add example

example/52_flash_atten_bias/CMakeLists.txt

 add_example_executable(example_batched_multihead_attention_bias_forward_v2 batched_multihead_attention_bias_forward_v2.cpp)
 add_example_executable(example_grouped_multihead_attention_bias_forward_v2 grouped_multihead_attention_bias_forward_v2.cpp)
+
+add_example_executable(example_batched_multihead_attention_bias_backward_v2 batched_multihead_attention_bias_backward_v2.cpp)
\ No newline at end of file

example/52_flash_atten_bias/batched_multihead_attention_bias_backward_v2.cpp

+// SPDX-License-Identifier: MIT
+// Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
+/*
+Backprop for Gemm + Softmax + Gemm fused operation, where forward prop is defined as:
+
+  Y_g_m_o = Softmax(alpha * Q_g_m_k * K_g_k_n) * V_g_n_o
+
+Computation graph:
+
+          K^T                   V
+          |                     |
+          |                     |
+    Q --- * ----- Softmax ----- * --> Y
+              S             P
+
+Kernel inputs:
+
+    Q, K, V, Y, dY, per-row softmax stats (LSE)
+
+Kernel outputs:
+
+    dQ, dK, dV
+
+*/
+
+#define PRINT_HOST 0
+#define USING_MASK 0
+#define DIM 128 // DIM should be a multiple of 8.
+
+#include <iostream>
+#include <numeric>
+#include <initializer_list>
+#include <cstdlib>
+#include <fstream>
+
+#include "ck/ck.hpp"
+#include "ck/tensor_operation/gpu/device/gemm_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/tensor_specialization.hpp"
+#include "ck/tensor_operation/gpu/device/impl/device_batched_mha_bwd_xdl_cshuffle_qloop_v1.hpp"
+#include "ck/tensor_operation/gpu/device/impl/device_batched_mha_bwd_xdl_cshuffle_qloop_v2.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"
+#include "ck/library/reference_tensor_operation/cpu/reference_dropout.hpp"
+
+template <ck::index_t... Is>
+using S = ck::Sequence<Is...>;
+
+using F16   = ck::half_t;
+using BF16  = ck::bhalf_t;
+using F32   = float;
+using U16   = unsigned short;
+using INT32 = int32_t;
+
+using PassThrough = ck::tensor_operation::element_wise::PassThrough;
+using Scale       = ck::tensor_operation::element_wise::Scale;
+
+using QKVElementOp = PassThrough;
+using YElementOp   = PassThrough;
+
+using InputDataType    = F16;
+using OutputDataType   = F16;
+using GemmDataType     = F16;
+using AccDataType      = F32;
+using ShuffleDataType  = F32;
+using LSEDataType      = F32;
+using ZDataType        = U16; // INT32
+using Acc0BiasDataType = ck::Tuple<>;
+using Acc1BiasDataType = ck::Tuple<>;
+
+static constexpr ck::index_t NumDimG = 2;
+static constexpr ck::index_t NumDimM = 1;
+static constexpr ck::index_t NumDimN = 1;
+static constexpr ck::index_t NumDimK = 1;
+static constexpr ck::index_t NumDimO = 1;
+// When OutputDataType == F32,      CShuffleBlockTransferScalarPerVector_NPerBlock = 4
+// When OutputDataType == F16/BF16, CShuffleBlockTransferScalarPerVector_NPerBlock = 8
+static constexpr ck::index_t CShuffleBlockTransferScalarPerVector_NPerBlock = 8;
+
+static constexpr auto GemmSpec = ck::tensor_operation::device::GemmSpecialization::MNKOPadding;
+#if USING_MASK
+static constexpr auto MaskingSpec =
+    ck::tensor_operation::device::MaskingSpecialization::MaskUpperTriangleFromBottomRight;
+#else
+static constexpr auto MaskingSpec =
+    ck::tensor_operation::device::MaskingSpecialization::MaskDisabled;
+#endif
+
+static constexpr auto TensorSpecQ   = ck::tensor_operation::device::TensorSpecialization::Default;
+static constexpr auto TensorSpecK   = ck::tensor_operation::device::TensorSpecialization::Default;
+static constexpr auto TensorSpecV   = ck::tensor_operation::device::TensorSpecialization::Default;
+static constexpr auto TensorSpecY   = ck::tensor_operation::device::TensorSpecialization::Default;
+static constexpr bool Deterministic = false;
+
+// DIM should be a multiple of 8.
+// If      DIM <= 32 , ues prototype1.
+// If 32 < DIM <= 64 , ues prototype1.
+// If 64 < DIM <= 128, ues prototype2.
+#if(DIM <= 32)
+// clang-format off
+using DeviceGemmInstance =
+    // ########################################################################################|  NumDimG| NumDimM| NumDimN| NumDimK| NumDimO| InputDataType| OutputDataType| GemmDataType| ZDataType| LSEDataType| Acc0BiasDataType| Acc1BiasDataType|     GemmAcc|        CShuffle|            A|            B|         Acc|           B1|           C|           GEMM|   ATensorSpec|  B0TensorSpec|  B1TensorSpec|   CTensorSpec| NumGemmK| Block| Gemm01| Gemm0| Gemm0| Gemm1| Gemm1| AK1| BK1| B1K1| MPer| NPer| Gemm0| Gemm0| Gemm1| Gemm2|  ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockLds|  B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockLds|    CShuffle|    CShuffle| CBlockTransferClusterLengths| CShuffleBlockTransferScalarPerVector_NPerBlock| MaskingSpec| Deterministic|
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |    DataType|        DataType|  Elementwise|  Elementwise| Elementwise|  Elementwise| Elementwise| Specialization|              |              |              |              | Prefetch|  Size|   MPer|  NPer|  KPer|  NPer|  KPer|    |    |     |  XDL|  XDL|  MXdl|  NXdl|  NXdl|  NXdl|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|    ThreadCluster|   ThreadCluster|  SrcAccessOrder|    SrcVectorDim|       SrcScalar|       DstScalar|  AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |    Operation|    Operation|   Operation|    Operation|   Operation|               |              |              |              |              |    Stage|      |  Block| Block| Block| Block| Block|    |    |     |     |     |   Per|   Per|   Per|   Per| Lengths_K0_M_K1|   ArrangeOrder|               |               |      PerVector|   PerVector_K1|          |  Lengths_K0_N_K1|    ArrangeOrder|                |                |       PerVector|    PerVector_K1|           |  PerShuffle|  PerShuffle|         _NBlock_NWaveNPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |             |             |            |             |            |               |              |              |              |              |         |      |       |      |      |      |      |    |    |     |     |     |  Wave|  Wave|  Wave|  Wave|                |               |               |               |               |               |          |                 |                |                |                |                |                |           |            |            |                             |                                               |            |              |
+    ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V1<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    32,    32,    32,   8,   8,    2,   32,   32,     4,     1,     1,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,           1,           1,               S<1, 64, 1, 4>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;
+// clang-format on
+#elif(DIM <= 64)
+// clang-format off
+using DeviceGemmInstance =
+    // ########################################################################################|  NumDimG| NumDimM| NumDimN| NumDimK| NumDimO| InputDataType| OutputDataType| GemmDataType| ZDataType| LSEDataType| Acc0BiasDataType| Acc1BiasDataType|     GemmAcc|        CShuffle|            A|            B|         Acc|           B1|           C|           GEMM|   ATensorSpec|  B0TensorSpec|  B1TensorSpec|   CTensorSpec| NumGemmK| Block| Gemm01| Gemm0| Gemm0| Gemm1| Gemm1| AK1| BK1| B1K1| MPer| NPer| Gemm0| Gemm0| Gemm1| Gemm2|  ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockLds|  B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockLds|    CShuffle|    CShuffle| CBlockTransferClusterLengths| CShuffleBlockTransferScalarPerVector_NPerBlock| MaskingSpec| Deterministic|
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |    DataType|        DataType|  Elementwise|  Elementwise| Elementwise|  Elementwise| Elementwise| Specialization|              |              |              |              | Prefetch|  Size|   MPer|  NPer|  KPer|  NPer|  KPer|    |    |     |  XDL|  XDL|  MXdl|  NXdl|  NXdl|  NXdl|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|    ThreadCluster|   ThreadCluster|  SrcAccessOrder|    SrcVectorDim|       SrcScalar|       DstScalar|  AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |    Operation|    Operation|   Operation|    Operation|   Operation|               |              |              |              |              |    Stage|      |  Block| Block| Block| Block| Block|    |    |     |     |     |   Per|   Per|   Per|   Per| Lengths_K0_M_K1|   ArrangeOrder|               |               |      PerVector|   PerVector_K1|          |  Lengths_K0_N_K1|    ArrangeOrder|                |                |       PerVector|    PerVector_K1|           |  PerShuffle|  PerShuffle|         _NBlock_NWaveNPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |             |             |            |             |            |               |              |              |              |              |         |      |       |      |      |      |      |    |    |     |     |     |  Wave|  Wave|  Wave|  Wave|                |               |               |               |               |               |          |                 |                |                |                |                |                |           |            |            |                             |                                               |            |              |
+    ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V1<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     64,   128,    64,    64,    32,   8,   8,    2,   32,   32,     2,     1,     2,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,           1,           2,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;
+    // ########################################################################################|  NumDimG| NumDimM| NumDimN| NumDimK| NumDimO| InputDataType| OutputDataType| GemmDataType| ZDataType| LSEDataType| Acc0BiasDataType| Acc1BiasDataType|     GemmAcc|        CShuffle|            A|            B|         Acc|           B1|           C|           GEMM|   ATensorSpec|  B0TensorSpec|  B1TensorSpec|   CTensorSpec| NumGemmK| Block| Gemm01| Gemm0| Gemm0| Gemm1| Gemm1| AK1| BK1| B1K1| MPer| NPer| Gemm0| Gemm0| Gemm1| Gemm2|  ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockLds|  B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockLds|  B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockLds|    CShuffle|    CShuffle| CBlockTransferClusterLengths| CShuffleBlockTransferScalarPerVector_NPerBlock| MaskingSpec| Deterministic|
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |    DataType|        DataType|  Elementwise|  Elementwise| Elementwise|  Elementwise| Elementwise| Specialization|              |              |              |              | Prefetch|  Size|   MPer|  NPer|  KPer|  NPer|  KPer|    |    |     |  XDL|  XDL|  MXdl|  NXdl|  NXdl|  NXdl|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|    ThreadCluster|   ThreadCluster|  SrcAccessOrder|    SrcVectorDim|       SrcScalar|       DstScalar|  AddExtraN|    ThreadCluster|   ThreadCluster|  SrcAccessOrder|    SrcVectorDim|       SrcScalar|       DstScalar|  AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |    Operation|    Operation|   Operation|    Operation|   Operation|               |              |              |              |              |    Stage|      |  Block| Block| Block| Block| Block|    |    |     |     |     |   Per|   Per|   Per|   Per| Lengths_K0_M_K1|   ArrangeOrder|               |               |      PerVector|   PerVector_K1|          |  Lengths_K0_N_K1|    ArrangeOrder|                |                |       PerVector|    PerVector_K1|           |  Lengths_K0_N_K1|    ArrangeOrder|                |                |       PerVector|    PerVector_K1|           |  PerShuffle|  PerShuffle|         _NBlock_NWaveNPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |             |             |            |             |            |               |              |              |              |              |         |      |       |      |      |      |      |    |    |     |     |     |  Wave|  Wave|  Wave|  Wave|                |               |               |               |               |               |          |                 |                |                |                |                |                |           |                 |                |                |                |                |                |           |            |            |                             |                                               |            |              |
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    64,    64,    32,   8,   8,    2,   32,   32,     4,     1,     2,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               2,               2,      false,           1,           2,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    32,    64,    32,   8,   8,    2,   32,   32,     4,     1,     2,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               2,               2,      false,           1,           2,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    64,    64,    32,   8,   8,    2,   32,   32,     4,     1,     2,     2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               2,               2,      false,           1,           2,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;
+// clang-format on
+#elif(DIM <= 128)
+// clang-format off
+using DeviceGemmInstance =
+    // ########################################################################################|  NumDimG| NumDimM| NumDimN| NumDimK| NumDimO| InputDataType| OutputDataType| GemmDataType| ZDataType| LSEDataType| Acc0BiasDataType| Acc1BiasDataType|     GemmAcc|        CShuffle|            A|            B|         Acc|           B1|           C|           GEMM|   ATensorSpec|  B0TensorSpec|  B1TensorSpec|   CTensorSpec| NumGemmK| Block| Gemm01| Gemm0| Gemm0| Gemm1| Gemm1| AK1| BK1| B1K1| MPer| NPer| Gemm0| Gemm0| Gemm1| Gemm2|  ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockTransfer| ABlockLds|  B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockTransfer| B0BlockLds|  B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockTransfer| B1BlockLds|    CShuffle|    CShuffle| CBlockTransferClusterLengths| CShuffleBlockTransferScalarPerVector_NPerBlock| MaskingSpec| Deterministic|
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |    DataType|        DataType|  Elementwise|  Elementwise| Elementwise|  Elementwise| Elementwise| Specialization|              |              |              |              | Prefetch|  Size|   MPer|  NPer|  KPer|  NPer|  KPer|    |    |     |  XDL|  XDL|  MXdl|  NXdl|  NXdl|  NXdl|   ThreadCluster|  ThreadCluster| SrcAccessOrder|   SrcVectorDim|      SrcScalar|      DstScalar| AddExtraM|    ThreadCluster|   ThreadCluster|  SrcAccessOrder|    SrcVectorDim|       SrcScalar|       DstScalar|  AddExtraN|    ThreadCluster|   ThreadCluster|  SrcAccessOrder|    SrcVectorDim|       SrcScalar|       DstScalar|  AddExtraN| MXdlPerWave| NXdlPerWave|         _MBlock_MWaveMPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |    Operation|    Operation|   Operation|    Operation|   Operation|               |              |              |              |              |    Stage|      |  Block| Block| Block| Block| Block|    |    |     |     |     |   Per|   Per|   Per|   Per| Lengths_K0_M_K1|   ArrangeOrder|               |               |      PerVector|   PerVector_K1|          |  Lengths_K0_N_K1|    ArrangeOrder|                |                |       PerVector|    PerVector_K1|           |  Lengths_K0_N_K1|    ArrangeOrder|                |                |       PerVector|    PerVector_K1|           |  PerShuffle|  PerShuffle|         _NBlock_NWaveNPerXdl|                                               |            |              |
+    // ########################################################################################|         |        |        |        |        |              |               |             |          |            |                 |                 |            |                |             |             |            |             |            |               |              |              |              |              |         |      |       |      |      |      |      |    |    |     |     |     |  Wave|  Wave|  Wave|  Wave|                |               |               |               |               |               |          |                 |                |                |                |                |                |           |                 |                |                |                |                |                |           |            |            |                             |                                               |            |              |
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    64,   128,    32,   8,   8,    2,   32,   32,     4,     1,     4,     2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    64,   128,    32,   8,   8,    2,   32,   32,     4,     1,     4,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    32,   128,    32,   8,   8,    2,   32,   32,     4,     1,     4,     2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    32,   128,    32,   8,   8,    2,   32,   32,     4,     1,     4,     4,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,    128,   128,    32,   128,    32,   8,   8,    2,   32,   32,     4,     1,     4,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     64,   128,    64,   128,    32,   8,   8,    2,   32,   32,     2,     1,     4,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     64,   128,    64,   128,    32,   8,   8,    2,   32,   32,     2,     1,     4,     2,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     64,   128,    32,   128,    32,   8,   8,    2,   32,   32,     2,     1,     4,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     64,   128,   128,   128,    32,   8,   8,    2,   32,   32,     2,     1,     4,     1,     S<4, 64, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     32,   128,   128,   128,    32,   8,   8,    2,   32,   32,     1,     1,     4,     1,     S<8, 32, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;               
+    // ck::tensor_operation::device::DeviceBatchedMultiheadAttentionBackward_Qloop_Xdl_CShuffle_V2<  NumDimG, NumDimM, NumDimN, NumDimK, NumDimO, InputDataType, OutputDataType, GemmDataType, ZDataType, LSEDataType, Acc0BiasDataType, Acc1BiasDataType, AccDataType, ShuffleDataType, QKVElementOp, QKVElementOp,       Scale, QKVElementOp,  YElementOp,       GemmSpec,   TensorSpecQ,   TensorSpecK,   TensorSpecV,   TensorSpecY,        1,   256,     32,   128,    64,   128,    32,   8,   8,    2,   32,   32,     1,     1,     4,     1,     S<8, 32, 1>,     S<1, 0, 2>,     S<1, 0, 2>,              2,              8,              8,      true,      S<4, 64, 1>,      S<1, 0, 2>,      S<1, 0, 2>,               2,               8,               8,       true,      S<8, 32, 1>,      S<0, 2, 1>,      S<0, 2, 1>,               1,               4,               2,      false,           1,           4,               S<1, 32, 1, 8>, CShuffleBlockTransferScalarPerVector_NPerBlock, MaskingSpec, Deterministic>;
+// clang-format on
+#endif
+
+// Ref Gemm0: S = alpha * Q * K^T
+// fp16 in, fp32 out
+using ReferenceGemm0Instance = ck::tensor_operation::host::ReferenceBatchedGemm<InputDataType,
+                                                                                InputDataType,
+                                                                                AccDataType,
+                                                                                AccDataType,
+                                                                                PassThrough,
+                                                                                PassThrough,
+                                                                                Scale>;
+
+// Ref Softmax: P = Softmax(S)
+// fp32 in, fp16 out
+using ReferenceSoftmaxInstance =
+    ck::tensor_operation::host::ReferenceSoftmax<AccDataType, InputDataType, AccDataType>;
+
+// Ref Gemm1: Y = P * V
+// fp16 in, fp16 out
+using ReferenceGemm1Instance = ck::tensor_operation::host::ReferenceBatchedGemm<InputDataType,
+                                                                                InputDataType,
+                                                                                InputDataType,
+                                                                                AccDataType,
+                                                                                PassThrough,
+                                                                                PassThrough,
+                                                                                PassThrough>;
+
+// Ref Gemm for backward pass
+// fp16 in, fp16 out
+using ReferenceGemm0GradInstance = ck::tensor_operation::host::ReferenceBatchedGemm<InputDataType,
+                                                                                    InputDataType,
+                                                                                    InputDataType,
+                                                                                    AccDataType,
+                                                                                    PassThrough,
+                                                                                    PassThrough,
+                                                                                    Scale>;
+
+using ReferenceGemm1GradInstance = ck::tensor_operation::host::ReferenceBatchedGemm<InputDataType,
+                                                                                    InputDataType,
+                                                                                    OutputDataType,
+                                                                                    AccDataType,
+                                                                                    PassThrough,
+                                                                                    PassThrough,
+                                                                                    Scale>;
+
+// Ref dropout
+using ReferenceDropoutInstance =
+    ck::tensor_operation::host::ReferenceDropout<ZDataType, InputDataType, InputDataType>;
+
+template <typename TensorQ,
+          typename TensorK,
+          typename TensorV,
+          typename TensorS,
+          typename TensorP,
+          typename TensorZ,
+          typename TensorY,
+          typename TensorLSE = TensorP>
+void run_attention_fwd_host(const TensorQ& q_g_m_k,
+                            const TensorK& k_g_n_k,
+                            const TensorV& v_g_n_o,
+                            const float alpha,
+                            TensorS& s_g_m_n,
+                            TensorP& p_g_m_n,
+                            TensorY& y_g_m_o,
+                            TensorLSE& lse_g_m,
+                            TensorP& p_drop_g_m_n,
+                            TensorZ& z_g_m_n,
+                            ZDataType p_dropout_in_16bits,
+                            float rp_dropout)
+{
+    // S = alpha * Q * K^T
+    auto k_g_k_n            = k_g_n_k.Transpose({0, 2, 1});
+    auto ref_gemm0          = ReferenceGemm0Instance{};
+    auto ref_gemm0_invoker  = ref_gemm0.MakeInvoker();
+    auto ref_gemm0_argument = ref_gemm0.MakeArgument(
+        q_g_m_k, k_g_k_n, s_g_m_n, PassThrough{}, PassThrough{}, Scale{alpha});
+
+    ref_gemm0_invoker.Run(ref_gemm0_argument);
+
+    // masking
+    auto M          = s_g_m_n.GetLengths()[1];
+    auto N          = s_g_m_n.GetLengths()[2];
+    const auto mask = DeviceGemmInstance::C0MatrixMask(M, N);
+    s_g_m_n.ForEach([&](auto& self, auto idx) {
+        if(mask.IsMaskedElement(idx[1], idx[2]))
+            self(idx) = -ck::NumericLimits<float>::Infinity();
+    });
+
+    // P = Softmax(S)
+    auto ref_softmax          = ReferenceSoftmaxInstance{};
+    auto ref_softmax_invoker  = ref_softmax.MakeInvoker();
+    auto ref_softmax_argument = ref_softmax.MakeArgument(s_g_m_n, p_g_m_n, 1, 0, {2}, &lse_g_m);
+
+    ref_softmax_invoker.Run(ref_softmax_argument);
+
+    // P_dropped
+    auto ref_dropout         = ReferenceDropoutInstance{};
+    auto ref_dropout_invoker = ref_dropout.MakeInvoker();
+    auto ref_dropout_argment =
+        ref_dropout.MakeArgument(z_g_m_n, p_g_m_n, p_drop_g_m_n, p_dropout_in_16bits, rp_dropout);
+    ref_dropout_invoker.Run(ref_dropout_argment);
+
+    // Y = P_dropout * V
+    auto ref_gemm1          = ReferenceGemm1Instance{};
+    auto ref_gemm1_invoker  = ref_gemm1.MakeInvoker();
+    auto ref_gemm1_argument = ref_gemm1.MakeArgument(
+        p_drop_g_m_n, v_g_n_o, y_g_m_o, PassThrough{}, PassThrough{}, PassThrough{});
+
+    ref_gemm1_invoker.Run(ref_gemm1_argument);
+}
+
+int run(int argc, char* argv[])
+{
+    bool do_verification = true;
+    int init_method      = 2; // method 1 will have slightly higher error; TODO: to investigate
+    bool time_kernel     = true;
+
+    // Overall QKV matrices shape
+    // y_g_m_o = Softmax(alpha * Q_g_m_k * K_g_k_n) * V_g_n_o
+    // y_g0_g1_m_o = reshape(y_g_m_o, [G0, G1, M, O])
+    // y_g0_m_g1_o = permute(y_g0_g1_m_o, [0, 2, 1, 3])
+    ck::index_t M  = 512;
+    ck::index_t N  = 512;
+    ck::index_t K  = DIM;
+    ck::index_t O  = DIM;
+    ck::index_t G0 = 4;
+    ck::index_t G1 = 6;
+
+    bool input_permute  = false;
+    bool output_permute = false;
+
+    float p_drop                    = 0.0;
+    const unsigned long long seed   = 1;
+    const unsigned long long offset = 0;
+
+    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 == 13)
+    {
+        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]);
+        G0 = std::stoi(argv[8]);
+        G1 = std::stoi(argv[9]);
+
+        p_drop = std::stof(argv[10]);
+
+        input_permute  = std::stoi(argv[11]);
+        output_permute = std::stoi(argv[12]);
+    }
+    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 11: M, N, K, O, G0, G1\n");
+        printf("arg10: scale (alpha)\n");
+        printf("arg11 to 12: input / output permute\n");
+        exit(0);
+    }
+
+    float p_dropout               = 1 - p_drop;
+    ZDataType p_dropout_in_16bits = ZDataType(std::floor(p_dropout * 65535.0));
+    float rp_dropout              = 1.0 / p_dropout;
+    float alpha                   = 1.f / std::sqrt(K);
+
+    std::cout << "do_verification: " << do_verification << std::endl;
+    std::cout << "init_method: " << init_method << std::endl;
+    std::cout << "time_kernel: " << time_kernel << std::endl;
+    std::cout << "M: " << M << std::endl;
+    std::cout << "N: " << N << std::endl;
+    std::cout << "K: " << K << std::endl;
+    std::cout << "O: " << O << std::endl;
+    std::cout << "G0: " << G0 << std::endl;
+    std::cout << "G1: " << G1 << std::endl;
+    std::cout << "alpha: " << alpha << std::endl;
+    std::cout << "input_permute: " << input_permute << std::endl;
+    std::cout << "output_permute: " << output_permute << std::endl;
+    std::cout << "p_drop: " << p_drop << std::endl;
+    std::cout << "seed: " << seed << std::endl;
+    std::cout << "offset: " << offset << std::endl;
+
+    const ck::index_t BatchCount = G0 * G1;
+
+    std::vector<ck::index_t> q_gs_ms_ks_lengths{G0, G1, M, K};
+    std::vector<ck::index_t> q_gs_ms_ks_strides =
+        input_permute
+            ? std::vector<ck::index_t>{M * G1 * K, K, G1 * K, 1} // Q layout [G0, M, G1, K]
+            : std::vector<ck::index_t>{G1 * M * K, M * K, K, 1}; // Q layout [G0, G1, M, K]
+
+    std::vector<ck::index_t> k_gs_ns_ks_lengths{G0, G1, N, K};
+    std::vector<ck::index_t> k_gs_ns_ks_strides =
+        input_permute
+            ? std::vector<ck::index_t>{N * G1 * K, K, G1 * K, 1} // K layout [G0, N, G1, K]
+            : std::vector<ck::index_t>{G1 * N * K, N * K, K, 1}; // K layout [G0, G1, N, K]
+
+    std::vector<ck::index_t> v_gs_os_ns_lengths{G0, G1, O, N};
+    std::vector<ck::index_t> v_gs_os_ns_strides =
+        input_permute
+            ? std::vector<ck::index_t>{N * G1 * O, O, 1, G1 * O} // V layout [G0, N, G1, O]
+            : std::vector<ck::index_t>{G1 * N * O, N * O, 1, O}; // V layout [G0, G1, N, O]
+
+    std::vector<ck::index_t> y_gs_ms_os_lengths{G0, G1, M, O};
+    std::vector<ck::index_t> y_gs_ms_os_strides =
+        output_permute
+            ? std::vector<ck::index_t>{M * G1 * O, O, G1 * O, 1} // Y layout [G0, M, G1, O]
+            : std::vector<ck::index_t>{G1 * M * O, M * O, O, 1}; // Y layout [G0, G1, M, O]
+
+    std::vector<ck::index_t> d_gs_ms_ns_lengths{G0, G1, M, N};
+    std::vector<ck::index_t> d_gs_ms_ns_strides =
+        input_permute
+            ? std::vector<ck::index_t>{M * G1 * N, N, G1 * N, 1} // D layout [G0, M, G1, N]
+            : std::vector<ck::index_t>{G1 * M * N, M * N, N, 1}; // D layout [G0, G1, M, N]
+
+    std::vector<ck::index_t> z_gs_ms_ns_lengths{G0, G1, M, N};
+    std::vector<ck::index_t> z_gs_ms_ns_strides =
+        input_permute
+            ? std::vector<ck::index_t>{M * G1 * N, N, G1 * N, 1} // Z layout [G0, M, G1, N]
+            : std::vector<ck::index_t>{G1 * M * N, M * N, N, 1}; // Z layout [G0, G1, M, N]
+    // The softmax stat log-sum-exp (LSE) is used to speed up softmax calculation in backward pass
+    // Pi = exp(Si) / sum(exp(S0) + exp(S1) + ...)
+    //    = exp(Si) / exp(log(sum(exp() + ...)))
+    //    = exp(Si - log(sum(exp() + ...)))
+    //               ^^^^^^^^^^^^^^^^^^^^^
+    //                       LSE
+    std::vector<ck::index_t> lse_gs_ms_lengths{G0, G1, M};
+    std::vector<ck::index_t> lse_gs_ms_strides{G1 * M, M, 1}; // LSE layout [G0, G1, M]
+
+    Tensor<InputDataType> q_gs_ms_ks(q_gs_ms_ks_lengths, q_gs_ms_ks_strides);
+    Tensor<InputDataType> k_gs_ns_ks(k_gs_ns_ks_lengths, k_gs_ns_ks_strides);
+    Tensor<ZDataType> z_gs_ms_ns(z_gs_ms_ns_lengths, z_gs_ms_ns_strides);
+    Tensor<InputDataType> v_gs_os_ns(v_gs_os_ns_lengths, v_gs_os_ns_strides);
+    Tensor<InputDataType> y_gs_ms_os(y_gs_ms_os_lengths, y_gs_ms_os_strides);
+    Tensor<InputDataType> ygrad_gs_ms_os(y_gs_ms_os_lengths, y_gs_ms_os_strides);
+    Tensor<LSEDataType> lse_gs_ms(lse_gs_ms_lengths, lse_gs_ms_strides);
+
+    std::cout << "q_gs_ms_ks: " << q_gs_ms_ks.mDesc << std::endl;
+    std::cout << "k_gs_ns_ks: " << k_gs_ns_ks.mDesc << std::endl;
+    std::cout << "z_gs_ms_ns: " << z_gs_ms_ns.mDesc << std::endl;
+    std::cout << "v_gs_os_ns: " << v_gs_os_ns.mDesc << std::endl;
+    std::cout << "y_gs_ms_os: " << y_gs_ms_os.mDesc << std::endl;
+    std::cout << "lse_gs_ms_os: " << lse_gs_ms.mDesc << std::endl;
+
+    z_gs_ms_ns.GenerateTensorValue(GeneratorTensor_1<InputDataType>{0});
+    switch(init_method)
+    {
+    case 0: break;
+    case 1:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_2<InputDataType>{-2, 2});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_2<InputDataType>{-2, 2});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_2<InputDataType>{-2, 2});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_2<InputDataType>{-2, 2});
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_2<DDataType>{-2, 2});
+        break;
+    case 2:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_3<InputDataType>{0.0, 1.0});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_3<InputDataType>{0.0, 1.0});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_3<InputDataType>{-0.5, 0.5});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_3<InputDataType>{-0.5, 0.5});
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_3<DDataType>{-0.5, 0.5});
+        break;
+    case 3:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_2<InputDataType>{-5, 5});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_1<DDataType>{1});
+        break;
+    case 4:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_1<DDataType>{1});
+        break;
+    case 5:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_Sequential<2>{}); // dy[g0, g1, m, o]
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_1<DDataType>{1});
+        // dO dot O = [0; 1; 2; ...]
+        break;
+    case 6:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_Sequential<3>{}); // dy[g0, g1, m, o]
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_1<DDataType>{1});
+        // assume mnko = 256
+        // P = softmax(QK) = 0.0039 * ones
+        // O = P V = 0.0039 * ones
+        // dP = dO V = [0, 1, 2, ...; 0, 1, 2, ...; ...]
+        // dO dot O = [127.5; ...]
+        // dS = P * (dP - dO dot O)
+        //
+        break;
+    default:
+        q_gs_ms_ks.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1});
+        k_gs_ns_ks.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        v_gs_os_ns.GenerateTensorValue(GeneratorTensor_Diagonal<InputDataType>{});
+        ygrad_gs_ms_os.GenerateTensorValue(GeneratorTensor_1<InputDataType>{1}); // dy[g0, g1, m, o]
+        d_gs_ms_ns.GenerateTensorValue(GeneratorTensor_1<DDataType>{1});
+        // assume mnko = 256
+        // P = softmax(QK) = 0.0039 * ones
+        // O = P V = 0.0039 * ones
+        // dP = dO V = ones
+        // dS = P * (dP - (dO dot O))
+        //    = 0.0039 * ones * (ones - 0.0039*256)
+        //    = 0.0039 * ones * (ones - 1)
+        //    = 0
+    }
+
+    Tensor<InputDataType> q_g_m_k({BatchCount, M, K});
+    Tensor<InputDataType> k_g_n_k({BatchCount, N, K});
+    Tensor<DDataType> d_g_m_n({G0 * G1, M, N});
+    Tensor<ZDataType> z_g_m_n({BatchCount, M, N});
+    Tensor<InputDataType> v_g_n_o({BatchCount, N, O});
+    Tensor<AccDataType> s_g_m_n({BatchCount, M, N});
+    Tensor<InputDataType> p_g_m_n({BatchCount, M, N});
+    Tensor<InputDataType> p_drop_g_m_n({BatchCount, M, N});
+    Tensor<InputDataType> y_g_m_o({BatchCount, M, O});
+    Tensor<LSEDataType> lse_g_m({BatchCount, M});
+
+    q_gs_ms_ks.ForEach(
+        [&](auto& self, auto idx) { q_g_m_k(idx[0] * G1 + idx[1], idx[2], idx[3]) = self(idx); });
+    k_gs_ns_ks.ForEach(
+        [&](auto& self, auto idx) { k_g_n_k(idx[0] * G1 + idx[1], idx[2], idx[3]) = self(idx); });
+    v_gs_os_ns.ForEach(
+        [&](auto& self, auto idx) { v_g_n_o(idx[0] * G1 + idx[1], idx[3], idx[2]) = self(idx); });
+    d_gs_ms_ns.ForEach(
+        [&](auto& self, auto idx) { d_g_m_n(idx[0] * G1 + idx[1], idx[2], idx[3]) = self(idx); });
+
+    // qkv gradients have the same descriptor as with qkv
+    DeviceMem q_device_buf(sizeof(InputDataType) * q_gs_ms_ks.mDesc.GetElementSpaceSize());
+    DeviceMem k_device_buf(sizeof(InputDataType) * k_gs_ns_ks.mDesc.GetElementSpaceSize());
+    DeviceMem d_device_buf(sizeof(DDataType) * d_gs_ms_ns.mDesc.GetElementSpaceSize());
+    DeviceMem z_device_buf(sizeof(ZDataType) * z_gs_ms_ns.mDesc.GetElementSpaceSize());
+    DeviceMem v_device_buf(sizeof(InputDataType) * v_gs_os_ns.mDesc.GetElementSpaceSize());
+    DeviceMem y_device_buf(sizeof(InputDataType) * y_gs_ms_os.mDesc.GetElementSpaceSize());
+    DeviceMem lse_device_buf(sizeof(LSEDataType) * lse_gs_ms.mDesc.GetElementSpaceSize());
+    DeviceMem qgrad_device_buf(sizeof(OutputDataType) * q_gs_ms_ks.mDesc.GetElementSpaceSize());
+    DeviceMem kgrad_device_buf(sizeof(OutputDataType) * k_gs_ns_ks.mDesc.GetElementSpaceSize());
+    DeviceMem vgrad_device_buf(sizeof(OutputDataType) * v_gs_os_ns.mDesc.GetElementSpaceSize());
+    DeviceMem ygrad_device_buf(sizeof(InputDataType) * y_gs_ms_os.mDesc.GetElementSpaceSize());
+
+    q_device_buf.ToDevice(q_gs_ms_ks.mData.data());
+    k_device_buf.ToDevice(k_gs_ns_ks.mData.data());
+    z_device_buf.ToDevice(z_gs_ms_ns.mData.data());
+    v_device_buf.ToDevice(v_gs_os_ns.mData.data());
+    ygrad_device_buf.ToDevice(ygrad_gs_ms_os.mData.data());
+
+    auto gemm    = DeviceGemmInstance{};
+    auto invoker = gemm.MakeInvoker();
+    // get z matrix
+    {
+        auto argument = gemm.MakeArgument(
+            static_cast<InputDataType*>(q_device_buf.GetDeviceBuffer()),
+            static_cast<InputDataType*>(k_device_buf.GetDeviceBuffer()),
+            static_cast<ZDataType*>(z_device_buf.GetDeviceBuffer()),
+            static_cast<InputDataType*>(v_device_buf.GetDeviceBuffer()),
+            static_cast<InputDataType*>(y_device_buf.GetDeviceBuffer()),
+            static_cast<LSEDataType*>(lse_device_buf.GetDeviceBuffer()),
+            static_cast<InputDataType*>(ygrad_device_buf.GetDeviceBuffer()),
+            static_cast<OutputDataType*>(qgrad_device_buf.GetDeviceBuffer()),
+            static_cast<OutputDataType*>(kgrad_device_buf.GetDeviceBuffer()),
+            static_cast<OutputDataType*>(vgrad_device_buf.GetDeviceBuffer()),
+            {}, // std::array<void*, 1> p_acc0_biases;
+            {}, // std::array<void*, 1> p_acc1_biases;
+            q_gs_ms_ks_lengths,
+            q_gs_ms_ks_strides,
+            k_gs_ns_ks_lengths,
+            k_gs_ns_ks_strides,
+            z_gs_ms_ns_lengths,
+            z_gs_ms_ns_strides,
+            v_gs_os_ns_lengths,
+            v_gs_os_ns_strides,
+            y_gs_ms_os_lengths,
+            y_gs_ms_os_strides,
+            lse_gs_ms_lengths,
+            {}, // std::array<std::vector<ck::index_t>, 1>{acc0_biases_gs_ms_ns_lengths},
+            {}, // std::array<std::vector<ck::index_t>, 1>{acc0_biases_gs_ms_ns_strides},
+            {}, // std::array<std::vector<ck::index_t>, 1>{acc1_biases_gs_ms_os_lengths},
+            {}, // std::array<std::vector<ck::index_t>, 1>{acc1_biases_gs_ms_os_strides},
+            QKVElementOp{},
+            QKVElementOp{},
+            Scale{alpha},
+            QKVElementOp{},
+            YElementOp{},
+            p_drop,
+            std::tuple<unsigned long long, unsigned long long>(seed, offset));
+
+        if(!gemm.IsSupportedArgument(argument))
+        {
+            std::cout << gemm.GetTypeString() << " does not support this problem" << std::endl;
+
+            return 0;
+        }
+        invoker.Run(argument, StreamConfig{nullptr, false});
+    }
+    // not need output z matrix
+    auto argument = gemm.MakeArgument(
+        static_cast<InputDataType*>(q_device_buf.GetDeviceBuffer()),
+        static_cast<InputDataType*>(k_device_buf.GetDeviceBuffer()),
+        static_cast<ZDataType*>(nullptr), // set to nullptr
+        static_cast<InputDataType*>(v_device_buf.GetDeviceBuffer()),
+        static_cast<InputDataType*>(y_device_buf.GetDeviceBuffer()),
+        static_cast<LSEDataType*>(lse_device_buf.GetDeviceBuffer()),
+        static_cast<InputDataType*>(ygrad_device_buf.GetDeviceBuffer()),
+        static_cast<OutputDataType*>(qgrad_device_buf.GetDeviceBuffer()),
+        static_cast<OutputDataType*>(kgrad_device_buf.GetDeviceBuffer()),
+        static_cast<OutputDataType*>(vgrad_device_buf.GetDeviceBuffer()),
+        {}, // std::array<void*, 1> p_acc0_biases;
+        {}, // std::array<void*, 1> p_acc1_biases;
+        q_gs_ms_ks_lengths,
+        q_gs_ms_ks_strides,
+        k_gs_ns_ks_lengths,
+        k_gs_ns_ks_strides,
+        z_gs_ms_ns_lengths,
+        z_gs_ms_ns_strides,
+        v_gs_os_ns_lengths,
+        v_gs_os_ns_strides,
+        y_gs_ms_os_lengths,
+        y_gs_ms_os_strides,
+        lse_gs_ms_lengths,
+        {}, // std::array<std::vector<ck::index_t>, 1>{acc0_biases_gs_ms_ns_lengths},
+        {}, // std::array<std::vector<ck::index_t>, 1>{acc0_biases_gs_ms_ns_strides},
+        {}, // std::array<std::vector<ck::index_t>, 1>{acc1_biases_gs_ms_os_lengths},
+        {}, // std::array<std::vector<ck::index_t>, 1>{acc1_biases_gs_ms_os_strides},
+        QKVElementOp{},
+        QKVElementOp{},
+        Scale{alpha},
+        QKVElementOp{},
+        YElementOp{},
+        p_drop,
+        std::tuple<unsigned long long, unsigned long long>(seed, offset));
+    qgrad_device_buf.SetZero();
+    float ave_time = invoker.Run(argument, StreamConfig{nullptr, time_kernel});
+
+    // 5 GEMM ops in total:
+    // S_MNK / dP_MNO Gemm (Gemm0 rcr)
+    // dQ_MKN Gemm (Gemm1 rrr)
+    // dV_NOM / dK_NKM Gemm (Gemm2 crr)
+    // 3x MNK + 2x MNO
+    std::size_t flop = (size_t(3) * M * N * K + size_t(2) * M * N * O) * 2 * BatchCount;
+    // Q/K/V/Y, dQ/dK/dV/dY, LSE
+    std::size_t num_btype =
+        (sizeof(InputDataType) * M * K + sizeof(InputDataType) * K * N +
+         sizeof(InputDataType) * N * O + sizeof(InputDataType) * M * O * size_t(2) +
+         sizeof(OutputDataType) * M * K + sizeof(OutputDataType) * K * N +
+         sizeof(OutputDataType) * N * O) *
+            BatchCount +
+        sizeof(LSEDataType) * M * 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;
+
+    // copy z matirx data form device
+    z_device_buf.FromDevice(z_gs_ms_ns.mData.data());
+    z_gs_ms_ns.ForEach(
+        [&](auto& self, auto idx) { z_g_m_n(idx[0] * G1 + idx[1], idx[2], idx[3]) = self(idx); });
+
+    //       std::cout << "z_g_m_n ref:\n" << z_g_m_n;
+    bool pass = true;
+    if(do_verification)
+    {
+        // run fwd again for y, cause z_g_m_n update
+        run_attention_fwd_host(q_g_m_k,
+                               k_g_n_k,
+                               v_g_n_o,
+                               alpha,
+                               s_g_m_n,
+                               p_g_m_n,
+                               y_g_m_o,
+                               lse_g_m,
+                               p_drop_g_m_n,
+                               z_g_m_n,
+                               p_dropout_in_16bits,
+                               rp_dropout);
+        y_gs_ms_os.ForEach([&](auto& self, auto idx) {
+            self(idx) = y_g_m_o(idx[0] * G1 + idx[1], idx[2], idx[3]);
+        });
+        lse_gs_ms.ForEach(
+            [&](auto& self, auto idx) { self(idx) = lse_g_m(idx[0] * G1 + idx[1], idx[2]); });
+        y_device_buf.ToDevice(y_gs_ms_os.mData.data());
+        lse_device_buf.ToDevice(lse_gs_ms.mData.data());
+
+        // call kernel again
+        qgrad_device_buf.SetZero();
+        invoker.Run(argument, StreamConfig{nullptr, false});
+
+        Tensor<OutputDataType> qgrad_g_m_k({BatchCount, M, K});
+        Tensor<OutputDataType> kgrad_g_n_k({BatchCount, N, K});
+        Tensor<OutputDataType> vgrad_g_n_o({BatchCount, N, O});
+        Tensor<InputDataType> sgrad_g_m_n({BatchCount, M, N});
+        Tensor<InputDataType> pgrad_g_m_n({BatchCount, M, N});
+        Tensor<InputDataType> pgrad_drop_g_m_n({BatchCount, M, N});
+        Tensor<InputDataType> ygrad_g_m_o({BatchCount, M, O});
+        Tensor<InputDataType> ygrad_dot_y_g_m({BatchCount, M});
+
+        ygrad_gs_ms_os.ForEach([&](auto& self, auto idx) {
+            ygrad_g_m_o(idx[0] * G1 + idx[1], idx[2], idx[3]) = self(idx);
+        });
+
+#if PRINT_HOST
+        {
+            std::cout << "q_g_m_k ref:\n" << q_g_m_k;
+            std::cout << "k_g_n_k ref:\n" << k_g_n_k;
+            std::cout << "v_g_n_o ref:\n" << v_g_n_o;
+            std::cout << "ygrad_g_m_o ref:\n" << ygrad_g_m_o;
+        }
+#endif
+
+        // Gradients
+        auto ref_gemm0_grad         = ReferenceGemm0GradInstance{};
+        auto ref_gemm0_grad_invoker = ref_gemm0_grad.MakeInvoker();
+        using RefGemm0GradArg       = ReferenceGemm0GradInstance::Argument;
+        auto ref_gemm1_grad         = ReferenceGemm1GradInstance{};
+        auto ref_gemm1_grad_invoker = ref_gemm1_grad.MakeInvoker();
+        using RefGemm1GradArg       = ReferenceGemm1GradInstance::Argument;
+
+        // dP_dropout = dY * V^T
+        auto v_g_o_n = v_g_n_o.Transpose({0, 2, 1});
+        ref_gemm0_grad_invoker.Run(RefGemm0GradArg{
+            ygrad_g_m_o, v_g_o_n, pgrad_drop_g_m_n, PassThrough{}, PassThrough{}, Scale{1.f}});
+#if PRINT_HOST
+        {
+            std::cout << "===== dP = dY * V^T\n";
+            std::cout << "ygrad_g_m_o ref:\n" << ygrad_g_m_o;
+            std::cout << "v_g_o_n ref:\n" << v_g_o_n;
+            std::cout << "pgrad_drop_g_m_n ref:\n" << pgrad_drop_g_m_n;
+        }
+#endif
+        // dP = dP_dropout x Z
+        auto ref_dropout         = ReferenceDropoutInstance{};
+        auto ref_dropout_invoker = ref_dropout.MakeInvoker();
+        auto ref_dropout_argment = ref_dropout.MakeArgument(
+            z_g_m_n, pgrad_drop_g_m_n, pgrad_g_m_n, p_dropout_in_16bits, rp_dropout);
+        ref_dropout_invoker.Run(ref_dropout_argment);
+
+        // dS_i_j = P_i_j .* (dP_i_j - dY_i dot Y_i)
+        sgrad_g_m_n.ForEach([&](auto& self, auto idx_gmn) {
+            float ygrad_dot_y = 0;
+            for(int o = 0; o < O; o++)
+            {
+                auto idx_gmo = idx_gmn;
+                idx_gmo[2]   = o;
+                ygrad_dot_y += ck::type_convert<AccDataType>(ygrad_g_m_o(idx_gmo)) *
+                               ck::type_convert<AccDataType>(y_g_m_o(idx_gmo));
+            }
+            self(idx_gmn) = ck::type_convert<InputDataType>(
+                ck::type_convert<AccDataType>(p_g_m_n(idx_gmn)) *
+                (ck::type_convert<AccDataType>(pgrad_g_m_n(idx_gmn)) - ygrad_dot_y));
+        });
+#if PRINT_HOST
+        {
+            std::cout << "===== dS_i_j = P_i_j .* (dP_i_j - dY_i dot Y_i)\n";
+            std::cout << "p_g_m_n ref:\n" << p_g_m_n;
+            std::cout << "pgrad_g_m_n ref:\n" << pgrad_g_m_n;
+            std::cout << "y_g_m_o ref:\n" << y_g_m_o;
+            std::cout << "ygrad_g_m_o ref:\n" << ygrad_g_m_o;
+            std::cout << "sgrad_g_m_n ref:\n" << sgrad_g_m_n;
+        }
+#endif
+        // dV = P_drop^T * dY
+        auto p_drop_g_n_m = p_drop_g_m_n.Transpose({0, 2, 1});
+        ref_gemm1_grad_invoker.Run(RefGemm1GradArg{
+            p_drop_g_n_m, ygrad_g_m_o, vgrad_g_n_o, PassThrough{}, PassThrough{}, Scale{1.0f}});
+#if PRINT_HOST
+        {
+            std::cout << "===== dV = P^T * dY\n";
+            std::cout << "p_drop_g_n_m ref:\n" << p_drop_g_n_m;
+            std::cout << "ygrad_g_m_o ref:\n" << ygrad_g_m_o;
+            std::cout << "vgrad_g_n_o ref:\n" << vgrad_g_n_o;
+        }
+#endif
+
+        // dQ = alpha * dS * K
+        ref_gemm1_grad_invoker.Run(RefGemm1GradArg{
+            sgrad_g_m_n, k_g_n_k, qgrad_g_m_k, PassThrough{}, PassThrough{}, Scale{alpha}});
+#if PRINT_HOST
+        {
+            std::cout << "===== dQ = alpha * dS * K\n";
+            std::cout << "sgrad_g_m_n ref:\n" << sgrad_g_m_n;
+            std::cout << "k_g_n_k ref:\n" << k_g_n_k;
+            std::cout << "qgrad_g_m_k ref:\n" << qgrad_g_m_k;
+        }
+#endif
+
+        // dK = alpha * dS^T * Q
+        auto sgrad_g_n_m = sgrad_g_m_n.Transpose({0, 2, 1});
+        ref_gemm1_grad_invoker.Run(RefGemm1GradArg{
+            sgrad_g_n_m, q_g_m_k, kgrad_g_n_k, PassThrough{}, PassThrough{}, Scale{alpha}});
+#if PRINT_HOST
+        {
+            std::cout << "===== dK = alpha * dS^T * Q\n";
+            std::cout << "sgrad_g_n_m ref:\n" << sgrad_g_n_m;
+            std::cout << "q_g_m_k ref:\n" << q_g_m_k;
+            std::cout << "kgrad_g_n_k ref:\n" << kgrad_g_n_k;
+        }
+#endif
+
+        Tensor<OutputDataType> qgrad_gs_ms_ks_host_result(q_gs_ms_ks_lengths, q_gs_ms_ks_strides);
+        Tensor<OutputDataType> kgrad_gs_ns_ks_host_result(k_gs_ns_ks_lengths, k_gs_ns_ks_strides);
+        Tensor<OutputDataType> vgrad_gs_os_ns_host_result(v_gs_os_ns_lengths, v_gs_os_ns_strides);
+
+        Tensor<OutputDataType> qgrad_gs_ms_ks_device_result(q_gs_ms_ks_lengths, q_gs_ms_ks_strides);
+        Tensor<OutputDataType> kgrad_gs_ns_ks_device_result(k_gs_ns_ks_lengths, k_gs_ns_ks_strides);
+        Tensor<OutputDataType> vgrad_gs_os_ns_device_result(v_gs_os_ns_lengths, v_gs_os_ns_strides);
+
+        qgrad_device_buf.FromDevice(qgrad_gs_ms_ks_device_result.mData.data());
+        kgrad_device_buf.FromDevice(kgrad_gs_ns_ks_device_result.mData.data());
+        vgrad_device_buf.FromDevice(vgrad_gs_os_ns_device_result.mData.data());
+
+        // permute
+        qgrad_gs_ms_ks_host_result.ForEach([&](auto& self, auto idx) {
+            const size_t& g0 = idx[0];
+            const size_t& g1 = idx[1];
+
+            const size_t g = g0 * G1 + g1;
+
+            self(idx) = qgrad_g_m_k(g, idx[2], idx[3]);
+        });
+        kgrad_gs_ns_ks_host_result.ForEach([&](auto& self, auto idx) {
+            const size_t& g0 = idx[0];
+            const size_t& g1 = idx[1];
+
+            const size_t g = g0 * G1 + g1;
+
+            self(idx) = kgrad_g_n_k(g, idx[2], idx[3]);
+        });
+        vgrad_gs_os_ns_host_result.ForEach([&](auto& self, auto idx) {
+            const size_t& g0 = idx[0];
+            const size_t& g1 = idx[1];
+
+            const size_t g = g0 * G1 + g1;
+
+            self(idx) = vgrad_g_n_o(g, idx[3], idx[2]);
+        });
+
+        std::cout << "Checking qgrad:\n";
+        pass &= ck::utils::check_err(qgrad_gs_ms_ks_device_result.mData,
+                                     qgrad_gs_ms_ks_host_result.mData,
+                                     "error",
+                                     1e-2,
+                                     1e-2);
+        std::cout << "Checking kgrad:\n";
+        pass &= ck::utils::check_err(kgrad_gs_ns_ks_device_result.mData,
+                                     kgrad_gs_ns_ks_host_result.mData,
+                                     "error",
+                                     1e-2,
+                                     1e-2);
+        std::cout << "Checking vgrad:\n";
+        pass &= ck::utils::check_err(vgrad_gs_os_ns_device_result.mData,
+                                     vgrad_gs_os_ns_host_result.mData,
+                                     "error",
+                                     1e-2,
+                                     1e-2);
+    }
+
+    return pass ? ((void)(std::cout << "pass\n"), 0) : ((void)(std::cout << "fail\n"), 1);
+}
+
+int main(int argc, char* argv[]) { return run(argc, argv); }