/home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-composable-kernel/checkouts/docs-6.4.3/include/ck/tensor_operation/gpu/warp/xdlops_gemm.hpp Source File

/home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-composable-kernel/checkouts/docs-6.4.3/include/ck/tensor_operation/gpu/warp/xdlops_gemm.hpp Source File#

Composable Kernel: /home/docs/checkouts/readthedocs.org/user_builds/advanced-micro-devices-composable-kernel/checkouts/docs-6.4.3/include/ck/tensor_operation/gpu/warp/xdlops_gemm.hpp Source File
Go to the documentation of this file.
 // 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/utility/math.hpp"
 #include "ck/utility/amd_xdlops.hpp"
  
 namespace ck {
  
 enum struct MfmaInstr
 {
     mfma_f32_32x32x1xf32 = 0,
     mfma_f32_16x16x1xf32,
     mfma_f32_4x4x1xf32,
     mfma_f32_32x32x2xf32,
     mfma_f32_16x16x4xf32,
     mfma_f32_32x32x4f16,
     mfma_f32_16x16x4f16,
     mfma_f32_4x4x4f16,
     mfma_f32_32x32x8f16,
     mfma_f32_16x16x16f16,
     mfma_f32_32x32x8bf16_1k,
     mfma_f32_16x16x16bf16_1k,
     mfma_f32_32x32x4bf16,
     mfma_f32_16x16x8bf16,
     mfma_i32_32x32x8i8,
     mfma_i32_16x16x16i8,
     mfma_i32_32x32x16i8,
     mfma_i32_16x16x32i8,
     mfma_f64_16x16x4f64,
     mfma_f32_32x32x16f8f8,
     mfma_f32_16x16x32f8f8,
     mfma_f32_32x32x16bf8bf8,
     mfma_f32_16x16x32bf8bf8,
     mfma_f32_32x32x16f8bf8,
     mfma_f32_16x16x32f8bf8,
     mfma_f32_32x32x16bf8f8,
     mfma_f32_16x16x32bf8f8,
     mfma_f32_32x32x16f16,
     mfma_f32_16x16x32f16,
     mfma_f32_32x32x16bf16,
     mfma_f32_16x16x32bf16,
     mfma_i32_32x32x32i8,
     mfma_i32_16x16x64i8,
     mfma_f32_32x32x64f8f6f4,
     mfma_f32_16x16x128f8f6f4,
     mfma_scale_f32_32x32x64f8f6f4,
     mfma_scale_f32_16x16x128f8f6f4
 };
  
 template <MfmaInstr instr>
 struct mfma_type;
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x1xf32>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 2;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 1;
     static constexpr bool is_k_reduction         = false;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x1f32<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x2xf32>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 1;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x2f32<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x4xf32>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 1;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x4f32<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x1xf32>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 4;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 1;
     static constexpr bool is_k_reduction         = false;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x1f32<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 // treat 4x4x1 as a single-blk 4x64 mfma
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_4x4x1xf32>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 64;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 1;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 4;
     static constexpr index_t n_per_blk           = 64;
     static constexpr index_t k_per_blk           = 1;
     static constexpr bool is_k_reduction         = false;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_4x4x1f32<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x4f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 2;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = false;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x4f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x8f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x8f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x16f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x16f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x32f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x32f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x16f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x16f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x4f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 4;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = false;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x4f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_4x4x4f16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 64;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 1;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 4;
     static constexpr index_t n_per_blk           = 64;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = false;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_4x4x4f16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x16bf16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x16bf16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x8bf16_1k>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x8bf16_1k<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x32bf16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x32bf16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x16bf16_1k>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x16bf16_1k<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x4bf16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 2;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x4bf16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x8bf16>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 2;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x8bf16<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_i32_32x32x8i8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_i32_32x32x8i8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_i32_16x16x16i8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 4;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_i32_16x16x16i8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_i32_32x32x16i8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_i32_32x32x16i8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_i32_16x16x32i8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_i32_16x16x32i8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_i32_32x32x32i8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 16;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_i32_32x32x32i8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_i32_16x16x64i8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 16;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_i32_16x16x64i8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f64_16x16x4f64>
 {
     static constexpr index_t group_size          = 1;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 4; // group_size * num_groups_per_blk;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4; // wave_size / num_threads_per_blk;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 1;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f64_16x16x4f64<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x16f8f8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x16f8f8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x32f8f8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x32f8f8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x16bf8bf8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x16bf8bf8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x32bf8bf8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x32bf8bf8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x16f8bf8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x16f8bf8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x32f8bf8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x32f8bf8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x16bf8f8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 4;
     static constexpr index_t num_regs_per_blk    = 16;
     static constexpr index_t num_threads_per_blk = 32;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 2;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 32;
     static constexpr index_t n_per_blk           = 32;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x16bf8f8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x32bf8f8>
 {
     static constexpr index_t group_size          = 4;
     static constexpr index_t num_groups_per_blk  = 1;
     static constexpr index_t num_regs_per_blk    = 4;
     static constexpr index_t num_threads_per_blk = 16;
     static constexpr index_t wave_size           = 64;
     static constexpr index_t num_input_blks      = 4;
     static constexpr index_t num_output_blks     = 1;
     static constexpr index_t m_per_blk           = 16;
     static constexpr index_t n_per_blk           = 16;
     static constexpr index_t k_per_blk           = 8;
     static constexpr bool is_k_reduction         = true;
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x32bf8f8<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 // TODO: fix mfma...f8f6f4 instructions
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_32x32x64f8f6f4>
 {
     // clang-format off
     static constexpr index_t group_size          = 4;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_groups_per_blk  = 4;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_regs_per_blk    = 16;   // m_per_blk * n_per_blk / wave_size
     static constexpr index_t num_threads_per_blk = 32;   // n_per_blk
     static constexpr index_t wave_size           = 64;   // fixed
     static constexpr index_t num_input_blks      = 2;    // m_per_blk / num_regs_per_blk
     static constexpr index_t num_output_blks     = 1;    // (is_k_reduction == true) ???
     static constexpr index_t m_per_blk           = 32;   // from the instruction
     static constexpr index_t n_per_blk           = 32;   // from the instruction
     static constexpr index_t k_per_blk           = 32;   // (is_k_reduction == true) ? 64 / num_input_blks
     static constexpr bool is_k_reduction         = true; // ???
     // clang-format on
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_32x32x64f8f6f4<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_f32_16x16x128f8f6f4>
 {
     // clang-format off
     static constexpr index_t group_size          = 4;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_groups_per_blk  = 1;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_regs_per_blk    = 4;    // m_per_blk * n_per_blk / wave_size
     static constexpr index_t num_threads_per_blk = 16;   // == n_per_blk
     static constexpr index_t wave_size           = 64;   // fixed
     static constexpr index_t num_input_blks      = 4;    // m_per_blk / num_regs_per_blk
     static constexpr index_t num_output_blks     = 1;    // (is_k_reduction == true) ???
     static constexpr index_t m_per_blk           = 16;   // from the instruction
     static constexpr index_t n_per_blk           = 16;   // from the instruction
     static constexpr index_t k_per_blk           = 32;   // (is_k_reduction == true) ? 128 / num_input_blks
     static constexpr bool is_k_reduction         = true; // ???
     // clang-format on
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_f32_16x16x128f8f6f4<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_scale_f32_32x32x64f8f6f4>
 {
     // clang-format off
     static constexpr index_t group_size          = 4;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_groups_per_blk  = 4;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_regs_per_blk    = 16;   // m_per_blk * n_per_blk / wave_size
     static constexpr index_t num_threads_per_blk = 32;   // n_per_blk
     static constexpr index_t wave_size           = 64;   // fixed
     static constexpr index_t num_input_blks      = 2;    // m_per_blk / num_regs_per_blk
     static constexpr index_t num_output_blks     = 1;    // (is_k_reduction == true) ???
     static constexpr index_t m_per_blk           = 32;   // from the instruction
     static constexpr index_t n_per_blk           = 32;   // from the instruction
     static constexpr index_t k_per_blk           = 32;   // (is_k_reduction == true) ? 64 / num_input_blks
     static constexpr bool is_k_reduction         = true; // ???
     // clang-format on
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_scale_f32_32x32x64f8f6f4<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <>
 struct mfma_type<MfmaInstr::mfma_scale_f32_16x16x128f8f6f4>
 {
     // clang-format off
     static constexpr index_t group_size          = 4;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_groups_per_blk  = 1;    // ??? group_size * num_groups_per_blk == num_regs_per_blk
     static constexpr index_t num_regs_per_blk    = 4;    // m_per_blk * n_per_blk / wave_size
     static constexpr index_t num_threads_per_blk = 16;   // == n_per_blk
     static constexpr index_t wave_size           = 64;   // fixed
     static constexpr index_t num_input_blks      = 4;    // m_per_blk / num_regs_per_blk
     static constexpr index_t num_output_blks     = 1;    // (is_k_reduction == true) ???
     static constexpr index_t m_per_blk           = 16;   // from the instruction
     static constexpr index_t n_per_blk           = 16;   // from the instruction
     static constexpr index_t k_per_blk           = 32;   // (is_k_reduction == true) ? 128 / num_input_blks
     static constexpr bool is_k_reduction         = true; // ???
     // clang-format on
  
     template <index_t MPerXdlops, index_t NPerXdlops, class FloatA, class FloatB, class FloatC>
     __device__ void run(const FloatA& a, const FloatB& b, FloatC& reg_c) const
     {
         intrin_mfma_scale_f32_16x16x128f8f6f4<MPerXdlops, NPerXdlops>::Run(a, b, reg_c);
     }
 };
  
 template <typename base_type,
           index_t MPerXdlops,
           index_t NPerXdlops,
           typename additional_type = base_type,
           bool is_single_rate_mfma = false>
 struct MfmaSelector
 {
     template <typename base_type_,
               index_t MPerXdlops_,
               index_t NPerXdlops_,
               typename additional_type_ = base_type_,
               bool is_single_rate_mfma_ = false>
     static constexpr auto GetMfma();
  
     template <>
     constexpr auto GetMfma<double, 16, 16>()
     {
         return MfmaInstr::mfma_f64_16x16x4f64;
     }
  
     template <>
     constexpr auto GetMfma<float, 64, 64>()
     {
         return MfmaInstr::mfma_f32_32x32x1xf32;
     }
  
     template <>
     constexpr auto GetMfma<float, 32, 64>()
     {
         return MfmaInstr::mfma_f32_32x32x1xf32;
     }
  
     template <>
     constexpr auto GetMfma<float, 16, 64>()
     {
         return MfmaInstr::mfma_f32_16x16x1xf32;
     }
  
     template <>
     constexpr auto GetMfma<float, 8, 64>()
     {
         return MfmaInstr::mfma_f32_4x4x1xf32;
     }
  
     template <>
     constexpr auto GetMfma<float, 4, 64>()
     {
         return MfmaInstr::mfma_f32_4x4x1xf32;
     }
  
     template <>
     constexpr auto GetMfma<float, 32, 32>()
     {
         return MfmaInstr::mfma_f32_32x32x2xf32;
     }
  
     template <>
     constexpr auto GetMfma<float, 16, 16>()
     {
         return MfmaInstr::mfma_f32_16x16x4xf32;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 64, 64>()
     {
         return MfmaInstr::mfma_f32_32x32x4f16;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 32, 64>()
     {
         return MfmaInstr::mfma_f32_32x32x4f16;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 32, 32, half_t, false>()
     {
 #if defined(__gfx950__)
         return MfmaInstr::mfma_f32_32x32x16f16;
 #else
         return MfmaInstr::mfma_f32_32x32x8f16;
 #endif
     }
     template <>
     constexpr auto GetMfma<half_t, 32, 32, half_t, true>()
     {
         return MfmaInstr::mfma_f32_32x32x8f16;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 16, 16, half_t, false>()
     {
 #if defined(__gfx950__)
         return MfmaInstr::mfma_f32_16x16x32f16;
 #else
         return MfmaInstr::mfma_f32_16x16x16f16;
 #endif
     }
  
     template <>
     constexpr auto GetMfma<half_t, 16, 16, half_t, true>()
     {
         return MfmaInstr::mfma_f32_16x16x16f16;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 16, 64>()
     {
         return MfmaInstr::mfma_f32_16x16x4f16;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 8, 64>()
     {
         return MfmaInstr::mfma_f32_4x4x4f16;
     }
  
     template <>
     constexpr auto GetMfma<half_t, 4, 64>()
     {
         return MfmaInstr::mfma_f32_4x4x4f16;
     }
  
     template <>
     constexpr auto GetMfma<bhalf_t, 32, 32, bhalf_t, false>()
     {
 #if defined(__gfx950__)
         return MfmaInstr::mfma_f32_32x32x16bf16;
 #elif defined(CK_USE_AMD_MFMA_BF16_1K_OP)
         return MfmaInstr::mfma_f32_32x32x8bf16_1k;
 #else
         return MfmaInstr::mfma_f32_32x32x4bf16;
 #endif
     }
  
     template <>
     constexpr auto GetMfma<bhalf_t, 32, 32, bhalf_t, true>()
     {
 #if defined(CK_USE_AMD_MFMA_BF16_1K_OP)
         return MfmaInstr::mfma_f32_32x32x8bf16_1k;
 #else
         return MfmaInstr::mfma_f32_32x32x4bf16;
 #endif
     }
  
     template <>
     constexpr auto GetMfma<bhalf_t, 16, 16, bhalf_t, false>()
     {
 #if defined(__gfx950__)
         return MfmaInstr::mfma_f32_16x16x32bf16;
 #elif defined(CK_USE_AMD_MFMA_BF16_1K_OP)
         return MfmaInstr::mfma_f32_16x16x16bf16_1k;
 #else
         return MfmaInstr::mfma_f32_16x16x8bf16;
 #endif
     }
  
     template <>
     constexpr auto GetMfma<bhalf_t, 16, 16, bhalf_t, true>()
     {
 #if defined(CK_USE_AMD_MFMA_BF16_1K_OP)
         return MfmaInstr::mfma_f32_16x16x16bf16_1k;
 #else
         return MfmaInstr::mfma_f32_16x16x8bf16;
 #endif
     }
  
 #if defined(__gfx950__)
     template <>
     constexpr auto GetMfma<int8_t, 32, 32>()
     {
         return MfmaInstr::mfma_i32_32x32x32i8;
     }
     template <>
     constexpr auto GetMfma<int8_t, 16, 16>()
     {
         return MfmaInstr::mfma_i32_16x16x64i8;
     }
 #elif defined(__gfx942__)
     template <>
     constexpr auto GetMfma<int8_t, 32, 32>()
     {
         return MfmaInstr::mfma_i32_32x32x16i8;
     }
     template <>
     constexpr auto GetMfma<int8_t, 16, 16>()
     {
         return MfmaInstr::mfma_i32_16x16x32i8;
     }
 #else
     template <>
     constexpr auto GetMfma<int8_t, 32, 32>()
     {
         return MfmaInstr::mfma_i32_32x32x8i8;
     }
     template <>
     constexpr auto GetMfma<int8_t, 16, 16>()
     {
         return MfmaInstr::mfma_i32_16x16x16i8;
     }
 #endif
  
     template <>
     constexpr auto GetMfma<f8_t, 32, 32>()
     {
         return MfmaInstr::mfma_f32_32x32x16f8f8;
     }
  
     template <>
     constexpr auto GetMfma<f8_t, 16, 16>()
     {
         return MfmaInstr::mfma_f32_16x16x32f8f8;
     }
  
     template <>
     constexpr auto GetMfma<bf8_t, 32, 32>()
     {
         return MfmaInstr::mfma_f32_32x32x16bf8bf8;
     }
  
     template <>
     constexpr auto GetMfma<bf8_t, 16, 16>()
     {
         return MfmaInstr::mfma_f32_16x16x32bf8bf8;
     }
  
     template <>
     constexpr auto GetMfma<f8_t, 32, 32, bf8_t>()
     {
         return MfmaInstr::mfma_f32_32x32x16f8bf8;
     }
  
     template <>
     constexpr auto GetMfma<f8_t, 16, 16, bf8_t>()
     {
         return MfmaInstr::mfma_f32_16x16x32f8bf8;
     }
  
     template <>
     constexpr auto GetMfma<bf8_t, 32, 32, f8_t>()
     {
         return MfmaInstr::mfma_f32_32x32x16bf8f8;
     }
  
     template <>
     constexpr auto GetMfma<bf8_t, 16, 16, f8_t>()
     {
         return MfmaInstr::mfma_f32_16x16x32bf8f8;
     }
  
     static constexpr auto selected_mfma = mfma_type<
         GetMfma<base_type, MPerXdlops, NPerXdlops, additional_type, is_single_rate_mfma>()>{};
  
     __host__ __device__ constexpr MfmaSelector()
     {
         static_assert(selected_mfma.group_size * selected_mfma.num_groups_per_blk ==
                           selected_mfma.num_regs_per_blk,
                       "wrong! num_regs_per_blk");
  
         static_assert(selected_mfma.num_threads_per_blk == selected_mfma.n_per_blk,
                       "n_per_blk != num_threads_per_blk");
  
         static_assert(selected_mfma.num_regs_per_blk * selected_mfma.num_input_blks ==
                           selected_mfma.m_per_blk,
                       "m_per_blk != num_input_blks * num_regs_per_blk");
  
         static_assert(selected_mfma.num_output_blks == selected_mfma.num_input_blks ||
                           selected_mfma.num_output_blks == 1,
                       "incorrect num_output_blks");
  
         static_assert(selected_mfma.num_regs_per_blk * selected_mfma.wave_size ==
                           selected_mfma.m_per_blk * selected_mfma.n_per_blk,
                       "num_regs_per_blk incorrect");
  
         static_assert(selected_mfma.is_k_reduction ||
                           (selected_mfma.num_input_blks == selected_mfma.num_output_blks),
                       "is_k_reduction wrong!");
     }
  
     static constexpr bool IsABroadcast()
     {
         static_assert(NPerXdlops >= MPerXdlops, "only support ABroadcast");
         return true;
     }
  
     static constexpr index_t GetKPerXdlops()
     {
         return (selected_mfma.is_k_reduction ? selected_mfma.num_input_blks : 1) *
                selected_mfma.k_per_blk;
     }
  
     static constexpr index_t GetK1PerXdlops() { return selected_mfma.k_per_blk; }
 };
  
 template <typename base_type,
           index_t MPerXdlops,
           index_t NPerXdlops,
           index_t KPack,
           typename additional_type = base_type,
           bool TransposeC          = false>
 struct XdlopsGemm
 {
     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>{};
  
     using CIndex   = MultiIndex<2>;
     using CIndex4D = MultiIndex<4>;
  
     __device__ static constexpr index_t GetNumBlks() { return mfma_instr.num_output_blks; }
  
     __device__ static constexpr index_t GetNumXdlops()
     {
         return MPerXdlops * NPerXdlops /
                (mfma_instr.m_per_blk * mfma_instr.n_per_blk * mfma_instr.num_output_blks);
     }
  
     __host__ __device__ constexpr XdlopsGemm()
     {
         static_assert(NPerXdlops == 4 || NPerXdlops == 8 || NPerXdlops == 16 || NPerXdlops == 32 ||
                           NPerXdlops == 64,
                       "Only support GemmNPerXdlops == 4, 8, 16, 32 or 64 for xdlops");
  
         static_assert(MPerXdlops == 4 || MPerXdlops == 8 || MPerXdlops == 16 || MPerXdlops == 32 ||
                           MPerXdlops == 64,
                       "Only support GemmMPerXdlops == 4, 8, 16, 32 or 64 for xdlops");
  
         static_assert(KPack % mfma_instr.k_per_blk == 0, "KPack cannot be divided by k_per_blk");
     }
  
     // XDL output supporting C = A * B
     // M2_N2 -> M2_M3_M4_N2
     template <typename CDesc_M0_N0_M1_N1_M2_N2>
     __host__ __device__ static constexpr auto
     MakeCDescriptor_M0_N0_M1_N1_M2_M3_M4_N2(const CDesc_M0_N0_M1_N1_M2_N2& c_desc_m0_n0_m1_n1_m2_n2)
     {
         const auto M0 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I0);
         const auto N0 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I1);
         const auto M1 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I2);
         const auto N1 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I3);
  
         return transform_tensor_descriptor(
             c_desc_m0_n0_m1_n1_m2_n2,
             make_tuple(make_pass_through_transform(M0),
                        make_pass_through_transform(N0),
                        make_pass_through_transform(M1),
                        make_pass_through_transform(N1),
                        make_unmerge_transform(make_tuple(Number<mfma_instr.num_groups_per_blk>{},
                                                          Number<mfma_instr.num_input_blks>{},
                                                          Number<mfma_instr.group_size>{})),
                        make_pass_through_transform(Number<mfma_instr.num_threads_per_blk>{})),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
                        Sequence<3>{},
                        Sequence<4>{},
                        Sequence<5>{}),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
                        Sequence<3>{},
                        Sequence<4, 5, 6>{},
                        Sequence<7>{}));
     }
  
     // transposed XDL output supporting C' = B' * A'
     // M2_N2 -> M2_N2_N3_N4
     template <typename CDesc_M0_N0_M1_N1_M2_N2>
     __host__ __device__ static constexpr auto
     MakeCDescriptor_M0_N0_M1_N1_M2_N2_N3_N4(const CDesc_M0_N0_M1_N1_M2_N2& c_desc_m0_n0_m1_n1_m2_n2)
     {
         const auto M0 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I0);
         const auto N0 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I1);
         const auto M1 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I2);
         const auto N1 = c_desc_m0_n0_m1_n1_m2_n2.GetLength(I3);
  
         return transform_tensor_descriptor(
             c_desc_m0_n0_m1_n1_m2_n2,
             make_tuple(make_pass_through_transform(M0),
                        make_pass_through_transform(N0),
                        make_pass_through_transform(M1),
                        make_pass_through_transform(N1),
                        make_pass_through_transform(Number<mfma_instr.num_threads_per_blk>{}),
                        make_unmerge_transform(make_tuple(Number<mfma_instr.num_groups_per_blk>{},
                                                          Number<mfma_instr.num_input_blks>{},
                                                          Number<mfma_instr.group_size>{}))),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
                        Sequence<3>{},
                        Sequence<4>{},
                        Sequence<5>{}),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
                        Sequence<3>{},
                        Sequence<4>{},
                        Sequence<5, 6, 7>{}));
     }
  
     template <typename CDesc_G_M0_N0_M1_N1_M2_N2>
     __host__ __device__ static constexpr auto MakeCDescriptor_G_M0_N0_M1_N1_M2_M3_M4_N2(
         const CDesc_G_M0_N0_M1_N1_M2_N2& c_desc_g_m0_n0_m1_n1_m2_n2)
     {
         const auto G  = c_desc_g_m0_n0_m1_n1_m2_n2.GetLength(I0);
         const auto M0 = c_desc_g_m0_n0_m1_n1_m2_n2.GetLength(I1);
         const auto N0 = c_desc_g_m0_n0_m1_n1_m2_n2.GetLength(I2);
         const auto M1 = c_desc_g_m0_n0_m1_n1_m2_n2.GetLength(I3);
         const auto N1 = c_desc_g_m0_n0_m1_n1_m2_n2.GetLength(I4);
  
         return transform_tensor_descriptor(
             c_desc_g_m0_n0_m1_n1_m2_n2,
             make_tuple(make_pass_through_transform(G),
                        make_pass_through_transform(M0),
                        make_pass_through_transform(N0),
                        make_pass_through_transform(M1),
                        make_pass_through_transform(N1),
                        make_unmerge_transform(make_tuple(mfma_instr.num_groups_per_blk,
                                                          mfma_instr.num_input_blks,
                                                          mfma_instr.group_size)),
                        make_pass_through_transform(mfma_instr.num_threads_per_blk)),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
                        Sequence<3>{},
                        Sequence<4>{},
                        Sequence<5>{},
                        Sequence<6>{}),
             make_tuple(Sequence<0>{},
                        Sequence<1>{},
                        Sequence<2>{},
                        Sequence<3>{},
                        Sequence<4>{},
                        Sequence<5, 6, 7>{},
                        Sequence<8>{}));
     }
  
     __device__ static constexpr index_t GetRegSizePerXdlops()
     {
         return MPerXdlops * NPerXdlops / mfma_instr.wave_size;
     }
  
     __device__ static constexpr index_t GetWaveSize() { return mfma_instr.wave_size; }
  
     template <class FloatA, class FloatB, class FloatC>
     __device__ void Run(const FloatA& p_a_wave, const FloatB& p_b_wave, FloatC& p_c_thread) const
     {
         static_assert(
             is_same<base_type, double>::value || is_same<base_type, float>::value ||
                 is_same<base_type, half_t>::value || is_same<base_type, bhalf_t>::value ||
                 is_same<base_type, int8_t>::value || is_same<base_type, f8_t>::value ||
                 is_same<base_type, bf8_t>::value ||
                 (is_same<base_type, f8_t>::value && is_same<additional_type, bf8_t>::value) ||
                 (is_same<base_type, bf8_t>::value && is_same<additional_type, f8_t>::value),
             "base base_type must be double, float, half, bfloat16, int8_t, f8_t or bf8_t!");
  
         static_for<0, KPack / mfma_instr.k_per_blk, 1>{}([&](auto k) {
             if constexpr(!TransposeC)
             {
                 mfma_instr.template run<MPerXdlops, NPerXdlops>(
                     p_a_wave[k], p_b_wave[k], p_c_thread);
             }
             else
             {
                 mfma_instr.template run<MPerXdlops, NPerXdlops>(
                     p_b_wave[k], p_a_wave[k], p_c_thread);
             }
         });
     }
  
     __device__ static auto GetLaneId() { return get_thread_local_1d_id() % mfma_instr.wave_size; }
  
     __device__ static auto GetBlkIdx()
     {
         const auto laneId = GetLaneId();
  
         constexpr auto threadidx_to_blk_idx_adaptor = make_single_stage_tensor_adaptor(
             make_tuple(make_merge_transform(
                 make_tuple(1, mfma_instr.num_input_blks, mfma_instr.num_threads_per_blk))),
             make_tuple(Sequence<0, 1, 2>{}),
             make_tuple(Sequence<0>{}));
  
         const auto blk_idx =
             threadidx_to_blk_idx_adaptor.CalculateBottomIndex(make_multi_index(laneId));
  
         const auto blk_id = blk_idx[I1];
         const auto blk_td = blk_idx[I2];
  
         return make_tuple(blk_id, blk_td);
     }
  
     __host__ __device__ static auto CalculateAThreadOriginDataIndex()
     {
         const auto laneId  = GetLaneId();
         const auto blk_idx = GetBlkIdx();
  
         const auto blk_id = blk_idx[I0];
         const auto blk_td = blk_idx[I1];
  
         if constexpr(mfma_instr.is_k_reduction)
         {
             return make_tuple(blk_id, blk_td);
         }
         else
         {
             return make_tuple(0, laneId);
         }
     }
  
     __host__ __device__ static auto CalculateBThreadOriginDataIndex()
     {
         const auto laneId  = GetLaneId();
         const auto blk_idx = GetBlkIdx();
  
         const auto blk_id = blk_idx[I0];
         const auto blk_td = blk_idx[I1];
  
         if constexpr(mfma_instr.is_k_reduction)
         {
             return make_tuple(blk_id, blk_td);
         }
         else
         {
             return make_tuple(0, laneId);
         }
     }
  
     __device__ static CIndex GetBeginOfThreadBlk(index_t xdlops_i, index_t blk_i)
     {
         const auto blk_idx = GetBlkIdx();
  
         const auto blk_id = blk_idx[I0];
         const auto blk_td = blk_idx[I1];
  
         index_t n_offset = blk_i * mfma_instr.n_per_blk + blk_td;
         index_t m_offset = xdlops_i * mfma_instr.m_per_blk + blk_id * mfma_instr.group_size;
  
         return TransposeC ? CIndex{n_offset, m_offset} : CIndex{m_offset, n_offset};
     }
  
     __device__ static CIndex4D GetBeginOfThreadBlk4D(index_t /* xdlops_i */, index_t /* blk_i */)
     {
         const auto blk_idx = GetBlkIdx();
  
         const auto blk_id = blk_idx[I0];
         const auto blk_td = blk_idx[I1];
  
         return TransposeC ? CIndex4D{blk_td, I0, blk_id, I0} : CIndex4D{I0, blk_id, I0, blk_td};
     }
  
     // Falls back to single rate instruction on gfx950 if KPack <= 4; no change on gfx942-
     static constexpr auto
         mfma = MfmaSelector < base_type,
         MPerXdlops, NPerXdlops, additional_type,
         ((is_same<base_type, half_t>::value || is_same<base_type, bhalf_t>::value) && KPack <= 4)
             ? true
             : false > {};
  
     static constexpr auto mfma_instr = mfma.selected_mfma;
  
     static constexpr auto KPerXdlops  = mfma.GetKPerXdlops();
     static constexpr auto K1PerXdlops = mfma.GetK1PerXdlops();
     static constexpr auto K0PerXdlops = KPerXdlops / K1PerXdlops;
  
     __host__ __device__ static constexpr auto GetCM0M1M2NThreadBlkLengths()
     {
         return make_tuple(
             Number<mfma_instr.num_groups_per_blk>{}, I1, Number<mfma_instr.group_size>{}, I1);
     }
 };
  
 } // namespace ck