Complex Contraction CK Bilinear Example (#1061)

* complex type contraction

* bug fix

* update

* Tensor Contraction Complex Data Type is working

* 4D Kernel

* some change

* validation check in progress

* validation issue

* fp32 verification error is fixed

* fp32 and fp64 are done

* remove old files

* remove cmake files

* remove cmake files

* Readme

* img verification

* CMakeList

* number changed

---------
Co-authored-by: Illia Silin <98187287+illsilin@users.noreply.github.com>
Co-authored-by: Emin Ozturk <emin.ozturk@utah.edu>

example/66_complex_contraction_bilinear/CMakeLists.txt

+add_example_executable(example_complex_contraction_bilinear_xdl_fp32 complex_contraction_bilinear_xdl_fp32.cpp)
+add_example_executable(example_complex_contraction_bilinear_xdl_fp64 complex_contraction_bilinear_xdl_fp64.cpp)
+

example/66_complex_contraction_bilinear/README.md

+# Instructions for ```example_complex_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
+```
+
+

example/66_complex_contraction_bilinear/common_instances.hpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/impl/device_contraction_multiple_d_xdl_cshuffle.hpp"
+
+using F16  = ck::half_t;
+using BF16 = ck::bhalf_t;
+using F32  = float;
+using F64  = double;
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+static constexpr auto GemmSpec = ck::tensor_operation::device::GemmSpecialization::MNKPadding;
+
+// Generic instances for fp32, fp16 and bf16 data types.
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceKK_Generic = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  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, ComputeDataType>;
+// clang-format on
+
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceKN_Generic = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  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, ComputeDataType>;
+// clang-format on
+
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceMK_Generic = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  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, ComputeDataType>;
+// clang-format on
+
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceMN_Generic = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  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, ComputeDataType>;
+// clang-format on
+
+// Fp64 instances.
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceKK_FP64 = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   128,   128,    16,   2,   2,   16,   16,    4,    4,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              2,              2,         1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              2,              2,         1,           1,           1,              S<1, 16, 1, 16>,               1, ComputeDataType>;
+// clang-format on
+
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceKN_FP64 = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   128,   128,    16,   2,   1,   16,   16,    4,    4,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              2,              2,         1,     S<8, 32, 1>,     S<0, 2, 1>,     S<0, 2, 1>,             1,              2,              1,         0,           1,           1,              S<1, 16, 1, 16>,               1, ComputeDataType>;
+// clang-format on
+
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceMK_FP64 = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   128,   128,    16,   1,   2,   16,   16,    4,    4,     S<4, 64, 1>,     S<0, 2, 1>,     S<0, 2, 1>,              1,              2,              1,         0,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,             2,              2,              2,         1,           1,           1,              S<1, 16, 1, 16>,               1, ComputeDataType>;
+// clang-format on
+
+template <ck::index_t NumDimM,
+          ck::index_t NumDimN,
+          ck::index_t NumDimK,
+          typename ADataType,
+          typename BDataType,
+          typename AccDataType,
+          typename CShuffleDataType,
+          typename DsDataType,
+          typename EDataType,
+          typename ComputeDataType,
+          typename AElementOp,
+          typename BElementOp,
+          typename CDEElementOp>
+// clang-format off
+using DeviceOpInstanceMN_FP64 = 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|         Compute|
+        //#####################################|        |        |        |      Type|      Type|        Type|         DataType|       Type|      Type| Elementwise| Elementwise|  Elementwise| Specialization| 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|            Data|
+        //#####################################|        |        |        |          |          |            |                 |           |          |   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|            Type|
+        //#####################################|        |        |        |          |          |            |                 |           |          |            |            |             |               |         |      |      |      |      |    |    |     |     |     |     |                |               |               |               |               |               |          |                |               |               |              |               |               |          |            |            |                             |                |                |
+        DeviceContractionMultipleD_Xdl_CShuffle< NumDimM, NumDimN, NumDimK, ADataType, BDataType, AccDataType, CShuffleDataType, DsDataType, EDataType,  AElementOp,  BElementOp, CDEElementOp,       GemmSpec,        1,   256,   128,   128,    16,   1,   1,   16,   16,    4,    4,     S<4, 64, 1>,     S<0, 2, 1>,     S<0, 2, 1>,              1,              2,              1,         0,     S<8, 32, 1>,     S<0, 2, 1>,     S<0, 2, 1>,             1,              2,              1,         0,           1,           1,              S<1, 16, 1, 16>,               1, ComputeDataType>;
+// clang-format on

example/66_complex_contraction_bilinear/complex_contraction_bilinear_xdl_fp32.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "common_instances.hpp"
+
+using ADataType        = F32;
+using BDataType        = F32;
+using AccDataType      = F32;
+using CShuffleDataType = F32;
+using DDataType        = F32;
+using DsDataType       = ck::Tuple<DDataType>;
+using EDataType        = F32;
+using ComputeDataType  = 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;
+
+using DeviceOpInstanceKKNN = DeviceOpInstanceKK_Generic<NumDimM,
+                                                        NumDimN,
+                                                        NumDimK,
+                                                        ADataType,
+                                                        BDataType,
+                                                        AccDataType,
+                                                        CShuffleDataType,
+                                                        DsDataType,
+                                                        EDataType,
+                                                        ComputeDataType,
+                                                        AElementOp,
+                                                        BElementOp,
+                                                        CDEElementOp>;
+
+using DeviceOpInstanceKNNN = DeviceOpInstanceKN_Generic<NumDimM,
+                                                        NumDimN,
+                                                        NumDimK,
+                                                        ADataType,
+                                                        BDataType,
+                                                        AccDataType,
+                                                        CShuffleDataType,
+                                                        DsDataType,
+                                                        EDataType,
+                                                        ComputeDataType,
+                                                        AElementOp,
+                                                        BElementOp,
+                                                        CDEElementOp>;
+
+using DeviceOpInstanceMKNN = DeviceOpInstanceMK_Generic<NumDimM,
+                                                        NumDimN,
+                                                        NumDimK,
+                                                        ADataType,
+                                                        BDataType,
+                                                        AccDataType,
+                                                        CShuffleDataType,
+                                                        DsDataType,
+                                                        EDataType,
+                                                        ComputeDataType,
+                                                        AElementOp,
+                                                        BElementOp,
+                                                        CDEElementOp>;
+
+using DeviceOpInstanceMNNN = DeviceOpInstanceMN_Generic<NumDimM,
+                                                        NumDimN,
+                                                        NumDimK,
+                                                        ADataType,
+                                                        BDataType,
+                                                        AccDataType,
+                                                        CShuffleDataType,
+                                                        DsDataType,
+                                                        EDataType,
+                                                        ComputeDataType,
+                                                        AElementOp,
+                                                        BElementOp,
+                                                        CDEElementOp>;
+
+using DeviceOpInstance = DeviceOpInstanceKKNN;
+
+#include "run_complex_contraction_bilinear_example.inc"
+
+int main(int argc, char* argv[]) { return run_complex_contraction_bilinear_example(argc, argv); }

example/66_complex_contraction_bilinear/complex_contraction_bilinear_xdl_fp64.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
+
+#include "common_instances.hpp"
+
+using ADataType        = F64;
+using BDataType        = F64;
+using AccDataType      = F64;
+using CShuffleDataType = F64;
+using DDataType        = F64;
+using DsDataType       = ck::Tuple<DDataType>;
+using EDataType        = F64;
+using ComputeDataType  = F64;
+
+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;
+
+using DeviceOpInstanceKKNN = DeviceOpInstanceKK_FP64<NumDimM,
+                                                     NumDimN,
+                                                     NumDimK,
+                                                     ADataType,
+                                                     BDataType,
+                                                     AccDataType,
+                                                     CShuffleDataType,
+                                                     DsDataType,
+                                                     EDataType,
+                                                     ComputeDataType,
+                                                     AElementOp,
+                                                     BElementOp,
+                                                     CDEElementOp>;
+
+using DeviceOpInstanceKNNN = DeviceOpInstanceKN_FP64<NumDimM,
+                                                     NumDimN,
+                                                     NumDimK,
+                                                     ADataType,
+                                                     BDataType,
+                                                     AccDataType,
+                                                     CShuffleDataType,
+                                                     DsDataType,
+                                                     EDataType,
+                                                     ComputeDataType,
+                                                     AElementOp,
+                                                     BElementOp,
+                                                     CDEElementOp>;
+
+using DeviceOpInstanceMKNN = DeviceOpInstanceMK_FP64<NumDimM,
+                                                     NumDimN,
+                                                     NumDimK,
+                                                     ADataType,
+                                                     BDataType,
+                                                     AccDataType,
+                                                     CShuffleDataType,
+                                                     DsDataType,
+                                                     EDataType,
+                                                     ComputeDataType,
+                                                     AElementOp,
+                                                     BElementOp,
+                                                     CDEElementOp>;
+
+using DeviceOpInstanceMNNN = DeviceOpInstanceMN_FP64<NumDimM,
+                                                     NumDimN,
+                                                     NumDimK,
+                                                     ADataType,
+                                                     BDataType,
+                                                     AccDataType,
+                                                     CShuffleDataType,
+                                                     DsDataType,
+                                                     EDataType,
+                                                     ComputeDataType,
+                                                     AElementOp,
+                                                     BElementOp,
+                                                     CDEElementOp>;
+
+using DeviceOpInstance = DeviceOpInstanceKKNN;
+
+#include "run_complex_contraction_bilinear_example.inc"
+
+int main(int argc, char* argv[]) { return run_complex_contraction_bilinear_example(argc, argv); }

example/66_complex_contraction_bilinear/run_complex_contraction_bilinear_example.inc

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+
+#pragma once
+
+#include <cstdlib>
+#include <iostream>
+#include <string>
+#include <vector>
+
+#include "ck/ck.hpp"
+#include "ck/library/utility/check_err.hpp"
+#include "ck/library/utility/device_memory.hpp"
+#include "ck/library/utility/host_tensor_generator.hpp"
+#include "ck/library/utility/numeric.hpp"
+#include "ck/library/reference_tensor_operation/cpu/reference_contraction.hpp"
+
+int run_complex_contraction_bilinear_example(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 9: 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);
+    }
+
+    // For Real Part of Complex Tensor
+    Tensor<ADataType> a_ms_ks_re(a_ms_ks_lengths, a_ms_ks_strides);
+    Tensor<BDataType> b_ns_ks_re(b_ns_ks_lengths, b_ns_ks_strides);
+    Tensor<EDataType> d_ms_ns_re(d_ms_ns_lengths, d_ms_ns_strides);
+
+    Tensor<EDataType> e_ms_ns_host_result_re(e_ms_ns_lengths, e_ms_ns_strides);
+    Tensor<EDataType> e_ms_ns_device_result_re(e_ms_ns_lengths, e_ms_ns_strides);
+
+    // For Imaginary Part of Complex Tensor
+    Tensor<ADataType> a_ms_ks_img(a_ms_ks_lengths, a_ms_ks_strides);
+    Tensor<BDataType> b_ns_ks_img(b_ns_ks_lengths, b_ns_ks_strides);
+    Tensor<EDataType> d_ms_ns_img(d_ms_ns_lengths, d_ms_ns_strides);
+
+    Tensor<EDataType> e_ms_ns_host_result_img(e_ms_ns_lengths, e_ms_ns_strides);
+    Tensor<EDataType> e_ms_ns_device_result_img(e_ms_ns_lengths, e_ms_ns_strides);
+
+    // Intermediate E tensor Definition
+    Tensor<EDataType> e_ms_ns_device_result_re1(e_ms_ns_lengths, e_ms_ns_strides);
+    Tensor<EDataType> e_ms_ns_device_result_img1(e_ms_ns_lengths, e_ms_ns_strides);
+
+    std::cout << "a_ms_ks_re: " << a_ms_ks_re.mDesc << std::endl;
+    std::cout << "b_ns_ks_re: " << b_ns_ks_re.mDesc << std::endl;
+    std::cout << "d_ms_ns_re: " << d_ms_ns_re.mDesc << std::endl;
+    std::cout << "e_ms_ns_re: " << e_ms_ns_host_result_re.mDesc << std::endl;
+
+    std::cout << "a_ms_ks_img: " << a_ms_ks_img.mDesc << std::endl;
+    std::cout << "b_ns_ks_img: " << b_ns_ks_img.mDesc << std::endl;
+    std::cout << "d_ms_ns_img: " << d_ms_ns_img.mDesc << std::endl;
+    std::cout << "e_ms_ns_img: " << e_ms_ns_host_result_img.mDesc << std::endl;
+
+    switch(init_method)
+    {
+        case 0: break;
+        case 1:
+
+            a_ms_ks_re.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
+            b_ns_ks_re.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+            d_ms_ns_re.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+
+            a_ms_ks_img.GenerateTensorValue(GeneratorTensor_2<ADataType>{-5, 5});
+            b_ns_ks_img.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+            d_ms_ns_img.GenerateTensorValue(GeneratorTensor_2<BDataType>{-5, 5});
+            break;
+
+        default:
+            a_ms_ks_re.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
+            b_ns_ks_re.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+            d_ms_ns_re.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+
+            a_ms_ks_img.GenerateTensorValue(GeneratorTensor_3<ADataType>{0.0, 1.0});
+            b_ns_ks_img.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+            d_ms_ns_img.GenerateTensorValue(GeneratorTensor_3<BDataType>{-0.5, 0.5});
+
+            break;
+    }
+
+    DeviceMem a_device_buf_re(sizeof(ADataType) * a_ms_ks_re.mDesc.GetElementSpaceSize());
+    DeviceMem b_device_buf_re(sizeof(BDataType) * b_ns_ks_re.mDesc.GetElementSpaceSize());
+    DeviceMem d_device_buf_re(sizeof(DDataType) * d_ms_ns_re.mDesc.GetElementSpaceSize());
+    DeviceMem e_device_buf_re(sizeof(EDataType) * e_ms_ns_device_result_re.mDesc.GetElementSpaceSize());
+
+    DeviceMem a_device_buf_img(sizeof(ADataType) * a_ms_ks_img.mDesc.GetElementSpaceSize());
+    DeviceMem b_device_buf_img(sizeof(BDataType) * b_ns_ks_img.mDesc.GetElementSpaceSize());
+    DeviceMem d_device_buf_img(sizeof(DDataType) * d_ms_ns_img.mDesc.GetElementSpaceSize());
+    DeviceMem e_device_buf_img(sizeof(EDataType) * e_ms_ns_device_result_img.mDesc.GetElementSpaceSize());
+
+    // Intermediate Value For E Real and Img
+    DeviceMem e_device_buf_re1(sizeof(EDataType) * e_ms_ns_device_result_re.mDesc.GetElementSpaceSize());
+    DeviceMem e_device_buf_img1(sizeof(EDataType) * e_ms_ns_device_result_img.mDesc.GetElementSpaceSize());
+
+
+    a_device_buf_re.ToDevice(a_ms_ks_re.mData.data());
+    b_device_buf_re.ToDevice(b_ns_ks_re.mData.data());
+    d_device_buf_re.ToDevice(d_ms_ns_re.mData.data());
+
+    a_device_buf_img.ToDevice(a_ms_ks_img.mData.data());
+    b_device_buf_img.ToDevice(b_ns_ks_img.mData.data());
+    d_device_buf_img.ToDevice(d_ms_ns_img.mData.data());
+
+    // set zero
+    e_device_buf_re.SetZero();
+    e_device_buf_img.SetZero();
+
+    // set zero for intermediate values
+    e_device_buf_re1.SetZero();
+    e_device_buf_img1.SetZero();
+ 
+    auto a_element_op   = AElementOp{};
+    auto b_element_op   = BElementOp{};
+    auto cde_element_op = CDEElementOp{alpha, beta};
+
+    // device operation
+    // For real Intermediate Value re_1
+
+    auto op       = DeviceOpInstance{};
+    auto invoker  = op.MakeInvoker();
+    auto argument_re1 = op.MakeArgument(a_device_buf_re.GetDeviceBuffer(),
+                                    b_device_buf_re.GetDeviceBuffer(),
+                                    std::array<const void*, 1>{d_device_buf_re.GetDeviceBuffer()},
+                                    e_device_buf_re1.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_re1))
+    {
+        std::cout << op.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time_re1 = invoker.Run(argument_re1, StreamConfig{nullptr, time_kernel});
+
+
+    alpha = -1.f;
+    beta  = 1.f;
+
+    a_element_op   = AElementOp{};
+    b_element_op   = BElementOp{};
+    cde_element_op = CDEElementOp{alpha, beta};
+
+    // device operation
+    // For real Intermediate Value re_2
+    // auto op       = DeviceOpInstance{};
+    // auto invoker  = op.MakeInvoker();
+    auto argument_re2 = op.MakeArgument(a_device_buf_img.GetDeviceBuffer(),
+                                    b_device_buf_img.GetDeviceBuffer(),
+                                    std::array<const void*, 1>{e_device_buf_re1.GetDeviceBuffer()},
+                                    e_device_buf_re.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_re2))
+    {
+        std::cout << op.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time_re2 = invoker.Run(argument_re2, StreamConfig{nullptr, time_kernel});
+
+    
+    alpha = 1.f;
+    beta  = 1.f;
+
+    a_element_op   = AElementOp{};
+    b_element_op   = BElementOp{};
+    cde_element_op = CDEElementOp{alpha, beta};
+
+    auto argument_img1 = op.MakeArgument(a_device_buf_re.GetDeviceBuffer(),
+                                b_device_buf_img.GetDeviceBuffer(),
+                                std::array<const void*, 1>{d_device_buf_img.GetDeviceBuffer()},
+                                e_device_buf_img1.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_img1))
+    {
+        std::cout << op.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time_img1 = invoker.Run(argument_img1, StreamConfig{nullptr, time_kernel});
+
+    alpha = 1.f;
+    beta  = 1.f;
+
+    auto argument_img2 = op.MakeArgument(a_device_buf_img.GetDeviceBuffer(),
+                                b_device_buf_re.GetDeviceBuffer(),
+                                std::array<const void*, 1>{e_device_buf_img1.GetDeviceBuffer()},
+                                e_device_buf_img.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_img2))
+    {
+        std::cout << op.GetTypeString() << " does not support this problem" << std::endl;
+
+        return 0;
+    }
+
+    float ave_time_img2 = invoker.Run(argument_img2, StreamConfig{nullptr, time_kernel});
+
+
+    ck::index_t M =
+        ck::accumulate_n<ck::index_t>(e_ms_ns_lengths.begin(), NumDimM, 1, std::multiplies<>{});
+
+    ck::index_t N = ck::accumulate_n<ck::index_t>(
+        e_ms_ns_lengths.begin() + NumDimM, NumDimN, 1, std::multiplies<>{});
+
+    ck::index_t K = ck::accumulate_n<ck::index_t>(
+        a_ms_ks_lengths.begin() + NumDimM, NumDimK, 1, std::multiplies<>{});
+
+    std::size_t flop      = std::size_t(2) * M * N * K * 2;
+    std::size_t num_btype = sizeof(ADataType) * M * K + sizeof(BDataType) * K * N +
+                            sizeof(DDataType) * M * N + sizeof(EDataType) * M * N * 2;
+
+    float ave_time = ave_time_img2 + ave_time_img1 + ave_time_re2 + ave_time_re1 ; 
+
+    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_re.FromDevice(e_ms_ns_device_result_re.mData.data());
+    e_device_buf_img.FromDevice(e_ms_ns_device_result_img.mData.data());
+
+    auto isRealOk = 0;
+    auto isImgOk = 0;
+
+    if(do_verification)
+    {
+        // Real Part Verification
+        Tensor<CShuffleDataType> c_ms_ns_host_result_re(e_ms_ns_lengths, e_ms_ns_strides);
+        Tensor<CShuffleDataType> c_ms_ns_host_result_re1(e_ms_ns_lengths, e_ms_ns_strides);
+
+        using ReferenceOpInstance =
+            ck::tensor_operation::host::ReferenceContraction_M2_N2_K2<NumDimM,
+                                                                      NumDimN,
+                                                                      NumDimK,
+                                                                      ADataType,
+                                                                      BDataType,
+                                                                      CShuffleDataType,
+                                                                      AccDataType,
+                                                                      F32,
+                                                                      AElementOp,
+                                                                      BElementOp>;
+
+        auto ref_op      = ReferenceOpInstance{};
+        auto ref_invoker = ref_op.MakeInvoker();
+
+        auto ref_argument_re =
+            ref_op.MakeArgument(a_ms_ks_re, b_ns_ks_re, c_ms_ns_host_result_re, a_element_op, b_element_op);
+
+        ref_invoker.Run(ref_argument_re);
+
+        alpha = 1.f;
+        beta  = 1.f;
+   
+        cde_element_op = CDEElementOp{alpha, beta};
+
+       
+        for(size_t m0 = 0; m0 < e_ms_ns_host_result_re.mDesc.GetLengths()[0]; ++m0)
+        {
+            for(size_t m1 = 0; m1 < e_ms_ns_host_result_re.mDesc.GetLengths()[1]; ++m1)
+            {
+                for(size_t n0 = 0; n0 < e_ms_ns_host_result_re.mDesc.GetLengths()[2]; ++n0)
+                {
+                    for(size_t n1 = 0; n1 < e_ms_ns_host_result_re.mDesc.GetLengths()[3]; ++n1)
+                    {
+                        cde_element_op(e_ms_ns_host_result_re(m0, m1, n0, n1),
+                                       c_ms_ns_host_result_re(m0, m1, n0, n1),
+                                       d_ms_ns_re(m0, m1, n0, n1));
+                    }
+                }
+            }
+        }
+
+        alpha = 1.f;
+        beta  = -1.f;
+   
+        cde_element_op = CDEElementOp{alpha, beta};
+
+        auto ref_argument_re1 =
+            ref_op.MakeArgument(a_ms_ks_img, b_ns_ks_img, c_ms_ns_host_result_re1, a_element_op, b_element_op);
+
+        ref_invoker.Run(ref_argument_re1);
+
+        for(size_t m0 = 0; m0 < e_ms_ns_host_result_re.mDesc.GetLengths()[0]; ++m0)
+        {
+            for(size_t m1 = 0; m1 < e_ms_ns_host_result_re.mDesc.GetLengths()[1]; ++m1)
+            {
+                for(size_t n0 = 0; n0 < e_ms_ns_host_result_re.mDesc.GetLengths()[2]; ++n0)
+                {
+                    for(size_t n1 = 0; n1 < e_ms_ns_host_result_re.mDesc.GetLengths()[3]; ++n1)
+                    {
+                        cde_element_op(e_ms_ns_host_result_re(m0, m1, n0, n1),
+                                       e_ms_ns_host_result_re(m0, m1, n0, n1),
+                                       c_ms_ns_host_result_re1(m0, m1, n0, n1));
+                    }
+                }
+            }
+        }
+
+        isRealOk =  ck::utils::check_err(e_ms_ns_device_result_re, e_ms_ns_host_result_re) ? 0 : 1;
+
+        
+
+
+        // Img Part Verification
+        Tensor<CShuffleDataType> c_ms_ns_host_result_img(e_ms_ns_lengths, e_ms_ns_strides);
+        Tensor<CShuffleDataType> c_ms_ns_host_result_img1(e_ms_ns_lengths, e_ms_ns_strides);
+
+        auto ref_argument_img =
+            ref_op.MakeArgument(a_ms_ks_re, b_ns_ks_img, c_ms_ns_host_result_img, a_element_op, b_element_op);
+            
+        ref_invoker.Run(ref_argument_img);
+
+        alpha = 1.f;
+        beta  = 1.f;
+   
+        cde_element_op = CDEElementOp{alpha, beta};
+
+        for(size_t m0 = 0; m0 < e_ms_ns_host_result_img.mDesc.GetLengths()[0]; ++m0)
+        {
+            for(size_t m1 = 0; m1 < e_ms_ns_host_result_img.mDesc.GetLengths()[1]; ++m1)
+            {
+                for(size_t n0 = 0; n0 < e_ms_ns_host_result_img.mDesc.GetLengths()[2]; ++n0)
+                {
+                    for(size_t n1 = 0; n1 < e_ms_ns_host_result_img.mDesc.GetLengths()[3]; ++n1)
+                    {
+                        cde_element_op(e_ms_ns_host_result_img(m0, m1, n0, n1),
+                                       c_ms_ns_host_result_img(m0, m1, n0, n1),
+                                       d_ms_ns_img(m0, m1, n0, n1));
+                    }
+                }
+            }
+        }
+
+        auto ref_argument_img1 =
+            ref_op.MakeArgument(a_ms_ks_img, b_ns_ks_re, c_ms_ns_host_result_img1, a_element_op, b_element_op);
+            
+        ref_invoker.Run(ref_argument_img1);
+
+        for(size_t m0 = 0; m0 < e_ms_ns_host_result_img.mDesc.GetLengths()[0]; ++m0)
+        {
+            for(size_t m1 = 0; m1 < e_ms_ns_host_result_img.mDesc.GetLengths()[1]; ++m1)
+            {
+                for(size_t n0 = 0; n0 < e_ms_ns_host_result_img.mDesc.GetLengths()[2]; ++n0)
+                {
+                    for(size_t n1 = 0; n1 < e_ms_ns_host_result_img.mDesc.GetLengths()[3]; ++n1)
+                    {
+                        cde_element_op(e_ms_ns_host_result_img(m0, m1, n0, n1),
+                                       e_ms_ns_host_result_img(m0, m1, n0, n1),
+                                       c_ms_ns_host_result_img1(m0, m1, n0, n1));
+                    }
+                }
+            }
+        }
+
+        isImgOk =  ck::utils::check_err(e_ms_ns_device_result_re, e_ms_ns_host_result_re) ? 0 : 1;
+
+        return (isRealOk && isImgOk);
+    }
+
+    return 0;
+}