CUDA编程接口：共享存储器实现矩阵相乘

转自http://cuda.it168.com/a2011/1207/1285/000001285186.shtml

正如在前面的文章提到的，共享存储器应当比全局存储器更快，详细内容将在后续文章中介绍。任何用访问共享存储器取代访问全局存储器的机会应当被发掘，如下面的矩阵相乘例子展示的那样。 下面的代码是矩阵相乘的一个直接的实现，没有利用到共享存储器。每个线程读入A的一行和B的一列，然后计算C中对应的元素，如图1所示。这样，A读了B.width次，B读了A.height次。

// Matrices are stored in row-major order:// M(row, col) = *(M.elements + row * M.width + col) typedef struct {int width;int height;float* elements; } Matrix; // Thread block size #define BLOCK_SIZE 16 // Forward declaration of the matrix multiplication kernel __global__ void MatMulKernel(const Matrix, const Matrix, Matrix); // Matrix multiplication - Host code // Matrix dimensions are assumed to be multiples of BLOCK_SIZE void MatMul(const Matrix A, const Matrix B, Matrix C) {    // Load A and B to device memory   Matrix d_A; d_A.width = A.width;   d_A.height = A.height;   size_t size = A.width * A.height * sizeof(float);   cudaMalloc((void**)&d_A.elements, size);    cudaMemcpy(d_A.elements, A.elements, size,    cudaMemcpyHostToDevice);   Matrix d_B;    d_B.width = B.width;   d_B.height = B.height; size = B.width * B.height * sizeof(float);   cudaMalloc((void**)&d_B.elements, size);   cudaMemcpy(d_B.elements, B.elements, size, cudaMemcpyHostToDevice);   // Allocate C in device memory Matrix d_C;    d_C.width = C.width;   d_C.height = C.height;   size = C.width * C.height * sizeof(float);    cudaMalloc((void**)&d_C.elements, size);   // Invoke kernel dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);   dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);   MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);   // Read C from device memory cudaMemcpy(C.elements, Cd.elements, size, cudaMemcpyDeviceToHost);   // Free device memory cudaFree(d_A.elements); cudaFree(d_B.elements);   cudaFree(d_C.elements);}// Matrix multiplication kernel called by MatMul() __global__ void MatMulKernel(Matrix A, Matrix B, Matrix C) {    // Each thread computes one element of C   // by accumulating results into Cvalue float Cvalue = 0;   int row = blockIdx.y * blockDim.y + threadIdx.y;   int col = blockIdx.x * blockDim.x + threadIdx.x;   for (int e = 0; e < A.width; ++e) Cvalue += A.elements[row * A.width + e] * B.elements[e * B.width + col];   C.elements[row * C.width + col] = Cvalue;}

　

　　▲图1 没有使用共享存储器的矩阵相乘

下面的例子代码利用了共享存储器实现矩阵相乘。本实现中，每个线程块负责计算一个小方阵Csub，Csub是C的一部分，而块内的每个线程计算Csub的一个元素。如图2所示。Csub等于两个长方形矩阵的乘积：A的子矩阵尺寸是(A.width,block_size)，行索引与Csub相同，B的子矩阵的尺寸是(block_size,A.width)，列索引与Csub相同。为了满足设备的资源，两个长方形的子矩阵分割为尺寸为block_size的方阵，Csub是这些方阵积的和。每次乘法的计算是这样的，首先从全局存储器中将二个对应的方阵载入共享存储器中，载入的方式是一个线程载入一个矩阵元素，然后一个线程计算乘积的一个元素。每个线程积累每次乘法的结果并写入寄存器中，结束后，再写入全局存储器。

　　采用这种将计算分块的方式，利用了快速的共享存储器，节约了许多全局存储器带宽，因为在全局存储器中，A只被读了(B.width/block_size)次同时B读了(A.height/block_size)次。

　　前面代码中的Matrix 类型增加了一个stride域，这样子矩阵能够用同样的类型有效表示。__device__函数(相关阅读的文章中提及)用于读写元素和从矩阵中建立子矩阵。

// Matrices are stored in row-major order:// M(row, col) = *(M.elements + row * M.stride + col)typedef struct {  int width;  int height; int stride;  float* elements;}Matrix; // Get a matrix element __device__ float GetElement(const Matrix A, int row, int col) {   return A.elements[row * A.stride + col];} // Set a matrix element __device__ void SetElement(Matrix A, int row, int col, float value) {A.elements[row * A.stride + col] = value;} // Get the BLOCK_SIZExBLOCK_SIZE sub-matrix Asub of A that is// located col sub-matrices to the right and row sub-matrices down // from the upper-left corner of A __device__ Matrix GetSubMatrix(Matrix A, int row, int col) {  Matrix Asub;  Asub.width = BLOCK_SIZE;   Asub.height = BLOCK_SIZE;  Asub.stride = A.stride;  Asub.elements = &A.elements[A.stride * BLOCK_SIZE * row + BLOCK_SIZE * col];  return Asub;} // Thread block size #define BLOCK_SIZE 16 // Forward declaration of the matrix multiplication kernel __global__ void MatMulKernel(const Matrix, const Matrix, Matrix); // Matrix multiplication - Host code // Matrix dimensions are assumed to be multiples of BLOCK_SIZEvoid MatMul(const Matrix A, const Matrix B, Matrix C) {   // Load A and B to device memory Matrix d_A;    d_A.width = d_A.stride = A.width;   d_A.height = A.height;   size_t size = A.width * A.height * sizeof(float);   cudaMalloc((void**)&d_A.elements, size);   cudaMemcpy(d_A.elements, A.elements, size, cudaMemcpyHostToDevice);   Matrix d_B;   d_B.width = d_B.stride = B.width;   d_B.height = B.height;   size = B.width * B.height * sizeof(float);      cudaMalloc((void**)&d_B.elements, size);   cudaMemcpy(d_B.elements, B.elements, size,cudaMemcpyHostToDevice);   // Allocate C in device memory Matrix d_C;   d_C.width = d_C.stride = C.width;   d_C.height = C.height;   size = C.width * C.height * sizeof(float); cudaMalloc((void**)&d_C.elements, size);   // Invoke kernel dim3 dimBlock(BLOCK_SIZE, BLOCK_SIZE);   dim3 dimGrid(B.width / dimBlock.x, A.height / dimBlock.y);   MatMulKernel<<<dimGrid, dimBlock>>>(d_A, d_B, d_C);   // Read C from device memory cudaMemcpy(C.elements, d_C.elements, size, cudaMemcpyDeviceToHost);   // Free device memory cudaFree(d_A.elements); cudaFree(d_B.elements);   cudaFree(d_C.elements);}// Matrix multiplication kernel called by MatMul() __global__ void MatMulKernel(Matrix A, Matrix B, Matrix C) {   // Block row and column    int blockRow = blockIdx.y;   int blockCol = blockIdx.x;   // Each thread block computes one sub-matrix Csub of C   Matrix Csub = GetSubMatrix(C, blockRow, blockCol);   // Each thread computes one element of Csub    // by accumulating results into Cvalue   float Cvalue = 0;   // Thread row and column within Csub   int row = threadIdx.y;   int col = threadIdx.x;   // Loop over all the sub-matrices of A and B that are   // required to compute Csub   // Multiply each pair of sub-matrices together   // and accumulate the results   for (int m = 0; m < (A.width / BLOCK_SIZE); ++m) {   // Get sub-matrix Asub of A   Matrix Asub = GetSubMatrix(A, blockRow, m);   // Get sub-matrix Bsub of B Matrix Bsub = GetSubMatrix(B, m, blockCol);   // Shared memory used to store Asub and Bsub respectively   __shared__ float As[BLOCK_SIZE][BLOCK_SIZE];   __shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];   // Load Asub and Bsub from device memory to shared memory   // Each thread loads one element of each sub-matrix   As[row][col] = GetElement(Asub, row, col);   Bs[row][col] = GetElement(Bsub, row, col);   // Synchronize to make sure the sub-matrices are loaded   // before starting the computation    __syncthreads();   // Multiply Asub and Bsub together   for (int e = 0; e < BLOCK_SIZE; ++e)   Cvalue += As[row][e] * Bs[e][col];   // Synchronize to make sure that the preceding   // computation is done before loading two new   // sub-matrices of A and B in the next iteration   __syncthreads(); }   // Write Csub to device memory   // Each thread writes one element   SetElement(Csub, row, col, Cvalue); }

　

　　▲图2 使用共享存储器的矩阵相乘