Fused attention (#345)

* initial stub for gemm_gemm_xdl_cshuffle

* set up example code

* compiles

* prevent integer overflow

* harmonize interface between ref_gemm and ref_batched_gemm

* batched_gemm_gemm

* fix example

* host tensor gen: diagonal pattern in lowest two-dimensions only

* make c descriptors containing only integral constants

* clean up

* add BlockwiseGemmXdlops_v2 while exploring an unified approach

* implement proper interface

* tidy up example

* fix compilation warnings

* coarsely controlled 2nd gemm padding

* remove rocm-cmake's hard requirement for certain revision

* clang-format

* resolve merge conflict

* fix compilation error on gfx10

* adds acc0 elementwise op to interface

* attention host validation

* add blockwsie softmax v1

* iteratively update softmax+gemm

* transpose both gemm0 and gemm1 xdl output so as to avoid broadcasting softmax max/sum

* add init method for easier debugging

* do away with manual thread cluster calculation

* generalize blockwise softmax interface

* row-wise softmax sum & max

* format

* rename to DeviceBatchedGemmSoftmaxGemm

* add gemm_softmax_gemm instances and tests

* comment
Co-authored-by: ltqin <letao.qin@amd.com>
Co-authored-by: Chao Liu <chao.liu2@amd.com>

CMakeLists.txt

@@ -8,7 +8,7 @@ list(APPEND CMAKE_MODULE_PATH "${PROJECT_SOURCE_DIR}/cmake")
 enable_testing()
 
 set(ROCM_SYMLINK_LIBS OFF)
-find_package(ROCM 0.8 REQUIRED PATHS /opt/rocm)
+find_package(ROCM REQUIRED PATHS /opt/rocm)
 
 include(ROCMInstallTargets)
 include(ROCMPackageConfigHelpers)

example/18_batched_gemm_reduce/batched_gemm_reduce_xdl_fp16.cpp

@@ -66,8 +66,14 @@ using DeviceBatchedGemmReduceInstance = ck::tensor_operation::device::DeviceBatc
         <     Row,     Col,     Row,  F16,   F16,   F16,      F32,      F32,       F32,   ReducePtrsGlobal,  AElementOp,  BElementOp,  CElementOp, ReduceOps, ReduceInElementOps, ReduceOutElementOps, ReduceGlobalMemOps, GemmSpecialization,        1,   256,   256,   128,    32,   8,   8,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,         1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              8,              8,         1,           1,           1,               S<1, 32, 1, 8>,               8,             S<64, 4>,                         4,                            1>;
 // clang-format on
 
-using ReferenceBatchedGemmInstance = ck::tensor_operation::host::
-    ReferenceBatchedGemm<ADataType, BDataType, CDataType, AElementOp, BElementOp, CElementOp>;
+using ReferenceBatchedGemmInstance =
+    ck::tensor_operation::host::ReferenceBatchedGemm<ADataType,
+                                                     BDataType,
+                                                     CDataType,
+                                                     ReduceAccDataType,
+                                                     AElementOp,
+                                                     BElementOp,
+                                                     CElementOp>;
 
 int main(int argc, char* argv[])
 {

example/24_batched_gemm_e_permute/batched_gemm_e_permute_xdl_fp16.cpp

@@ -51,8 +51,13 @@ using DeviceGemmInstance = ck::tensor_operation::device::DeviceBatchedGemmEPermu
         < ALayout, BLayout, ELayout, ADataType, BDataType, AccDataType, CShuffleDataType, EDataType,  AElementOp,  BElementOp, CDEElementOp,    GemmDefault,        1,   256,   256,   128,    32,   8,   8,   32,   32,    4,    2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,         1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              8,              8,         1,           1,           1,               S<1, 32, 1, 8>,               8>;
 // clang-format on
 
-using ReferenceBatchedGemmInstance = ck::tensor_operation::host::
-    ReferenceBatchedGemm<ADataType, BDataType, EDataType, AElementOp, BElementOp, CDEElementOp>;
+using ReferenceBatchedGemmInstance = ck::tensor_operation::host::ReferenceBatchedGemm<ADataType,
+                                                                                      BDataType,
+                                                                                      EDataType,
+                                                                                      AccDataType,
+                                                                                      AElementOp,
+                                                                                      BElementOp,
+                                                                                      CDEElementOp>;
 
 int main(int argc, char* argv[])
 {

example/32_batched_gemm_gemm/CMakeLists.txt

+# TODO: add example batched_gemm_gemm_xdl_fp16
+add_example_executable(example_batched_gemm_softmax_gemm_xdl_fp16 batched_gemm_softmax_gemm_xdl_fp16.cpp)

example/32_batched_gemm_gemm/batched_gemm_softmax_gemm_xdl_fp16.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+/*
+Gemm + Gemm fused operation. Computes C_m_o = A_m_k * B0_k_n * B1_n_o
+                                              |------------|
+                                                   Gemm0
+                                              |---------------------|
+                                                       Gemm1
+*/
+
+#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_batched_gemm_softmax_gemm_xdl_cshuffle.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/utility/check_err.hpp"
+#include "ck/library/utility/device_memory.hpp"
+#include "ck/library/utility/host_tensor.hpp"
+#include "ck/library/utility/host_tensor_generator.hpp"
+#include "ck/library/reference_tensor_operation/cpu/reference_batched_gemm.hpp"
+#include "ck/library/reference_tensor_operation/cpu/reference_softmax.hpp"
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+using F16 = ck::half_t;
+using F32 = float;
+
+using Row = ck::tensor_layout::gemm::RowMajor;
+using Col = ck::tensor_layout::gemm::ColumnMajor;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+
+using ADataType        = F16;
+using B0DataType       = F16;
+using B1DataType       = F16;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using CDataType        = F16;
+
+using ALayout  = Row;
+using B0Layout = Col;
+using B1Layout = Row;
+using CLayout  = Row;
+
+using AElementOp    = PassThrough;
+using B0ElementOp   = PassThrough;
+using Acc0ElementOp = PassThrough;
+using B1ElementOp   = PassThrough;
+using CElementOp    = PassThrough;
+
+static constexpr auto GemmDefault = ck::tensor_operation::device::GemmSpecialization::Default;
+
+using DeviceGemmInstance = ck::tensor_operation::device::DeviceBatchedGemmSoftmaxGemm_Xdl_CShuffle<
+    ALayout,
+    B0Layout,
+    B1Layout,
+    CLayout,
+    ADataType,
+    B0DataType,
+    B1DataType,
+    CDataType,
+    AccDataType,
+    CShuffleDataType,
+    AElementOp,
+    B0ElementOp,
+    Acc0ElementOp,
+    B1ElementOp,
+    CElementOp,
+    GemmDefault,
+    1,
+    256,
+    128,         // MPerBlock
+    128,         // NPerBlock
+    32,          // KPerBlock
+    64,          // Gemm1NPerBlock
+    32,          // Gemm1KPerBlock
+    8,           // AK1
+    8,           // BK1
+    2,           // B1K1
+    32,          // MPerXDL
+    32,          // NPerXDL
+    1,           // MXdlPerWave
+    4,           // NXdlPerWave
+    2,           // Gemm1NXdlPerWave
+    S<4, 64, 1>, // ABlockTransfer
+    S<1, 0, 2>,
+    S<1, 0, 2>,
+    2,
+    8,
+    8,
+    true,
+    S<4, 64, 1>, // BBlockTransfer
+    S<1, 0, 2>,
+    S<1, 0, 2>,
+    2,
+    8,
+    8,
+    true,
+    S<16, 16, 1>, // B1BlockTransfer
+    S<0, 2, 1>,
+    S<0, 2, 1>,
+    1,
+    4,
+    2,
+    false,
+    1,              // CShuffleMXdlPerWavePerShuffle
+    2,              // CShuffleNXdlPerWavePerShuffle
+    S<1, 32, 1, 8>, // CShuffleBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock
+    8>;             // CShuffleBlockTransferScalarPerVector_NPerBlock
+
+// Ref Gemm0: fp16 in, fp32 out
+using ReferenceGemm0Instance = ck::tensor_operation::host::ReferenceBatchedGemm<ADataType,
+                                                                                B0DataType,
+                                                                                AccDataType,
+                                                                                AccDataType,
+                                                                                AElementOp,
+                                                                                B0ElementOp,
+                                                                                CElementOp>;
+
+// Ref Softmax: fp32 in, fp16 out
+using ReferenceSoftmaxInstance =
+    ck::tensor_operation::host::ReferenceSoftmax<AccDataType, ADataType, AccDataType>;
+
+// Ref Gemm1: fp16 in, fp16 out
+using ReferenceGemm1Instance = ck::tensor_operation::host::ReferenceBatchedGemm<ADataType,
+                                                                                B1DataType,
+                                                                                CDataType,
+                                                                                AccDataType,
+                                                                                AElementOp,
+                                                                                B1ElementOp,
+                                                                                CElementOp>;
+
+int main(int argc, char* argv[])
+{
+    bool do_verification = true;
+    int init_method      = 1;
+    bool time_kernel     = false;
+
+    // GEMM shape
+    ck::index_t M             = 1024;
+    ck::index_t N             = 1024;
+    ck::index_t K             = 64;
+    ck::index_t O             = 128;
+    ck::index_t BatchCount    = 4;
+    ck::index_t StrideA       = -1;
+    ck::index_t StrideB0      = -1;
+    ck::index_t StrideB1      = -1;
+    ck::index_t StrideC       = -1;
+    ck::index_t BatchStrideA  = -1;
+    ck::index_t BatchStrideB0 = -1;
+    ck::index_t BatchStrideB1 = -1;
+    ck::index_t BatchStrideC  = -1;
+
+    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 == 9)
+    {
+        do_verification = std::stoi(argv[1]);
+        init_method     = std::stoi(argv[2]);
+        time_kernel     = std::stoi(argv[3]);
+
+        M = std::stoi(argv[4]);
+        N = std::stoi(argv[5]);
+        K = std::stoi(argv[6]);
+        O = std::stoi(argv[7]);
+
+        BatchCount = std::stoi(argv[8]);
+    }
+    else if(argc == 17)
+    {
+        do_verification = std::stoi(argv[1]);
+        init_method     = std::stoi(argv[2]);
+        time_kernel     = std::stoi(argv[3]);
+
+        M = std::stoi(argv[4]);
+        N = std::stoi(argv[5]);
+        K = std::stoi(argv[6]);
+        O = std::stoi(argv[7]);
+
+        BatchCount = std::stoi(argv[8]);
+
+        StrideA  = std::stoi(argv[9]);
+        StrideB0 = std::stoi(argv[10]);
+        StrideB1 = std::stoi(argv[11]);
+        StrideC  = std::stoi(argv[12]);
+
+        BatchStrideA  = std::stoi(argv[13]);
+        BatchStrideB0 = std::stoi(argv[14]);
+        BatchStrideB1 = std::stoi(argv[15]);
+        BatchStrideC  = std::stoi(argv[16]);
+    }
+    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 17: M, N, K, O, Batch, StrideA, StrideB0, StrideB1, StrideC, BatchStrideA, "
+               "BatchStrideB0, BatchStrideB1, BatchStrideC\n");
+        exit(0);
+    }
+
+    const int DefaultStrideA  = ck::is_same_v<ALayout, Row> ? K : M;
+    const int DefaultStrideB0 = ck::is_same_v<B0Layout, Row> ? N : K;
+    const int DefaultStrideB1 = ck::is_same_v<B1Layout, Row> ? O : N;
+    const int DefaultStrideC  = ck::is_same_v<CLayout, Row> ? O : M;
+
+    StrideA  = (StrideA < 0) ? DefaultStrideA : StrideA;
+    StrideB0 = (StrideB0 < 0) ? DefaultStrideB0 : StrideB0;
+    StrideB1 = (StrideB1 < 0) ? DefaultStrideB1 : StrideB1;
+    StrideC  = (StrideC < 0) ? DefaultStrideC : StrideC;
+
+    const int DefaultBatchStrideA  = (ck::is_same_v<ALayout, Col> ? K : M) * StrideA;
+    const int DefaultBatchStrideB0 = (ck::is_same_v<B0Layout, Col> ? N : K) * StrideB0;
+    const int DefaultBatchStrideB1 = (ck::is_same_v<B1Layout, Col> ? O : N) * StrideB1;
+    const int DefaultBatchStrideC  = (ck::is_same_v<CLayout, Col> ? O : M) * StrideC;
+
+    BatchStrideA  = BatchStrideA < 0 ? DefaultBatchStrideA : BatchStrideA;
+    BatchStrideB0 = BatchStrideB0 < 0 ? DefaultBatchStrideB0 : BatchStrideB0;
+    BatchStrideB1 = BatchStrideB1 < 0 ? DefaultBatchStrideB1 : BatchStrideB1;
+    BatchStrideC  = BatchStrideC < 0 ? DefaultBatchStrideC : BatchStrideC;
+
+    auto f_host_tensor_descriptor = [](std::size_t batch_count,
+                                       std::size_t row,
+                                       std::size_t col,
+                                       std::size_t stride,
+                                       std::size_t batch_stride,
+                                       auto layout) {
+        if(std::is_same<decltype(layout), Row>::value)
+        {
+            return HostTensorDescriptor(std::vector<std::size_t>({batch_count, row, col}),
+                                        std::vector<std::size_t>({batch_stride, stride, 1}));
+        }
+        else
+        {
+            return HostTensorDescriptor(std::vector<std::size_t>({batch_count, row, col}),
+                                        std::vector<std::size_t>({batch_stride, 1, stride}));
+        }
+    };
+
+    // C_m_o = A_m_k * B0_k_n * B1_n_o
+    Tensor<ADataType> a_g_m_k(
+        f_host_tensor_descriptor(BatchCount, M, K, StrideA, BatchStrideA, ALayout{}));
+    Tensor<B0DataType> b0_g_k_n(
+        f_host_tensor_descriptor(BatchCount, K, N, StrideB0, BatchStrideB0, B0Layout{}));
+    Tensor<B1DataType> b1_g_n_o(
+        f_host_tensor_descriptor(BatchCount, N, O, StrideB1, BatchStrideB1, B1Layout{}));
+    Tensor<CDataType> c_g_m_o_host_result(
+        f_host_tensor_descriptor(BatchCount, M, O, StrideC, BatchStrideC, CLayout{}));
+    Tensor<CDataType> c_g_m_o_device_result(
+        f_host_tensor_descriptor(BatchCount, M, O, StrideC, BatchStrideC, CLayout{}));
+
+    std::cout << "a_g_m_k: " << a_g_m_k.mDesc << std::endl;
+    std::cout << "b0_g_k_n: " << b0_g_k_n.mDesc << std::endl;
+    std::cout << "b1_g_n_o: " << b1_g_n_o.mDesc << std::endl;
+    std::cout << "c_g_m_o: " << c_g_m_o_host_result.mDesc << std::endl;
+
+    switch(init_method)
+    {
+    case 0: break;
+    case 1:
+        a_g_m_k.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
+        b0_g_k_n.GenerateTensorValue(GeneratorTensor_2<B0DataType>{-5, 5});
+        b1_g_n_o.GenerateTensorValue(GeneratorTensor_2<B1DataType>{-5, 5});
+        break;
+    case 2:
+        a_g_m_k.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
+        b0_g_k_n.GenerateTensorValue(GeneratorTensor_3<B0DataType>{0.0, 1.0});
+        b1_g_n_o.GenerateTensorValue(GeneratorTensor_3<B1DataType>{-0.5, 0.5});
+        break;
+    case 3:
+        a_g_m_k.GenerateTensorValue(GeneratorTensor_2<ADataType>{-2, 2});
+        b0_g_k_n.GenerateTensorValue(GeneratorTensor_Diagonal<B0DataType>{});
+        b1_g_n_o.GenerateTensorValue(GeneratorTensor_Diagonal<B1DataType>{});
+        break;
+    default:
+        a_g_m_k.GenerateTensorValue(GeneratorTensor_1<ADataType>{1});
+        b0_g_k_n.GenerateTensorValue(GeneratorTensor_Sequential<1>{});
+        b1_g_n_o.GenerateTensorValue(GeneratorTensor_Diagonal<B1DataType>{});
+    }
+
+    DeviceMem a_g_m_k_device_buf(sizeof(ADataType) * a_g_m_k.mDesc.GetElementSize());
+    DeviceMem b0_g_k_n_device_buf(sizeof(B0DataType) * b0_g_k_n.mDesc.GetElementSize());
+    DeviceMem b1_g_n_o_device_buf(sizeof(B1DataType) * b1_g_n_o.mDesc.GetElementSize());
+    DeviceMem c_g_m_o_device_buf(sizeof(CDataType) * c_g_m_o_device_result.mDesc.GetElementSize());
+
+    a_g_m_k_device_buf.ToDevice(a_g_m_k.mData.data());
+    b0_g_k_n_device_buf.ToDevice(b0_g_k_n.mData.data());
+    b1_g_n_o_device_buf.ToDevice(b1_g_n_o.mData.data());
+
+    auto a_element_op    = AElementOp{};
+    auto b0_element_op   = B0ElementOp{};
+    auto acc0_element_op = Acc0ElementOp{};
+    auto b1_element_op   = B1ElementOp{};
+    auto c_element_op    = CElementOp{};
+
+    // do GEMM
+    auto gemm    = DeviceGemmInstance{};
+    auto invoker = gemm.MakeInvoker();
+    auto argument =
+        gemm.MakeArgument(static_cast<ADataType*>(a_g_m_k_device_buf.GetDeviceBuffer()),
+                          static_cast<B0DataType*>(b0_g_k_n_device_buf.GetDeviceBuffer()),
+                          static_cast<B1DataType*>(b1_g_n_o_device_buf.GetDeviceBuffer()),
+                          static_cast<CDataType*>(c_g_m_o_device_buf.GetDeviceBuffer()),
+                          M,
+                          N,
+                          K,
+                          O,
+                          BatchCount,
+                          StrideA,
+                          StrideB0,
+                          StrideB1,
+                          StrideC,
+                          BatchStrideA,
+                          BatchStrideB0,
+                          BatchStrideB1,
+                          BatchStrideC,
+                          a_element_op,
+                          b0_element_op,
+                          acc0_element_op,
+                          b1_element_op,
+                          c_element_op);
+
+    if(!gemm.IsSupportedArgument(argument))
+    {
+        std::cout << gemm.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+
+    std::size_t flop      = (size_t(M) * N * K * 2 + size_t(M) * N * O * 2) * BatchCount;
+    std::size_t num_btype = (sizeof(ADataType) * M * K + sizeof(B0DataType) * K * N +
+                             sizeof(B1DataType) * N * O + sizeof(CDataType) * M * O) *
+                            BatchCount;
+
+    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, "
+              << gemm.GetTypeString() << std::endl;
+
+    c_g_m_o_device_buf.FromDevice(c_g_m_o_device_result.mData.data());
+
+    if(do_verification)
+    {
+        // Output of Gemm0 is input A of Gemm1
+        Tensor<AccDataType> acc0_g_m_n(f_host_tensor_descriptor(BatchCount, M, N, N, M * N, Row{}));
+
+        Tensor<ADataType> a1_g_m_n(f_host_tensor_descriptor(BatchCount, M, N, N, M * N, Row{}));
+
+        auto ref_gemm0          = ReferenceGemm0Instance{};
+        auto ref_gemm0_invoker  = ref_gemm0.MakeInvoker();
+        auto ref_gemm0_argument = ref_gemm0.MakeArgument(
+            a_g_m_k, b0_g_k_n, acc0_g_m_n, a_element_op, b0_element_op, PassThrough{});
+
+        ref_gemm0_invoker.Run(ref_gemm0_argument);
+
+        auto ref_softmax          = ReferenceSoftmaxInstance{};
+        auto ref_softmax_invoker  = ref_softmax.MakeInvoker();
+        auto ref_softmax_argument = ref_softmax.MakeArgument(acc0_g_m_n, a1_g_m_n, 1, 0, {2});
+
+        ref_softmax_invoker.Run(ref_softmax_argument);
+
+        auto ref_gemm1          = ReferenceGemm1Instance{};
+        auto ref_gemm1_invoker  = ref_gemm1.MakeInvoker();
+        auto ref_gemm1_argument = ref_gemm1.MakeArgument(
+            a1_g_m_n, b1_g_n_o, c_g_m_o_host_result, PassThrough{}, b1_element_op, c_element_op);
+
+        ref_gemm1_invoker.Run(ref_gemm1_argument);
+
+        return ck::utils::check_err(c_g_m_o_device_result.mData, c_g_m_o_host_result.mData) ? 0 : 1;
+    }
+
+    return 0;
+}

example/CMakeLists.txt

@@ -46,3 +46,4 @@ add_subdirectory(28_grouped_gemm_bias_e_permute)
 add_subdirectory(29_batched_gemm_bias_e_permute)
 add_subdirectory(30_grouped_convnd_fwd_bias_relu)
 add_subdirectory(31_grouped_convnd_fwd_bias_relu_add)
+add_subdirectory(32_batched_gemm_gemm)

include/ck/tensor_description/tensor_descriptor.hpp

@@ -4,6 +4,7 @@
 #pragma once
 
 #include "ck/utility/common_header.hpp"
+#include "ck/utility/sequence_helper.hpp"
 #include "ck/tensor_description/multi_index_transform.hpp"
 
 namespace ck {
@@ -159,6 +160,12 @@ struct TensorDescriptor
         return transforms_[Number<itran>{}].GetUpperLengths()[Number<idim_up>{}];
     }
 
+    __host__ __device__ constexpr auto GetLengths() const
+    {
+        // FIXME: use Tuple of reference instead
+        return generate_sequence_v2([&](auto I) { return GetLength(I); }, Number<ndim_visible_>{});
+    }
+
     __host__ __device__ constexpr auto GetElementSize() const { return element_size_; }
 
     __host__ __device__ constexpr auto GetElementSpaceSize() const { return element_space_size_; }

include/ck/tensor_operation/gpu/block/blockwise_gemm_xdlops.hpp

@@ -25,6 +25,22 @@ constexpr LoopScheduler make_default_loop_scheduler()
 #endif // if CK_EXPERIMENTAL_INTER_WAVE_SCHEDULING
 }
 
+template <index_t MNXdlPerWave, index_t MNWaves, index_t MNPerXdl, typename TileDesc_K0_MN_K1>
+__host__ __device__ static constexpr auto
+MakeGemmMmaTileDescriptor_MN0_MN1_MN2_K(const TileDesc_K0_MN_K1&)
+{
+    constexpr index_t K0 = TileDesc_K0_MN_K1{}.GetLength(Number<0>{});
+    constexpr index_t K1 = TileDesc_K0_MN_K1{}.GetLength(Number<2>{});
+
+    return transform_tensor_descriptor(
+        TileDesc_K0_MN_K1{},
+        make_tuple(make_merge_transform_v3_division_mod(make_tuple(Number<K0>{}, Number<K1>{})),
+                   make_unmerge_transform(
+                       make_tuple(Number<MNXdlPerWave>{}, Number<MNWaves>{}, Number<MNPerXdl>{}))),
+        make_tuple(Sequence<0, 2>{}, Sequence<1>{}),
+        make_tuple(Sequence<3>{}, Sequence<0, 1, 2>{}));
+}
+
 template <index_t BlockSize,
           typename FloatAB,
           typename FloatAcc,
@@ -585,4 +601,361 @@ constexpr auto BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_Selector()
     }
 };
 
+// Blockwise gemm supporting
+// 1. regular XDL output M2_M3_M4_M2 and transposed XDL output M2_N2_N3_N4
+// 2. decoupled input tile descriptor and mma tile descriptor in order to support both vgpr and LDS
+// source buffer
+// 3. configurable k index starting position and step size after each FMA/XDL instruction
+template <index_t BlockSize,
+          typename FloatAB,
+          typename FloatAcc,
+          typename ATileDesc,
+          typename BTileDesc,
+          typename AMmaTileDesc,
+          typename BMmaTileDesc,
+          index_t MPerBlock,
+          index_t NPerBlock,
+          index_t KPerBlock,
+          index_t MPerXDL,
+          index_t NPerXDL,
+          index_t MRepeat,
+          index_t NRepeat,
+          index_t KPack,
+          bool TransposeC = false,
+          index_t AMmaKStride =
+              KPack* XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack, TransposeC>{}.K0PerXdlops,
+          index_t BMmaKStride =
+              KPack* XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack, TransposeC>{}.K0PerXdlops>
+struct BlockwiseGemmXdlops_v2
+{
+    static constexpr auto I0 = Number<0>{};
+    static constexpr auto I1 = Number<1>{};
+    static constexpr auto I2 = Number<2>{};
+    static constexpr auto I3 = Number<3>{};
+
+    using ThisThreadBlock = ThisThreadBlock<BlockSize>;
+
+    static constexpr index_t WaveSize = get_warp_size();
+
+    static constexpr index_t A_K0 = ATileDesc{}.GetLength(I0);
+    static constexpr index_t B_K0 = BTileDesc{}.GetLength(I0);
+    static constexpr index_t A_K1 = ATileDesc{}.GetLength(I2);
+    static constexpr index_t B_K1 = BTileDesc{}.GetLength(I2);
+
+    static constexpr auto xdlops_gemm = XdlopsGemm<FloatAB, MPerXDL, NPerXDL, KPack, TransposeC>{};
+
+    static constexpr index_t KPerThread = KPerBlock / xdlops_gemm.K0PerXdlops;
+
+    static constexpr index_t MWaves = MPerBlock / (MRepeat * MPerXDL);
+    static constexpr index_t NWaves = NPerBlock / (NRepeat * NPerXDL);
+
+    StaticBufferTupleOfVector<AddressSpaceEnum::Vgpr,
+                              FloatAcc,
+                              MRepeat * NRepeat,
+                              xdlops_gemm.GetRegSizePerXdlops(),
+                              true>
+        c_thread_buf_;
+
+    __host__ __device__ constexpr auto& GetCThreadBuffer() { return c_thread_buf_; }
+
+    __device__ static auto GetWaveIdx()
+    {
+        const index_t thread_id = ThisThreadBlock::GetThreadId();
+
+        constexpr auto threadid_to_wave_idx_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_merge_transform(make_tuple(MWaves, NWaves, WaveSize))),
+            make_tuple(Sequence<0, 1, 2>{}),
+            make_tuple(Sequence<0>{}));
+
+        return threadid_to_wave_idx_adaptor.CalculateBottomIndex(make_multi_index(thread_id));
+    }
+
+    __device__ static auto CalculateAThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+
+        const auto xdlops_a_idx = xdlops_gemm.CalculateAThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_m, xdlops_a_idx[I1], KPack * xdlops_a_idx[I0]);
+    }
+
+    __device__ static auto CalculateBThreadOriginDataIndex()
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_n = wave_idx[I1];
+
+        const auto xdlops_b_idx = xdlops_gemm.CalculateBThreadOriginDataIndex();
+
+        return make_tuple(0, waveId_n, xdlops_b_idx[I1], KPack * xdlops_b_idx[I0]);
+    }
+
+    template <index_t m0, index_t n0, index_t xdlops_i, index_t blk_i>
+    __device__ static auto
+        CalculateCThreadOriginDataIndex(Number<m0>, Number<n0>, Number<xdlops_i>, Number<blk_i>)
+    {
+        const auto wave_idx = GetWaveIdx();
+
+        const auto waveId_m = wave_idx[I0];
+        const auto waveId_n = wave_idx[I1];
+
+        const auto tmp = xdlops_gemm.GetBeginOfThreadBlk(xdlops_i, blk_i);
+        const auto blk_idx =
+            TransposeC ? make_multi_index(tmp[I1], tmp[I0]) : make_multi_index(tmp[I0], tmp[I1]);
+
+        constexpr auto mrepeat_mwave_mperxdl_to_m_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(MRepeat, MWaves, MPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        constexpr auto nrepeat_nwave_nperxdl_to_n_adaptor = make_single_stage_tensor_adaptor(
+            make_tuple(make_unmerge_transform(make_tuple(NRepeat, NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}),
+            make_tuple(Sequence<0, 1, 2>{}));
+
+        const index_t c_thread_m = mrepeat_mwave_mperxdl_to_m_adaptor.CalculateBottomIndex(
+            make_tuple(m0, waveId_m, blk_idx[I0]))[I0];
+        const index_t c_thread_n = nrepeat_nwave_nperxdl_to_n_adaptor.CalculateBottomIndex(
+            make_tuple(n0, waveId_n, blk_idx[I1]))[I0];
+
+        return make_tuple(c_thread_m, c_thread_n);
+    }
+
+    using Tuple4 = decltype(CalculateAThreadOriginDataIndex());
+
+    __host__ __device__ BlockwiseGemmXdlops_v2(Tuple4 a_origin = CalculateAThreadOriginDataIndex(),
+                                               Tuple4 b_origin = CalculateBThreadOriginDataIndex())
+        : a_thread_copy_(a_origin), b_thread_copy_(b_origin)
+    {
+        static_assert(AMmaTileDesc::IsKnownAtCompileTime() && BMmaTileDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc should be known at compile-time");
+
+        static_assert(ThisThreadBlock::GetNumOfThread() == MWaves * NWaves * WaveSize,
+                      "ThisThreadBlock::GetNumOfThread() != MWaves * NWaves * WaveSize\n");
+
+        static_assert(MPerBlock % (MPerXDL * MRepeat) == 0 && NPerBlock % (NPerXDL * NRepeat) == 0,
+                      "wrong!");
+    }
+
+    __host__ __device__ BlockwiseGemmXdlops_v2(const BlockwiseGemmXdlops_v2& other)
+        : a_thread_copy_(other.a_origin), b_thread_copy_(other.b_origin)
+    {
+    }
+
+    // transposed XDL output supporting C_xdl' = B_xdl' * A_xdl'
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_M0_N0_M1_N1_M2_N2_N3_N4()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, N, M0, M1, M2));
+    }
+
+    // XDL output supporting C_xdl = A_xdl * B_xdl
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    __host__ __device__ static constexpr auto GetCThreadDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_m0_m1_m2_n_tblk_lens = xdlops_gemm.GetCM0M1M2NThreadBlkLengths();
+
+        constexpr auto M0 = c_m0_m1_m2_n_tblk_lens[I0];
+        constexpr auto M1 = c_m0_m1_m2_n_tblk_lens[I1];
+        constexpr auto M2 = c_m0_m1_m2_n_tblk_lens[I2];
+        constexpr auto N  = c_m0_m1_m2_n_tblk_lens[I3];
+
+        return make_naive_tensor_descriptor_packed(
+            make_tuple(I1, Number<MRepeat>{}, Number<NRepeat>{}, I1, I1, M0, M1, M2, N));
+    }
+
+    // transposed XDL output supporting C_xdl' = B_xdl' * A_xdl'
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_M0_N0_M1_N1_M2_N2_N3_N4()
+    {
+        constexpr auto c_block_desc_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_N2_N3_N4(c_block_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    // XDL output supporting C_xdl = A_xdl * B_xdl
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_block_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    __host__ __device__ static constexpr auto GetCBlockDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2()
+    {
+        constexpr auto c_block_desc_g_m0_n0_m1_n1_m2_n2 =
+            make_naive_tensor_descriptor_packed(make_tuple(I1,
+                                                           Number<MRepeat>{},
+                                                           Number<NRepeat>{},
+                                                           Number<MWaves>{},
+                                                           Number<NWaves>{},
+                                                           Number<MPerXDL>{},
+                                                           Number<NPerXDL>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_block_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_M_N& c_grid_desc_m_n)
+    {
+        const auto M = c_grid_desc_m_n.GetLength(I0);
+        const auto N = c_grid_desc_m_n.GetLength(I1);
+
+        const auto c_grid_desc_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_m_n,
+            make_tuple(make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}),
+            make_tuple(Sequence<0, 2, 4>{}, Sequence<1, 3, 5>{}));
+
+        return xdlops_gemm.MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(c_grid_desc_m0_n0_m1_n1_m2_n2);
+    }
+
+    template <typename CGridDesc_G_M_N>
+    __host__ __device__ static constexpr auto
+    MakeCGridDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(const CGridDesc_G_M_N& c_grid_desc_g_m_n)
+    {
+        const auto G = c_grid_desc_g_m_n.GetLength(I0);
+        const auto M = c_grid_desc_g_m_n.GetLength(I1);
+        const auto N = c_grid_desc_g_m_n.GetLength(I2);
+
+        const auto c_grid_desc_g_m0_n0_m1_n1_m2_n2 = transform_tensor_descriptor(
+            c_grid_desc_g_m_n,
+            make_tuple(make_pass_through_transform(G),
+                       make_unmerge_transform(make_tuple(M / (MWaves * MPerXDL), MWaves, MPerXDL)),
+                       make_unmerge_transform(make_tuple(N / (NWaves * NPerXDL), NWaves, NPerXDL))),
+            make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}),
+            make_tuple(Sequence<0>{}, Sequence<1, 3, 5>{}, Sequence<2, 4, 6>{}));
+
+        return xdlops_gemm.MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
+            c_grid_desc_g_m0_n0_m1_n1_m2_n2);
+    }
+
+    static constexpr AMmaTileDesc a_block_desc_m0_m1_m2_k;
+    static constexpr BMmaTileDesc b_block_desc_n0_n1_n2_k;
+
+    template <typename ABlockBuffer, typename BBlockBuffer, typename CThreadBuffer>
+    __device__ void Run(const ABlockBuffer& a_block_buf,
+                        const BBlockBuffer& b_block_buf,
+                        CThreadBuffer& c_thread_buf) const
+    {
+        auto a_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            a_thread_desc_.GetElementSpaceSize());
+        auto b_thread_buf = make_static_buffer<AddressSpaceEnum::Vgpr, FloatAB>(
+            b_thread_desc_.GetElementSpaceSize());
+
+        static_for<0, KPerThread / KPack, 1>{}([&](auto k) { // k=0,1,2 instead of k=0,kpack*1, ...
+            static_for<0, MRepeat, 1>{}([&](auto m0) {
+                // read A
+                a_thread_copy_.Run(a_block_desc_m0_m1_m2_k,
+                                   make_tuple(m0, I0, I0, Number<k * AMmaKStride>{}),
+                                   a_block_buf,
+                                   a_thread_desc_,
+                                   make_tuple(I0, I0, I0, I0),
+                                   a_thread_buf);
+
+                static_for<0, NRepeat, 1>{}([&](auto n0) {
+                    // read B
+                    b_thread_copy_.Run(b_block_desc_n0_n1_n2_k,
+                                       make_tuple(n0, I0, I0, Number<k * BMmaKStride>{}),
+                                       b_block_buf,
+                                       b_thread_desc_,
+                                       make_tuple(I0, I0, I0, I0),
+                                       b_thread_buf);
+                    vector_type<FloatAB, KPack> a_thread_vec;
+                    vector_type<FloatAB, KPack> b_thread_vec;
+
+                    static_for<0, KPack, 1>{}([&](auto i) {
+                        a_thread_vec.template AsType<FloatAB>()(i) = a_thread_buf
+                            [Number<a_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, i))>{}];
+                        b_thread_vec.template AsType<FloatAB>()(i) = b_thread_buf
+                            [Number<b_thread_desc_.CalculateOffset(make_tuple(0, 0, 0, i))>{}];
+                    });
+
+                    using mfma_input_type =
+                        typename vector_type<FloatAB, xdlops_gemm.K1PerXdlops>::type;
+
+                    constexpr index_t c_offset =
+                        c_thread_desc_.CalculateOffset(make_tuple(m0, n0, 0));
+
+                    xdlops_gemm.template Run(
+                        a_thread_vec.template AsType<mfma_input_type>(),
+                        b_thread_vec.template AsType<mfma_input_type>(),
+                        c_thread_buf.GetVectorTypeReference(Number<c_offset>{}));
+                });
+            });
+        });
+    }
+
+    protected:
+    // A[M0, M1, M2, KPerThread]
+    static constexpr auto a_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPerThread>{}));
+
+    // B[N0, N1, N2, KPerThread]
+    static constexpr auto b_thread_desc_ =
+        make_naive_tensor_descriptor_packed(make_tuple(I1, I1, I1, Number<KPerThread>{}));
+
+    // C[M, N, NumRegXdlops]
+    static constexpr auto c_thread_desc_ = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<MRepeat>{}, Number<NRepeat>{}, xdlops_gemm.GetRegSizePerXdlops()));
+
+    using AThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(a_block_desc_m0_m1_m2_k),
+                                                         decltype(a_thread_desc_),
+                                                         Sequence<1, 1, 1, KPack>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         A_K1,
+                                                         A_K1>;
+
+    using BThreadCopy = ThreadwiseTensorSliceTransfer_v4<FloatAB,
+                                                         FloatAB,
+                                                         decltype(b_block_desc_n0_n1_n2_k),
+                                                         decltype(b_thread_desc_),
+                                                         Sequence<1, 1, 1, KPack>,
+                                                         Sequence<0, 1, 2, 3>,
+                                                         3,
+                                                         B_K1,
+                                                         B_K1>;
+
+    AThreadCopy a_thread_copy_;
+    BThreadCopy b_thread_copy_;
+};
+
 } // namespace ck

include/ck/tensor_operation/gpu/block/blockwise_softmax.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/utility/data_type.hpp"
+#include "ck/utility/reduction_common.hpp"
+#include "ck/utility/reduction_operator.hpp"
+#include "ck/utility/reduction_functions_accumulate.hpp"
+#include "ck/tensor_operation/gpu/block/reduction_functions_blockwise.hpp"
+#include "ck/tensor_operation/gpu/thread/reduction_functions_threadwise.hpp"
+
+namespace ck {
+
+template <index_t BlockSize,
+          typename AccDataType,
+          typename ThreadMap_M_K, // thread_id to m_k
+          typename ThreadClusterDesc_M_K,
+          typename ThreadSliceDesc_M_K>
+struct BlockwiseSoftmax
+{
+    static constexpr auto I0         = Number<0>{};
+    static constexpr auto I1         = Number<1>{};
+    static constexpr index_t MRepeat = ThreadSliceDesc_M_K{}.GetLength(I0);
+    static constexpr index_t KRepeat = ThreadSliceDesc_M_K{}.GetLength(I1);
+
+    using ThreadSliceDesc_M = decltype(
+        make_naive_tensor_descriptor_packed(make_tuple(ThreadSliceDesc_M_K{}.GetLength(I0))));
+
+    using ThreadwiseMaxReduce = ThreadwiseReduction<AccDataType,
+                                                    ThreadSliceDesc_M_K,
+                                                    ThreadSliceDesc_M,
+                                                    reduce::Max,
+                                                    false>;
+
+    using ThreadClusterLengths_M_K = decltype(ThreadClusterDesc_M_K{}.GetLengths());
+
+    using BlockwiseMaxReduce = PartitionedBlockwiseReduction_v2<AccDataType,
+                                                                BlockSize,
+                                                                ThreadClusterLengths_M_K,
+                                                                ThreadMap_M_K,
+                                                                reduce::Max,
+                                                                false>;
+
+    using BlockwiseSumReduce = PartitionedBlockwiseReduction_v2<AccDataType,
+                                                                BlockSize,
+                                                                ThreadClusterLengths_M_K,
+                                                                ThreadMap_M_K,
+                                                                reduce::Add,
+                                                                false>;
+
+    using ThreadwiseSumReduce = ThreadwiseReduction<AccDataType,
+                                                    ThreadSliceDesc_M_K,
+                                                    ThreadSliceDesc_M,
+                                                    reduce::Add,
+                                                    false>;
+
+    using BufferType = StaticBuffer<AddressSpaceEnum::Vgpr, AccDataType, MRepeat, true>;
+
+    template <typename CThreadBuffer, typename WorkspaceBuffer>
+    __host__ __device__ void Run(CThreadBuffer& in_thread_buf, WorkspaceBuffer& reduce_work_buf)
+    {
+        // find max value
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            max_value_buf(I) = reduce::Max::template GetIdentityValue<AccDataType>();
+        });
+        ThreadwiseMaxReduce::Reduce(in_thread_buf, max_value_buf);
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            BlockwiseMaxReduce::Reduce(reduce_work_buf, max_value_buf(I));
+            block_sync_lds();
+        });
+
+        // calculate exp for elements, P=exp(s-max)
+        static_for<0, MRepeat, 1>{}([&](auto iM) {
+            static_for<0, KRepeat, 1>{}([&](auto iK) {
+                auto offset = Number<ThreadSliceDesc_M_K{}.CalculateOffset(make_tuple(iM, iK))>{};
+                in_thread_buf(offset) = math::exp(in_thread_buf[offset] - max_value_buf(iM));
+            });
+        });
+
+        // sum data
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            sum_value_buf(I) = reduce::Add::template GetIdentityValue<AccDataType>();
+        });
+        ThreadwiseSumReduce::Reduce(in_thread_buf, sum_value_buf);
+        static_for<0, MRepeat, 1>{}([&](auto I) {
+            BlockwiseSumReduce::Reduce(reduce_work_buf, sum_value_buf(I));
+            block_sync_lds();
+        });
+    }
+
+    BufferType max_value_buf;
+    BufferType sum_value_buf;
+};
+
+} // namespace ck

include/ck/tensor_operation/gpu/block/reduction_functions_blockwise.hpp

@@ -82,6 +82,78 @@ struct PartitionedBlockwiseReduction
     };
 };
 
+// clang-format off
+// Assume:
+//  1) work_buffer is buffer (typically LDS) allocated outside as workspace, does not include any in/out data
+//  2) work_buffer has AccDataType elements, and space size is no less than BlockSize
+//  3) in_out_value is the input data in vgpr from each thread
+//  4) in_out_value is the over-written reduced output in vgpr for each thread
+// clang-format on
+template <typename AccDataType,
+          index_t BlockSize,
+          typename ThreadClusterLengths_M_K,
+          typename ThreadClusterDesc,
+          typename OpReduce,
+          bool PropagateNan,
+          typename Accumulation =
+              detail::AccumulateWithNanCheck<PropagateNan, OpReduce, AccDataType>>
+struct PartitionedBlockwiseReduction_v2
+{
+    static_assert(BlockSize == ThreadClusterLengths_M_K::At(0) * ThreadClusterLengths_M_K::At(1),
+                  "The product of cluster lengths should be same as BlockSize!");
+
+    static constexpr auto BufferLength_M = ThreadClusterLengths_M_K::At(0);
+    static constexpr auto BufferLength_K = ThreadClusterLengths_M_K::At(1);
+
+    static_assert(BufferLength_K > 1, "Parallel reduction need work on at least two elements");
+
+    static constexpr auto block_buf_desc_m_k = make_naive_tensor_descriptor_packed(
+        make_tuple(Number<BufferLength_M>{}, Number<BufferLength_K>{}));
+
+    static constexpr auto thread_cluster_desc = ThreadClusterDesc{};
+
+    template <typename BufferType>
+    __device__ static void Reduce(BufferType& work_buffer, AccDataType& in_out_value)
+    {
+        static_assert(is_same<typename BufferType::type, AccDataType>{},
+                      "Buffer data type should be consistent as AccDataType!");
+
+        constexpr auto cluster_len_shift = get_shift<BufferLength_K>();
+
+        const auto thread_cluster_idx =
+            thread_cluster_desc.CalculateBottomIndex(make_multi_index(get_thread_local_1d_id()));
+
+        const auto thread_m_cluster_id = thread_cluster_idx[Number<0>{}];
+        const auto thread_k_cluster_id = thread_cluster_idx[Number<1>{}];
+
+        work_buffer(block_buf_desc_m_k.CalculateOffset(thread_cluster_idx)) = in_out_value;
+
+        __syncthreads();
+
+        static_for<0, cluster_len_shift, 1>{}([&](auto I) {
+            constexpr index_t indOffset = 1 << (cluster_len_shift - 1 - I());
+
+            if(thread_k_cluster_id < indOffset)
+            {
+                index_t offset1 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx);
+                index_t offset2 = block_buf_desc_m_k.CalculateOffset(thread_cluster_idx +
+                                                                     make_tuple(0, indOffset));
+
+                AccDataType opData1 = work_buffer[offset1];
+                AccDataType opData2 = work_buffer[offset2];
+                Accumulation::Calculate(opData1, opData2);
+                work_buffer(offset1) = opData1;
+            }
+
+            __syncthreads();
+        });
+
+        index_t offset = block_buf_desc_m_k.CalculateOffset(make_tuple(thread_m_cluster_id, 0));
+
+        in_out_value = work_buffer[offset];
+    };
+};
+
 // clang-format off
 // Assume:
 //  1) work_val_buffer/work_idx_buffer is buffer (typically LDS) allocated outside as workspace, does not include any in/out data

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

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <vector>
+
+#include "device_base.hpp"
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+template <typename ALayout,
+          typename B0Layout,
+          typename B1Layout,
+          typename CLayout,
+          typename ADataType,
+          typename B0DataType,
+          typename B1DataType,
+          typename CDataType,
+          typename AElementwiseOperation,
+          typename B0ElementwiseOperation,
+          typename Acc0ElementwiseOperation,
+          typename B1ElementwiseOperation,
+          typename CElementwiseOperation>
+struct DeviceBatchedGemmGemm : public BaseOperator
+{
+    virtual std::unique_ptr<BaseArgument>
+    MakeArgumentPointer(const void* p_a,
+                        const void* p_b0,
+                        const void* p_b1,
+                        void* p_c,
+                        ck::index_t M,
+                        ck::index_t N,
+                        ck::index_t K,
+                        ck::index_t O,
+                        ck::index_t Batch,
+                        ck::index_t StrideA,
+                        ck::index_t StrideB0,
+                        ck::index_t StrideB1,
+                        ck::index_t StrideC,
+                        ck::index_t BatchStrideA,
+                        ck::index_t BatchStrideB0,
+                        ck::index_t BatchStrideB1,
+                        ck::index_t BatchStrideC,
+                        AElementwiseOperation a_element_op,
+                        B0ElementwiseOperation b0_element_op,
+                        Acc0ElementwiseOperation acc0_element_op,
+                        B1ElementwiseOperation b1_element_op,
+                        CElementwiseOperation c_element_op) = 0;
+
+    virtual std::unique_ptr<BaseInvoker> MakeInvokerPointer() = 0;
+};
+
+template <typename ALayout,
+          typename B0Layout,
+          typename B1Layout,
+          typename CLayout,
+          typename ADataType,
+          typename B0DataType,
+          typename B1DataType,
+          typename CDataType,
+          typename AElementwiseOperation,
+          typename B0ElementwiseOperation,
+          typename Acc0ElementwiseOperation,
+          typename B1ElementwiseOperation,
+          typename CElementwiseOperation>
+using DeviceBatchedGemmGemmPtr = std::unique_ptr<DeviceBatchedGemmGemm<ALayout,
+                                                                       B0Layout,
+                                                                       B1Layout,
+                                                                       CLayout,
+                                                                       ADataType,
+                                                                       B0DataType,
+                                                                       B1DataType,
+                                                                       CDataType,
+                                                                       AElementwiseOperation,
+                                                                       B0ElementwiseOperation,
+                                                                       Acc0ElementwiseOperation,
+                                                                       B1ElementwiseOperation,
+                                                                       CElementwiseOperation>>;
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

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

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <iostream>
+#include <vector>
+
+#include "device_base.hpp"
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+
+template <typename ALayout,
+          typename B0Layout,
+          typename B1Layout,
+          typename CLayout,
+          typename ADataType,
+          typename B0DataType,
+          typename B1DataType,
+          typename CDataType,
+          typename AElementwiseOperation,
+          typename B0ElementwiseOperation,
+          typename Acc0ElementwiseOperation,
+          typename B1ElementwiseOperation,
+          typename CElementwiseOperation>
+struct DeviceBatchedGemmSoftmaxGemm : public BaseOperator
+{
+    virtual std::unique_ptr<BaseArgument>
+    MakeArgumentPointer(const void* p_a,
+                        const void* p_b0,
+                        const void* p_b1,
+                        void* p_c,
+                        ck::index_t M,
+                        ck::index_t N,
+                        ck::index_t K,
+                        ck::index_t O,
+                        ck::index_t Batch,
+                        ck::index_t StrideA,
+                        ck::index_t StrideB0,
+                        ck::index_t StrideB1,
+                        ck::index_t StrideC,
+                        ck::index_t BatchStrideA,
+                        ck::index_t BatchStrideB0,
+                        ck::index_t BatchStrideB1,
+                        ck::index_t BatchStrideC,
+                        AElementwiseOperation a_element_op,
+                        B0ElementwiseOperation b0_element_op,
+                        Acc0ElementwiseOperation acc0_element_op,
+                        B1ElementwiseOperation b1_element_op,
+                        CElementwiseOperation c_element_op) = 0;
+
+    virtual std::unique_ptr<BaseInvoker> MakeInvokerPointer() = 0;
+};
+
+template <typename ALayout,
+          typename B0Layout,
+          typename B1Layout,
+          typename CLayout,
+          typename ADataType,
+          typename B0DataType,
+          typename B1DataType,
+          typename CDataType,
+          typename AElementwiseOperation,
+          typename B0ElementwiseOperation,
+          typename Acc0ElementwiseOperation,
+          typename B1ElementwiseOperation,
+          typename CElementwiseOperation>
+using DeviceBatchedGemmSoftmaxGemmPtr =
+    std::unique_ptr<DeviceBatchedGemmSoftmaxGemm<ALayout,
+                                                 B0Layout,
+                                                 B1Layout,
+                                                 CLayout,
+                                                 ADataType,
+                                                 B0DataType,
+                                                 B1DataType,
+                                                 CDataType,
+                                                 AElementwiseOperation,
+                                                 B0ElementwiseOperation,
+                                                 Acc0ElementwiseOperation,
+                                                 B1ElementwiseOperation,
+                                                 CElementwiseOperation>>;
+
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck

include/ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp

@@ -1145,9 +1145,22 @@ struct ThreadwiseTensorSliceTransfer_v4
                 src_desc, src_data_coord);
 
             // copy data from src_buf into src_tmp_vector
-            src_tmp_vector.template AsType<src_vector_t>()(Number<0>{}) =
-                src_buf.template Get<src_vector_t>(src_data_coord.GetOffset(), is_src_valid);
+            if constexpr(SrcBuffer::IsDynamicBuffer())
+            {
+                src_tmp_vector.template AsType<src_vector_t>()(Number<0>{}) =
+                    src_buf.template Get<src_vector_t>(src_data_coord.GetOffset(), is_src_valid);
+            }
+            else if constexpr(SrcBuffer::IsStaticBuffer())
+            {
+                static_for<0, SrcScalarPerVector, 1>{}([&](auto i) {
+                    constexpr index_t src_offset = src_desc.CalculateOffset(
+                        src_ref_to_origin_disp_idx + data_to_origin_disp_idx +
+                        i * src_scalar_step_in_vector);
 
+                    // apply type convert
+                    src_tmp_vector.template AsType<SrcData>()(i) = src_buf[Number<src_offset>{}];
+                });
+            }
             // copy data from src_tmp_vector to dst_tmp_vector (data cast data from SrcData to
             // DstData)
             vector_type_maker_t<DstData, SrcScalarPerVector> dst_tmp_vector;
@@ -1184,4 +1197,101 @@ struct ThreadwiseTensorSliceTransfer_v4
     SrcCoord src_ref_coord_;
 };
 
+// Do NOT involve any tensor coordinates with StaticBuffer
+template <typename SrcData,
+          typename DstData,
+          typename SrcDesc,
+          typename DstDesc,
+          typename ElementwiseOperation,
+          typename SliceLengths,
+          typename DimAccessOrder,
+          index_t DstVectorDim,
+          index_t DstScalarPerVector,
+          typename enable_if<SrcDesc::IsKnownAtCompileTime() && DstDesc::IsKnownAtCompileTime(),
+                             bool>::type = false>
+struct ThreadwiseTensorSliceTransfer_StaticToStatic
+{
+    static constexpr index_t nDim = SliceLengths::Size();
+
+    using Index = MultiIndex<nDim>;
+
+    __device__ constexpr ThreadwiseTensorSliceTransfer_StaticToStatic(
+        const ElementwiseOperation& element_op)
+        : element_op_{element_op}
+    {
+        static_assert(SrcDesc::IsKnownAtCompileTime() && DstDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc need to known at compile-time");
+
+        static_assert(SliceLengths::At(Number<DstVectorDim>{}) % DstScalarPerVector == 0,
+                      "wrong! Not divisible");
+    }
+
+    template <typename SrcSliceOriginIdx,
+              typename DstSliceOriginIdx,
+              typename SrcBuffer,
+              typename DstBuffer>
+    __device__ void Run(const SrcDesc&,
+                        const SrcSliceOriginIdx&,
+                        const SrcBuffer& src_buf,
+                        const DstDesc&,
+                        const DstSliceOriginIdx&,
+                        DstBuffer& dst_buf)
+    {
+        static_assert(SrcDesc::IsKnownAtCompileTime() && DstDesc::IsKnownAtCompileTime(),
+                      "wrong! Desc need to known at compile-time");
+
+        static_assert(is_known_at_compile_time<remove_cvref_t<SrcSliceOriginIdx>>::value &&
+                          is_known_at_compile_time<remove_cvref_t<DstSliceOriginIdx>>::value,
+                      "wrong! SliceOrigin need to known at compile-time");
+
+        static_assert(SrcBuffer::IsStaticBuffer() && DstBuffer::IsStaticBuffer(),
+                      "wrong! Buffer need to be StaticBuffer");
+
+        // SrcDesc and src_slice_origin_idx are known at compile-time
+        constexpr auto src_desc             = remove_cvref_t<SrcDesc>{};
+        constexpr auto dst_desc             = remove_cvref_t<DstDesc>{};
+        constexpr auto src_slice_origin_idx = to_multi_index(SrcSliceOriginIdx{});
+        constexpr auto dst_slice_origin_idx = to_multi_index(DstSliceOriginIdx{});
+
+        // scalar per access on each dim
+        constexpr auto dst_scalar_per_access = generate_sequence(
+            detail::lambda_scalar_per_access<DstVectorDim, DstScalarPerVector>{}, Number<nDim>{});
+
+        constexpr auto dst_scalar_step_in_vector =
+            generate_sequence(detail::lambda_scalar_step_in_vector<DstVectorDim>{}, Number<nDim>{});
+
+        using SpaceFillingCurve = SpaceFillingCurve<SliceLengths,
+                                                    DimAccessOrder,
+                                                    remove_cv_t<decltype(dst_scalar_per_access)>>;
+
+        static_assert(DstScalarPerVector == SpaceFillingCurve::ScalarPerVector,
+                      "wrong!DstScalarPerVector != SpaceFillingCurve::ScalarPerVector");
+
+        constexpr auto num_access = SpaceFillingCurve::GetNumOfAccess();
+
+        static_for<0, num_access, 1>{}([&](auto idx_1d) {
+            constexpr auto idx_md = SpaceFillingCurve::GetIndex(idx_1d);
+
+            // copy data from src_buf into dst_vector
+            static_for<0, DstScalarPerVector, 1>{}([&](auto i) {
+                constexpr index_t src_offset = src_desc.CalculateOffset(
+                    src_slice_origin_idx + idx_md + i * dst_scalar_step_in_vector);
+
+                constexpr index_t dst_offset = dst_desc.CalculateOffset(
+                    dst_slice_origin_idx + idx_md + i * dst_scalar_step_in_vector);
+
+                SrcData v;
+
+                // apply element-wise operation
+                element_op_(v, src_buf[Number<src_offset>{}]);
+
+                // apply type convert
+                dst_buf(Number<dst_offset>{}) = type_convert<DstData>(v);
+            });
+        });
+    }
+
+    ElementwiseOperation element_op_;
+};
+
 } // namespace ck

include/ck/tensor_operation/gpu/warp/xdlops_gemm.hpp

@@ -579,7 +579,11 @@ struct MfmaSelector
     static constexpr index_t GetK1PerXdlops() { return selected_mfma.k_per_blk; }
 };
 
-template <typename base_type, index_t MPerXdlops, index_t NPerXdlops, index_t KPack>
+template <typename base_type,
+          index_t MPerXdlops,
+          index_t NPerXdlops,
+          index_t KPack,
+          bool TransposeC = false>
 struct XdlopsGemm
 {
     static constexpr auto I0 = Number<0>{};
@@ -612,6 +616,8 @@ struct XdlopsGemm
         static_assert(KPack % mfma_instr.k_per_blk == 0, "KPack cannot be divided by k_per_blk");
     }
 
+    // XDL output supporting C = A * B
+    // M2_N2 -> M2_M3_M4_N2
     template <typename CDesc_M0_N0_M1_N1_M2_N2>
     __host__ __device__ static constexpr auto
     MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(const CDesc_M0_N0_M1_N1_M2_N2& c_desc_m0_n0_m1_n1_m2_n2)
@@ -627,10 +633,10 @@ struct XdlopsGemm
                        make_pass_through_transform(N0),
                        make_pass_through_transform(M1),
                        make_pass_through_transform(N1),
-                       make_unmerge_transform(make_tuple(mfma_instr.num_groups_per_blk,
-                                                         mfma_instr.num_input_blks,
-                                                         mfma_instr.group_size)),
-                       make_pass_through_transform(mfma_instr.num_threads_per_blk)),
+                       make_unmerge_transform(make_tuple(Number<mfma_instr.num_groups_per_blk>{},
+                                                         Number<mfma_instr.num_input_blks>{},
+                                                         Number<mfma_instr.group_size>{})),
+                       make_pass_through_transform(Number<mfma_instr.num_threads_per_blk>{})),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
@@ -645,6 +651,41 @@ struct XdlopsGemm
                        Sequence<7>{}));
     }
 
+    // transposed XDL output supporting C' = B' * A'
+    // M2_N2 -> M2_N2_N3_N4
+    template <typename CDesc_M0_N0_M1_N1_M2_N2>
+    __host__ __device__ static constexpr auto
+    MakeCDescriptor_M0_N0_M1_N1_M2_N2_N3_N4(const CDesc_M0_N0_M1_N1_M2_N2& c_desc_m0_n0_m1_n1_m2_n2)
+    {
+        const auto M0 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I0);
+        const auto N0 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I1);
+        const auto M1 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I2);
+        const auto N1 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I3);
+
+        return transform_tensor_descriptor(
+            c_desc_m0_n0_m1_n1_m2_n2,
+            make_tuple(make_pass_through_transform(M0),
+                       make_pass_through_transform(N0),
+                       make_pass_through_transform(M1),
+                       make_pass_through_transform(N1),
+                       make_pass_through_transform(Number<mfma_instr.num_threads_per_blk>{}),
+                       make_unmerge_transform(make_tuple(Number<mfma_instr.num_groups_per_blk>{},
+                                                         Number<mfma_instr.num_input_blks>{},
+                                                         Number<mfma_instr.group_size>{}))),
+            make_tuple(Sequence<0>{},
+                       Sequence<1>{},
+                       Sequence<2>{},
+                       Sequence<3>{},
+                       Sequence<4>{},
+                       Sequence<5>{}),
+            make_tuple(Sequence<0>{},
+                       Sequence<1>{},
+                       Sequence<2>{},
+                       Sequence<3>{},
+                       Sequence<4>{},
+                       Sequence<5, 6, 7>{}));
+    }
+
     template <typename CDesc_G_M0_N0_M1_N1_M2_N2>
     __host__ __device__ static constexpr auto MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
         const CDesc_G_M0_N0_M1_N1_M2_N2& c_desc_g_m0_n0_m1_n1_m2_n2)
@@ -698,7 +739,16 @@ struct XdlopsGemm
                       "base base_type must be double, float, half, bfloat16, and int8_t!");
 
         static_for<0, KPack / mfma_instr.k_per_blk, 1>{}([&](auto k) {
-            mfma_instr.template run<MPerXdlops, NPerXdlops>(p_a_wave[k], p_b_wave[k], p_c_thread);
+            if constexpr(!TransposeC)
+            {
+                mfma_instr.template run<MPerXdlops, NPerXdlops>(
+                    p_a_wave[k], p_b_wave[k], p_c_thread);
+            }
+            else
+            {
+                mfma_instr.template run<MPerXdlops, NPerXdlops>(
+                    p_b_wave[k], p_a_wave[k], p_c_thread);
+            }
         });
     }
 

include/ck/utility/static_buffer.hpp

@@ -20,6 +20,29 @@ struct StaticBuffer : public StaticallyIndexedArray<T, N>
 
     __host__ __device__ constexpr StaticBuffer() : base{} {}
 
+    __host__ __device__ constexpr StaticBuffer& operator=(StaticBuffer& y)
+    {
+        StaticBuffer& x = *this;
+        static_for<0, base::Size(), 1>{}([&](auto i) { x(i) = y[i]; });
+        return x;
+    }
+
+    template <typename... Ys>
+    __host__ __device__ constexpr StaticBuffer& operator=(const Tuple<Ys...>& y)
+    {
+        static_assert(base::Size() == sizeof...(Ys), "wrong! size not the same");
+        StaticBuffer& x = *this;
+        static_for<0, base::Size(), 1>{}([&](auto i) { x(i) = y[i]; });
+        return x;
+    }
+
+    __host__ __device__ constexpr StaticBuffer& operator=(const T& y)
+    {
+        StaticBuffer& x = *this;
+        static_for<0, base::Size(), 1>{}([&](auto i) { x(i) = y; });
+        return x;
+    }
+
     __host__ __device__ static constexpr AddressSpaceEnum GetAddressSpace() { return AddressSpace; }
 
     __host__ __device__ static constexpr bool IsStaticBuffer() { return true; }
@@ -40,10 +63,12 @@ struct StaticBuffer : public StaticallyIndexedArray<T, N>
         return base::operator()(i);
     }
 
-    __host__ __device__ void Clear()
+    __host__ __device__ void Set(T x)
     {
-        static_for<0, N, 1>{}([&](auto i) { operator()(i) = T{0}; });
+        static_for<0, N, 1>{}([&](auto i) { operator()(i) = T{x}; });
     }
+
+    __host__ __device__ void Clear() { Set(T{0}); }
 };
 
 // static buffer for vector
@@ -61,6 +86,7 @@ struct StaticBufferTupleOfVector
 
     static constexpr auto s_per_v   = Number<ScalarPerVector>{};
     static constexpr auto num_of_v_ = Number<NumOfVector>{};
+    static constexpr auto s_per_buf = s_per_v * num_of_v_;
 
     __host__ __device__ constexpr StaticBufferTupleOfVector() : base{} {}
 
@@ -70,6 +96,8 @@ struct StaticBufferTupleOfVector
 
     __host__ __device__ static constexpr bool IsDynamicBuffer() { return false; }
 
+    __host__ __device__ static constexpr index_t Size() { return s_per_buf; };
+
     // Get S
     // i is offset of S
     template <index_t I>

include/ck/utility/statically_indexed_array_multi_index.hpp

@@ -34,7 +34,10 @@ __host__ __device__ constexpr auto to_multi_index(const T& x)
 // is the alias of the latter. This is because compiler cannot infer the NSize if
 // using MultiIndex<NSize>
 // TODO: how to fix this?
-template <typename... Ys, typename X>
+template <
+    typename... Ys,
+    typename X,
+    enable_if_t<!std::is_integral<X>::value && !std::is_floating_point<X>::value, bool> = false>
 __host__ __device__ constexpr auto operator+=(Tuple<Ys...>& y, const X& x)
 {
     static_assert(X::Size() == sizeof...(Ys), "wrong! size not the same");
@@ -43,7 +46,10 @@ __host__ __device__ constexpr auto operator+=(Tuple<Ys...>& y, const X& x)
     return y;
 }
 
-template <typename... Ys, typename X>
+template <
+    typename... Ys,
+    typename X,
+    enable_if_t<!std::is_integral<X>::value && !std::is_floating_point<X>::value, bool> = false>
 __host__ __device__ constexpr auto operator-=(Tuple<Ys...>& y, const X& x)
 {
     static_assert(X::Size() == sizeof...(Ys), "wrong! size not the same");
@@ -52,7 +58,10 @@ __host__ __device__ constexpr auto operator-=(Tuple<Ys...>& y, const X& x)
     return y;
 }
 
-template <typename... Xs, typename Y>
+template <
+    typename... Xs,
+    typename Y,
+    enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> = false>
 __host__ __device__ constexpr auto operator+(const Tuple<Xs...>& x, const Y& y)
 {
     static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
@@ -63,7 +72,10 @@ __host__ __device__ constexpr auto operator+(const Tuple<Xs...>& x, const Y& y)
     return r;
 }
 
-template <typename... Xs, typename Y>
+template <
+    typename... Xs,
+    typename Y,
+    enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> = false>
 __host__ __device__ constexpr auto operator-(const Tuple<Xs...>& x, const Y& y)
 {
     static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
@@ -74,7 +86,10 @@ __host__ __device__ constexpr auto operator-(const Tuple<Xs...>& x, const Y& y)
     return r;
 }
 
-template <typename... Xs, typename Y>
+template <
+    typename... Xs,
+    typename Y,
+    enable_if_t<!std::is_integral<Y>::value && !std::is_floating_point<Y>::value, bool> = false>
 __host__ __device__ constexpr auto operator*(const Tuple<Xs...>& x, const Y& y)
 {
     static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
@@ -85,9 +100,11 @@ __host__ __device__ constexpr auto operator*(const Tuple<Xs...>& x, const Y& y)
     return r;
 }
 
-// MultiIndex = index_t * MultiIndex
-template <typename... Xs>
-__host__ __device__ constexpr auto operator*(index_t a, const Tuple<Xs...>& x)
+// MultiIndex = scalar * MultiIndex
+template <typename... Xs,
+          typename Y,
+          enable_if_t<std::is_integral<Y>::value || std::is_floating_point<Y>::value, bool> = false>
+__host__ __device__ constexpr auto operator*(Y a, const Tuple<Xs...>& x)
 {
     constexpr index_t NSize = sizeof...(Xs);
 
@@ -96,13 +113,40 @@ __host__ __device__ constexpr auto operator*(index_t a, const Tuple<Xs...>& x)
     return r;
 }
 
-// MultiIndex = MultiIndex * index_t
-template <typename... Xs>
-__host__ __device__ constexpr auto operator*(const Tuple<Xs...>& x, index_t a)
+// MultiIndex = MultiIndex * scalar
+template <typename... Xs,
+          typename Y,
+          enable_if_t<std::is_integral<Y>::value || std::is_floating_point<Y>::value, bool> = false>
+__host__ __device__ constexpr auto operator*(const Tuple<Xs...>& x, Y a)
 {
     return a * x;
 }
 
+namespace mathext {
+
+template <typename... Xs>
+__host__ __device__ constexpr auto exp(const Tuple<Xs...>& x)
+{
+    constexpr index_t NSize = sizeof...(Xs);
+
+    Tuple<Xs...> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r(i) = math::exp(x[i]); });
+    return r;
+}
+
+template <typename... Xs, typename Y>
+__host__ __device__ constexpr auto max(const Tuple<Xs...>& x, const Y& y)
+{
+    static_assert(Y::Size() == sizeof...(Xs), "wrong! size not the same");
+    constexpr index_t NSize = sizeof...(Xs);
+
+    Tuple<Xs...> r;
+    static_for<0, NSize, 1>{}([&](auto i) { r(i) = math::max(x[i], y[i]); });
+    return r;
+}
+
+} // namespace mathext
+
 template <typename... Xs>
 __host__ __device__ void print_multi_index(const Tuple<Xs...>& x)
 {

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

@@ -16,6 +16,7 @@ namespace host {
 template <typename ADataType,
           typename BDataType,
           typename CDataType,
+          typename AccDataType,
           typename AElementwiseOperation,
           typename BElementwiseOperation,
           typename CElementwiseOperation>
@@ -58,7 +59,7 @@ struct ReferenceBatchedGemm : public device::BaseOperator
             auto f_gmk_gkn_gmn = [&](auto g, auto m, auto n) {
                 const int K = arg.a_g_m_k_.mDesc.GetLengths()[2];
 
-                float v_acc = 0;
+                AccDataType v_acc = 0;
 
                 for(int k = 0; k < K; ++k)
                 {
@@ -68,10 +69,11 @@ struct ReferenceBatchedGemm : public device::BaseOperator
                     arg.a_element_op_(v_a, arg.a_g_m_k_(g, m, k));
                     arg.b_element_op_(v_b, arg.b_g_k_n_(g, k, n));
 
-                    v_acc += ck::type_convert<float>(v_a) * ck::type_convert<float>(v_b);
+                    v_acc +=
+                        ck::type_convert<AccDataType>(v_a) * ck::type_convert<AccDataType>(v_b);
                 }
 
-                float v_c;
+                AccDataType v_c;
 
                 arg.c_element_op_(v_c, v_acc);
 
@@ -81,8 +83,7 @@ struct ReferenceBatchedGemm : public device::BaseOperator
             make_ParallelTensorFunctor(f_gmk_gkn_gmn,
                                        arg.c_g_m_n_.mDesc.GetLengths()[0],
                                        arg.c_g_m_n_.mDesc.GetLengths()[1],
-                                       arg.c_g_m_n_.mDesc.GetLengths()[2])(
-                std::thread::hardware_concurrency());
+                                       arg.c_g_m_n_.mDesc.GetLengths()[2])();
 
             return 0;
         }

library/include/ck/library/tensor_operation_instance/gpu/batched_gemm_softmax_gemm.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2022, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <cstdlib>
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/device/tensor_layout.hpp"
+#include "ck/tensor_operation/gpu/device/device_batched_gemm_softmax_gemm.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "ck/library/tensor_operation_instance/device_operation_instance_factory.hpp"
+
+namespace ck {
+namespace tensor_operation {
+namespace device {
+namespace instance {
+
+void add_device_batched_gemm_softmax_gemm_xdl_cshuffle_f16_f16_f16_f16_gmk_gnk_gno_gmo_instance(
+    std::vector<std::unique_ptr<DeviceBatchedGemmSoftmaxGemm<Row,
+                                                             Col,
+                                                             Row,
+                                                             Row,
+                                                             F16,
+                                                             F16,
+                                                             F16,
+                                                             F16,
+                                                             PassThrough,
+                                                             PassThrough,
+                                                             PassThrough,
+                                                             PassThrough,
+                                                             PassThrough>>>& instances);
+
+template <typename ALayout,
+          typename B0Layout,
+          typename B1Layout,
+          typename CLayout,
+          typename ADataType,
+          typename B0DataType,
+          typename B1DataType,
+          typename CDataType>
+struct DeviceOperationInstanceFactory<
+    ck::tensor_operation::device::DeviceBatchedGemmSoftmaxGemm<ALayout,
+                                                               B0Layout,
+                                                               B1Layout,
+                                                               CLayout,
+                                                               ADataType,
+                                                               B0DataType,
+                                                               B1DataType,
+                                                               CDataType,
+                                                               PassThrough,
+                                                               PassThrough,
+                                                               PassThrough,
+                                                               PassThrough,
+                                                               PassThrough>>
+{
+    using DeviceOp = DeviceBatchedGemmSoftmaxGemm<ALayout,
+                                                  B0Layout,
+                                                  B1Layout,
+                                                  CLayout,
+                                                  ADataType,
+                                                  B0DataType,
+                                                  B1DataType,
+                                                  CDataType,
+                                                  PassThrough,
+                                                  PassThrough,
+                                                  PassThrough,
+                                                  PassThrough,
+                                                  PassThrough>;
+
+    static auto GetInstances()
+    {
+        std::vector<std::unique_ptr<DeviceOp>> op_ptrs;
+
+        if constexpr(is_same_v<ADataType, half_t> && is_same_v<B0DataType, half_t> &&
+                     is_same_v<B1DataType, half_t> && is_same_v<CDataType, half_t>)
+        {
+            if constexpr(is_same_v<ALayout, Row> && is_same_v<B0Layout, Col> &&
+                         is_same_v<B1Layout, Row> && is_same_v<CLayout, Row>)
+            {
+                add_device_batched_gemm_softmax_gemm_xdl_cshuffle_f16_f16_f16_f16_gmk_gnk_gno_gmo_instance(
+                    op_ptrs);
+            }
+        }
+        return op_ptrs;
+    }
+};
+
+} // namespace instance
+} // namespace device
+} // namespace tensor_operation
+} // namespace ck