S<0, 2, 1>,             1,              4,              1,         0,           1,           1,              S<1, 16, 1, 16>,               4>;
+
+using DeviceOpInstanceMKNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   1,   4,   32,   32,    4,    2,     S<4, 64, 1>,     S<0, 2, 1>,     S<0, 2, 1>,              1,              4,              1,         0,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              4,              4,         1,           1,           1,              S<1, 16, 1, 16>,               4>;
+
+using DeviceOpInstanceMNNN = ck::tensor_operation::device::
+        //#####################################| NumDimM| NumDimN| NumDimK| AData| BData| AccData| CShuffle|     DsData| EData|            A|           B|          CDE|           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|
+        //#####################################|        |        |        |  Type|  Type|    Type| DataType|       Type|  Type|  Elementwise| Elementwise|  Elementwise| Spacialization| Prefetch|  Size| Block| Block| Block|    |    |  XDL|  XDL|  Per|  Per|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|   ThreadCluster|  ThreadCluster| SrcAccessOrder|  SrcVectorDim|      SrcScalar|      DstScalar| AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl| ScalarPerVector|
+        //#####################################|        |        |        |      |      |        |         |           |      |    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_NWaveNPerXdl|   _NWaveNPerXdl|
+        //#####################################|        |        |        |      |      |        |         |           |      |             |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK,   F32,   F32,     F32,      F32, DsDataType,   F32,   AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   256,   128,    16,   1,   1,   32,   32,    4,    2,     S<4, 64, 1>,     S<0, 2, 1>,     S<0, 2, 1>,              1,              4,              1,         0,     S<8, 32, 1>,     S<0, 2, 1>,     S<0, 2, 1>,             1,              4,              1,         0,           1,           1,              S<1, 16, 1, 16>,               4>;
+// clang-format on
+
+using DeviceOpInstance = DeviceOpInstanceKKNN;
+
+// hardcoded for NumDimM == NumDimN == NumDimK == 2
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename EDataType,
+          typename AccDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          ck::enable_if_t<NumDimM == 2 && NumDimN == 2 && NumDimK == 2, bool> = false>
+struct ReferenceContraction_M2_N2_K2 : public ck::tensor_operation::device::BaseOperator
+{
+    // Argument
+    struct Argument : public ck::tensor_operation::device::BaseArgument
+    {
+        Argument(const Tensor<ADataType>& a_ms_ks,
+                 const Tensor<BDataType>& b_ns_ks,
+                 Tensor<EDataType>& e_ms_ns,
+                 AElementwiseOperation a_element_op,
+                 BElementwiseOperation b_element_op,
+                 CDEElementwiseOperation cde_element_op)
+            : a_ms_ks_{a_ms_ks},
+              b_ns_ks_{b_ns_ks},
+              e_ms_ns_{e_ms_ns},
+              a_element_op_{a_element_op},
+              b_element_op_{b_element_op},
+              cde_element_op_{cde_element_op}
+        {
+        }
+
+        const Tensor<ADataType>& a_ms_ks_;
+        const Tensor<BDataType>& b_ns_ks_;
+        Tensor<EDataType>& e_ms_ns_;
+
+        AElementwiseOperation a_element_op_;
+        BElementwiseOperation b_element_op_;
+        CDEElementwiseOperation cde_element_op_;
+    };
+
+    // Invoker
+    struct Invoker : public ck::tensor_operation::device::BaseInvoker
+    {
+        using Argument = ReferenceContraction_M2_N2_K2::Argument;
+
+        float Run(const Argument& arg)
+        {
+            auto f_ms_ns = [&](auto m0, auto m1, auto n0, auto n1) {
+                const int K0 = arg.a_ms_ks_.mDesc.GetLengths()[2];
+                const int K1 = arg.a_ms_ks_.mDesc.GetLengths()[3];
+
+                AccDataType v_acc = 0;
+
+                for(int k0 = 0; k0 < K0; ++k0)
+                {
+                    for(int k1 = 0; k1 < K1; ++k1)
+                    {
+                        AccDataType v_a;
+                        AccDataType v_b;
+
+                        arg.a_element_op_(
+                            v_a, ck::type_convert<const AccDataType>(arg.a_ms_ks_(m0, m1, k0, k1)));
+                        arg.b_element_op_(
+                            v_b, ck::type_convert<const AccDataType>(arg.b_ns_ks_(n0, n1, k0, k1)));
+
+                        v_acc += v_a * v_b;
+                    }
+                }
+
+                AccDataType v_c;
+
+                arg.cde_element_op_(v_c, v_acc);
+
+                arg.e_ms_ns_(m0, m1, n0, n1) = v_c;
+            };
+
+            make_ParallelTensorFunctor(f_ms_ns,
+                                       arg.e_ms_ns_.mDesc.GetLengths()[0],
+                                       arg.e_ms_ns_.mDesc.GetLengths()[1],
+                                       arg.e_ms_ns_.mDesc.GetLengths()[2],
+                                       arg.e_ms_ns_.mDesc.GetLengths()[3])(
+                std::thread::hardware_concurrency());
+
+            return 0;
+        }
+
+        float Run(const ck::tensor_operation::device::BaseArgument* p_arg,
+                  const StreamConfig& /* stream_config */ = StreamConfig{}) override
+        {
+            return Run(*dynamic_cast<const Argument*>(p_arg));
+        }
+    };
+
+    static constexpr bool IsValidCompilationParameter()
+    {
+        // TODO: properly implement this check
+        return true;
+    }
+
+    bool IsSupportedArgument(const ck::tensor_operation::device::BaseArgument*) override
+    {
+        return true;
+    }
+
+    static auto MakeArgument(const Tensor<ADataType>& a_ms_ks,
+                             const Tensor<BDataType>& b_ns_ks,
+                             Tensor<EDataType>& e_ms_ns,
+                             AElementwiseOperation a_element_op,
+                             BElementwiseOperation b_element_op,
+                             CDEElementwiseOperation cde_element_op)
+    {
+        return Argument{a_ms_ks, b_ns_ks, e_ms_ns, a_element_op, b_element_op, cde_element_op};
+    }
+
+    static auto MakeInvoker() { return Invoker{}; }
+
+    virtual std::unique_ptr<ck::tensor_operation::device::BaseInvoker> MakeInvokerPointer()
+    {
+        return std::make_unique<Invoker>(Invoker{});
+    }
+
+    std::string GetTypeString() const override
+    {
+        auto str = std::stringstream();
+
+        // clang-format off
+        str << "ReferenceContraction_M2_N2_K2"
+            << std::endl;
+        // clang-format on
+
+        return str.str();
+    }
+};
+
+int main(int argc, char* argv[])
+{
+    bool do_verification = true;
+    int init_method      = 1;
+    bool time_kernel     = false;
+
+    // A[M0, M1, K0, K1]
+    std::vector<ck::index_t> a_ms_ks_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> a_ms_ks_strides{524288, 4096, 128, 1};
+    // B[N0, N1, K0, K1]
+    std::vector<ck::index_t> b_ns_ks_lengths{32, 64, 32, 64};
+    std::vector<ck::index_t> b_ns_ks_strides{524288, 4096, 128, 1};
+    // E[M0, M1, N0, N1]
+    std::vector<ck::index_t> e_ms_ns_lengths{30, 128, 32, 64};
+    std::vector<ck::index_t> e_ms_ns_strides{524288, 4096, 128, 1};
+
+    float scale = 1.f;
+
+    if(argc == 1)
+    {
+        // use default case
+    }
+    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 == 23)
+    {
+        do_verification = std::stoi(argv[1]);
+        init_method     = std::stoi(argv[2]);
+        time_kernel     = std::stoi(argv[3]);
+
+        const ck::index_t M0 = std::stoi(argv[4]);
+        const ck::index_t M1 = std::stoi(argv[5]);
+
+        const ck::index_t N0 = std::stoi(argv[6]);
+        const ck::index_t N1 = std::stoi(argv[7]);
+
+        const ck::index_t K0 = std::stoi(argv[8]);
+        const ck::index_t K1 = std::stoi(argv[9]);
+
+        a_ms_ks_lengths = {M0, M1, K0, K1};
+        a_ms_ks_strides = {
+            std::stoi(argv[10]), std::stoi(argv[11]), std::stoi(argv[12]), std::stoi(argv[13])};
+
+        b_ns_ks_lengths = {N0, N1, K0, K1};
+        b_ns_ks_strides = {
+            std::stoi(argv[14]), std::stoi(argv[15]), std::stoi(argv[16]), std::stoi(argv[17])};
+
+        e_ms_ns_lengths = {M0, M1, N0, N1};
+        e_ms_ns_strides = {
+            std::stoi(argv[22]), std::stoi(argv[23]), std::stoi(argv[24]), std::stoi(argv[25])};
+
+        scale = std::stof(argv[26]);
+    }
+    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=no, 1=yes)\n");
+        printf("arg4 to 7: M0, M1, N0, N1, K0, K1\n");
+        printf("arg10 to 13: Stride_A_M0, Stride_A_M1, Stride_A_K0, Stride_A_K1\n");
+        printf("arg14 to 17: Stride_B_N0, Stride_B_N1, Stride_B_K0, Stride_B_K1\n");
+        printf("arg18 to 21: Stride_E_M0, Stride_E_M1, Stride_E_N0, Stride_E_N1\n");
+        printf("arg22: scale\n");
+        exit(0);
+    }
+
+    Tensor<ADataType> a_ms_ks(
+        std::vector<std::size_t>(a_ms_ks_lengths.begin(), a_ms_ks_lengths.end()),
+        std::vector<std::size_t>(a_ms_ks_strides.begin(), a_ms_ks_strides.end()));
+    Tensor<BDataType> b_ns_ks(
+        std::vector<std::size_t>(b_ns_ks_lengths.begin(), b_ns_ks_lengths.end()),
+        std::vector<std::size_t>(b_ns_ks_strides.begin(), b_ns_ks_strides.end()));
+    Tensor<EDataType> e_ms_ns_host_result(
+        std::vector<std::size_t>(e_ms_ns_lengths.begin(), e_ms_ns_lengths.end()),
+        std::vector<std::size_t>(e_ms_ns_strides.begin(), e_ms_ns_strides.end()));
+    Tensor<EDataType> e_ms_ns_device_result(
+        std::vector<std::size_t>(e_ms_ns_lengths.begin(), e_ms_ns_lengths.end()),
+        std::vector<std::size_t>(e_ms_ns_strides.begin(), e_ms_ns_strides.end()));
+
+    std::cout << "a_ms_ks: " << a_ms_ks.mDesc << std::endl;
+    std::cout << "b_ns_ks: " << b_ns_ks.mDesc << std::endl;
+    std::cout << "e_ms_ns: " << e_ms_ns_host_result.mDesc << std::endl;
+
+    switch(init_method)
+    {
+    case 0: break;
+    case 1:
+        a_ms_ks.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
+        b_ns_ks.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+        break;
+    default:
+        a_ms_ks.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
+        b_ns_ks.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+        break;
+    }
+
+    DeviceMem a_device_buf(sizeof(ADataType) * a_ms_ks.mDesc.GetElementSpace());
+    DeviceMem b_device_buf(sizeof(BDataType) * b_ns_ks.mDesc.GetElementSpace());
+    DeviceMem e_device_buf(sizeof(EDataType) * e_ms_ns_device_result.mDesc.GetElementSpace());
+
+    a_device_buf.ToDevice(a_ms_ks.mData.data());
+    b_device_buf.ToDevice(b_ns_ks.mData.data());
+
+    // set zero
+    e_device_buf.SetZero();
+
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{scale};
+
+    // device operation
+    auto op       = DeviceOpInstance{};
+    auto invoker  = op.MakeInvoker();
+    auto argument = op.MakeArgument(a_device_buf.GetDeviceBuffer(),
+                                    b_device_buf.GetDeviceBuffer(),
+                                    std::array<const void*, 0>{},
+                                    e_device_buf.GetDeviceBuffer(),
+                                    a_ms_ks_lengths,
+                                    a_ms_ks_strides,
+                                    b_ns_ks_lengths,
+                                    b_ns_ks_strides,
+                                    std::array<std::vector<ck::index_t>, 0>{},
+                                    std::array<std::vector<ck::index_t>, 0>{},
+                                    e_ms_ns_lengths,
+                                    e_ms_ns_strides,
+                                    a_element_op,
+                                    b_element_op,
+                                    cde_element_op);
+
+    if(!op.IsSupportedArgument(argument))
+    {
+        std::cout << op.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+
+    ck::index_t M = std::accumulate(e_ms_ns_lengths.begin(),
+                                    e_ms_ns_lengths.begin() + NumDimM,
+                                    ck::index_t{1},
+                                    std::multiplies<ck::index_t>{});
+
+    ck::index_t N = std::accumulate(e_ms_ns_lengths.begin() + NumDimM,
+                                    e_ms_ns_lengths.begin() + NumDimM + NumDimN,
+                                    ck::index_t{1},
+                                    std::multiplies<ck::index_t>{});
+
+    ck::index_t K = std::accumulate(a_ms_ks_lengths.begin() + NumDimM,
+                                    a_ms_ks_lengths.begin() + NumDimM + NumDimK,
+                                    ck::index_t{1},
+                                    std::multiplies<ck::index_t>{});
+
+    std::size_t flop = std::size_t(2) * M * N * K;
+    std::size_t num_btype =
+        sizeof(ADataType) * M * K + sizeof(BDataType) * K * N + +sizeof(EDataType) * M * N;
+
+    float tflops = static_cast<float>(flop) / 1.E9 / ave_time;
+
+    float gb_per_sec = num_btype / 1.E6 / ave_time;
+
+    std::cout << "Perf: " << ave_time << " ms, " << tflops << " TFlops, " << gb_per_sec << " GB/s, "
+              << op.GetTypeString() << std::endl;
+
+    e_device_buf.FromDevice(e_ms_ns_device_result.mData.data());
+
+    if(do_verification)
+    {
+        Tensor<CShuffleDataType> c_ms_ns_host_result(
+            std::vector<std::size_t>(e_ms_ns_lengths.begin(), e_ms_ns_lengths.end()),
+            std::vector<std::size_t>(e_ms_ns_strides.begin(), e_ms_ns_strides.end()));
+
+        using ReferenceOpInstance = ReferenceContraction_M2_N2_K2<NumDimM,
+                                                                  NumDimN,
+                                                                  NumDimK,
+                                                                  ADataType,
+                                                                  BDataType,
+                                                                  CShuffleDataType,
+                                                                  AccDataType,
+                                                                  AElementOp,
+                                                                  BElementOp,
+                                                                  PassThrough>;
+
+        auto ref_gemm    = ReferenceOpInstance{};
+        auto ref_invoker = ref_gemm.MakeInvoker();
+
+        auto ref_argument = ref_gemm.MakeArgument(
+            a_ms_ks, b_ns_ks, c_ms_ns_host_result, a_element_op, b_element_op, PassThrough{});
+
+        ref_invoker.Run(ref_argument);
+
+        for(size_t m0 = 0; m0 < e_ms_ns_host_result.mDesc.GetLengths()[0]; ++m0)
+        {
+            for(size_t m1 = 0; m1 < e_ms_ns_host_result.mDesc.GetLengths()[1]; ++m1)
+            {
+                for(size_t n0 = 0; n0 < e_ms_ns_host_result.mDesc.GetLengths()[2]; ++n0)
+                {
+                    for(size_t n1 = 0; n1 < e_ms_ns_host_result.mDesc.GetLengths()[3]; ++n1)
+                    {
+                        cde_element_op(e_ms_ns_host_result(m0, m1, n0, n1),
+                                       c_ms_ns_host_result(m0, m1, n0, n1));
+                    }
+                }
+            }
+        }
+
+        return ck::utils::check_err(e_ms_ns_device_result.mData, e_ms_ns_host_result.mData) ? 0 : 1;
+    }
+
+    return 0;
+}

example/CMakeLists.txt

@@ -44,3 +44,4 @@ add_subdirectory(22_cgemm)
 add_subdirectory(23_softmax)
 add_subdirectory(24_batched_gemm_c_permute)
 add_subdirectory(25_gemm_bias_c_permute)
+add_subdirectory(26_contraction)

include/ck/ck.hpp

@@ -102,7 +102,12 @@
 #define CK_EXPERIMENTAL_STATIC_TENSOR_DESCRIPTOR 0
 
 // experimental feature: buffer load/store/atomic-add/ OOB trick
+// This (ifndef) is a hack to use customized behavior for buffer load rather than using default
+// setting Don't use this hack unless absolutely necessary!
+// FIXME: make the behavior of buffer load a configurable (template) parameter of each device op
+#ifndef CK_EXPERIMENTAL_USE_BUFFER_LOAD_OOB_CHECK_OFFSET_TRICK
 #define CK_EXPERIMENTAL_USE_BUFFER_LOAD_OOB_CHECK_OFFSET_TRICK 0
+#endif
 #define CK_EXPERIMENTAL_USE_BUFFER_STORE_OOB_CHECK_OFFSET_TRICK 1
 #define CK_EXPERIMENTAL_USE_BUFFER_ATOMIC_ADD_OOB_CHECK_OFFSET_TRICK 1
 #define CK_EXPERIMENTAL_USE_BUFFER_ATOMIC_MAX_OOB_CHECK_OFFSET_TRICK 1

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

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <vector>
+
+#include "ck/tensor_operation/gpu/device/device_base.hpp"
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+// Tensor Contraction:
+//   input : A
+//   input : B
+//   input : D0, D1, ...
+//   output : E
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+// Assume:
+//   A[M0, M1, M2, ..., K0, K1, K2, ...]
+//   B[N0, N1, N2, ..., K0, K1, K2, ...]
+//   D[M0, M1, M2, ..., N0, N1, N2, ...]
+//   E[M0, M1, M2, ..., N0, N1, N2, ...]
+template <index_t NumDimM,
+          index_t NumDimN,
+          index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation>
+struct DeviceContractionMultipleD : public BaseOperator
+{
+    static constexpr index_t NumDTensor = DsDataType::Size();
+
+    virtual std::unique_ptr<BaseArgument>
+    MakeArgumentPointer(const void* p_a,
+                        const void* p_b,
+                        std::array<const void*, NumDTensor> p_ds,
+                        void* p_e,
+                        std::vector<index_t> a_ms_ks_lengths,
+                        std::vector<index_t> a_ms_ks_strides,
+                        std::vector<index_t> b_ns_ks_lengths,
+                        std::vector<index_t> b_ns_ks_strides,
+                        std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_lengths,
+                        std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_strides,
+                        std::vector<index_t> e_ms_ns_lengths,
+                        std::vector<index_t> e_ms_ns_strides,
+                        AElementwiseOperation a_element_op,
+                        BElementwiseOperation b_element_op,
+                        CDEElementwiseOperation cde_element_op) = 0;
+
+    virtual std::unique_ptr<BaseInvoker> MakeInvokerPointer() = 0;
+};
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

include/ck/tensor_operation/gpu/device/device_contraction_multiple_d_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_contraction_multiple_d.hpp"
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/grid/gridwise_gemm_multiple_d_xdl_cshuffle.hpp"
+#include "ck/device_utility/device_prop.hpp"
+#include "ck/device_utility/kernel_launch.hpp"
+
+namespace ck {
+
+template <typename GridwiseGemm,
+          typename FloatAB,
+          typename FloatDsPointer,
+          typename FloatE,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          typename AGridDesc_AK0_M_AK1,
+          typename BGridDesc_BK0_N_BK1,
+          typename DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+          typename EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock,
+          typename Block2ETileMap,
+          bool HasMainKBlockLoop>
+__global__ void
+#if CK_USE_LAUNCH_BOUNDS
+    __launch_bounds__(CK_MAX_THREAD_PER_BLOCK, CK_MIN_BLOCK_PER_CU)
+#endif
+        kernel_contraction_multiple_d_xdl_cshuffle(
+            const FloatAB* __restrict__ p_a_grid,
+            const FloatAB* __restrict__ p_b_grid,
+            FloatDsPointer p_ds_grid,
+            FloatE* __restrict__ p_e_grid,
+            const AElementwiseOperation a_element_op,
+            const BElementwiseOperation b_element_op,
+            const CDEElementwiseOperation cde_element_op,
+            const AGridDesc_AK0_M_AK1 a_grid_desc_ak0_m_ak1,
+            const BGridDesc_BK0_N_BK1 b_grid_desc_bk0_n_bk1,
+            const DsGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+                ds_grid_desc_mblock_mperblock_nblock_nperblock,
+            const EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
+                e_grid_desc_mblock_mperblock_nblock_nperblock,
+            const 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_shared,
+                                                  a_element_op,
+                                                  b_element_op,
+                                                  cde_element_op,
+                                                  a_grid_desc_ak0_m_ak1,
+                                                  b_grid_desc_bk0_n_bk1,
+                                                  ds_grid_desc_mblock_mperblock_nblock_nperblock,
+                                                  e_grid_desc_mblock_mperblock_nblock_nperblock,
+                                                  block_2_etile_map);
+#else
+    ignore = p_a_grid;
+    ignore = p_b_grid;
+    ignore = p_ds_grid;
+    ignore = p_e_grid;
+    ignore = a_element_op;
+    ignore = b_element_op;
+    ignore = cde_element_op;
+    ignore = a_grid_desc_ak0_m_ak1;
+    ignore = b_grid_desc_bk0_n_bk1;
+    ignore = ds_grid_desc_mblock_mperblock_nblock_nperblock;
+    ignore = e_grid_desc_mblock_mperblock_nblock_nperblock;
+    ignore = block_2_etile_map;
+#endif
+}
+
+} // namespace ck
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+// Tensor Contraction:
+//   input : A
+//   input : B
+//   input : D0, D1, ...
+//   output : E
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+// Assume:
+//   A[M0, M1, M2, ..., K0, K1, K2, ...]
+//   B[N0, N1, N2, ..., K0, K1, K2, ...]
+//   D[M0, M1, M2, ..., N0, N1, N2, ...]
+//   E[M0, M1, M2, ..., N0, N1, N2, ...]
+template <index_t NumDimM,
+          index_t NumDimN,
+          index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename GemmAccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename AElementwiseOperation,
+          typename BElementwiseOperation,
+          typename CDEElementwiseOperation,
+          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 CDEBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
+          index_t CDEBlockTransferScalarPerVector_NPerBlock,
+          LoopScheduler LoopSched = make_default_loop_scheduler()>
+struct DeviceContractionMultipleD_Xdl_CShuffle
+    : public DeviceContractionMultipleD<NumDimM,
+                                        NumDimN,
+                                        NumDimK,
+                                        ADataType,
+                                        BDataType,
+                                        DsDataType,
+                                        EDataType,
+                                        AElementwiseOperation,
+                                        BElementwiseOperation,
+                                        CDEElementwiseOperation>
+{
+    using DeviceOp = DeviceContractionMultipleD_Xdl_CShuffle;
+
+    static constexpr index_t NumDTensor = DsDataType::Size();
+
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    // Assume: A[M0, M1, M2, ..., K0, K1, K2, ...]
+    static auto MakeAGridDescriptor_AK0_M_AK1(const std::vector<index_t>& a_ms_ks_lengths_vec,
+                                              const std::vector<index_t>& a_ms_ks_strides_vec)
+    {
+        assert(a_ms_ks_lengths_vec.size() == NumDimM + NumDimK &&
+               a_ms_ks_strides_vec.size() == NumDimM + NumDimK);
+
+        const auto to_tuple = [&](auto& vec, auto num) {
+            return generate_tuple([&](auto i) { return vec[i]; }, num);
+        };
+
+        const auto a_ms_ns_lengths = to_tuple(a_ms_ks_lengths_vec, Number<NumDimM + NumDimK>{});
+        const auto a_ms_ks_strides = to_tuple(a_ms_ks_strides_vec, Number<NumDimM + NumDimK>{});
+
+        // dimension Ids for M0, M1, ...
+        constexpr auto mDimIds = typename arithmetic_sequence_gen<0, NumDimM, 1>::type{};
+
+        // dimension Ids for K0, K1, ...
+        constexpr auto kDimIds =
+            typename arithmetic_sequence_gen<NumDimM, NumDimM + NumDimK, 1>::type{};
+
+        // lengths for M0, M1, ...
+        const auto mLengths = get_container_subset(a_ms_ns_lengths, mDimIds);
+
+        // lengths for K0, K1, ...
+        const auto kLengths = get_container_subset(a_ms_ns_lengths, kDimIds);
+
+        // naive tensor A[M0, M1, M2, ..., K0, K1, K2...]
+        const auto a_grid_desc_ms_ks =
+            make_naive_tensor_descriptor(a_ms_ns_lengths, a_ms_ks_strides);
+
+        // transformed tensor A[MRaw = M0 * M1 * M2 * ... , KRaw = K0 * K1 * K2 * ...]
+        const auto a_grid_desc_mraw_kraw = transform_tensor_descriptor(
+            a_grid_desc_ms_ks,
+            make_tuple(make_merge_transform(mLengths), make_merge_transform(kLengths)),
+            make_tuple(mDimIds, kDimIds),
+            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+        const auto MRaw = a_grid_desc_mraw_kraw.GetLength(I0);
+        const auto KRaw = a_grid_desc_mraw_kraw.GetLength(I1);
+
+        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;
+        }
+    }
+
+    // Assume: B[N0, N1, N2, ..., K0, K1, K2, ...]
+    static auto MakeBGridDescriptor_BK0_N_BK1(const std::vector<index_t>& b_ns_ks_lengths_vec,
+                                              const std::vector<index_t>& b_ns_ks_strides_vec)
+    {
+        assert(b_ns_ks_lengths_vec.size() == NumDimN + NumDimK &&
+               b_ns_ks_strides_vec.size() == NumDimN + NumDimK);
+
+        const auto to_tuple = [&](auto& vec, auto num) {
+            return generate_tuple([&](auto i) { return vec[i]; }, num);
+        };
+
+        const auto b_ns_ks_lengths = to_tuple(b_ns_ks_lengths_vec, Number<NumDimN + NumDimK>{});
+        const auto b_ns_ks_strides = to_tuple(b_ns_ks_strides_vec, Number<NumDimN + NumDimK>{});
+
+        // dimension Ids for N0, N1, ...
+        constexpr auto nDimIds = typename arithmetic_sequence_gen<0, NumDimN, 1>::type{};
+
+        // dimension Ids for K0, K1, ...
+        constexpr auto kDimIds =
+            typename arithmetic_sequence_gen<NumDimN, NumDimN + NumDimK, 1>::type{};
+
+        // lengths for K0, K1, ...
+        const auto kLengths = get_container_subset(b_ns_ks_lengths, kDimIds);
+
+        // lengths for N0, N1, ...
+        const auto nLengths = get_container_subset(b_ns_ks_lengths, nDimIds);
+
+        // naive tensor B[N0, N1, N2, ..., K0, K1, K2, ...]
+        const auto b_grid_desc_ns_ks =
+            make_naive_tensor_descriptor(b_ns_ks_lengths, b_ns_ks_strides);
+
+        // transformed tensor B[NRaw = N0 * N1 * N2 * ..., KRaw = K0 * K1 * K2 * ...]
+        const auto b_grid_desc_nraw_kraw = transform_tensor_descriptor(
+            b_grid_desc_ns_ks,
+            make_tuple(make_merge_transform(nLengths), make_merge_transform(kLengths)),
+            make_tuple(nDimIds, kDimIds),
+            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+        const auto NRaw = b_grid_desc_nraw_kraw.GetLength(I0);
+        const auto KRaw = b_grid_desc_nraw_kraw.GetLength(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;
+        }
+    }
+
+    // assume E[M0, M1, M2, ..., N0, N1, N2...]
+    static auto MakeEGridDescriptor_M_N(const std::vector<index_t>& e_ms_ns_lengths_vec,
+                                        const std::vector<index_t>& e_ms_ns_strides_vec)
+    {
+        assert(e_ms_ns_lengths_vec.size() == NumDimM + NumDimN &&
+               e_ms_ns_strides_vec.size() == NumDimM + NumDimN);
+
+        const auto to_tuple = [&](auto& vec, auto num) {
+            return generate_tuple([&](auto i) { return vec[i]; }, num);
+        };
+
+        const auto e_ms_ns_lengths = to_tuple(e_ms_ns_lengths_vec, Number<NumDimM + NumDimN>{});
+        const auto e_ms_ns_strides = to_tuple(e_ms_ns_strides_vec, Number<NumDimM + NumDimN>{});
+
+        // dimension Ids for M0, M1, ...
+        constexpr auto mDimIds = typename arithmetic_sequence_gen<0, NumDimM, 1>::type{};
+
+        // dimension Ids for N0, N1, ...
+        constexpr auto nDimIds =
+            typename arithmetic_sequence_gen<NumDimM, NumDimM + NumDimN, 1>::type{};
+
+        // lengths for M0, M1, ...
+        const auto mLengths = get_container_subset(e_ms_ns_lengths, mDimIds);
+
+        // lengths for K0, K1, ...
+        const auto nLengths = get_container_subset(e_ms_ns_lengths, nDimIds);
+
+        // naive tensor E[M0, M1, M2, ..., N0, N1, N2...]
+        const auto e_grid_desc_ms_ns =
+            make_naive_tensor_descriptor(e_ms_ns_lengths, e_ms_ns_strides);
+
+        // transformed tensor E[MRaw = M0 * M1 * M2 * ... , NRaw = N0 * N1 * N2 * ...]
+        const auto e_grid_desc_mraw_nraw = transform_tensor_descriptor(
+            e_grid_desc_ms_ns,
+            make_tuple(make_merge_transform(mLengths), make_merge_transform(nLengths)),
+            make_tuple(mDimIds, nDimIds),
+            make_tuple(Sequence<0>{}, Sequence<1>{}));
+
+        const auto MRaw = e_grid_desc_mraw_nraw.GetLength(I0);
+        const auto NRaw = e_grid_desc_mraw_nraw.GetLength(I1);
+
+        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;
+        }
+    }
+
+    using AGridDesc_AK0_M_AK1 =
+        decltype(MakeAGridDescriptor_AK0_M_AK1(std::vector<index_t>{}, std::vector<index_t>{}));
+    using BGridDesc_BK0_N_BK1 =
+        decltype(MakeBGridDescriptor_BK0_N_BK1(std::vector<index_t>{}, std::vector<index_t>{}));
+    using EGridDesc_M_N =
+        decltype(MakeEGridDescriptor_M_N(std::vector<index_t>{}, std::vector<index_t>{}));
+
+    // GridwiseGemm
+    using GridwiseGemm = GridwiseGemmMultipleD_k0mk1_k0nk1_mn_xdl_cshuffle<
+        ADataType, // TODO: distinguish A/B datatype
+        GemmAccDataType,
+        CShuffleDataType,
+        DsDataType,
+        EDataType,
+        AElementwiseOperation,
+        BElementwiseOperation,
+        CDEElementwiseOperation,
+        InMemoryDataOperationEnum::Set,
+        AGridDesc_AK0_M_AK1,
+        BGridDesc_BK0_N_BK1,
+        EGridDesc_M_N,
+        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,
+        CDEBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
+        CDEBlockTransferScalarPerVector_NPerBlock,
+        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::vector<index_t> a_ms_ns_lengths,
+                 std::vector<index_t> a_ms_ks_strides,
+                 std::vector<index_t> b_ns_ks_lengths,
+                 std::vector<index_t> b_ns_ks_strides,
+                 std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_lengths,
+                 std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_strides,
+                 std::vector<index_t> e_ms_ns_lengths,
+                 std::vector<index_t> e_ms_ns_strides,
+                 AElementwiseOperation a_element_op,
+                 BElementwiseOperation b_element_op,
+                 CDEElementwiseOperation cde_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)},
+              a_grid_desc_ak0_m_ak1_{
+                  DeviceOp::MakeAGridDescriptor_AK0_M_AK1(a_ms_ns_lengths, a_ms_ks_strides)},
+              b_grid_desc_bk0_n_bk1_{
+                  DeviceOp::MakeBGridDescriptor_BK0_N_BK1(b_ns_ks_lengths, b_ns_ks_strides)},
+              ds_grid_desc_mblock_mperblock_nblock_nperblock_{},
+              e_grid_desc_m_n_{DeviceOp::MakeEGridDescriptor_M_N(e_ms_ns_lengths, e_ms_ns_strides)},
+              e_grid_desc_mblock_mperblock_nblock_nperblock_{},
+              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},
+              a_mz_stride_{},
+              a_kz_stride_{},
+              b_nz_stride_{},
+              b_kz_stride_{},
+              ds_nz_stride_{},
+              e_nz_stride_{}
+        {
+            if(GridwiseGemm::CheckValidity(a_grid_desc_ak0_m_ak1_,
+                                           b_grid_desc_bk0_n_bk1_,
+                                           e_grid_desc_m_n_,
+                                           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(ds_ms_ns_lengths[i], ds_ms_ns_strides[i]);
+
+                    ds_grid_desc_mblock_mperblock_nblock_nperblock_(i) =
+                        GridwiseGemm::MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
+                            d_grid_desc_m_n);
+                });
+            }
+
+            // for sanity check of vector memory access
+            a_mz_stride_ = a_ms_ks_strides[NumDimM - 1];
+            a_kz_stride_ = a_ms_ks_strides[NumDimM + NumDimK - 1];
+
+            b_nz_stride_ = b_ns_ks_strides[NumDimN - 1];
+            b_kz_stride_ = b_ns_ks_strides[NumDimN + NumDimK - 1];
+
+            for(index_t i = 0; i < NumDTensor; ++i)
+            {
+                ds_nz_stride_[i] = ds_ms_ns_strides[i][NumDimM + NumDimN - 1];
+            }
+
+            e_nz_stride_ = e_ms_ns_strides[NumDimM + NumDimN - 1];
+        }
+
+        //  private:
+        // pointers
+        const ADataType* p_a_grid_;
+        const BDataType* p_b_grid_;
+        typename GridwiseGemm::DsGridPointer p_ds_grid_;
+        EDataType* p_e_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_;
+
+        // 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_;
+
+        // Strides for the last M/N/K dimensions of A/B/Ds/E
+        //   for sanity check of vector load/store
+        index_t a_mz_stride_;
+        index_t a_kz_stride_;
+        index_t b_nz_stride_;
+        index_t b_kz_stride_;
+        std::array<index_t, NumDTensor> ds_nz_stride_;
+        index_t e_mz_stride_;
+        index_t e_nz_stride_;
+    };
+
+    // Invoker
+    struct Invoker : public BaseInvoker
+    {
+        using Argument = DeviceOp::Argument;
+
+        float Run(const Argument& arg, const StreamConfig& stream_config = StreamConfig{})
+        {
+#if 0
+            {
+                std::cout << "arg.a_grid_desc_ak0_m_ak1_{"
+                          << arg.a_grid_desc_ak0_m_ak1_.GetLength(I0) << ", "
+                          << arg.a_grid_desc_ak0_m_ak1_.GetLength(I1) << ", "
+                          << arg.a_grid_desc_ak0_m_ak1_.GetLength(I2) << "}" << std::endl;
+
+                std::cout << "arg.b_grid_desc_bk0_n_bk1_{"
+                          << arg.b_grid_desc_bk0_n_bk1_.GetLength(I0) << ", "
+                          << arg.b_grid_desc_bk0_n_bk1_.GetLength(I1) << ", "
+                          << arg.b_grid_desc_bk0_n_bk1_.GetLength(I2) << "}" << std::endl;
+
+                std::cout << "arg.e_grid_desc_m_n_{ " << arg.e_grid_desc_m_n_.GetLength(I0) << ", "
+                          << arg.e_grid_desc_m_n_.GetLength(I1) << "}" << std::endl;
+            }
+#endif
+
+            if(!GridwiseGemm::CheckValidity(arg.a_grid_desc_ak0_m_ak1_,
+                                            arg.b_grid_desc_bk0_n_bk1_,
+                                            arg.e_grid_desc_m_n_,
+                                            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_contraction_multiple_d_xdl_cshuffle<
+                    GridwiseGemm,
+                    ADataType, // TODO: distiguish A/B datatype
+                    typename GridwiseGemm::DsGridPointer,
+                    EDataType,
+                    AElementwiseOperation,
+                    BElementwiseOperation,
+                    CDEElementwiseOperation,
+                    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,
+                    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.a_element_op_,
+                                              arg.b_element_op_,
+                                              arg.cde_element_op_,
+                                              arg.a_grid_desc_ak0_m_ak1_,
+                                              arg.b_grid_desc_bk0_n_bk1_,
+                                              arg.ds_grid_desc_mblock_mperblock_nblock_nperblock_,
+                                              arg.e_grid_desc_mblock_mperblock_nblock_nperblock_,
+                                              arg.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 constexpr bool IsValidCompilationParameter()
+    {
+        // TODO: properly implement this check
+        return true;
+    }
+
+    static bool IsSupportedArgument(const Argument& arg)
+    {
+        if(!(ck::get_device_name() == "gfx908" || ck::get_device_name() == "gfx90a"))
+        {
+            return false;
+        }
+
+        if(!GridwiseGemm::CheckValidity(arg.a_grid_desc_ak0_m_ak1_,
+                                        arg.b_grid_desc_bk0_n_bk1_,
+                                        arg.e_grid_desc_m_n_,
+                                        arg.block_2_etile_map_))
+        {
+            return false;
+        }
+
+        // check vector access
+        static_assert((ABlockTransferSrcVectorDim == 1 || ABlockTransferSrcVectorDim == 2) &&
+                          (BBlockTransferSrcVectorDim == 1 || BBlockTransferSrcVectorDim == 2),
+                      "wrong!");
+
+        // vector memory access of A: could be on M or AK1 dimension
+        if constexpr(ABlockTransferSrcVectorDim == 1)
+        {
+            if(!(arg.a_mz_stride_ == 1 &&
+                 arg.a_grid_desc_ak0_m_ak1_.GetLength(I1) % ABlockTransferSrcScalarPerVector == 0))
+            {
+                return false;
+            }
+        }
+        else
+        {
+            if(!(arg.a_kz_stride_ == 1 &&
+                 arg.a_grid_desc_ak0_m_ak1_.GetLength(I2) % ABlockTransferSrcScalarPerVector == 0))
+            {
+                return false;
+            }
+        }
+
+        // vector memory access of B: could be on N or BK1 dimension
+        if constexpr(BBlockTransferSrcVectorDim == 1)
+        {
+            if(!(arg.b_nz_stride_ == 1 &&
+                 arg.b_grid_desc_bk0_n_bk1_.GetLength(I1) % BBlockTransferSrcScalarPerVector == 0))
+            {
+                return false;
+            }
+        }
+        else
+        {
+            if(!(arg.b_kz_stride_ == 1 &&
+                 arg.b_grid_desc_bk0_n_bk1_.GetLength(I2) % BBlockTransferSrcScalarPerVector == 0))
+            {
+                return false;
+            }
+        }
+
+        // vector memory access of Ds: always on NPerBlock dimension
+        bool valid_d_access = true;
+
+        static_for<0, NumDTensor, 1>{}([&](auto i) {
+            if(!(arg.ds_nz_stride_[i] == 1 &&
+                 arg.ds_grid_desc_mblock_mperblock_nblock_nperblock_[i].GetLength(I3) %
+                         CDEBlockTransferScalarPerVector_NPerBlock ==
+                     0))
+            {
+                valid_d_access = false;
+            }
+        });
+
+        if(valid_d_access == false)
+        {
+            return false;
+        }
+
+        // vector memory access of E: always on NPerBlock dimension
+        if(!(arg.e_nz_stride_ == 1 &&
+             arg.e_grid_desc_mblock_mperblock_nblock_nperblock_.GetLength(I3) %
+                     CDEBlockTransferScalarPerVector_NPerBlock ==
+                 0))
+        {
+            return false;
+        }
+
+        return true;
+    }
+
+    // polymorphic
+    bool IsSupportedArgument(const BaseArgument* p_arg) override
+    {
+        return IsSupportedArgument(*dynamic_cast<const Argument*>(p_arg));
+    }
+
+    static auto MakeArgument(const void* p_a,
+                             const void* p_b,
+                             std::array<const void*, NumDTensor> p_ds,
+                             void* p_e,
+                             std::vector<index_t> a_ms_ns_lengths,
+                             std::vector<index_t> a_ms_ks_strides,
+                             std::vector<index_t> b_ns_ks_lengths,
+                             std::vector<index_t> b_ns_ks_strides,
+                             std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_lengths,
+                             std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_strides,
+                             std::vector<index_t> e_ms_ns_lengths,
+                             std::vector<index_t> e_ms_ns_strides,
+                             AElementwiseOperation a_element_op,
+                             BElementwiseOperation b_element_op,
+                             CDEElementwiseOperation cde_element_op)
+    {
+        return Argument{p_a,
+                        p_b,
+                        p_ds,
+                        p_e,
+                        a_ms_ns_lengths,
+                        a_ms_ks_strides,
+                        b_ns_ks_lengths,
+                        b_ns_ks_strides,
+                        ds_ms_ns_lengths,
+                        ds_ms_ns_strides,
+                        e_ms_ns_lengths,
+                        e_ms_ns_strides,
+                        a_element_op,
+                        b_element_op,
+                        cde_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::vector<index_t> a_ms_ns_lengths,
+                        std::vector<index_t> a_ms_ks_strides,
+                        std::vector<index_t> b_ns_ks_lengths,
+                        std::vector<index_t> b_ns_ks_strides,
+                        std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_lengths,
+                        std::array<std::vector<index_t>, NumDTensor> ds_ms_ns_strides,
+                        std::vector<index_t> e_ms_ns_lengths,
+                        std::vector<index_t> e_ms_ns_strides,
+                        AElementwiseOperation a_element_op,
+                        BElementwiseOperation b_element_op,
+                        CDEElementwiseOperation cde_element_op) override
+    {
+        return std::make_unique<Argument>(p_a,
+                                          p_b,
+                                          p_ds,
+                                          p_e,
+                                          a_ms_ns_lengths,
+                                          a_ms_ks_strides,
+                                          b_ns_ks_lengths,
+                                          b_ns_ks_strides,
+                                          ds_ms_ns_lengths,
+                                          ds_ms_ns_strides,
+                                          e_ms_ns_lengths,
+                                          e_ms_ns_strides,
+                                          a_element_op,
+                                          b_element_op,
+                                          cde_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 << "DeviceContractionMultipleD_Xdl_CShuffle"
+            << "<"
+            << NumDimM << ", "
+            << NumDimN << ", "
+            << NumDimK << ", "
+            << BlockSize << ", "
+            << MPerBlock << ", "
+            << NPerBlock << ", "
+            << KPerBlock << ", "
+            << AK1 << ", "
+            << BK1 << ", "
+            << ABlockTransferSrcVectorDim << ", "
+            << BBlockTransferSrcVectorDim
+            << ">";
+        // clang-format on
+
+        return str.str();
+    }
+};
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

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

@@ -2,10 +2,11 @@
 // Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
 
 #pragma once
+
 #include <iostream>
 #include <vector>
 
-#include "device_base.hpp"
+#include "ck/tensor_operation/gpu/device/device_base.hpp"
 
 namespace ck {
 namespace tensor_operation {

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

@@ -11,11 +11,14 @@ namespace ck {
 namespace tensor_operation {
 namespace device {
 
-// input : A[M, K], B[K, N],
-// input : D0[M, N], D1[M, N], ...
-// output : E[M, N]
-// C = a_op(A) * b_op(B)
-// E = cde_op(C, D0, D1, ...)
+// GEMM:
+//   input : A[M, K], B[K, N],
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+// Assume:
+//   D0, D1, ... and E have the same layout
 template <typename ALayout,
           typename BLayout,
           typename DELayout,

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

@@ -88,12 +88,15 @@ namespace ck {
 namespace tensor_operation {
 namespace device {
 
-// input : A[M, K], or A[K, N]
-// input : B[K, N], or A[N, K]
-// input : D0[M, N], D1[M, N], ...
-// output : E[M, N]
-// C = a_op(A) * b_op(B)
-// E = cde_op(C, D0, D1, ...)
+// GEMM:
+//   input : A[AK0, M, AK1]
+//   input : B[AK0, N, AK1]
+//   input : D0[M, N], D1[M, N], ...
+//   output : E[M, N]
+//   C = a_op(A) * b_op(B)
+//   E = cde_op(C, D0, D1, ...)
+// Assume:
+//   D0, D1, ... and E have the same layout
 template <typename ALayout,
           typename BLayout,
           typename DELayout,
@@ -363,7 +366,7 @@ struct DeviceGemmMultipleD_Xdl_CShuffle : public DeviceGemmMultipleD<ALayout,
         }
     }
 
-    static auto MakeCGridDescriptor_M_N(index_t MRaw, index_t NRaw, index_t StrideE)
+    static auto MakeEGridDescriptor_M_N(index_t MRaw, index_t NRaw, index_t StrideE)
     {
         const auto c_grid_desc_mraw_nraw = [&]() {
             if constexpr(is_same<tensor_layout::gemm::RowMajor, DELayout>::value)
@@ -423,7 +426,7 @@ struct DeviceGemmMultipleD_Xdl_CShuffle : public DeviceGemmMultipleD<ALayout,
 
     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(MakeCGridDescriptor_M_N(1, 1, 1));
+    using EGridDesc_M_N       = decltype(MakeEGridDescriptor_M_N(1, 1, 1));
 
     // GridwiseGemm
     using GridwiseGemm = GridwiseGemmMultipleD_k0mk1_k0nk1_mn_xdl_cshuffle<
@@ -496,7 +499,7 @@ struct DeviceGemmMultipleD_Xdl_CShuffle : public DeviceGemmMultipleD<ALayout,
               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::MakeCGridDescriptor_M_N(MRaw, NRaw, StrideE)},
+              e_grid_desc_m_n_{DeviceOp::MakeEGridDescriptor_M_N(MRaw, NRaw, StrideE)},
               e_grid_desc_mblock_mperblock_nblock_nperblock_{},
               block_2_etile_map_{GridwiseGemm::MakeDefaultBlock2ETileMap(e_grid_desc_m_n_)},
               a_element_op_{a_element_op},
@@ -518,7 +521,7 @@ struct DeviceGemmMultipleD_Xdl_CShuffle : public DeviceGemmMultipleD<ALayout,
                     p_ds_grid_(i) = static_cast<const DDataType*>(p_ds_grid[i]);
 
                     const auto d_grid_desc_m_n =
-                        DeviceOp::MakeCGridDescriptor_M_N(MRaw, NRaw, StrideDs[i]);
+                        DeviceOp::MakeEGridDescriptor_M_N(MRaw, NRaw, StrideDs[i]);
 
                     ds_grid_desc_mblock_mperblock_nblock_nperblock_(i) =
                         GridwiseGemm::MakeEGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock(
@@ -527,23 +530,14 @@ struct DeviceGemmMultipleD_Xdl_CShuffle : public DeviceGemmMultipleD<ALayout,
             }
         }
 
-        // ck::Tuple<const DsDataType*...>
-        static constexpr auto MakeDsGridPointer()
-        {
-            return generate_tuple(
-                [&](auto i) {
-                    using DDataType = remove_cv_t<decltype(DsDataType{}.At(i))>;
-
-                    return static_cast<const DDataType*>(nullptr);
-                },
-                Number<NumDTensor>{});
-        }
-
         //  private:
+        // pointers
         const ADataType* p_a_grid_;
         const BDataType* p_b_grid_;
         typename GridwiseGemm::DsGridPointer p_ds_grid_;
         EDataType* p_e_grid_;
+
+        // tensor descriptors
         AGridDesc_AK0_M_AK1 a_grid_desc_ak0_m_ak1_;
         BGridDesc_BK0_N_BK1 b_grid_desc_bk0_n_bk1_;
         StaticallyIndexedArray<
@@ -554,7 +548,11 @@ struct DeviceGemmMultipleD_Xdl_CShuffle : public DeviceGemmMultipleD<ALayout,
         EGridDesc_M_N e_grid_desc_m_n_;
         typename GridwiseGemm::EGridDescriptor_MBlock_MPerBlock_NBlock_NPerBlock
             e_grid_desc_mblock_mperblock_nblock_nperblock_;
+
+        // 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_;

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

@@ -24,9 +24,25 @@ struct PassThrough
     };
 };
 
+struct Scale
+{
+    __host__ __device__ Scale(float scale) : scale_(scale) {}
+
+    template <typename Y, typename X>
+    __host__ __device__ void operator()(Y& y, const X& x) const;
+
+    template <>
+    __host__ __device__ void operator()<float, float>(float& y, const float& x) const
+    {
+        y = scale_ * x;
+    };
+
+    float scale_;
+};
+
 struct UnaryDivide
 {
-    __host__ __device__ UnaryDivide(const int32_t divider = 1) : divider_(divider){};
+    __host__ __device__ UnaryDivide(const int32_t divider = 1) : divider_(divider) {}
 
     template <typename T>
     __host__ __device__ void operator()(T& y, const T& x) const