/*
 * Copyright (c) 2020-2023, NVIDIA CORPORATION.  All rights reserved.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
#pragma once

#include "src/turbomind/kernels/decoder_masked_multihead_attention.h"
#include "src/turbomind/kernels/decoder_masked_multihead_attention_utils.h"
#include "src/turbomind/macro.h"
#include "src/turbomind/utils/cuda_type_utils.cuh"
#include <assert.h>
#include <float.h>
#include <type_traits>

// #define MMHA_USE_HMMA_FOR_REDUCTION

// Below are knobs to extend FP32 accumulation for higher FP16 accuracy

// Does not seem to affect the accuracy that much
// #define MMHA_USE_FP32_ACUM_FOR_FMA

// Seems to slightly improve the accuracy
#define MMHA_USE_FP32_ACUM_FOR_OUT

#if 0 && defined(MMHA_USE_FP32_ACUM_FOR_OUT)
 // Does not seem to improve the accuracy
 //#define MMHA_USE_FP32_ACUM_FOR_LOGITS
#endif

namespace mmha {

////////////////////////////////////////////////////////////////////////////////////////////////////

//
// We use the following terminology to describe the different dimensions.
//
// B:  Batch size (number of sequences),
// L:  Sequence length,
// D:  Hidden dimension,
// H:  Number of heads,
// Dh: Hidden dimension per head - Dh = D / H.
//
// The different kernels assign a threadblock for B x H pair. The grid has size (1, B, H). We use
// 64, 128 and 256 threads per block.
//
// Each threadblock loads Dh values from Q and its associated bias. The kernels run a loop to
// compute Q * K^T where K is loaded from a cache buffer -- except for the current timestep. The
// cache buffer helps with memory accesses and contains keys with bias.
//
// The layout of the cache buffer for the keys is [B, H, Dh/x, L, x] where x == 8 for FP16 and
// x == 4 for FP32 where the fastest moving dimension (contiguous data) is the rightmost one. The
// values for x are chosen to create chunks of 16 bytes.
//
// The different kernels use 1, 2 or 4 threads per key (THREADS_PER_KEY). The size of the LDGs
// depends on the number of threads per key. Each thread sums Dh / THREADS_PER_KEY elements. At
// the end of each iteration of the Q * K^T loop, we perform a reduction between lanes using an
// HMMA instruction (Tensor Core). Each Q * K^T valuey is stored in shared memory in FP32.
//
// After that loop, a parallel softmax is computed across the different Q * K^T values stored in
// shared memory.
//
// The kernel ends with a loop over the values in V. We use THREADS_PER_VALUE to control how many
// timesteps are computed by loop iteration. As with the keys, the values are read from a cache
// except for the current timestep. The layout of the cache buffer for the values is much simpler
// as it is [B, H, L, Dh].
//

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int Dh>
struct Qk_vec_m_ {
};

template<>
struct Qk_vec_m_<float, 32> {
    using Type = float;
};
template<>
struct Qk_vec_m_<float, 64> {
    using Type = float2;
};
template<>
struct Qk_vec_m_<float, 128> {
    using Type = float4;
};
template<>
struct Qk_vec_m_<float, 256> {
    using Type = float4;
};
template<>
struct Qk_vec_m_<uint16_t, 32> {
    using Type = uint32_t;
};
template<>
struct Qk_vec_m_<uint16_t, 64> {
    using Type = uint32_t;
};
template<>
struct Qk_vec_m_<uint16_t, 128> {
    using Type = uint2;
};
template<>
struct Qk_vec_m_<uint16_t, 256> {
    using Type = uint4;
};
#ifdef ENABLE_BF16
template<>
struct Qk_vec_m_<__nv_bfloat16, 32> {
    using Type = __nv_bfloat162;
};
template<>
struct Qk_vec_m_<__nv_bfloat16, 64> {
    using Type = __nv_bfloat162;
};
template<>
struct Qk_vec_m_<__nv_bfloat16, 128> {
    using Type = bf16_4_t;
};
template<>
struct Qk_vec_m_<__nv_bfloat16, 256> {
    using Type = bf16_8_t;
};
#endif  // ENABLE_BF16

#ifdef ENABLE_FP8
template<>
struct Qk_vec_m_<__nv_fp8_e4m3, 32> {
    using Type = fp8_4_t;
};
template<>
struct Qk_vec_m_<__nv_fp8_e4m3, 64> {
    using Type = fp8_4_t;
};
template<>
struct Qk_vec_m_<__nv_fp8_e4m3, 128> {
    using Type = fp8_4_t;
};
template<>
struct Qk_vec_m_<__nv_fp8_e4m3, 256> {
    using Type = fp8_4_t;
};
#endif  // ENABLE_FP8

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int Dh>
struct Qk_vec_k_ {
    using Type = typename Qk_vec_m_<T, Dh>::Type;
};
#ifdef ENABLE_FP8
template<>
struct Qk_vec_k_<__nv_fp8_e4m3, 32> {
    using Type = float4;
};
template<>
struct Qk_vec_k_<__nv_fp8_e4m3, 64> {
    using Type = float4;
};
template<>
struct Qk_vec_k_<__nv_fp8_e4m3, 128> {
    using Type = float4;
};
template<>
struct Qk_vec_k_<__nv_fp8_e4m3, 256> {
    using Type = float4;
};
#endif  // ENABLE_FP8

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int THREADS_PER_KEY>
struct K_vec_m_ {
};

template<>
struct K_vec_m_<float, 4> {
    using Type = float;
};
template<>
struct K_vec_m_<float, 2> {
    using Type = float2;
};
template<>
struct K_vec_m_<float, 1> {
    using Type = float4;
};
template<>
struct K_vec_m_<uint16_t, 4> {
    using Type = uint32_t;
};
template<>
struct K_vec_m_<uint16_t, 2> {
    using Type = uint2;
};
template<>
struct K_vec_m_<uint16_t, 1> {
    using Type = uint4;
};
#ifdef ENABLE_BF16
template<>
struct K_vec_m_<__nv_bfloat16, 4> {
    using Type = __nv_bfloat162;
};
template<>
struct K_vec_m_<__nv_bfloat16, 2> {
    using Type = bf16_4_t;
};
template<>
struct K_vec_m_<__nv_bfloat16, 1> {
    using Type = bf16_8_t;
};
#endif  // ENABLE_BF16

// NOTE: THREADS_PER_KEY * sizeof(K_vec_m_) = 128 bytes
#ifdef ENABLE_FP8
template<>
struct K_vec_m_<__nv_fp8_e4m3, 4> {
    using Type = fp8_4_t;
};
template<>
struct K_vec_m_<__nv_fp8_e4m3, 2> {
    using Type = fp8_4_t;
};  // Defined for compilation-purpose only, do not use
template<>
struct K_vec_m_<__nv_fp8_e4m3, 1> {
    using Type = fp8_4_t;
};      // Defined for compilation-purpose only, do not use
#endif  // ENABLE_FP8

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int THREADS_PER_KEY>
struct K_vec_k_ {
    using Type = typename K_vec_m_<T, THREADS_PER_KEY>::Type;
};
#ifdef ENABLE_FP8
template<>
struct K_vec_k_<__nv_fp8_e4m3, 4> {
    using Type = float4;
};
template<>
struct K_vec_k_<__nv_fp8_e4m3, 2> {
    using Type = float4;
};  // Defined for compilation-purpose only, do not use
template<>
struct K_vec_k_<__nv_fp8_e4m3, 1> {
    using Type = float4;
};      // Defined for compilation-purpose only, do not use
#endif  // ENABLE_FP8

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int V_VEC_SIZE>
struct V_vec_m_ {
};

template<>
struct V_vec_m_<float, 1> {
    using Type = float;
};
template<>
struct V_vec_m_<float, 2> {
    using Type = float2;
};
template<>
struct V_vec_m_<float, 4> {
    using Type = float4;
};
template<>
struct V_vec_m_<uint16_t, 2> {
    using Type = uint32_t;
};
template<>
struct V_vec_m_<uint16_t, 4> {
    using Type = uint2;
};
template<>
struct V_vec_m_<uint16_t, 8> {
    using Type = uint4;
};
#ifdef ENABLE_BF16
template<>
struct V_vec_m_<__nv_bfloat16, 2> {
    using Type = __nv_bfloat162;
};
template<>
struct V_vec_m_<__nv_bfloat16, 4> {
    using Type = bf16_4_t;
};
template<>
struct V_vec_m_<__nv_bfloat16, 8> {
    using Type = bf16_8_t;
};
#endif  // ENABLE_BF16
#ifdef ENABLE_FP8
template<>
struct V_vec_m_<__nv_fp8_e4m3, 4> {
    using Type = fp8_4_t;
};
template<>
struct V_vec_m_<__nv_fp8_e4m3, 8> {
    using Type = fp8_4_t;
};
template<>
struct V_vec_m_<__nv_fp8_e4m3, 16> {
    using Type = fp8_4_t;
};
#endif  // ENABLE_FP8

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int V_VEC_SIZE>
struct V_vec_k_ {
    using Type = typename V_vec_m_<T, V_VEC_SIZE>::Type;
};
#ifdef ENABLE_FP8
template<>
struct V_vec_k_<__nv_fp8_e4m3, 4> {
    using Type = float4;
};
template<>
struct V_vec_k_<__nv_fp8_e4m3, 8> {
    using Type = float4;
};
template<>
struct V_vec_k_<__nv_fp8_e4m3, 16> {
    using Type = float4;
};
#endif

////////////////////////////////////////////////////////////////////////////////////////////////////

#ifdef MMHA_USE_FP32_ACUM_FOR_FMA
template<typename T>
struct Qk_vec_acum_fp32_ {
};

template<>
struct Qk_vec_acum_fp32_<float> {
    using Type = float;
};
template<>
struct Qk_vec_acum_fp32_<float2> {
    using Type = float2;
};
template<>
struct Qk_vec_acum_fp32_<float4> {
    using Type = float4;
};
// template<> struct Qk_vec_acum_fp32_<uint16_t> { using Type = float;        };
template<>
struct Qk_vec_acum_fp32_<uint32_t> {
    using Type = float2;
};
template<>
struct Qk_vec_acum_fp32_<uint2> {
    using Type = Float4_;
};
template<>
struct Qk_vec_acum_fp32_<uint4> {
    using Type = Float8_;
};
template<>
struct Qk_vec_acum_fp32_<__nv_bfloat16> {
    using Type = float;
};
template<>
struct Qk_vec_acum_fp32_<__nv_bfloat162> {
    using Type = float2;
};
template<>
struct Qk_vec_acum_fp32_<bf16_4_t> {
    using Type = Float4_;
};
template<>
struct Qk_vec_acum_fp32_<bf16_8_t> {
    using Type = Float8_;
};

template<>
struct Qk_vec_acum_fp32_<uint4> {
    using Type = Float8_;
};
template<>
struct Qk_vec_acum_fp32_<__nv_bfloat16> {
    using Type = float;
};
template<>
struct Qk_vec_acum_fp32_<__nv_bfloat162> {
    using Type = float2;
};
template<>
struct Qk_vec_acum_fp32_<bf16_4_t> {
    using Type = Float4_;
};
template<>
struct Qk_vec_acum_fp32_<bf16_8_t> {
    using Type = Float8_;
};
#ifdef ENABLE_FP8
// template<>
// struct Qk_vec_acum_fp32_<fp8_2_t> {
//     using Type = float2;
// };
template<>
struct Qk_vec_acum_fp32_<fp8_4_t> {
    using Type = Float4_;
};
// template<>
// struct Qk_vec_acum_fp32_<fp8_8_t> {
//     using Type = Float4_;
// };
#endif  // ENABLE_FP8

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T>
struct K_vec_acum_fp32_ {
};

template<>
struct K_vec_acum_fp32_<float> {
    using Type = float;
};
template<>
struct K_vec_acum_fp32_<float2> {
    using Type = float2;
};
template<>
struct K_vec_acum_fp32_<float4> {
    using Type = float4;
};
template<>
struct K_vec_acum_fp32_<uint32_t> {
    using Type = float2;
};
template<>
struct K_vec_acum_fp32_<uint2> {
    using Type = Float4_;
};
template<>
struct K_vec_acum_fp32_<uint4> {
    using Type = Float8_;
};
template<>
struct K_vec_acum_fp32_<__nv_bfloat16> {
    using Type = float;
};
template<>
struct K_vec_acum_fp32_<__nv_bfloat162> {
    using Type = float2;
};
template<>
struct K_vec_acum_fp32_<bf16_4_t> {
    using Type = Float4_;
};
template<>
struct K_vec_acum_fp32_<bf16_8_t> {
    using Type = Float8_;
};
#ifdef ENABLE_FP8
// template<>
// struct K_vec_acum_fp32_<fp8_2_t> {
//     using Type = float2;
// };
template<>
struct K_vec_acum_fp32_<fp8_4_t> {
    using Type = Float4_;
};
// template<>
// struct K_vec_acum_fp32_<fp8_8_t> {
//     using Type = Float4_;
// };
#endif  // ENABLE_FP8
#endif  // MMHA_USE_FP32_ACUM_FOR_FMA

////////////////////////////////////////////////////////////////////////////////////////////////////

#ifdef MMHA_USE_FP32_ACUM_FOR_OUT
template<typename T>
struct V_vec_acum_fp32_ {
};

template<>
struct V_vec_acum_fp32_<float> {
    using Type = float;
};
template<>
struct V_vec_acum_fp32_<float2> {
    using Type = float2;
};
template<>
struct V_vec_acum_fp32_<float4> {
    using Type = float4;
};
template<>
struct V_vec_acum_fp32_<uint32_t> {
    using Type = float2;
};
template<>
struct V_vec_acum_fp32_<uint2> {
    using Type = Float4_;
};
template<>
struct V_vec_acum_fp32_<uint4> {
    using Type = Float8_;
};
#ifdef ENABLE_BF16
template<>
struct V_vec_acum_fp32_<__nv_bfloat162> {
    using Type = float2;
};
template<>
struct V_vec_acum_fp32_<bf16_4_t> {
    using Type = Float4_;
};
template<>
struct V_vec_acum_fp32_<bf16_8_t> {
    using Type = Float8_;
};
#endif  // ENABLE_BF16
#ifdef ENABLE_FP8
// template<>
// struct V_vec_acum_fp32_<fp8_2_t> {
//     using Type = float2;
// };
template<>
struct V_vec_acum_fp32_<fp8_4_t> {
    using Type = Float4_;
};
// template<>
// struct V_vec_acum_fp32_<fp8_8_t> {
//     using Type = Float4_;
// };
#endif  // ENABLE_FP8
#endif

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename Tout, typename Tin>
__inline__ __device__ Tout vec_conversion(const Tin& x)
{
    return x;
}
template<>
__inline__ __device__ uint32_t vec_conversion<uint32_t, float2>(const float2& a)
{
    union {
        half2    float16;
        uint32_t uint32;
    };

    float16 = __float22half2_rn(a);
    return uint32;
}
template<>
__inline__ __device__ uint2 vec_conversion<uint2, float4>(const float4& a)
{
    uint2  b;
    float2 val;
    val.x = a.x;
    val.y = a.y;
    b.x   = vec_conversion<uint32_t, float2>(val);

    val.x = a.z;
    val.y = a.w;
    b.y   = vec_conversion<uint32_t, float2>(val);

    return b;
}
template<>
__inline__ __device__ uint4 vec_conversion<uint4, Float8_>(const Float8_& a)
{
    uint4 b;
    b.x = vec_conversion<uint32_t, float2>(a.x);
    b.y = vec_conversion<uint32_t, float2>(a.y);
    b.z = vec_conversion<uint32_t, float2>(a.z);
    b.w = vec_conversion<uint32_t, float2>(a.w);
    return b;
}

#ifdef ENABLE_BF16
template<>
__inline__ __device__ __nv_bfloat162 vec_conversion<__nv_bfloat162, float2>(const float2& a)
{
    return cuda_cast<__nv_bfloat162, float2>(a);
}
template<>
__inline__ __device__ bf16_4_t vec_conversion<bf16_4_t, float4>(const float4& a)
{
    bf16_4_t b;
    float2   val;
    val.x = a.x;
    val.y = a.y;
    b.x   = vec_conversion<__nv_bfloat162, float2>(val);

    val.x = a.z;
    val.y = a.w;
    b.y   = vec_conversion<__nv_bfloat162, float2>(val);

    return b;
}
template<>
__inline__ __device__ bf16_8_t vec_conversion<bf16_8_t, Float8_>(const Float8_& a)
{
    bf16_8_t b;
    b.x = vec_conversion<__nv_bfloat162, float2>(a.x);
    b.y = vec_conversion<__nv_bfloat162, float2>(a.y);
    b.z = vec_conversion<__nv_bfloat162, float2>(a.z);
    b.w = vec_conversion<__nv_bfloat162, float2>(a.w);
    return b;
}
#endif

////////////////////////////////////////////////////////////////////////////////////////////////////

template<int THREADS_PER_KEY, typename K_vec, int N>
inline __device__ float qk_dot_(const K_vec (&q)[N], const K_vec (&k)[N])
{
#ifdef MMHA_USE_FP32_ACUM_FOR_FMA
    using K_vec_acum = typename K_vec_acum_fp32_<K_vec>::Type;
#else
    using K_vec_acum = K_vec;
#endif
    // Compute the parallel products for Q*K^T (treat vector lanes separately).
    K_vec_acum qk_vec = mul<K_vec_acum, K_vec, K_vec>(q[0], k[0]);
#pragma unroll
    for (int ii = 1; ii < N; ++ii) {
        qk_vec = fma(q[ii], k[ii], qk_vec);
    }

    // Finalize the reduction across lanes.
    float qk = sum(qk_vec);
#pragma unroll
    for (int mask = THREADS_PER_KEY / 2; mask >= 1; mask /= 2) {
        qk += __shfl_xor_sync(uint32_t(-1), qk, mask);
    }
    return qk;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int THREADS_PER_KEY>
struct Qk_dot {
    template<typename K_vec, int N>
    static inline __device__ float dot(const K_vec (&q)[N], const K_vec (&k)[N])
    {
        return qk_dot_<THREADS_PER_KEY>(q, k);
    }
};

////////////////////////////////////////////////////////////////////////////////////////////////////
__device__ inline void f16mulf16addf32(uint32_t & a, uint32_t & b, const float * c, float * d){

//   uint32_t res = 0;
//   asm volatile("v_pk_fma_f16 %0, %1,%2,%3" : "=v"(res) : "v"(a), "v"(b), "v"(res));
//   __half * h = reinterpret_cast<__half*>(&res);
  __half * ha = reinterpret_cast<__half*>(&a);
  __half * hb = reinterpret_cast<__half*>(&b);

  *d = *c + __half2float(ha[0])*__half2float(hb[0]) + __half2float(ha[1])*__half2float(hb[1]);

}

// row 8 col 4
__device__ inline void m16n8k8(const uint32_t * A, const uint32_t * B, /*const float * C,*/ float * D) {
  int tid = threadIdx.x;
  int baseId = tid / 32 * 32;
  __shared__ uint32_t smem[1024*3];

  int base = tid*3;
  __builtin_memcpy(smem+base, A, sizeof(uint32_t));
  __builtin_memcpy(smem+(base+1), A+1, sizeof(uint32_t));
  __builtin_memcpy(smem+(base+2), B, sizeof(uint32_t));
  __syncthreads();

  /* 站在D的视角，每个进程负责D数据的计算，从0线程开始循环，获取一行A和两列B
     s为B矩阵的线程号
     baseA为A的线程号
     baseB0为当前线程获取B的第一列，baseB1为当前线程获取B的第二列
  */
  int s = baseId+(tid%4)*8, e = s+4;
  for (int i = s; i < e; ++i) {
    // A[0]->i A[1]->i+1 B[0]->i+2 
    int baseA = (tid-tid%4+i-s)*3;  // 当前tid所处行的第一列的进程号+stride 再*3
    int baseB0 = i*3, baseB1 = (i+4)*3;
   
    f16mulf16addf32(smem[baseA], smem[baseB0+2], D, D);

    f16mulf16addf32(smem[baseA], smem[baseB1+2], D+1, D+1);

    f16mulf16addf32(smem[baseA+1], smem[baseB0+2], D+2, D+2);

    f16mulf16addf32(smem[baseA+1], smem[baseB1+2], D+3, D+3);
  }
}


inline __device__ float4 hmma_fp32(const uint2& a, uint32_t b)
{
    float4 c;
    float  zero = 0.f;
    const uint32_t * A = reinterpret_cast<const uint32_t*>(&a);
    const uint32_t * B = reinterpret_cast<const uint32_t*>(b);
    float * C = reinterpret_cast<float*>(&c);
    m16n8k8(A, B, C);
    // asm volatile("mma.sync.aligned.m16n8k8.row.col.f32.f16.f16.f32 \n"
    //              "    {%0, %1, %2, %3}, \n"
    //              "    {%4, %5}, \n"
    //              "    {%6}, \n"
    //              "    {%7, %7, %7, %7}; \n"

    //              : "=f"(c.x), "=f"(c.y), "=f"(c.z), "=f"(c.w)
    //              : "r"(a.x), "r"(a.y), "r"(b), "f"(zero));
    return c;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<int N>
inline __device__ float qk_hmma_dot_(const uint32_t (&q)[N], const uint32_t (&k)[N])
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 750
#ifdef MMHA_USE_FP32_ACUM_FOR_FMA
    using K_vec_acum = typename K_vec_acum_fp32_<uint32_t>::Type;
#else
    using K_vec_acum = uint32_t;
#endif
    K_vec_acum qk_vec = mul<K_vec_acum, uint32_t, uint32_t>(q[0], k[0]);
#pragma unroll
    for (int ii = 1; ii < N; ++ii) {
        qk_vec = fma(q[ii], k[ii], qk_vec);
    }
#ifdef MMHA_USE_FP32_ACUM_FOR_FMA
    uint32_t qk_vec_ = float2_to_half2(qk_vec);
    return hmma_fp32(make_uint2(qk_vec_, 0u), 0x3c003c00u).x;
#else
    return hmma_fp32(make_uint2(qk_vec, 0u), 0x3c003c00u).x;
#endif
#else
    return 0.f;
#endif
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<>
struct Qk_dot<uint16_t, 4> {
    template<int N>
    static inline __device__ float dot(const uint32_t (&q)[N], const uint32_t (&k)[N])
    {
#if __CUDA_ARCH__ >= 750 && defined(MMHA_USE_HMMA_FOR_REDUCTION)
        return qk_hmma_dot_(q, k);
#else
        return qk_dot_<4>(q, k);
#endif  // defined MMHA_USE_HMMA_FOR_REDUCTION
    }
};

////////////////////////////////////////////////////////////////////////////////////////////////////

// template<int WARPS_PER_BLOCK, int WARP_SIZE = 32>
template<int WARPS_PER_BLOCK, int WARP_SIZE = 64>
inline __device__ float block_sum(float* red_smem, float sum)
{

    // Decompose the thread index into warp / lane.
    int warp = threadIdx.x / WARP_SIZE;
    int lane = threadIdx.x % WARP_SIZE;

// Compute the sum per warp.
#pragma unroll
    for (int mask = WARP_SIZE / 2; mask >= 1; mask /= 2) {
        sum += __shfl_xor_sync(uint32_t(-1), sum, mask);
    }

    // Warp leaders store the data to shared memory.
    if (lane == 0) {
        red_smem[warp] = sum;
    }

    // Make sure the data is in shared memory.
    __syncthreads();

    // The warps compute the final sums.
    if (lane < WARPS_PER_BLOCK) {
        sum = red_smem[lane];
    }

// Parallel reduction inside the warp.
#pragma unroll
    for (int mask = WARPS_PER_BLOCK / 2; mask >= 1; mask /= 2) {
        sum += __shfl_xor_sync(uint32_t(-1), sum, mask);
    }

    // Broadcast to other threads.
    return __shfl_sync(uint32_t(-1), sum, 0);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(float& dst, float src)
{
    dst = src;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(uint16_t& dst, float src)
{
    dst = float_to_half(src);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(uint32_t& dst, float2 src)
{
    dst = float2_to_half2(src);
}

////////////////////////////////////////////////////////////////////////////////////////////////////
#ifdef ENABLE_BF16
inline __device__ void convert_from_float(__nv_bfloat16& dst, float src)
{
    dst = __float2bfloat16(src);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(__nv_bfloat162& dst, float2 src)
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
    dst = __float22bfloat162_rn(src);
#else
    dst   = __floats2bfloat162_rn(src.x, src.y);
#endif
}
#endif  // ENABLE_BF16
////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(uint2& dst, Float4_ src)
{
    dst.x = float2_to_half2(src.x);
    dst.y = float2_to_half2(src.y);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(uint2& dst, float4 src)
{
    convert_from_float(dst, Float4_{make_float2(src.x, src.y), make_float2(src.z, src.w)});
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(uint4& dst, Float8_ src)
{
    dst.x = float2_to_half2(src.x);
    dst.y = float2_to_half2(src.y);
    dst.z = float2_to_half2(src.z);
    dst.w = float2_to_half2(src.w);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

#ifdef ENABLE_BF16
inline __device__ void convert_from_float(bf16_4_t& dst, Float4_ src)
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
    dst.x = __float22bfloat162_rn(src.x);
    dst.y = __float22bfloat162_rn(src.y);
#else
    dst.x = __floats2bfloat162_rn(src.x.x, src.x.y);
    dst.y = __floats2bfloat162_rn(src.y.x, src.y.y);
#endif
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(bf16_4_t& dst, float4 src)
{
    convert_from_float(dst, Float4_{make_float2(src.x, src.y), make_float2(src.z, src.w)});
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(bf16_8_t& dst, Float8_ src)
{
#if defined(__CUDA_ARCH__) && __CUDA_ARCH__ >= 800
    dst.x = __float22bfloat162_rn(src.x);
    dst.y = __float22bfloat162_rn(src.y);
    dst.z = __float22bfloat162_rn(src.z);
    dst.w = __float22bfloat162_rn(src.w);
#else
    dst.x = __floats2bfloat162_rn(src.x.x, src.x.y);
    dst.y = __floats2bfloat162_rn(src.y.x, src.y.y);
    dst.z = __floats2bfloat162_rn(src.z.x, src.z.y);
    dst.w = __floats2bfloat162_rn(src.w.x, src.w.y);
#endif
}
#endif  // ENABLE_BF16

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(float2& dst, float2 src)
{
    dst = src;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ void convert_from_float(float4& dst, float4 src)
{
    dst = src;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float convert_to_float(float4 u)
{
    return u.x;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float convert_to_float(uint4 u)
{
    float2 tmp = half2_to_float2(u.x);
    return tmp.x;
}

#if defined(MMHA_USE_FP32_ACUM_FOR_LOGITS)

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float cast_to_float(float u)
{
    return u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float2 cast_to_float(float2 u)
{
    return u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float4 cast_to_float(float4 u)
{
    return u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ Float4_ cast_to_float(Float4_ u)
{
    return u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ Float8_ cast_to_float(Float8_ u)
{
    return u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float2 cast_to_float(uint32_t u)
{
    return half2_to_float2(u);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ Float4_ cast_to_float(uint2 u)
{
    Float4_ tmp;
    tmp.x = half2_to_float2(u.x);
    tmp.y = half2_to_float2(u.y);
    return tmp;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ Float8_ cast_to_float(uint4 u)
{
    Float8_ tmp;
    tmp.x = half2_to_float2(u.x);
    tmp.y = half2_to_float2(u.y);
    tmp.z = half2_to_float2(u.z);
    tmp.w = half2_to_float2(u.w);
    return tmp;
}

#endif

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float float_from_int8(int8_t u)
{
    return u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float2 float_from_int8(int16_t u)
{
    union {
        int16_t int16;
        int8_t  int8[2];
    };
    int16 = u;
    return make_float2(int8[0], int8[1]);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ float4 float_from_int8(int32_t u)
{
    union {
        int32_t int32;
        int8_t  int8[4];
    };
    int32 = u;
    return make_float4(int8[0], int8[1], int8[2], int8[3]);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

// clang-format off
inline __device__ Float8_ float_from_int8(int64_t u)
{
    union {
        int64_t int64;
        int16_t int16[4];
    };
    int64 = u;
    return Float8_ {float_from_int8(int16[0]),
                    float_from_int8(int16[1]),
                    float_from_int8(int16[2]),
                    float_from_int8(int16[3])};
}
// clang-format on

inline __device__ int8_t quant(float a, const float scale, const float zp)
{
    int8_t int8;
    int8 = round(max(-128.f, min(127.f, (a - zp) / scale)));
    return int8;
}

inline __device__ short quant(float2 a, const float scale, const float zp)
{
    union {
        int8_t int8[2];
        short  int16;
    };

    int8[0] = round(max(-128.f, min(127.f, (a.x - zp) / scale)));
    int8[1] = round(max(-128.f, min(127.f, (a.y - zp) / scale)));
    return int16;
}

inline __device__ int32_t quant(float4 a, const float scale, const float zp)
{
    union {
        int8_t  int8[4];
        int32_t int32;
    };

    int8[0] = round(max(-128.f, min(127.f, (a.x - zp) / scale)));
    int8[1] = round(max(-128.f, min(127.f, (a.y - zp) / scale)));
    int8[2] = round(max(-128.f, min(127.f, (a.z - zp) / scale)));
    int8[3] = round(max(-128.f, min(127.f, (a.w - zp) / scale)));
    return int32;
}

// float16 to int8
inline __device__ int8_t quant(uint16_t a, const float scale, const float zp)
{
    int8_t int8;
    float  b = half_to_float(a);
    int8     = round(max(-128.f, min(127.f, (b - zp) / scale)));
    return int8;
}
// float16x2 to int8x2
inline __device__ int16_t quant(uint a, const float scale, const float zp)
{
    union {
        int8_t int8[2];
        short  int16;
    };
    float2 b = half2_to_float2(a);

    int8[0] = round(max(-128.f, min(127.f, (b.x - zp) / scale)));
    int8[1] = round(max(-128.f, min(127.f, (b.y - zp) / scale)));
    return int16;
}
// float16x4 to int8x4
inline __device__ int32_t quant(uint2 a, const float scale, const float zp)
{
    union {
        int16_t int16[2];
        int32_t int32;
    };

    int16[0] = quant(a.x, scale, zp);
    int16[1] = quant(a.y, scale, zp);
    return int32;
}
// float16x8 to int8x8
inline __device__ int64_t quant(uint4 a, const float scale, const float zp)
{
    union {
        int16_t int16[4];
        int64_t int64;
    };

    int16[0] = quant(a.x, scale, zp);
    int16[1] = quant(a.y, scale, zp);
    int16[2] = quant(a.z, scale, zp);
    int16[3] = quant(a.w, scale, zp);
    return int64;
}

// bfloat16 to int8
inline __device__ int8_t quant(__nv_bfloat16 a, const float scale, const float zp)
{
    int8_t int8;
    float  b = bfloat16_to_float(a);
    int8     = round(max(-128.f, min(127.f, (b - zp) / scale)));
    return int8;
}
// bfloat16x2 to int8x2
inline __device__ int16_t quant(__nv_bfloat162 a, const float scale, const float zp)
{
    union {
        int8_t int8[2];
        short  int16;
    };
    float2 b = bfloat162_to_float2(a);

    int8[0] = round(max(-128.f, min(127.f, (b.x - zp) / scale)));
    int8[1] = round(max(-128.f, min(127.f, (b.y - zp) / scale)));
    return int16;
}
// bfloat16x4 to int8x4
inline __device__ int32_t quant(bf16_4_t a, const float scale, const float zp)
{
    union {
        int16_t int16[2];
        int32_t int32;
    };

    int16[0] = quant(a.x, scale, zp);
    int16[1] = quant(a.y, scale, zp);
    return int32;
}
// bfloat16x8 to int8x8
inline __device__ int64_t quant(bf16_8_t a, const float scale, const float zp)
{
    union {
        int16_t int16[4];
        int64_t int64;
    };

    int16[0] = quant(a.x, scale, zp);
    int16[1] = quant(a.y, scale, zp);
    int16[2] = quant(a.z, scale, zp);
    int16[3] = quant(a.w, scale, zp);
    return int64;
}

// int8 to float32, then `vec_conversion` to target format
inline __device__ float dequant(int8_t a, const float scale, const float zp)
{
    float b = a * scale + zp;
    return b;
}
// int8x2 to float32x2
inline __device__ float2 dequant(int16_t a, const float scale, const float zp)
{
    union {
        int8_t  int8[2];
        int16_t int16;
    };
    int16 = a;

    float2 b;
    b.x = int8[0] * scale + zp;
    b.y = int8[1] * scale + zp;
    return b;
}
// int8x4 to float32x4
inline __device__ float4 dequant(int32_t a, const float scale, const float zp)
{
    union {
        int8_t  int8[4];
        int32_t int32;
    };
    int32 = a;

    float4 b;
    b.x = (int8[0] * scale) + zp;
    b.y = (int8[1] * scale) + zp;
    b.z = (int8[2] * scale) + zp;
    b.w = (int8[3] * scale) + zp;
    return b;
}

inline __device__ Float8_ dequant(int64_t a, const float scale, const float zp)
{
    union {
        int16_t int16[4];
        int64_t int64;
    };
    int64 = a;

    Float8_ b;
    b.x = dequant(int16[0], scale, zp);
    b.y = dequant(int16[1], scale, zp);
    b.z = dequant(int16[2], scale, zp);
    b.w = dequant(int16[3], scale, zp);
    return b;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ int8_t cast_to_int8(float val)
{
    // union {
    //     int8_t  int8[2];
    //     int16_t int16;
    // };
    // asm volatile("cvt.rni.sat.s8.f32 %0, %1;" : "=h"(int16) : "f"(val));
    // return int8[0];
    int8_t dst;
    if (val >= 128){
        dst = 127;
    }else if (val < -128){
        dst = -128;
    }else{
        dst = static_cast<int8_t>(val);
    }
    return dst;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ int32_t cast_to_int8(float4 val)
{
    union {
        int8_t  int8[4];
        int32_t int32;
    };
    int8[0] = cast_to_int8(val.x);
    int8[1] = cast_to_int8(val.y);
    int8[2] = cast_to_int8(val.z);
    int8[3] = cast_to_int8(val.w);
    return int32;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ int64_t cast_to_int8(Float8_ val)
{
    union {
        int8_t  int8[8];
        int64_t int64;
    };
    int8[0] = cast_to_int8(val.x.x);
    int8[1] = cast_to_int8(val.x.y);
    int8[2] = cast_to_int8(val.y.x);
    int8[3] = cast_to_int8(val.y.y);
    int8[4] = cast_to_int8(val.z.x);
    int8[5] = cast_to_int8(val.z.y);
    int8[6] = cast_to_int8(val.w.x);
    int8[7] = cast_to_int8(val.w.y);
    return int64;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T>
inline __device__ __host__ T div_up(T m, T n)
{
    return (m + n - 1) / n;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T>
struct kernel_type_t {
    using Type = T;
};

#ifdef ENABLE_FP8
template<>
struct kernel_type_t<__nv_fp8_e4m3> {
    using Type = float;
};
#endif

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T>
inline size_t
smem_size_in_bytes(const Multihead_attention_params<T>& params, int threads_per_value, int threads_per_block)
{
    using Tk = typename kernel_type_t<T>::Type;
    // The amount of shared memory needed to store the Q*K^T values in float.
    const int max_timesteps = min(params.timestep, params.memory_max_len);
    size_t    qk_sz         = div_up(max_timesteps + 1, 4) * 16;

    // The extra memory needed if we are not using floats for the final logits.
    size_t logits_sz = 0;
#ifndef MMHA_USE_FP32_ACUM_FOR_LOGITS
    if (sizeof(Tk) != 4) {
        // TDOD
        logits_sz = div_up(max_timesteps + 1, 4) * 4 * sizeof(Tk);
    }
#endif

    // The total size needed during softmax.
    size_t softmax_sz = qk_sz + logits_sz;

    // The number of partial rows to reduce in the final reduction.
    int rows_per_red = threads_per_block / threads_per_value;
    // The amount of storage needed to finalize the outputs.
    size_t red_sz = rows_per_red * params.hidden_size_per_head * sizeof(Tk) / 2;

    // The max.
    return max(softmax_sz, red_sz);
}

////////////////////////////////////////////////////////////////////////////////////////////////////

inline __device__ constexpr uint32_t shfl_mask(int threads)
{
    return threads == 32 ? uint32_t(-1) : (1u << threads) - 1u;
}

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T,  // The type of the inputs. Supported types: float and half.
         int  Dh,     // The hidden dimension per head.
         int  Dh_MAX,
         int  THREADS_PER_KEY,    // The number of threads per key.
         int  THREADS_PER_VALUE,  // The number of threads per value.
         int  THREADS_PER_BLOCK,  // The number of threads in a threadblock.
         bool HAS_BEAMS,
         int  QUANT_POLICY>  // quantization method
__global__ void masked_multihead_attention_kernel(Multihead_attention_params<T> params)
{

    using Tk = typename kernel_type_t<T>::Type;
#ifdef ENABLE_FP8
    // FP8 MHA Scales
    constexpr bool FP8_MHA_KERNEL = std::is_same<T, __nv_fp8_e4m3>::value;
#else
    constexpr bool FP8_MHA_KERNEL = false;
#endif
    // Make sure the hidden dimension per head is a multiple of the number of threads per key.
    static_assert(Dh_MAX % THREADS_PER_KEY == 0, "");
    // Make sure the hidden dimension per head is a multiple of the number of threads per value.
    static_assert(Dh_MAX % THREADS_PER_VALUE == 0, "");

    // The size of a warp.
    // constexpr int WARP_SIZE = 32;
    constexpr int WARP_SIZE = 64;
    // The number of warps in a threadblock.
    constexpr int WARPS_PER_BLOCK = THREADS_PER_BLOCK / WARP_SIZE;

    // Use smem_size_in_bytes (above) to determine the amount of shared memory.
    extern __shared__ char smem_[];

    // The shared memory for the Q*K^T values and partial logits in softmax.
    float* qk_smem = reinterpret_cast<float*>(smem_);

    // The shared memory for the logits. For FP32, that's the same buffer as qk_smem.
    char* logits_smem_ = smem_;
#ifndef MMHA_USE_FP32_ACUM_FOR_LOGITS
    if (sizeof(Tk) != 4) {
        // TODO - change to tlength
        const int max_timesteps = min(params.timestep, params.memory_max_len);
        logits_smem_ += div_up(max_timesteps + 1, 4) * 16;
    }
    Tk* logits_smem = reinterpret_cast<Tk*>(logits_smem_);
#else
    float*         logits_smem    = reinterpret_cast<float*>(logits_smem_);
#endif

    // The shared memory to do the final reduction for the output values. Reuse qk_smem.
    Tk* out_smem = reinterpret_cast<Tk*>(smem_);

    // The shared memory buffers for the block-wide reductions. One for max, one for sum.
    __shared__ float red_smem[WARPS_PER_BLOCK * 2];

    // A vector of Q or K elements for the current timestep.
    using Qk_vec_k = typename Qk_vec_k_<T, Dh_MAX>::Type;  // with kernel-used precision
    using Qk_vec_m = typename Qk_vec_m_<T, Dh_MAX>::Type;  // with memory-used precision

    // Use alignment for safely casting the shared buffers as Qk_vec_k.
    // Shared memory to store Q inputs.
    __shared__ __align__(sizeof(Qk_vec_k)) Tk q_smem[Dh_MAX];

    // The number of elements per vector.
    constexpr int QK_VEC_SIZE = sizeof(Qk_vec_m) / sizeof(T);
    // Make sure the hidden size per head is a multiple of the vector size.
    static_assert(Dh_MAX % QK_VEC_SIZE == 0, "");
    // We will use block wide reduction if needed
    // static_assert(Dh_MAX / QK_VEC_SIZE <= WARP_SIZE, "");
    // The number of vectors per warp.
    constexpr int QK_VECS_PER_WARP = Dh_MAX / QK_VEC_SIZE;

    // The layout of the cache is [B, H, Dh/x, L, x] with x == 4/8/16 for FP32/FP16/FP8. Since each thread
    // owns x elements, we have to decompose the linear index into chunks of x values and the posi-
    // tion of the thread in that chunk.

    // The number of elements in a chunk of 16B (that's the x in the above formula).
    constexpr int QK_ELTS_IN_16B = 16 / sizeof(T);
    // The number of K vectors in 16B.
    constexpr int QK_VECS_IN_16B = 16 / sizeof(Qk_vec_m);

    // The batch/beam idx
    const int bi = blockIdx.y;
    if (params.finished != nullptr && params.finished[bi] == true) {
        return;
    }

    // The head.
    const int hi = blockIdx.x;
    // Combine the batch and the head indices.
    const int bhi = bi * params.num_heads + hi;

    const int head_n_rep = params.num_heads / params.num_kv_heads;

    const int kvhi = hi / head_n_rep;  // heads in the same group collapse to the same kv head

    const bool group_leader = hi % head_n_rep == 0;  // only group leader writes to kv cache

    // The thread in the block.
    const int tidx = threadIdx.x;

    // While doing the product Q*K^T for the different keys we track the max.
    float qk_max = -FLT_MAX;

    float qk = 0.0F;

    const size_t bi_seq_len_offset = bi * params.memory_max_len;

    const int tlength      = params.length_per_sample[bi] + params.max_prefix_prompt_length;
    const int first_step   = max(0, tlength + 1 - params.memory_max_len);
    const int tlength_circ = tlength % params.memory_max_len;

    // First QK_VECS_PER_WARP load Q and K + the bias values for the current timestep.
    const bool is_masked = tidx >= QK_VECS_PER_WARP;

    const int q_base_offset = bi * params.stride + hi * Dh;
    const int k_base_offset = bi * params.stride + kvhi * Dh;

    // The offset in the Q and K buffer also accounts for the batch.
    const int q_offset = q_base_offset + tidx * QK_VEC_SIZE;
    const int k_offset = k_base_offset + tidx * QK_VEC_SIZE;

    // The offset in the bias buffer.
    const int q_bias_offset = hi * Dh + tidx * QK_VEC_SIZE;
    const int k_bias_offset = kvhi * Dh + tidx * QK_VEC_SIZE;

    // past kv quant param
    const float k_scale = params.attention_k_scale;
    const float k_zp    = params.attention_k_zp;
    const float v_scale = params.attention_v_scale;
    const float v_zp    = params.attention_v_zp;

    // Trigger the loads from the Q and K buffers.
    Qk_vec_k q;
    zero(q);
    if (!is_masked && (Dh == Dh_MAX || tidx * QK_VEC_SIZE < Dh)) {
        q = vec_conversion<Qk_vec_k, Qk_vec_m>(*reinterpret_cast<const Qk_vec_m*>(&params.q[q_offset]));
    }

    Qk_vec_k k;
    zero(k);
    {
        k = !is_masked && (Dh == Dh_MAX || tidx * QK_VEC_SIZE < Dh) ?
                vec_conversion<Qk_vec_k, Qk_vec_m>(*reinterpret_cast<const Qk_vec_m*>(&params.k[k_offset])) :
                k;
    }

    // Trigger the loads from the Q and K bias buffers.
    Qk_vec_k q_bias;
    zero(q_bias);
    q_bias = (!is_masked && Dh == Dh_MAX || tidx * QK_VEC_SIZE < Dh) && params.q_bias != nullptr ?
                 vec_conversion<Qk_vec_k, Qk_vec_m>(*reinterpret_cast<const Qk_vec_m*>(&params.q_bias[q_bias_offset])) :
                 q_bias;

    Qk_vec_k k_bias;
    zero(k_bias);

    k_bias = !is_masked && (Dh == Dh_MAX || tidx * QK_VEC_SIZE < Dh) && params.k_bias != nullptr ?
                 vec_conversion<Qk_vec_k, Qk_vec_m>(*reinterpret_cast<const Qk_vec_m*>(&params.k_bias[k_bias_offset])) :
                 k_bias;

    // Computes the Q/K values with bias.
    q = add(q, q_bias);
    k = add(k, k_bias);

    float rotary_embedding_base = params.rotary_embedding_base;
    if (params.use_dynamic_ntk) {
        // +1 because of `length_per_sample == context_length - 1`
        rotary_embedding_base = rotary_embedding_get_base(params.length_per_sample[bi] + 1,
                                                          params.max_position_embeddings,
                                                          params.rotary_embedding_dim,
                                                          rotary_embedding_base);
    }

    // Padded len
    const int padd_len = (params.total_padding_tokens == nullptr) ? 0 : params.total_padding_tokens[bi];
    if (params.rotary_embedding_dim > 0) {
        apply_rotary_embedding(
            q, k, tidx, params.rotary_embedding_dim, rotary_embedding_base, params.timestep - padd_len);
    }

    if (params.use_logn_attn) {
        T log_n_scaling;
        // +1 because of `length_per_sample == context_length - 1`
        convert_from_float(log_n_scaling,
                           logn_attn_get_scaling(params.length_per_sample[bi] + 1, params.max_position_embeddings));
        q = mul<Qk_vec_k, T, Qk_vec_k>(log_n_scaling, q);
    }

    if (!is_masked) {
        // Store the Q values to shared memory.
        *reinterpret_cast<Qk_vec_k*>(&q_smem[tidx * QK_VEC_SIZE]) = q;

        // Write the K values to the global memory cache.
        //
        // NOTE: The stores are uncoalesced as we have multiple chunks of 16B spread across the memory
        // system. We designed it this way as it allows much better memory loads (and there are many
        // more loads) + the stores are really "write and forget" since we won't need the ack before
        // the end of the kernel. There's plenty of time for the transactions to complete.

        // The 16B chunk written by the thread.
        int co = tidx / QK_VECS_IN_16B;
        // The position of the thread in that 16B chunk.
        int ci = tidx % QK_VECS_IN_16B * QK_VEC_SIZE;

        if (group_leader) {
            // Trigger the stores to global memory.
            if (Dh == Dh_MAX || co < Dh / QK_ELTS_IN_16B) {

                size_t offset = params.kv_cache_per_sample_offset + kvhi * params.memory_max_len * Dh
                                + tlength_circ * Dh + co * QK_ELTS_IN_16B + ci;

                if (!QUANT_POLICY) {
                    *reinterpret_cast<Qk_vec_m*>(&params.k_cache_per_sample[bi][offset]) =
                        vec_conversion<Qk_vec_m, Qk_vec_k>(k);
                }
                else if (QUANT_POLICY == 4) {
                    using Packed_Int8_t  = typename packed_type<int8_t, num_elems<Qk_vec_k>::value>::type;
                    Packed_Int8_t k_int8 = quant(k, k_scale, k_zp);

                    int8_t* dst_ptr = reinterpret_cast<int8_t*>(params.k_cache_per_sample[bi]);
                    *reinterpret_cast<Packed_Int8_t*>(&dst_ptr[offset]) = k_int8;
                }
            }
        }

        // Compute \sum_i Q[i] * K^T[i] for the current timestep.
#ifdef MMHA_USE_FP32_ACUM_FOR_FMA
        using Qk_vec_acum = typename Qk_vec_acum_fp32_<Qk_vec_k>::Type;
#else
        using Qk_vec_acum = Qk_vec_k;
#endif
        qk = dot<Qk_vec_acum, Qk_vec_k>(q, k);
        if (QK_VECS_PER_WARP <= WARP_SIZE) {
#pragma unroll
            for (int mask = QK_VECS_PER_WARP / 2; mask >= 1; mask /= 2) {
                qk += __shfl_xor_sync(shfl_mask(QK_VECS_PER_WARP), qk, mask);
            }
        }
    }

    if (QK_VECS_PER_WARP > WARP_SIZE) {
        constexpr int WARPS_PER_RED = (QK_VECS_PER_WARP + WARP_SIZE - 1) / WARP_SIZE;
        qk                          = block_sum<WARPS_PER_RED>(&red_smem[WARPS_PER_RED], qk);
    }

    // Store that value in shared memory. Keep the Q*K^T value in register for softmax.
    if (tidx == 0) {
        // Normalize qk.
        qk *= params.inv_sqrt_dh;
        if (params.relative_attention_bias != nullptr) {
            qk = add(qk,
                     params.relative_attention_bias[hi * params.relative_attention_bias_stride
                                                        * params.relative_attention_bias_stride
                                                    + (tlength - padd_len) * params.relative_attention_bias_stride
                                                    + (tlength - padd_len)]);
        }
        // We don't need to apply the linear position bias here since qi - ki = 0 yields the position bias 0.

        //printf("QK_last[%d] = %f\n", hi, qk);

        qk_max                        = qk;
        qk_smem[tlength - first_step] = qk;
        // qk_smem[params.timestep] = qk;
    }

    // Make sure the data is in shared memory.
    __syncthreads();

    // The type of queries and keys for the math in the Q*K^T product.
    using K_vec_k = typename K_vec_k_<T, THREADS_PER_KEY>::Type;
    using K_vec_m = typename K_vec_m_<T, THREADS_PER_KEY>::Type;
    // The number of elements per vector.
    constexpr int K_VEC_SIZE = sizeof(K_vec_m) / sizeof(T);
    // Make sure the hidden size per head is a multiple of the vector size.
    static_assert(Dh_MAX % K_VEC_SIZE == 0, "");
    // The number of elements per thread.
    constexpr int K_ELTS_PER_THREAD = Dh_MAX / THREADS_PER_KEY;
    // The number of vectors per thread.
    constexpr int K_VECS_PER_THREAD = K_ELTS_PER_THREAD / K_VEC_SIZE;

    // The position the first key loaded by each thread from the cache buffer (for this B * H).
    int ko = tidx / THREADS_PER_KEY;
    // The position of the thread in the chunk of keys.
    int ki = tidx % THREADS_PER_KEY * K_VEC_SIZE;

    static_assert(Dh_MAX == THREADS_PER_KEY * K_VEC_SIZE * K_VECS_PER_THREAD);

    // Load the Q values from shared memory. The values are reused during the loop on K.
    K_vec_k q_vec[K_VECS_PER_THREAD];
#pragma unroll
    for (int ii = 0; ii < K_VECS_PER_THREAD; ++ii) {
        q_vec[ii] = *reinterpret_cast<const K_vec_k*>(&q_smem[ki + ii * THREADS_PER_KEY * K_VEC_SIZE]);
    }

    // The number of timesteps loaded per iteration.
    constexpr int K_PER_ITER = THREADS_PER_BLOCK / THREADS_PER_KEY;
    // The number of keys per warp.
    constexpr int K_PER_WARP = WARP_SIZE / THREADS_PER_KEY;

    // The base pointer for the key in the cache buffer.
    T*      k_cache_batch      = nullptr;
    int8_t* k_cache_batch_int8 = nullptr;

    if (!QUANT_POLICY) {
        k_cache_batch =
            params.k_cache_per_sample[bi] + params.kv_cache_per_sample_offset + kvhi * params.memory_max_len * Dh + ki;
    }
    else if (QUANT_POLICY == 4) {
        // convert k_cache_per_sample to int8
        int8_t* ptr        = reinterpret_cast<int8_t*>(params.k_cache_per_sample[bi]);
        k_cache_batch_int8 = ptr + params.kv_cache_per_sample_offset + kvhi * params.memory_max_len * Dh + ki;
    }

    // Pick a number of keys to make sure all the threads of a warp enter (due to shfl_sync).
    // int ti_end = div_up(params.timestep, K_PER_WARP) * K_PER_WARP;
    int ti_end = div_up(tlength - first_step, K_PER_WARP) * K_PER_WARP + first_step;

    // Iterate over the keys/timesteps to compute the various (Q*K^T)_{ti} values.
    // const int* beam_indices = HAS_BEAMS ? &params.cache_indir[bi_seq_len_offset] : nullptr;

    for (int ti = first_step + ko; ti < ti_end; ti += K_PER_ITER) {
        const int ti_circ = ti % params.memory_max_len;
        bool      is_mask = (params.masked_tokens != nullptr) && params.masked_tokens[bi_seq_len_offset + ti];

        // The keys loaded from the key cache.
        K_vec_k k[K_VECS_PER_THREAD];
        K_vec_k k_vec_zero;
        zero(k_vec_zero);
#pragma unroll
        for (int ii = 0; ii < K_VECS_PER_THREAD; ++ii) {
            int jj = ti_circ * Dh / QK_ELTS_IN_16B + ii;
            // if( ti < params.timestep ) {
            const bool within_bounds = (Dh == Dh_MAX || jj * QK_ELTS_IN_16B < Dh * params.memory_max_len);
            if (ti < tlength) {
                if (!within_bounds) {
                    k[ii] = k_vec_zero;
                }
                else {
                    int beam_offset = 0;

                    if (!QUANT_POLICY) {
                        k[ii] = vec_conversion<K_vec_k, K_vec_m>(
                            (*reinterpret_cast<const K_vec_m*>(&k_cache_batch[beam_offset + jj * QK_ELTS_IN_16B])));
                    }
                    else if (QUANT_POLICY == 4) {
                        using Packed_Int8_t  = typename packed_type<int8_t, num_elems<K_vec_m>::value>::type;
                        using Packed_Float_t = typename packed_type<float, num_elems<K_vec_m>::value>::type;

                        Packed_Int8_t k_vec_m_int8 = *reinterpret_cast<const Packed_Int8_t*>(
                            &k_cache_batch_int8[beam_offset + jj * QK_ELTS_IN_16B]);
                        Packed_Float_t k_vec_m_float = dequant(k_vec_m_int8, k_scale, k_zp);

                        k[ii] = vec_conversion<K_vec_k, Packed_Float_t>(k_vec_m_float);
                    }
                }
            }
        }

        // Perform the dot product and normalize qk.
        //
        // WARNING: ALL THE THREADS OF A WARP MUST ENTER!!!
        float qk = Qk_dot<T, THREADS_PER_KEY>::dot(q_vec, k) * params.inv_sqrt_dh;

        // Store the product to shared memory. There's one qk value per timestep. Update the max.
        // if( ti < params.timestep && tidx % THREADS_PER_KEY == 0 ) {
        if (ti < tlength && tidx % THREADS_PER_KEY == 0) {
            if (params.relative_attention_bias != nullptr) {
                qk = add(qk,
                         params.relative_attention_bias[hi * params.relative_attention_bias_stride
                                                            * params.relative_attention_bias_stride
                                                        + tlength * params.relative_attention_bias_stride + ti]);
            }
            if (params.linear_bias_slopes != nullptr) {
                // Apply the linear position bias: (ki - qi) * slope[hi].
                // The padding token locates between the input context and the generated tokens.
                // We need to remove the number of padding tokens in the distance computation.
                //   ti   : 0 1 2 3 4 5 6 7 8 9(tlength)
                //   token: i i i i p p p o o o where i=input, p=pad, o=output.
                // e.g. ti = 2, dist = (9 - 3) - 2 = 4.
                int   max_context_length = params.max_prefix_prompt_length + params.max_input_length;
                float dist               = (ti < max_context_length ? ti + padd_len : ti) - tlength;

                qk += mul<float, T, float>(params.linear_bias_slopes[hi], dist);
            }
            // printf("QK_%d = %f\n", (int)ti, qk);
            qk_max                   = is_mask ? qk_max : fmaxf(qk_max, qk);
            qk_smem[ti - first_step] = qk;
        }
    }

// Perform the final reduction to compute the max inside each warp.
//
// NOTE: In a group of THREADS_PER_KEY threads, the leader already has the max value for the
// group so it's not needed to run the reduction inside the group (again).
#pragma unroll
    for (int mask = WARP_SIZE / 2; mask >= THREADS_PER_KEY; mask /= 2) {
        qk_max = fmaxf(qk_max, __shfl_xor_sync(uint32_t(-1), qk_max, mask));
    }

    // Decompose the thread index into warp and lane.
    const int warp = tidx / WARP_SIZE;
    const int lane = tidx % WARP_SIZE;

    // The warp leader writes the max to shared memory.
    if (lane == 0) {
        red_smem[warp] = qk_max;
    }

    // Make sure the products are in shared memory.
    __syncthreads();

    // The warps finalize the reduction.
    qk_max = lane < WARPS_PER_BLOCK ? red_smem[lane] : -FLT_MAX;
#pragma unroll
    for (int mask = WARPS_PER_BLOCK / 2; mask >= 1; mask /= 2) {
        qk_max = fmaxf(qk_max, __shfl_xor_sync(uint32_t(-1), qk_max, mask));
    }

    // Broadcast to all the threads in the warp.
    qk_max = __shfl_sync(uint32_t(-1), qk_max, 0);

//    if (threadIdx.x == 0) {
//        printf("QK_MAX[%d] = %f\n", hi, (float)qk_max);
//    }

    // Compute the logits and start the sum.
    float sum = 0.f;
    // for( int ti = tidx; ti <= params.timestep; ti += THREADS_PER_BLOCK ) {
    for (int ti = first_step + tidx; ti <= tlength; ti += THREADS_PER_BLOCK) {
        bool is_mask = (params.masked_tokens != nullptr) && params.masked_tokens[bi_seq_len_offset + ti];
#ifdef FP8_MHA
        float logit = 0.f;
        if (FP8_MHA_KERNEL) {
            logit = is_mask ? 0.f :
                              __expf((qk_smem[ti - first_step] - qk_max) * params.query_weight_output_scale[0]
                                     * params.query_weight_output_scale[0]);
        }
        else {
            logit = is_mask ? 0.f : __expf(qk_smem[ti - first_step] - qk_max);
        }
#else
        float logit       = is_mask ? 0.f : __expf(qk_smem[ti - first_step] - qk_max);
#endif
        sum += logit;
        qk_smem[ti - first_step] = logit;
    }

    // Compute the sum.
    sum = block_sum<WARPS_PER_BLOCK>(&red_smem[WARPS_PER_BLOCK], sum);

//   if (threadIdx.x == 0) {
//        printf("SUM[%d] = %f\n", hi, (float)sum);
//    }

    // Normalize the logits.
    float inv_sum = __fdividef(1.f, sum + 1.e-6f);

    for (int ti = first_step + tidx; ti <= tlength; ti += THREADS_PER_BLOCK) {
        float logit = qk_smem[ti - first_step] * inv_sum;
        convert_from_float(logits_smem[ti - first_step], logit);
    }

    // Put Values part below so we leverage __syncthreads
    // from the previous step

    // The number of elements per vector.
    constexpr int V_VEC_SIZE = Dh_MAX / THREADS_PER_VALUE;
    // A vector of V elements for the current timestep.
    using V_vec_k = typename V_vec_k_<T, V_VEC_SIZE>::Type;
    using V_vec_m = typename V_vec_m_<T, V_VEC_SIZE>::Type;

    // The value computed by this thread.
    int vo = tidx / THREADS_PER_VALUE;
    // The hidden dimensions computed by this particular thread.
    int vi = tidx % THREADS_PER_VALUE * V_VEC_SIZE;

    // The base pointer for the value in the cache buffer.
    T* v_cache       = nullptr;
    T* v_cache_batch = nullptr;

    int8_t* v_cache_int8       = nullptr;
    int8_t* v_cache_batch_int8 = nullptr;

    if (!QUANT_POLICY) {
        v_cache =
            params.v_cache_per_sample[bi] + params.kv_cache_per_sample_offset + kvhi * params.memory_max_len * Dh + vi;
        // Base pointer for the beam's batch, before offsetting with indirection buffer
        // T* v_cache_batch = &params.v_cache[bbhi * params.memory_max_len * Dh + vi];
        v_cache_batch = v_cache;
    }
    else if (QUANT_POLICY == 4) {
        int8_t* ptr        = reinterpret_cast<int8_t*>(params.v_cache_per_sample[bi]);
        v_cache_int8       = ptr + params.kv_cache_per_sample_offset + kvhi * params.memory_max_len * Dh + vi;
        v_cache_batch_int8 = v_cache_int8;
    }

    // The number of values processed per iteration of the loop.
    constexpr int V_PER_ITER = THREADS_PER_BLOCK / THREADS_PER_VALUE;

    // From previous, before values, step
    // Also make sure the logits are in shared memory.
    __syncthreads();

    // Values continued
#ifdef MMHA_USE_FP32_ACUM_FOR_OUT
    using V_vec_acum = typename V_vec_acum_fp32_<V_vec_k>::Type;
#else
    using V_vec_acum = V_vec_k;
#endif
    // The partial outputs computed by each thread.
    V_vec_acum out;
    zero(out);

    // Loop over the timesteps to compute the partial outputs.
    // for( int ti = vo; ti < params.timestep; ti += V_PER_ITER ) {
    if (Dh == Dh_MAX || vi < Dh) {
        using Packed_Int8_t  = typename packed_type<int8_t, num_elems<V_vec_m>::value>::type;
        using Packed_Float_t = typename packed_type<float, num_elems<V_vec_m>::value>::type;
        // Separate the ti < memory_max_len and ti > memory_max_len
        // to prevent ti % memory_len when ti < memory_len, and
        // the compiler cannot optimize the codes automatically.
        const int min_length = min(tlength, params.memory_max_len);
        for (int ti = first_step + vo; ti < min_length; ti += V_PER_ITER) {
            // Load the values from the cache.
            V_vec_k v;

            if (!QUANT_POLICY) {
                v = vec_conversion<V_vec_k, V_vec_m>(*reinterpret_cast<const V_vec_m*>(&v_cache_batch[ti * Dh]));
            }
            else if (QUANT_POLICY == 4) {
                Packed_Int8_t  v_vec_m_int8  = *reinterpret_cast<const Packed_Int8_t*>(&v_cache_batch_int8[ti * Dh]);
                Packed_Float_t v_vec_m_float = dequant(v_vec_m_int8, v_scale, v_zp);

                v = vec_conversion<V_vec_k, Packed_Float_t>(v_vec_m_float);
            }

            // Load the logits from shared memory.
#if defined(MMHA_USE_FP32_ACUM_FOR_LOGITS)
            float logit = logits_smem[ti - first_step];
            out         = fma(logit, cast_to_float(v), out);
#else  // MMHA_USE_FP32_ACUM_FOR_LOGITS
#ifdef FP8_MHA
            Tk logit;
            if (FP8_MHA_KERNEL) {
                // NOTE: fake quantization
                // logit = vec_conversion<Tk, Tquant>(vec_conversion<Tquant, Tk>(mul<Tk, float, Tk>(1.0f /
                // params.attention_qk_scale[0], logits_smem[ti])));
                logit = logits_smem[ti - first_step];
            }
            else {
                logit = logits_smem[ti - first_step];
            }
            out = fma(logit, v, out);
#else   // FP8_MHA
            Tk logit = logits_smem[ti - first_step];
            out      = fma(logit, v, out);
#endif  // FP8_MHA
#endif  // MMHA_USE_FP32_ACUM_FOR_LOGITS
        }
        for (int ti = first_step + vo; ti < tlength; ti += V_PER_ITER) {
            if (ti < params.memory_max_len) {
                // handled by previous loop
                continue;
            }
            const int ti_circ = ti % params.memory_max_len;

            // Load the values from the cache.
            V_vec_k v;
            if (!QUANT_POLICY) {
                v = vec_conversion<V_vec_k, V_vec_m>(*reinterpret_cast<const V_vec_m*>(&v_cache_batch[ti_circ * Dh]));
            }
            else if (QUANT_POLICY == 4) {
                Packed_Int8_t v_vec_m_int8 = *reinterpret_cast<const Packed_Int8_t*>(&v_cache_batch_int8[ti_circ * Dh]);
                Packed_Float_t v_vec_m_float = dequant(v_vec_m_int8, v_scale, v_zp);

                v = vec_conversion<V_vec_k, Packed_Float_t>(v_vec_m_float);
            }

            // Load the logits from shared memory.
#if defined(MMHA_USE_FP32_ACUM_FOR_LOGITS)
            float logit = logits_smem[ti - first_step];
            out         = fma(logit, cast_to_float(v), out);
#else  // MMHA_USE_FP32_ACUM_FOR_LOGITS
#ifdef FP8_MHA
            Tk logit;
            if (FP8_MHA_KERNEL) {
                // NOTE: fake quantization
                // logit = vec_conversion<Tk, Tquant>(vec_conversion<Tquant, Tk>(mul<Tk, float, Tk>(1.0f /
                // params.attention_qk_scale[0], logits_smem[ti])));
                logit = logits_smem[ti - first_step];
            }
            else {
                logit = logits_smem[ti - first_step];
            }
            out = fma(logit, v, out);
#else   // FP8_MHA
            Tk logit = logits_smem[ti - first_step];
            out      = fma(logit, v, out);
#endif  // FP8_MHA
#endif  // MMHA_USE_FP32_ACUM_FOR_LOGITS
        }
    }

    // One group of threads computes the product(s) for the current timestep.
    // if( vo == params.timestep % V_PER_ITER ) {
    if (vo == tlength % V_PER_ITER && (Dh == Dh_MAX || vi < Dh)) {

        V_vec_k v;

        // Trigger the loads from the V buffer.
        const auto v_offset = k_base_offset + vi;

        v = vec_conversion<V_vec_k, V_vec_m>(*reinterpret_cast<const V_vec_m*>(&params.v[v_offset]));

        // Trigger the loads from the V bias buffer.
        if (params.v_bias != nullptr) {
            V_vec_k v_bias = *reinterpret_cast<const V_vec_k*>(&params.v_bias[kvhi * Dh + vi]);
            v              = add(v, v_bias);
        }

        // Store the V values to cache
        if (group_leader) {

            // Store the values with bias back to global memory in the cache for V.
            if (!QUANT_POLICY) {
                *reinterpret_cast<V_vec_m*>(&v_cache[tlength_circ * Dh]) = vec_conversion<V_vec_m, V_vec_k>(v);
            }
            else if (QUANT_POLICY == 4) {
                using Packed_Int8_t  = typename packed_type<int8_t, num_elems<V_vec_k>::value>::type;
                Packed_Int8_t v_int8 = quant(v, v_scale, v_zp);
                *reinterpret_cast<Packed_Int8_t*>(&v_cache_int8[tlength_circ * Dh]) = v_int8;
            }
        }

        // Initialize the output value with the current timestep.
#if defined(MMHA_USE_FP32_ACUM_FOR_LOGITS)
        // out = fma(logits_smem[params.timestep], cast_to_float(v), out);
        out = fma(logits_smem[tlength - first_step], cast_to_float(v), out);
#else  // MMHA_USE_FP32_ACUM_FOR_LOGITS
       // out = fma(logits_smem[params.timestep], v, out);
#ifdef FP8_MHA
        Tk logit;
        if (FP8_MHA_KERNEL) {
            // NOTE: fake quantization
            // logit = mul<Tk, float, Tk>(1.0f / params.attention_qk_scale[0], logits_smem[tlength]);
            logit = logits_smem[tlength - first_step];
        }
        else {
            logit = logits_smem[tlength - first_step];
        }
        out = fma(logit, v, out);
#else   // FP8_MHA
        out = fma(logits_smem[tlength - first_step], v, out);
#endif  // FP8_MHA
#endif  // MMHA_USE_FP32_ACUM_FOR_LOGITS
    }

    // Make sure we can start writing to shared memory.
    __syncthreads();

    // Run the final reduction amongst the different groups computing different partial outputs.
    if (Dh == Dh_MAX || vi < Dh) {
#pragma unroll
        for (int active_groups = V_PER_ITER; active_groups >= 2; active_groups /= 2) {

            // The midpoint in the number of active groups.
            int midpoint = active_groups / 2;

            // The upper part of active threads store to shared memory.
            if (vo >= midpoint && vo < active_groups && (Dh == Dh_MAX || vi < Dh)) {
#ifdef MMHA_USE_FP32_ACUM_FOR_OUT
                convert_from_float(*reinterpret_cast<V_vec_k*>(&out_smem[(vo - midpoint) * Dh + vi]), out);
#else
                *reinterpret_cast<V_vec_k*>(&out_smem[(vo - midpoint) * Dh + vi]) = out;
#endif
            }
            __syncthreads();

            // The bottom warps update their values.
            if (vo < midpoint && (Dh == Dh_MAX || vi < Dh)) {
                out = add(*reinterpret_cast<const V_vec_k*>(&out_smem[vo * Dh + vi]), out);
            }
            __syncthreads();
        }
    }

    // Output the final values.
    if (vo == 0 && (Dh == Dh_MAX || vi < Dh)) {
#ifdef MMHA_USE_FP32_ACUM_FOR_OUT
        if (FP8_MHA_KERNEL) {
#ifdef FP8_MHA
            // float result_scale = params.attention_qk_scale[0] * params.query_weight_output_scale[0] *
            // params.attention_output_weight_input_scale_inv[0];
            float result_scale =
                params.query_weight_output_scale[0] * params.attention_output_weight_input_scale_inv[0];
            convert_from_float(*reinterpret_cast<V_vec_m*>(&params.out[bhi * Dh + vi]),
                               mul<V_vec_acum, float, V_vec_acum>(result_scale, out));
#endif  // FP8_MHA
        }
        else {
            convert_from_float(*reinterpret_cast<V_vec_m*>(&params.out[bhi * Dh + vi]), out);
        }
#else   // MMHA_USE_FP32_ACUM_FOR_OUT
        // TODO: support int8_mode?
        *reinterpret_cast<V_vec_m*>(&params.out[bhi * Dh + vi]) = vec_conversion<V_vec_m, V_vec_acum>(out);
#endif  // MMHA_USE_FP32_ACUM_FOR_OUT
    }
}

////////////////////////////////////////////////////////////////////////////////////////////////////

}  // namespace mmha

////////////////////////////////////////////////////////////////////////////////////////////////////

template<typename T, int Dh_MAX>
struct threads_per_value_t {
    static const int value = Dh_MAX * sizeof(T) / 16;
};
#ifdef ENABLE_FP8
template<int Dh_MAX>
struct threads_per_value_t<__nv_fp8_e4m3, Dh_MAX> {
    static const int value = Dh_MAX * 4 / 16;  // DEBUG: float v
};
#endif

template<typename T, int Dh, int Dh_MAX, typename KERNEL_PARAMS_TYPE>
void mmha_launch_kernel(const KERNEL_PARAMS_TYPE& params, const cudaStream_t& stream);
