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《CuTe C++ 简介01，从示例开始 》 中，最后看到了 计算 gemm 的cuda kernel，使用 NVIDIA CUTLASS 的 CUTe (CUDA Tile) 库实现的高性能 GEMM (通用矩阵乘法) CUDA kernel。接下来解释一下这个内核的各个部分。文末再贴一遍代码，方便查看。
1. 模板参数和函数签名
template <class ProblemShape, class CtaTiler,class TA, class AStride, class ASmemLayout, class AThreadLayout,class TB, class BStride, class BSmemLayout, class BThreadLayout,class TC, class CStride, class CSmemLayout, class CThreadLayout,class Alpha, class Beta>这个内核高度模板化，支持配置，
任意数据类型 (TA, TB, TC)；
任意矩阵形状和步长；
任意内存布局和线程映射；
不同的标量类型 (Alpha, Beta)；
2. 静态断言和预条件检查
大量的 CUTE_STATIC_ASSERT_V 和 static_assert 确保在编译时验证如下内容，
正确的张量维度；
线程布局和数据分块的兼容性；
内存布局的一致性；
3. 张量创建和分块
Tensor mA = make_tensor(make_gmem_ptr(A), select<0,2>(shape_MNK), dA);
Tensor gA = local_tile(mA, cta_tiler, cta_coord, Step<_1, X,_1>{});创建全局内存中的矩阵张量；
使用 local_tile 将大矩阵分块为线程 block 处理的子块；
4. 共享内存分配
__shared__ TA smemA[cosize_v<ASmemLayout>];
Tensor sA = make_tensor(make_smem_ptr(smemA), sA_layout);为矩阵 A 和 B 分配共享内存；
使用模板化的布局确保内存访问的高效性；
5. 数据分区
Tensor tAgA = local_partition(gA, tA, threadIdx.x);
Tensor tAsA = local_partition(sA, tA, threadIdx.x);将全局内存和共享内存的数据分区给各个线程；
每个线程负责加载特定的数据块；
6. 累加器分配和初始化
Tensor tCrC = make_tensor_like(tCgC);
clear(tCrC);为每个线程创建寄存器中的累加器；
初始化为零；
7. 主循环 (核心计算部分)
for (int k_tile = 0; k_tile < K_TILE_MAX; ++k_tile)
{copy(tAgA(_,_,k_tile), tAsA);copy(tBgB(_,_,k_tile), tBsB);cp_async_fence();cp_async_wait<0>();__syncthreads();gemm(tCsA, tCsB, tCrC);__syncthreads();
}这是内核的核心部分：
-
数据加载: 将全局内存中的数据拷贝到共享内存；
-
异步等待: 使用
cp_async指令实现异步数据加载； -
同步: 确保所有线程完成数据加载；
-
计算: 从共享内存加载数据并进行矩阵乘法计算；
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再次同步: 确保所有线程完成计算；
8. 收尾处理
axpby(alpha, tCrC, beta, tCgC);应用缩放因子 alpha 和 beta；
将计算结果写回全局内存；
关键点复盘
-
双缓冲机制: 通过循环处理 K 维度，实现计算和数据加载的重叠；
-
高效内存访问: 使用共享内存减少全局内存访问；
-
线程级并行: 精细的线程调度和数据分区；
-
模板元编程: 编译时优化，生成高度特化的代码；
-
异步拷贝: 使用
cp_async指令隐藏内存延迟；
评价：这个内核展示了现代 GPU 编程的最佳实践，通过精细的内存层次管理和线程调度来实现高性能的矩阵乘法运算。
template <class ProblemShape, class CtaTiler,class TA, class AStride, class ASmemLayout, class AThreadLayout,class TB, class BStride, class BSmemLayout, class BThreadLayout,class TC, class CStride, class CSmemLayout, class CThreadLayout,class Alpha, class Beta>
__global__ static
__launch_bounds__(decltype(size(CThreadLayout{}))::value)
void
gemm_device(ProblemShape shape_MNK, CtaTiler cta_tiler,TA const* A, AStride dA, ASmemLayout sA_layout, AThreadLayout tA,TB const* B, BStride dB, BSmemLayout sB_layout, BThreadLayout tB,TC * C, CStride dC, CSmemLayout , CThreadLayout tC,Alpha alpha, Beta beta)
{using namespace cute;// PreconditionsCUTE_STATIC_ASSERT_V(rank(shape_MNK) == Int<3>{}); // (M, N, K)CUTE_STATIC_ASSERT_V(rank(cta_tiler) == Int<3>{}); // (BLK_M, BLK_N, BLK_K)static_assert(is_static<AThreadLayout>::value);static_assert(is_static<BThreadLayout>::value);static_assert(is_static<CThreadLayout>::value);CUTE_STATIC_ASSERT_V(size(tA) == size(tB)); // NumThreadsCUTE_STATIC_ASSERT_V(size(tC) == size(tA)); // NumThreadsCUTE_STATIC_ASSERT_V(size<0>(cta_tiler) % size<0>(tA) == Int<0>{}); // BLK_M / THR_MCUTE_STATIC_ASSERT_V(size<2>(cta_tiler) % size<1>(tA) == Int<0>{}); // BLK_K / THR_KCUTE_STATIC_ASSERT_V(size<1>(cta_tiler) % size<0>(tB) == Int<0>{}); // BLK_N / THR_NCUTE_STATIC_ASSERT_V(size<2>(cta_tiler) % size<1>(tB) == Int<0>{}); // BLK_K / THR_KCUTE_STATIC_ASSERT_V(size<0>(cta_tiler) % size<0>(tC) == Int<0>{}); // BLK_M / THR_MCUTE_STATIC_ASSERT_V(size<1>(cta_tiler) % size<1>(tC) == Int<0>{}); // BLK_N / THR_Nstatic_assert(is_static<ASmemLayout>::value);static_assert(is_static<BSmemLayout>::value);static_assert(is_static<CSmemLayout>::value);CUTE_STATIC_ASSERT_V(size<0>(ASmemLayout{}) == size<0>(cta_tiler)); // BLK_MCUTE_STATIC_ASSERT_V(size<0>(CSmemLayout{}) == size<0>(cta_tiler)); // BLK_MCUTE_STATIC_ASSERT_V(size<0>(BSmemLayout{}) == size<1>(cta_tiler)); // BLK_NCUTE_STATIC_ASSERT_V(size<1>(CSmemLayout{}) == size<1>(cta_tiler)); // BLK_NCUTE_STATIC_ASSERT_V(size<1>(ASmemLayout{}) == size<2>(cta_tiler)); // BLK_KCUTE_STATIC_ASSERT_V(size<1>(BSmemLayout{}) == size<2>(cta_tiler)); // BLK_KCUTE_STATIC_ASSERT_V(congruent(select<0,2>(shape_MNK), dA)); // dA strides for shape MKCUTE_STATIC_ASSERT_V(congruent(select<1,2>(shape_MNK), dB)); // dB strides for shape NKCUTE_STATIC_ASSERT_V(congruent(select<0,1>(shape_MNK), dC)); // dC strides for shape MN//// Full and Tiled Tensors//// Represent the full tensorsTensor mA = make_tensor(make_gmem_ptr(A), select<0,2>(shape_MNK), dA); // (M,K)Tensor mB = make_tensor(make_gmem_ptr(B), select<1,2>(shape_MNK), dB); // (N,K)Tensor mC = make_tensor(make_gmem_ptr(C), select<0,1>(shape_MNK), dC); // (M,N)// Get the appropriate blocks for this thread blockauto cta_coord = make_coord(blockIdx.x, blockIdx.y, _); // (m,n,k)Tensor gA = local_tile(mA, cta_tiler, cta_coord, Step<_1, X,_1>{}); // (BLK_M,BLK_K,k)Tensor gB = local_tile(mB, cta_tiler, cta_coord, Step< X,_1,_1>{}); // (BLK_N,BLK_K,k)Tensor gC = local_tile(mC, cta_tiler, cta_coord, Step<_1,_1, X>{}); // (BLK_M,BLK_N)// Shared memory buffers__shared__ TA smemA[cosize_v<ASmemLayout>];__shared__ TB smemB[cosize_v<BSmemLayout>];Tensor sA = make_tensor(make_smem_ptr(smemA), sA_layout); // (BLK_M,BLK_K)Tensor sB = make_tensor(make_smem_ptr(smemB), sB_layout); // (BLK_N,BLK_K)//// Partition the copying of A and B tiles across the threads//// TUTORIAL: Example of simple raked partitioning of ThreadLayouts tA|tB over data A|B tilesTensor tAgA = local_partition(gA, tA, threadIdx.x); // (THR_M,THR_K,k)Tensor tAsA = local_partition(sA, tA, threadIdx.x); // (THR_M,THR_K)Tensor tBgB = local_partition(gB, tB, threadIdx.x); // (THR_N,THR_K,k)Tensor tBsB = local_partition(sB, tB, threadIdx.x); // (THR_N,THR_K)CUTE_STATIC_ASSERT_V(size<0>(tAgA) == size<0>(tAsA)); // THR_MCUTE_STATIC_ASSERT_V(size<1>(tAgA) == size<1>(tAsA)); // THR_KCUTE_STATIC_ASSERT_V(size<0>(tBgB) == size<0>(tBsB)); // THR_NCUTE_STATIC_ASSERT_V(size<1>(tBgB) == size<1>(tBsB)); // THR_K//// Define A/B partitioning and C accumulators//// TUTORIAL: Example of partitioning via projections of a ThreadLayout tC// Partition sA (BLK_M, BLK_K) by the rows of tCTensor tCsA = local_partition(sA, tC, threadIdx.x, Step<_1, X>{}); // (THR_M,BLK_K)// Partition sB (BLK_N, BLK_K) by the cols of tCTensor tCsB = local_partition(sB, tC, threadIdx.x, Step< X,_1>{}); // (THR_N,BLK_K)// Partition gC (M,N) by the tile of tCTensor tCgC = local_partition(gC, tC, threadIdx.x, Step<_1,_1>{}); // (THR_M,THR_N)// Allocate the accumulators -- same shape/layout as the partitioned dataTensor tCrC = make_tensor_like(tCgC); // (THR_M,THR_N)CUTE_STATIC_ASSERT_V(size<0>(tCrC) == size<0>(tCgC)); // THR_MCUTE_STATIC_ASSERT_V(size<0>(tCrC) == size<0>(tCsA)); // THR_MCUTE_STATIC_ASSERT_V(size<1>(tCrC) == size<1>(tCgC)); // THR_NCUTE_STATIC_ASSERT_V(size<1>(tCrC) == size<0>(tCsB)); // THR_NCUTE_STATIC_ASSERT_V(size<1>(tCsA) == size<1>(tCsB)); // BLK_K// Clear the accumulatorsclear(tCrC);#if 0if(thread0()) {print(" mA : "); print( mA); print("\n");print(" gA : "); print( gA); print("\n");print(" sA : "); print( sA); print("\n");print("tAgA : "); print(tAgA); print("\n");print("tAsA : "); print(tAsA); print("\n");}
#endif#if 0if(thread0()) {print(" mB : "); print( mB); print("\n");print(" gB : "); print( gB); print("\n");print(" sB : "); print( sB); print("\n");print("tBgB : "); print(tBgB); print("\n");print("tBsB : "); print(tBsB); print("\n");}
#endif#if 0if(thread0()) {print(" mC : "); print( mC); print("\n");print(" gC : "); print( gC); print("\n");print("tCsA : "); print(tCsA); print("\n");print("tCsB : "); print(tCsB); print("\n");print("tCgC : "); print(tCgC); print("\n");print("tCrC : "); print(tCrC); print("\n");}
#endif#if 1// TUTORIAL: Example of a simple mainloop that read tiles of data into shared memory,// and then computes on those tiles.// copy(.) operates on the global and shared memory via the tA|tB partitioning// gemm(.) operates on the shared and register memory via the tC partitioningauto K_TILE_MAX = size<2>(tAgA);for (int k_tile = 0; k_tile < K_TILE_MAX; ++k_tile){// Copy gmem to smem with tA|tB thread-partitioned tensorscopy(tAgA(_,_,k_tile), tAsA); // A (THR_M,THR_K) -> (THR_M,THR_K)copy(tBgB(_,_,k_tile), tBsB); // B (THR_N,THR_K) -> (THR_N,THR_K)// TUTORIAL: The above call to copy(tAgA(_,_,k_tile), tAsA) is equivalent to// Tensor tAgAk = tAgA(_,_,k_tile);// CUTE_UNROLL// for (int i = 0; i < size(tAsA); ++i) {// tAsA(i) = tAgAk(i);// }cp_async_fence(); // Label the end of (potential) cp.async instructionscp_async_wait<0>(); // Sync on all (potential) cp.async instructions__syncthreads(); // Wait for all threads to write to smem// Compute gemm on tC thread-partitioned smemgemm(tCsA, tCsB, tCrC); // (THR_M,THR_N) += (THR_M,BLK_K) * (THR_N,BLK_K)// TUTORIAL: The above call to gemm(tCsA, tCsB, tCrC) is equivalent to// CUTE_UNROLL// for (int k = 0; k < size<1>(tCsA); ++k) {// CUTE_UNROLL// for (int m = 0; m < size<0>(tCrC); ++m) {// CUTE_UNROLL// for (int n = 0; n < size<1>(tCrC); ++n) {// tCrC(m,n) += tCsA(m,k) * tCsB(n,k);// }// }// }__syncthreads(); // Wait for all threads to read from smem}#endif//// Epilogue//axpby(alpha, tCrC, beta, tCgC);// TUTORIAL: The above call to axpby(alpha, tCrC, beta, tCgC) is equivalent to// CUTE_UNROLL// for (int i = 0; i < size(tCrC); ++i) {// tCgC(i) = alpha * tCrC(i) + beta * tCgC(i);// }
}