CUDA编程接口：共享存储器实现矩阵相乘

左手的ㄟ右手 2022-08-01 12:15 172阅读 0赞

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;
    }

![CUDA编程接口：共享存储器实现矩阵相乘][CUDA]

▲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_SIZE
    void 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); 
    }

![CUDA编程接口：共享存储器实现矩阵相乘][CUDA 1]

▲图2 使用共享存储器的矩阵相乘

[CUDA]: /images/20220731/0ed67550ce354fbfa85bda3ccc4af923.png
[CUDA 1]: /images/20220731/2f1784cd5a74424b8bd5abcfd1671f0c.png