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 // SPDX-License-Identifier: MIT
 // Copyright (c) 2018-2023, Advanced Micro Devices, Inc. All rights reserved.
  
 #pragma once
  
 #include "ck/utility/common_header.hpp"
 #include "ck/tensor_description/multi_index_transform_helper.hpp"
 #include "ck/tensor_description/tensor_descriptor.hpp"
 #include "ck/tensor_description/tensor_descriptor_helper.hpp"
 #include "ck/tensor_operation/gpu/grid/block_to_ctile_map.hpp"
 #include "ck/tensor_operation/gpu/grid/gridwise_gemm_pipeline_selector.hpp"
 #include "ck/tensor_operation/gpu/block/blockwise_gemm_xdlops.hpp"
 #include "ck/tensor_operation/gpu/block/thread_group_tensor_slice_transfer_v4r1.hpp"
 #include "ck/tensor_operation/gpu/block/thread_group_tensor_slice_transfer_v6r1.hpp"
 #include "ck/tensor_operation/gpu/thread/threadwise_tensor_slice_transfer.hpp"
 #include "ck/tensor_operation/gpu/element/element_wise_operation.hpp"
  
 namespace ck {
  
 // Implementation of "Merge" transformation primitive that uses division and mod. It is supposed to
 // be used for low_lengths that are known at compile time and are power of 2, otherwise performance
 // will be very bad
 template <typename LowLengths>
 struct Merge_v4_no_carry
 {
     static constexpr index_t NDimLow = LowLengths::Size();
  
     using LowerIndex = MultiIndex<NDimLow>;
     using UpperIndex = MultiIndex<1>;
  
     using LowLengthsScan =
         decltype(container_reverse_exclusive_scan(LowLengths{}, math::multiplies{}, Number<1>{}));
  
     using UpLengths =
         decltype(make_tuple(container_reduce(LowLengths{}, math::multiplies{}, Number<1>{})));
  
     LowLengths low_lengths_;
     LowLengthsScan low_lengths_scan_;
     UpLengths up_lengths_;
  
     __host__ __device__ constexpr Merge_v4_no_carry() = default;
  
     __host__ __device__ constexpr Merge_v4_no_carry(const LowLengths& low_lengths)
         : low_lengths_{low_lengths},
           low_lengths_scan_{
               container_reverse_exclusive_scan(low_lengths, math::multiplies{}, Number<1>{})},
           up_lengths_{make_tuple(container_reduce(low_lengths, math::multiplies{}, Number<1>{}))}
     {
         static_assert(LowerIndex::Size() == NDimLow, "wrong!");
     }
  
     __host__ __device__ static constexpr index_t GetNumOfLowerDimension() { return NDimLow; }
  
     __host__ __device__ static constexpr index_t GetNumOfUpperDimension() { return 1; }
  
     __host__ __device__ constexpr const auto& GetUpperLengths() const { return up_lengths_; }
  
     template <typename LowIdx, typename UpIdx>
     __host__ __device__ constexpr void CalculateLowerIndex(LowIdx& idx_low,
                                                            const UpIdx& idx_up) const
     {
         static_assert(LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
                       "wrong! inconsistent # of dimension");
  
         index_t tmp = idx_up[Number<0>{}];
  
         // division and mod
         static_for<0, NDimLow - 1, 1>{}([&](auto i) {
             idx_low(i) = tmp / this->low_lengths_scan_[i];
             tmp %= this->low_lengths_scan_[i];
         });
  
         idx_low(Number<NDimLow - 1>{}) = tmp;
     }
  
     template <typename LowIdxDiff,
               typename UpIdxDiff,
               typename LowIdx,
               typename UpIdx,
               index_t Hack>
     __host__ __device__ void UpdateLowerIndex(LowIdxDiff& idx_diff_low,
                                               const UpIdxDiff& idx_up_diff,
                                               LowIdx& idx_low,
                                               const UpIdx& idx_up_new,
                                               Number<Hack>) const
     {
         static_assert(LowIdxDiff::Size() == NDimLow && UpIdxDiff::Size() == 1 &&
                           LowIdx::Size() == NDimLow && UpIdx::Size() == 1,
                       "wrong! inconsistent # of dimension");
  
         constexpr auto I0   = Number<0>{};
         constexpr auto INm1 = Number<NDimLow - 1>{};
  
         index_t tmp = idx_up_new[I0];
  
         idx_low(INm1)      = tmp;
         idx_diff_low(INm1) = idx_up_diff[I0];
     }
  
     __host__ __device__ static constexpr bool IsLinearTransform() { return false; }
  
     __host__ __device__ static constexpr bool IsValidUpperIndexAlwaysMappedToValidLowerIndex()
     {
         return true;
     }
  
     __host__ __device__ static constexpr bool IsKnownAtCompileTime()
     {
         return is_known_at_compile_time<LowLengths>::value &&
                is_known_at_compile_time<LowLengthsScan>::value &&
                is_known_at_compile_time<UpLengths>::value;
     }
  
     template <typename UpIdx>
     __host__ __device__ static constexpr bool
     IsValidUpperIndexMappedToValidLowerIndex(const UpIdx& /* idx_up */)
     {
         return true;
     }
  
     __host__ __device__ void Print() const
     {
         printf("{");
         printf("Merge_v3_direct_division_mod_wrw, ");
         printf("low_lengths_ ");
         print_multi_index(low_lengths_);
         printf("low_lengths_scan_ ");
         print_multi_index(low_lengths_scan_);
         printf("up_lengths_ ");
         print_multi_index(up_lengths_);
         printf("}");
     }
 };
  
 template <typename LowLengths>
 __host__ __device__ constexpr auto make_merge_transform_v4_no_carry(const LowLengths& low_lengths)
 {
     return Merge_v4_no_carry<LowLengths>{low_lengths};
 }
  
 template <typename GridwiseGemm,
           typename FloatA,
           typename FloatB,
           typename FloatC,
           typename AGridDesc_B_K0_M_K1,
           typename BGridDesc_B_K0_N_K1,
           typename CGridDesc_MBlock_MPerBlock_NBlock_NPerBlock,
           typename AElementwiseOperation,
           typename BElementwiseOperation,
           typename CElementwiseOperation,
           typename CBlockClusterAdaptor,
           bool HasMainKBlockLoop>
 __global__ void
 #if CK_USE_LAUNCH_BOUNDS
 __launch_bounds__(CK_MAX_THREAD_PER_BLOCK, CK_MIN_BLOCK_PER_CU)
 #endif
     kernel_gemm_xdlops_bwd_weight(const FloatA* __restrict__ p_a_grid,
                                   const FloatB* __restrict__ p_b_grid,
                                   FloatC* __restrict__ p_c_grid,
                                   const AGridDesc_B_K0_M_K1 a_b_k0_m_k1_grid_desc,
                                   const BGridDesc_B_K0_N_K1 b_b_k0_n_k1_grid_desc,
                                   const CGridDesc_MBlock_MPerBlock_NBlock_NPerBlock
                                       c_grid_desc_mblock_mperblock_nblock_nperblock,
                                   const AElementwiseOperation a_element_op,
                                   const BElementwiseOperation b_element_op,
                                   const CElementwiseOperation c_element_op,
                                   const CBlockClusterAdaptor c_block_cluster_adaptor)
 {
 #if(defined(__gfx908__) || defined(__gfx90a__) || defined(__gfx94__))
     __shared__ char p_shared[GridwiseGemm::GetSharedMemoryNumberOfByte()];
  
     GridwiseGemm::template Run<HasMainKBlockLoop>(p_a_grid,
                                                   p_b_grid,
                                                   p_c_grid,
                                                   p_shared,
                                                   a_b_k0_m_k1_grid_desc,
                                                   b_b_k0_n_k1_grid_desc,
                                                   c_grid_desc_mblock_mperblock_nblock_nperblock,
                                                   a_element_op,
                                                   b_element_op,
                                                   c_element_op,
                                                   c_block_cluster_adaptor);
 #else
     ignore = p_a_grid;
     ignore = p_b_grid;
     ignore = p_c_grid;
     ignore = a_b_k0_m_k1_grid_desc;
     ignore = b_b_k0_n_k1_grid_desc;
     ignore = c_grid_desc_mblock_mperblock_nblock_nperblock;
     ignore = a_element_op;
     ignore = b_element_op;
     ignore = c_element_op;
     ignore = c_block_cluster_adaptor;
 #endif // end of if (defined(__gfx908__) || defined(__gfx90a__))
 }
  
 template <index_t BlockSize,
           typename FloatA,
           typename FloatB,
           typename FloatAcc,
           typename FloatC,
           InMemoryDataOperationEnum CGlobalMemoryDataOperation,
           typename AGridDesc_B_K0_M_K1,
           typename BGridDesc_B_K0_N_K1,
           typename CMNGridDesc,
           typename AElementwiseOperation,
           typename BElementwiseOperation,
           typename CElementwiseOperation,
           index_t MPerBlock,
           index_t NPerBlock,
           index_t K0PerBlock,
           index_t MPerXDL,
           index_t NPerXDL,
           index_t K1Value,
           index_t MRepeat,
           index_t NRepeat,
           typename ABlockTransferThreadClusterLengths_K0_M_K1,
           typename ABlockTransferThreadClusterArrangeOrder,
           typename ABlockTransferSrcAccessOrder,
           index_t ABlockTransferSrcVectorDim,
           index_t ABlockTransferSrcScalarPerVector,
           index_t ABlockTransferDstScalarPerVector_K1,
           bool AThreadTransferSrcResetCoordinateAfterRun,
           bool ABlockLdsExtraM,
           index_t ABlockLdsM1PerBlock,
           index_t ABlockLdsM0PerBlock,
           index_t ABlockLdsM1Padding,
           typename BBlockTransferThreadClusterLengths_K0_N_K1,
           typename BBlockTransferThreadClusterArrangeOrder,
           typename BBlockTransferSrcAccessOrder,
           index_t BBlockTransferSrcVectorDim,
           index_t BBlockTransferSrcScalarPerVector,
           index_t BBlockTransferDstScalarPerVector_K1,
           bool BThreadTransferSrcResetCoordinateAfterRun,
           bool BBlockLdsExtraN,
           index_t BBlockLdsN1PerBlock,
           index_t BBlockLdsN0PerBlock,
           index_t BBlockLdsN1Padding,
           index_t CShuffleMRepeatPerShuffle,
           index_t CShuffleNRepeatPerShuffle,
           index_t CBlockTransferScalarPerVector_NWaveNPerXDL,
           typename CBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
           bool ABlockLdsExtraM1Wrw      = false,
           bool BBlockLdsExtraN1Wrw      = false,
           index_t NumGemmKPrefetchStage = 1,
           PipelineVersion PipelineVer   = PipelineVersion::v1,
           typename ComputeTypeA         = FloatA,
           typename ComputeTypeB         = ComputeTypeA>
 struct GridwiseGemm_bk0mk1_bk0nk1_mn_xdlops_bwd_weight
 {
     static constexpr auto I0 = Number<0>{};
     static constexpr auto I1 = Number<1>{};
     static constexpr auto I2 = Number<2>{};
     static constexpr auto I3 = Number<3>{};
     static constexpr auto I4 = Number<4>{};
     static constexpr auto I5 = Number<5>{};
     static constexpr auto I6 = Number<6>{};
     static constexpr auto I7 = Number<7>{};
  
     // K1 should be Number<...>
     static constexpr auto K1 = Number<K1Value>{};
  
     using ThisThreadBlock = ThisThreadBlock<BlockSize>;
  
     using GridwiseGemmPipe = remove_cvref_t<
         decltype(GridwiseGemmPipeline_Selector<PipelineVer, NumGemmKPrefetchStage>())>;
  
     // denorm test fix, required to work around fp16 mfma issue
     // we convert fp16->fp32->bf16 and execute bf16 mfma instruction
     // when mfma if fixed, remove this section and update
     // FloatAAdjusted -> ComputeTypeA, FloatBAdjusted -> ComputeTypeB,
     // throughout this file
 #if CK_GFX90A_DENORM_WORKAROUND
     using FloatAAdjusted =
         conditional_t<is_same_v<ComputeTypeA, ck::half_t>, ck::bhalf_t, ComputeTypeA>;
     using FloatBAdjusted =
         conditional_t<is_same_v<ComputeTypeB, ck::half_t>, ck::bhalf_t, ComputeTypeB>;
 #else
     using FloatAAdjusted = ComputeTypeA;
     using FloatBAdjusted = ComputeTypeB;
 #endif
  
     // M0/M1/M1Padding
     static constexpr auto M1PerBlock = Number<ABlockLdsM1PerBlock>{};
     static constexpr auto M0PerBlock = Number<ABlockLdsM0PerBlock>{};
     static constexpr auto M1Padding  = Number<ABlockLdsM1Padding>{};
  
     // N0/N1/N1Padding
     static constexpr auto N1PerBlock = Number<BBlockLdsN1PerBlock>{};
     static constexpr auto N0PerBlock = Number<BBlockLdsN0PerBlock>{};
     static constexpr auto N1Padding  = Number<BBlockLdsN1Padding>{};
  
     __host__ __device__ static constexpr auto GetABlockDescriptor_K0PerBlock_MPerBlock_K1()
     {
         constexpr auto max_lds_align = K1;
  
         // A matrix in LDS memory, dst of blockwise copy
         constexpr auto a_block_desc_k0_m_k1 = [&]() {
             if constexpr(ABlockLdsExtraM)
             {
                 if constexpr(ABlockLdsExtraM1Wrw)
                 {
                     constexpr auto a_block_desc_k0_m0_m1_k1 = make_naive_tensor_descriptor(
                         make_tuple(
                             Number<K0PerBlock>{}, Number<M0PerBlock>{}, Number<M1PerBlock>{}, K1),
                         make_tuple(Number<M0PerBlock>{} * (Number<M1PerBlock>{} * K1 + M1Padding),
                                    Number<M1PerBlock>{} * K1 + M1Padding,
                                    K1,
                                    I1));
  
                     constexpr auto a_block_desc_k0_m_k1_tmp = transform_tensor_descriptor(
                         a_block_desc_k0_m0_m1_k1,
                         make_tuple(make_pass_through_transform(Number<K0PerBlock>{}),
                                    make_merge_transform_v3_division_mod(
                                        make_tuple(Number<M0PerBlock>{}, Number<M1PerBlock>{})),
                                    make_pass_through_transform(K1)),
                         make_tuple(Sequence<0>{}, Sequence<1, 2>{}, Sequence<3>{}),
                         make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}));
  
                     return a_block_desc_k0_m_k1_tmp;
                 }
                 else
                 {
                     return make_naive_tensor_descriptor(
                         make_tuple(Number<K0PerBlock>{}, Number<MPerBlock>{}, K1),
                         make_tuple(Number<MPerBlock + 1>{} * K1, K1, I1));
                 }
             }
             else
             {
                 return make_naive_tensor_descriptor_aligned(
                     make_tuple(Number<K0PerBlock>{}, Number<MPerBlock>{}, K1), max_lds_align);
             }
         }();
  
         return a_block_desc_k0_m_k1;
     }
  
     __host__ __device__ static constexpr auto GetABlockDescriptor_Batch_K0PerBlock_MPerBlock_K1()
     {
         constexpr auto max_lds_align = K1;
  
         // A matrix in LDS memory, dst of blockwise copy
         constexpr auto a_block_desc_b_k0_m_k1 = [&]() {
             if constexpr(ABlockLdsExtraM)
             {
                 if constexpr(ABlockLdsExtraM1Wrw)
                 {
                     constexpr auto a_block_desc_b_k0_m0_m1_k1 = make_naive_tensor_descriptor(
                         make_tuple(Number<1>{},
                                    Number<K0PerBlock>{},
                                    Number<M0PerBlock>{},
                                    Number<M1PerBlock>{},
                                    K1),
                         make_tuple(Number<K0PerBlock>{} * Number<M0PerBlock>{} *
                                        (Number<M1PerBlock>{} * K1 + M1Padding),
                                    Number<M0PerBlock>{} * (Number<M1PerBlock>{} * K1 + M1Padding),
                                    Number<M1PerBlock>{} * K1 + M1Padding,
                                    K1,
                                    I1));
  
                     constexpr auto a_block_desc_b_k0_m_k1_tmp = transform_tensor_descriptor(
                         a_block_desc_b_k0_m0_m1_k1,
                         make_tuple(make_pass_through_transform(Number<1>{}),
                                    make_pass_through_transform(Number<K0PerBlock>{}),
                                    make_merge_transform_v4_no_carry(
                                        make_tuple(Number<M0PerBlock>{}, Number<M1PerBlock>{})),
                                    make_pass_through_transform(K1)),
                         make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2, 3>{}, Sequence<4>{}),
                         make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}));
  
                     return a_block_desc_b_k0_m_k1_tmp;
                 }
                 else
                 {
                     return make_naive_tensor_descriptor(
                         make_tuple(Number<1>{}, Number<K0PerBlock>{}, Number<MPerBlock>{}, K1),
                         make_tuple(Number<K0PerBlock>{} * Number<MPerBlock + 1>{} * K1,
                                    Number<MPerBlock + 1>{} * K1,
                                    K1,
                                    I1));
                 }
             }
             else
             {
                 return make_naive_tensor_descriptor_aligned(
                     make_tuple(Number<1>{}, Number<K0PerBlock>{}, Number<MPerBlock>{}, K1),
                     max_lds_align);
             }
         }();
  
         return a_block_desc_b_k0_m_k1;
     }
  
     __host__ __device__ static constexpr auto GetBBlockDescriptor_K0PerBlock_NPerBlock_K1()
     {
         constexpr auto max_lds_align = K1;
  
         // B matrix in LDS memory, dst of blockwise copy
         constexpr auto b_block_desc_k0_n_k1 = [&]() {
             if constexpr(BBlockLdsExtraN)
             {
                 if constexpr(BBlockLdsExtraN1Wrw)
                 {
                     constexpr auto b_block_desc_k0_n0_n1_k1 = make_naive_tensor_descriptor(
                         make_tuple(
                             Number<K0PerBlock>{}, Number<N0PerBlock>{}, Number<N1PerBlock>{}, K1),
                         make_tuple(Number<N0PerBlock>{} * (Number<N1PerBlock>{} * K1 + N1Padding),
                                    Number<N1PerBlock>{} * K1 + N1Padding,
                                    K1,
                                    I1));
  
                     constexpr auto b_block_desc_k0_n_k1_tmp = transform_tensor_descriptor(
                         b_block_desc_k0_n0_n1_k1,
                         make_tuple(make_pass_through_transform(Number<K0PerBlock>{}),
                                    make_merge_transform_v3_division_mod(
                                        make_tuple(Number<N0PerBlock>{}, Number<N1PerBlock>{})),
                                    make_pass_through_transform(K1)),
                         make_tuple(Sequence<0>{}, Sequence<1, 2>{}, Sequence<3>{}),
                         make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}));
  
                     return b_block_desc_k0_n_k1_tmp;
                 }
                 else
                 {
                     return make_naive_tensor_descriptor(
                         make_tuple(Number<K0PerBlock>{}, Number<NPerBlock>{}, K1),
                         make_tuple(Number<NPerBlock + 1>{} * K1, K1, I1));
                 }
             }
             else
             {
                 return make_naive_tensor_descriptor_aligned(
                     make_tuple(Number<K0PerBlock>{}, Number<NPerBlock>{}, K1), max_lds_align);
             }
         }();
  
         return b_block_desc_k0_n_k1;
     }
  
     __host__ __device__ static constexpr auto GetBBlockDescriptor_Batch_K0PerBlock_NPerBlock_K1()
     {
         constexpr auto max_lds_align = K1;
  
         // B matrix in LDS memory, dst of blockwise copy
         constexpr auto b_block_desc_b_k0_n_k1 = [&]() {
             if constexpr(BBlockLdsExtraN)
             {
                 if constexpr(BBlockLdsExtraN1Wrw)
                 {
                     constexpr auto b_block_desc_b_k0_n0_n1_k1 = make_naive_tensor_descriptor(
                         make_tuple(Number<1>{},
                                    Number<K0PerBlock>{},
                                    Number<N0PerBlock>{},
                                    Number<N1PerBlock>{},
                                    K1),
                         make_tuple(Number<K0PerBlock>{} * Number<N0PerBlock>{} *
                                        (Number<N1PerBlock>{} * K1 + N1Padding),
                                    Number<N0PerBlock>{} * (Number<N1PerBlock>{} * K1 + N1Padding),
                                    Number<N1PerBlock>{} * K1 + N1Padding,
                                    K1,
                                    I1));
  
                     constexpr auto b_block_desc_b_k0_n_k1_tmp = transform_tensor_descriptor(
                         b_block_desc_b_k0_n0_n1_k1,
                         make_tuple(make_pass_through_transform(Number<1>{}),
                                    make_pass_through_transform(Number<K0PerBlock>{}),
                                    make_merge_transform_v4_no_carry(
                                        make_tuple(Number<N0PerBlock>{}, Number<N1PerBlock>{})),
                                    make_pass_through_transform(K1)),
                         make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2, 3>{}, Sequence<4>{}),
                         make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}));
  
                     return b_block_desc_b_k0_n_k1_tmp;
                 }
                 else
                 {
                     return make_naive_tensor_descriptor(
                         make_tuple(Number<1>{}, Number<K0PerBlock>{}, Number<NPerBlock>{}, K1),
                         make_tuple(Number<K0PerBlock>{} * Number<NPerBlock + 1>{} * K1,
                                    Number<NPerBlock + 1>{} * K1,
                                    K1,
                                    I1));
                 }
             }
             else
             {
                 return make_naive_tensor_descriptor_aligned(
                     make_tuple(Number<1>{}, Number<K0PerBlock>{}, Number<NPerBlock>{}, K1),
                     max_lds_align);
             }
         }();
  
         return b_block_desc_b_k0_n_k1;
     }
  
     __host__ __device__ static constexpr index_t GetSharedMemoryNumberOfByte()
     {
         constexpr auto max_lds_align = K1;
  
         // A matrix in LDS memory, dst of blockwise copy
         constexpr auto a_b_k0_m_k1_block_desc = GetABlockDescriptor_Batch_K0PerBlock_MPerBlock_K1();
  
         // B matrix in LDS memory, dst of blockwise copy
         constexpr auto b_b_k0_n_k1_block_desc = GetBBlockDescriptor_Batch_K0PerBlock_NPerBlock_K1();
  
         // LDS allocation for A and B: be careful of alignment
         constexpr auto a_block_space_size = math::integer_least_multiple(
             a_b_k0_m_k1_block_desc.GetElementSpaceSize(), max_lds_align);
  
         constexpr auto b_block_space_size = math::integer_least_multiple(
             b_b_k0_n_k1_block_desc.GetElementSpaceSize(), max_lds_align);
  
         constexpr auto c_block_size =
             GetCBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock().GetElementSpaceSize();
  
         return math::max((a_block_space_size * sizeof(FloatAAdjusted) +
                           b_block_space_size * sizeof(FloatBAdjusted)),
                          c_block_size * sizeof(FloatC));
     }
  
     // block_id to matrix tile idx (m0, n0) mapping are controlled by {M01, N01}
     template <typename Block2CTileMap>
     __host__ __device__ static constexpr bool
     CheckValidity(const AGridDesc_B_K0_M_K1& a_b_k0_m_k1_grid_desc,
                   const BGridDesc_B_K0_N_K1& b_b_k0_n_k1_grid_desc,
                   const CMNGridDesc& c_m_n_grid_desc,
                   const Block2CTileMap& block_2_ctile_map)
     {
         static_assert(is_known_at_compile_time<remove_cv_t<decltype(K1)>>::value,
                       "wrong! K1 need to be known at compile-time");
  
         static_assert((MPerBlock % (MPerXDL * MRepeat) == 0) &&
                           (NPerBlock % (NRepeat * NPerXDL)) == 0,
                       "Invalid tuning param!");
  
         const auto M      = a_b_k0_m_k1_grid_desc.GetLength(I2);
         const auto N      = b_b_k0_n_k1_grid_desc.GetLength(I2);
         const auto K0     = a_b_k0_m_k1_grid_desc.GetLength(I1);
         const auto KBatch = a_b_k0_m_k1_grid_desc.GetLength(I0);
  
         // check gridwise gemm pipeline
         const auto num_k_loop = K0 / K0PerBlock;
  
         if(!GridwiseGemmPipe::IsSupported(num_k_loop))
         {
             return false;
         }
  
         if(!(M == c_m_n_grid_desc.GetLength(I0) && N == c_m_n_grid_desc.GetLength(I1) &&
              K0 == b_b_k0_n_k1_grid_desc.GetLength(I1) &&
              K1 == a_b_k0_m_k1_grid_desc.GetLength(I3) &&
              K1 == b_b_k0_n_k1_grid_desc.GetLength(I3) &&
              KBatch == b_b_k0_n_k1_grid_desc.GetLength(I0)))
             return false;
  
         if(!(M % MPerBlock == 0 && N % NPerBlock == 0 && K0 % K0PerBlock == 0))
             return false;
  
         if(!block_2_ctile_map.CheckValidity(c_m_n_grid_desc))
         {
             return false;
         }
  
         // TODO: also check validity of all components (blockwise-copy, threadwise-copy, etc)
         return true;
     }
  
     __host__ __device__ static constexpr bool CalculateHasMainK0BlockLoop(index_t K0)
     {
         // const bool has_main_k0_block_loop = K0 > K0PerBlock;
         const index_t num_loop = K0 / K0PerBlock;
  
         return GridwiseGemmPipe::CalculateHasMainLoop(num_loop);
  
         // return has_main_k0_block_loop;
     }
  
     __host__ __device__ static constexpr auto
     MakeCGridDesc_MBlock_MPerBlock_NBlock_NPerBlock(const CMNGridDesc& c_m_n_grid_desc)
     {
         const auto M = c_m_n_grid_desc.GetLength(I0);
         const auto N = c_m_n_grid_desc.GetLength(I1);
  
         const auto MBlock = M / MPerBlock;
         const auto NBlock = N / NPerBlock;
  
         return transform_tensor_descriptor(
             c_m_n_grid_desc,
             make_tuple(make_unmerge_transform(make_tuple(MBlock, Number<MPerBlock>{})),
                        make_unmerge_transform(make_tuple(NBlock, Number<NPerBlock>{}))),
             make_tuple(Sequence<0>{}, Sequence<1>{}),
             make_tuple(Sequence<0, 1>{}, Sequence<2, 3>{}));
     }
  
     // return block_id to C matrix tile idx (m0, n0) mapping
     __host__ __device__ static constexpr auto MakeCBlockClusterAdaptor(
         const CMNGridDesc& c_m_n_grid_desc, index_t M01, index_t N01, index_t KBatch)
     {
         return BlockToCTileMap_KSplit_M00_N00_M01_N01<MPerBlock, NPerBlock, CMNGridDesc>(
             c_m_n_grid_desc, M01, N01, KBatch);
     }
  
     __host__ __device__ static constexpr auto
     GetCBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock()
     {
         constexpr index_t MWave = MPerBlock / (MRepeat * MPerXDL);
         constexpr index_t NWave = NPerBlock / (NRepeat * NPerXDL);
  
         return make_naive_tensor_descriptor_packed(
             make_tuple(I1,
                        Number<CShuffleMRepeatPerShuffle * MWave * MPerXDL>{},
                        I1,
                        Number<CShuffleNRepeatPerShuffle * NWave * NPerXDL>{}));
     }
  
     using CGridDesc_MBlock_MPerBlock_NBlock_NPerBlock =
         decltype(MakeCGridDesc_MBlock_MPerBlock_NBlock_NPerBlock(CMNGridDesc{}));
     using CBlockClusterAdaptor = decltype(MakeCBlockClusterAdaptor(CMNGridDesc{}, 1, 1, 1));
  
     template <bool HasMainKBlockLoop>
     __device__ static void Run(const FloatA* __restrict__ p_a_grid,
                                const FloatB* __restrict__ p_b_grid,
                                FloatC* __restrict__ p_c_grid,
                                void* __restrict__ p_shared,
                                const AGridDesc_B_K0_M_K1& a_b_k0_m_k1_grid_desc,
                                const BGridDesc_B_K0_N_K1& b_b_k0_n_k1_grid_desc,
                                const CGridDesc_MBlock_MPerBlock_NBlock_NPerBlock&
                                    c_grid_desc_mblock_mperblock_nblock_nperblock,
                                const AElementwiseOperation& a_element_op,
                                const BElementwiseOperation& b_element_op,
                                const CElementwiseOperation& c_element_op,
                                const CBlockClusterAdaptor& c_block_cluster_adaptor)
     {
         const auto a_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
             p_a_grid, a_b_k0_m_k1_grid_desc.GetElementSpaceSize());
         const auto b_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
             p_b_grid, b_b_k0_n_k1_grid_desc.GetElementSpaceSize());
         auto c_grid_buf = make_dynamic_buffer<AddressSpaceEnum::Global>(
             p_c_grid, c_grid_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize());
  
         const auto K0 = a_b_k0_m_k1_grid_desc.GetLength(I1);
  
         // divide block work by [M, N]
         const auto block_work_idx =
             c_block_cluster_adaptor.CalculateBottomIndex(make_multi_index(get_block_1d_id()));
  
         const index_t k_batch_id = block_work_idx[I0];
  
         if(!c_block_cluster_adaptor.ValidCTileIndex(
                make_tuple(block_work_idx[I1], block_work_idx[I2]),
                make_tuple(c_grid_desc_mblock_mperblock_nblock_nperblock.GetLength(I0),
                           c_grid_desc_mblock_mperblock_nblock_nperblock.GetLength(I2))))
         {
             return;
         }
  
         // HACK: this force m/n_block_data_idx_on_grid into SGPR
         const index_t m_block_data_idx_on_grid =
             __builtin_amdgcn_readfirstlane(block_work_idx[I1] * MPerBlock);
  
         const index_t n_block_data_idx_on_grid =
             __builtin_amdgcn_readfirstlane(block_work_idx[I2] * NPerBlock);
  
         // lds max alignment
         constexpr auto max_lds_align = K1;
  
         // A matrix in LDS memory, dst of blockwise copy
         constexpr auto a_k0_m_k1_block_desc = GetABlockDescriptor_K0PerBlock_MPerBlock_K1();
  
         constexpr auto a_b_k0_m_k1_block_desc = GetABlockDescriptor_Batch_K0PerBlock_MPerBlock_K1();
         // B matrix in LDS memory, dst of blockwise copy
         constexpr auto b_k0_n_k1_block_desc = GetBBlockDescriptor_K0PerBlock_NPerBlock_K1();
  
         constexpr auto b_b_k0_n_k1_block_desc = GetBBlockDescriptor_Batch_K0PerBlock_NPerBlock_K1();
         // A matrix blockwise copy
         auto a_blockwise_copy =
             ThreadGroupTensorSliceTransfer_v4r1<ThisThreadBlock,
                                                 AElementwiseOperation,
                                                 ck::tensor_operation::element_wise::PassThrough,
                                                 InMemoryDataOperationEnum::Set,
                                                 Sequence<1, K0PerBlock, MPerBlock, K1>,
                                                 ABlockTransferThreadClusterLengths_K0_M_K1,
                                                 ABlockTransferThreadClusterArrangeOrder,
                                                 FloatA,
                                                 FloatAAdjusted,
                                                 decltype(a_b_k0_m_k1_grid_desc),
                                                 decltype(a_b_k0_m_k1_block_desc),
                                                 ABlockTransferSrcAccessOrder,
                                                 Sequence<0, 2, 1, 3>,
                                                 ABlockTransferSrcVectorDim,
                                                 3,
                                                 ABlockTransferSrcScalarPerVector,
                                                 ABlockTransferDstScalarPerVector_K1,
                                                 1,
                                                 1,
                                                 AThreadTransferSrcResetCoordinateAfterRun,
                                                 true>(
                 a_b_k0_m_k1_grid_desc,
                 make_multi_index(k_batch_id, 0, m_block_data_idx_on_grid, 0),
                 a_element_op,
                 a_b_k0_m_k1_block_desc,
                 make_multi_index(0, 0, 0, 0),
                 ck::tensor_operation::element_wise::PassThrough{});
  
         // B matrix blockwise copy
         auto b_blockwise_copy =
             ThreadGroupTensorSliceTransfer_v4r1<ThisThreadBlock,
                                                 BElementwiseOperation,
                                                 ck::tensor_operation::element_wise::PassThrough,
                                                 InMemoryDataOperationEnum::Set,
                                                 Sequence<1, K0PerBlock, NPerBlock, K1>,
                                                 BBlockTransferThreadClusterLengths_K0_N_K1,
                                                 BBlockTransferThreadClusterArrangeOrder,
                                                 FloatB,
                                                 FloatBAdjusted,
                                                 decltype(b_b_k0_n_k1_grid_desc),
                                                 decltype(b_b_k0_n_k1_block_desc),
                                                 BBlockTransferSrcAccessOrder,
                                                 Sequence<0, 2, 1, 3>,
                                                 BBlockTransferSrcVectorDim,
                                                 3,
                                                 BBlockTransferSrcScalarPerVector,
                                                 BBlockTransferDstScalarPerVector_K1,
                                                 1,
                                                 1,
                                                 BThreadTransferSrcResetCoordinateAfterRun,
                                                 true>(
                 b_b_k0_n_k1_grid_desc,
                 make_multi_index(k_batch_id, 0, n_block_data_idx_on_grid, 0),
                 b_element_op,
                 b_b_k0_n_k1_block_desc,
                 make_multi_index(0, 0, 0, 0),
                 ck::tensor_operation::element_wise::PassThrough{});
  
         // GEMM definition
         //   c_mtx += transpose(a_mtx) * b_mtx
         //     a_mtx[K0PerBlock, MPerBlock] is in LDS
         //     b_mtx[K0PerBlock, NPerBlock] is in LDS
         //     c_mtx[MPerBlock, NPerBlock] is distributed among threads, and saved in
         //       register
         // sanity check
         constexpr bool is_single_rate_mfma =
             (((is_same<FloatAAdjusted, half_t>::value || is_same<FloatAAdjusted, bhalf_t>::value) &&
               K1 <= 4) ||
              (is_same<FloatAAdjusted, int8_t>::value && K1 <= 8) ||
              ((is_same<FloatAAdjusted, f8_t>::value || is_same<FloatAAdjusted, bf8_t>::value) &&
               K1 < 32))
                 ? true
                 : false;
         constexpr auto is_scale_mfma = false;
         constexpr index_t KPack      = math::max(K1,
                                             MfmaSelector<FloatAAdjusted,
                                                               MPerXDL,
                                                               NPerXDL,
                                                               FloatBAdjusted,
                                                               is_single_rate_mfma,
                                                               is_scale_mfma>::selected_mfma.k_per_blk);
  
         auto blockwise_gemm =
             BlockwiseGemmXdlops_k0mk1_k0nk1_m0n0m1n1m2m3m4n2_v1<BlockSize,
                                                                 FloatAAdjusted,
                                                                 FloatBAdjusted,
                                                                 FloatAcc,
                                                                 decltype(a_k0_m_k1_block_desc),
                                                                 decltype(b_k0_n_k1_block_desc),
                                                                 MPerXDL,
                                                                 NPerXDL,
                                                                 MRepeat,
                                                                 NRepeat,
                                                                 KPack>{};
  
         auto c_thread_buf = blockwise_gemm.GetCThreadBuffer();
  
         // LDS allocation for A and B: be careful of alignment
         constexpr auto a_block_space_size =
             math::integer_least_multiple(a_k0_m_k1_block_desc.GetElementSpaceSize(), max_lds_align);
  
         constexpr auto a_block_slice_copy_step = make_multi_index(0, K0PerBlock, 0, 0);
         constexpr auto b_block_slice_copy_step = make_multi_index(0, K0PerBlock, 0, 0);
  
         auto a_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
             static_cast<FloatAAdjusted*>(p_shared), a_k0_m_k1_block_desc.GetElementSpaceSize());
  
         auto b_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
             static_cast<FloatBAdjusted*>(p_shared) + a_block_space_size,
             b_k0_n_k1_block_desc.GetElementSpaceSize());
  
         // gridwise GEMM pipeline
         const index_t K0BlockMainLoop = __builtin_amdgcn_readfirstlane(K0 / K0PerBlock);
  
         GridwiseGemmPipe::template Run<HasMainKBlockLoop>(a_b_k0_m_k1_grid_desc,
                                                           a_b_k0_m_k1_block_desc,
                                                           a_blockwise_copy,
                                                           a_grid_buf,
                                                           a_block_buf,
                                                           a_block_slice_copy_step,
                                                           b_b_k0_n_k1_grid_desc,
                                                           b_b_k0_n_k1_block_desc,
                                                           b_blockwise_copy,
                                                           b_grid_buf,
                                                           b_block_buf,
                                                           b_block_slice_copy_step,
                                                           blockwise_gemm,
                                                           c_thread_buf,
                                                           K0BlockMainLoop);
  
         // output: register to global memory
         {
             constexpr index_t MWave = MPerBlock / (MRepeat * MPerXDL);
             constexpr index_t NWave = NPerBlock / (NRepeat * NPerXDL);
  
             constexpr auto c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc =
                 blockwise_gemm.GetCBlockDescriptor_M0_N0_M1_N1_M2_M3_M4_N2();
  
             constexpr auto c_m0_n0_m1_n1_m2_m3_m4_n2_thread_desc =
                 blockwise_gemm.GetCThreadDescriptor_M0_N0_M1_N1_M2_M3_M4_N2();
  
             constexpr auto M0 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I0);
             constexpr auto N0 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I1);
             constexpr auto M1 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I2);
             constexpr auto N1 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I3);
             constexpr auto M2 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I4);
             constexpr auto M3 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I5);
             constexpr auto M4 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I6);
             constexpr auto N2 = c_m0_n0_m1_n1_m2_m3_m4_n2_block_desc.GetLength(I7);
  
             constexpr auto c_block_desc_mblock_mperblock_nblock_nperblock =
                 GetCBlockDescriptor_MBlock_MPerBlock_NBlock_NPerBlock();
  
             auto c_block_buf = make_dynamic_buffer<AddressSpaceEnum::Lds>(
                 static_cast<FloatC*>(p_shared),
                 c_block_desc_mblock_mperblock_nblock_nperblock.GetElementSpaceSize());
  
             static_assert(M1 == MWave, "");
             static_assert(N1 == NWave, "");
             static_assert(M2 * M3 * M4 == MPerXDL, "");
             static_assert(N2 == NPerXDL, "");
  
             constexpr auto c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2 = transform_tensor_descriptor(
                 c_block_desc_mblock_mperblock_nblock_nperblock,
                 make_tuple(
                     make_freeze_transform(I0), // freeze mblock
                     make_unmerge_transform(make_tuple(CShuffleMRepeatPerShuffle,
                                                       M1,
                                                       M2,
                                                       M3,
                                                       M4)), // M1 = MWave, M2 * M3 * M4 = MPerXDL
                     make_freeze_transform(I0),              // freeze nblock
                     make_unmerge_transform(make_tuple(CShuffleNRepeatPerShuffle,
                                                       N1,
                                                       N2))), // M1 = MWave, M2 * M3 * M4 = MPerXDL
                 make_tuple(Sequence<0>{}, Sequence<1>{}, Sequence<2>{}, Sequence<3>{}),
                 make_tuple(
                     Sequence<>{}, Sequence<0, 2, 4, 5, 6>{}, Sequence<>{}, Sequence<1, 3, 7>{}));
  
             // calculate origin of thread output tensor on global memory
             //     blockwise GEMM c matrix starting index
             const auto c_thread_mtx_on_block =
                 blockwise_gemm.CalculateCThreadOriginDataIndex(I0, I0, I0, I0);
  
             const index_t m_thread_data_on_block = c_thread_mtx_on_block[I0];
             const index_t n_thread_data_on_block = c_thread_mtx_on_block[I1];
  
             const auto m_thread_data_on_block_to_m0_m1_m2_m3_m4_adaptor =
                 make_single_stage_tensor_adaptor(
                     make_tuple(make_merge_transform(make_tuple(M0, M1, M2, M3, M4))),
                     make_tuple(Sequence<0, 1, 2, 3, 4>{}),
                     make_tuple(Sequence<0>{}));
  
             const auto m_thread_data_on_block_idx =
                 m_thread_data_on_block_to_m0_m1_m2_m3_m4_adaptor.CalculateBottomIndex(
                     make_multi_index(m_thread_data_on_block));
  
             const auto n_thread_data_on_block_to_n0_n1_n2_adaptor =
                 make_single_stage_tensor_adaptor(
                     make_tuple(make_merge_transform(make_tuple(N0, N1, N2))),
                     make_tuple(Sequence<0, 1, 2>{}),
                     make_tuple(Sequence<0>{}));
  
             const auto n_thread_data_on_block_idx =
                 n_thread_data_on_block_to_n0_n1_n2_adaptor.CalculateBottomIndex(
                     make_multi_index(n_thread_data_on_block));
  
             // VGPR to LDS
             auto c_thread_copy_vgpr_to_lds =
                 ThreadwiseTensorSliceTransfer_v1r3<FloatAcc,
                                                    FloatC,
                                                    decltype(c_m0_n0_m1_n1_m2_m3_m4_n2_thread_desc),
                                                    decltype(c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2),
                                                    ck::tensor_operation::element_wise::PassThrough,
                                                    Sequence<CShuffleMRepeatPerShuffle,
                                                             CShuffleNRepeatPerShuffle,
                                                             I1,
                                                             I1,
                                                             M2,
                                                             I1,
                                                             M4,
                                                             I1>,
                                                    Sequence<0, 1, 2, 3, 4, 5, 6, 7>,
                                                    7,
                                                    1,
                                                    InMemoryDataOperationEnum::Set,
                                                    1,
                                                    true>{
                     c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2,
                     make_multi_index(0,
                                      0,
                                      m_thread_data_on_block_idx[I1],
                                      n_thread_data_on_block_idx[I1],
                                      m_thread_data_on_block_idx[I2],
                                      m_thread_data_on_block_idx[I3],
                                      m_thread_data_on_block_idx[I4],
                                      n_thread_data_on_block_idx[I2]),
                     ck::tensor_operation::element_wise::PassThrough{}};
  
             // LDS to global
             auto c_block_copy_lds_to_global = ThreadGroupTensorSliceTransfer_v6r1<
                 ThisThreadBlock,            // index_t BlockSize,
                 CElementwiseOperation,      // ElementwiseOperation,
                 CGlobalMemoryDataOperation, // DstInMemOp,
                 Sequence<1,
                          CShuffleMRepeatPerShuffle * MWave * MPerXDL,
                          1,
                          CShuffleNRepeatPerShuffle * NWave * NPerXDL>, // BlockSliceLengths,
                 CBlockTransferClusterLengths_MBlock_MPerBlock_NBlock_NPerBlock,
                 Sequence<0, 1, 2, 3>, // typename ThreadClusterArrangeOrder,
                 FloatC,               // typename SrcData,
                 FloatC,               // typename DstData,
                 decltype(c_block_desc_mblock_mperblock_nblock_nperblock),
                 decltype(c_grid_desc_mblock_mperblock_nblock_nperblock),
                 Sequence<0, 1, 2, 3>,                       // typename DimAccessOrder,
                 3,                                          // index_t VectorDim,
                 CBlockTransferScalarPerVector_NWaveNPerXDL, // index_t ScalarPerVector,
                 true,  // bool ThreadTransferSrcResetCoordinateAfterRun,
                 false> // bool ThreadTransferDstResetCoordinateAfterRun
                 {c_block_desc_mblock_mperblock_nblock_nperblock,
                  make_multi_index(0, 0, 0, 0),
                  c_grid_desc_mblock_mperblock_nblock_nperblock,
                  make_multi_index(block_work_idx[I1], 0, block_work_idx[I2], 0),
                  c_element_op};
  
             constexpr auto mxdlperwave_forward_step =
                 make_multi_index(0, CShuffleMRepeatPerShuffle * MWave * MPerXDL, 0, 0);
             constexpr auto nxdlperwave_forward_step =
                 make_multi_index(0, 0, 0, CShuffleNRepeatPerShuffle * NWave * NPerXDL);
             constexpr auto nxdlperwave_backward_step =
                 make_multi_index(0, 0, 0, -CShuffleNRepeatPerShuffle * NWave * NPerXDL);
  
             static_for<0, MRepeat, CShuffleMRepeatPerShuffle>{}([&](auto mxdlperwave_iter) {
                 constexpr auto mxdlperwave = mxdlperwave_iter;
  
                 static_for<0, NRepeat, CShuffleNRepeatPerShuffle>{}([&](auto nxdlperwave_iter) {
                     constexpr bool nxdlperwave_forward_sweep =
                         (mxdlperwave % (2 * CShuffleMRepeatPerShuffle) == 0);
  
                     constexpr index_t nxdlperwave_value =
                         nxdlperwave_forward_sweep
                             ? nxdlperwave_iter
                             : (NRepeat - nxdlperwave_iter - CShuffleNRepeatPerShuffle);
  
                     constexpr auto nxdlperwave = Number<nxdlperwave_value>{};
  
                     // make sure it's safe to do ds_write
                     block_sync_lds();
  
                     // VGPR to LDS
                     c_thread_copy_vgpr_to_lds.Run(
                         c_m0_n0_m1_n1_m2_m3_m4_n2_thread_desc,
                         make_tuple(mxdlperwave, nxdlperwave, I0, I0, I0, I0, I0, I0),
                         c_thread_buf,
                         c_block_desc_m0_n0_m1_n1_m2_m3_m4_n2,
                         c_block_buf);
  
                     // make sure it's safe to do ds_read
                     block_sync_lds();
  
                     // LDS to global
                     c_block_copy_lds_to_global.Run(c_block_desc_mblock_mperblock_nblock_nperblock,
                                                    c_block_buf,
                                                    c_grid_desc_mblock_mperblock_nblock_nperblock,
                                                    c_grid_buf);
  
                     // move on nxdlperwave dimension
                     if constexpr(nxdlperwave_forward_sweep &&
                                  (nxdlperwave < NRepeat - CShuffleNRepeatPerShuffle))
                     {
                         c_block_copy_lds_to_global.MoveDstSliceWindow(
                             c_grid_desc_mblock_mperblock_nblock_nperblock,
                             nxdlperwave_forward_step);
                     }
                     else if constexpr((!nxdlperwave_forward_sweep) && (nxdlperwave > 0))
                     {
                         c_block_copy_lds_to_global.MoveDstSliceWindow(
                             c_grid_desc_mblock_mperblock_nblock_nperblock,
                             nxdlperwave_backward_step);
                     }
                 });
  
                 // move on mxdlperwave dimension
                 if constexpr(mxdlperwave < MRepeat - CShuffleMRepeatPerShuffle)
                 {
                     c_block_copy_lds_to_global.MoveDstSliceWindow(
                         c_grid_desc_mblock_mperblock_nblock_nperblock, mxdlperwave_forward_step);
                 }
             });
         }
     }
 }; // namespace ck
  
 } // namespace ck