CUDA: 共享存储器实现矩阵相乘

共享存储器使用__shared__限定词分配。

　　相关阅读：

       CUDA编程接口：运行初始化与设备存储器

　　CUDA编程接口：使用nvcc编译器的兼容性

　　CUDA编程接口：如何用nvcc编译CUDA程序

　　CUDA编程模型：存储器层次和异构编程

　　CUDA编程模型：内核与线程层次概述

　　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。

#include<stdio.h>#include<cutil.h>#include<cuda_runtime.h>
#pragma comment(lib, "cudart.lib")#pragma comment(lib, "cutil32.lib")
bool InitCUDA(void){ int count = 0; int i = 0;
 cudaGetDeviceCount(&count); if(count == 0) {  fprintf(stderr, "There is no device.\n");  return false; }
 for(i = 0; i < count; i++) {  cudaDeviceProp prop;  if(cudaGetDeviceProperties(&prop, i) == cudaSuccess)  {   if(prop.major >= 1)   {    break;   }  } } if(i == count) {  fprintf(stderr, "There is no device supporting CUDA.\n");  return false; } cudaSetDevice(i);
 printf("CUDA initialized.\n"); return true;  }///////////////////////////////////////////////////////////////////////////////////////////#define THREAD_NUM 256
#define MATRIX_SIZE 100 //方阵阶
float a[MATRIX_SIZE][MATRIX_SIZE], b[MATRIX_SIZE][MATRIX_SIZE], c[MATRIX_SIZE][MATRIX_SIZE];
void Random_Number(float source[][MATRIX_SIZE]){ for(int i = 0; i < MATRIX_SIZE; i++) {  for(int j = 0; j < MATRIX_SIZE; j++)  {   source[i][j] = float(rand() % 10) / 10;  } }}
__global__ static void Matrix_Mul(const float* source1, const float* source2, float* result){ const int tid = threadIdx.x; const int bid = blockIdx.x; const int id = bid * blockDim.x + tid; const int row = id / MATRIX_SIZE; const int col = id % MATRIX_SIZE;
 if(row < MATRIX_SIZE && col < MATRIX_SIZE) {  float t = 0;  for(int i = 0; i < MATRIX_SIZE; i++)  {   t += source1[row * MATRIX_SIZE + i] * source2[i * MATRIX_SIZE + col];  }  result[row * MATRIX_SIZE + col] = t; }}
int main(int argc,char* argv[]){ InitCUDA();//初始化CUDA
 float *ac, *bc, *cc; size_t lda, ldb, ldc;
 srand(0);
 Random_Number(a); Random_Number(b);
 unsigned int timer = 0; CUT_SAFE_CALL( cutCreateTimer(&timer)); CUT_SAFE_CALL( cutStartTimer(timer));//define in cutil.h //到显存中申请空间,其中lda,ldb,ldc为显存中的行间距 cudaMallocPitch((void**)&ac, &lda, sizeof(float) * MATRIX_SIZE, MATRIX_SIZE); cudaMallocPitch((void**)&bc, &ldb, sizeof(float) * MATRIX_SIZE, MATRIX_SIZE); cudaMallocPitch((void**)&cc, &ldc, sizeof(float) * MATRIX_SIZE, MATRIX_SIZE); //复制内存元素到显存 cudaMemcpy2D(ac, lda, a, sizeof(float) * MATRIX_SIZE, sizeof(float) * MATRIX_SIZE, MATRIX_SIZE, cudaMemcpyHostToDevice); cudaMemcpy2D(bc, ldb, b, sizeof(float) * MATRIX_SIZE, sizeof(float) * MATRIX_SIZE, MATRIX_SIZE, cudaMemcpyHostToDevice);
 int BLOCK_NUM = (MATRIX_SIZE + THREAD_NUM - 1) / THREAD_NUM;
 Matrix_Mul<<<BLOCK_NUM * MATRIX_SIZE, THREAD_NUM, 0>>>(ac, bc, cc); //把处理结果从显存中取出,其中c对应sizeof(float)*MATRIX_SIZE,cc对应ldc cudaMemcpy2D(c, sizeof(float) * MATRIX_SIZE, cc, ldc, sizeof(float) * MATRIX_SIZE, MATRIX_SIZE, cudaMemcpyDeviceToHost);
 cutStopTimer(timer);
 printf("Processing time: %f (ms)\n", cutGetTimerValue(timer));
 for(int j = 0; j < MATRIX_SIZE; j++) {  float temp = 0;  for(int i = 0; i < MATRIX_SIZE; i++)  {   temp += a[0][i] * b[i][j];  }
  printf ("CPU:c[0][%d]=%f\n", j, temp);  printf ("GPU:c[0][%d]=%f\n", j, c[0][j]); }
 system("PAUSE");
 return 0;}

 　　

　　▲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。

#define BLOCK_SIZE 16// 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 CMatrix Csub = GetSubMatrix(C, blockRow, blockCol);// Each thread computes one element of Csub // by accumulating results into Cvaluefloat Cvalue = 0;// Thread row and column within Csubint 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 resultsfor (int m = 0; m < (A.width / BLOCK_SIZE); ++m){// Get sub-matrix Asub of AMatrix 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-matrixAs[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 togetherfor (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 elementSetElement(Csub, row, col, Cvalue); }

　　

　　▲图2 使用共享存储器的矩阵相乘

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