CPU 矩阵乘法
能相乘的两个矩阵，必须满足一个矩阵的行数和第二个矩阵的列数相同.
A(N*P) * B(P*M) = C(N*M). 其中P是行数，N是列数， 从宽高的角度来说，即 A的宽度和B的高度是相同的．C矩阵 = ha * wb.
其中C(i,j) = A矩阵中的i行和B矩阵中的j列进行点乘得到该点的值．
//C = A*B
void MatrixMulCPU(float* _C,const float *_A,const float *_B,int _wa,int _ha,int _wb)
{
float sum = 0;
for (int i = 0; i < _ha; ++i)
{
for (int j = 0; j < _wb; ++j)
{
sum = 0;
for (int k = 0; k < _wa; ++k)
{ //i*_wa得到当前对应的是A矩阵中的哪一行，+k对应当前行的哪一列．矩阵Ａ的stride是wa //j对应当前矩阵Ｂ的哪一列，＋k*wb依次表示第０行的j列,第１行的j列...第wa-1行的j列．矩阵Ｂ的stride是wb
sum += (float)_A[i*_wa+k]*(float)_B[k*_wb+ j];
}
_C[i*_wb+j] = (float)sum;
}
}
}
简单矩阵乘法
C(i,j) = sum { A(i,k)*B(k,j) } 0<=k < _wa;耦合程度很小，所以我们可以通过划分区域的方法，让每个线程负责一个区域。
怎么划分呢？首先最初的想法是让每一个线程计算一个C(i,j)，那么估算一下，应该需要height_c*width_c，也就是ha*wb个线程。进一步，我们将矩阵按一个大方格Block划分，如果一个方格Block大小是16*16，那么矩阵80*48的可以表示为5(*16) * 3(*16)，即5*3个大格子(Grid)，所以grid的划分自然就是(height_c/16) *(width_c/16)个线程了。
好了，划分完后，内核代码如下： 这个kernel的代码只是把外层两个循环变成
计算版本0：
__global__ void matrix_kernel_0(float* _C,const float* _A,const float *_B,int _wa,int _wb)
{
float sum = 0;
//找出该线程所在的行列
int row = blockIdx.y*blockDim.y + threadIdx.y;
int col = blockIdx.x*blockDim.x + threadIdx.x;
//线程Thread(row,col)负责计算C(row,col)
for (int i = 0; i < _wa; ++i)
{
sum += _A[row*_wa + i]*_B[i*_wb + col];
}
_C[row*_wb + col] = sum;
}
这个是Heterogeneous Parallel Programming lab3:Basic Matrix Matrix Multiplication的代码：
#include <wb.h>
#define wbCheck(stmt) do { cudaError_t err = stmt; if (err != cudaSuccess) { wbLog(ERROR, "Failed to run stmt ", #stmt); wbLog(ERROR, "Got CUDA error ... ", cudaGetErrorString(err)); return -1; } } while (0)
#if 0 //This is C verison matrixMUl
//C = A*B
void MatrixMulCPU(float* _C,const float *_A,const float *_B,int _wa,int _ha,int _wb)
{
float sum = 0;
for (int i = 0; i < _ha; ++i)
{
for (int j = 0; j < _wb; ++j)
{
sum = 0;
for (int k = 0; k < _wa; ++k)
{
sum += (float)_A[i*_wa+k]*(float)_B[k*_wb+ j];
}
_C[i*_wb+j] = (float)sum;
}
}
}
#endif
// Compute C = A * B , Matrix C = hA * wB = rowA * columnB
__global__ void matrixMultiply(float *A, float *B, float *C, int numARows,
int numAColumns, int numBRows, int numBColumns,
int numCRows, int numCColumns) {
//@@ Insert code to implement matrix multiplication here
float sum = 0.0f;
int row = blockIdx.y*blockDim.y + threadIdx.y;
int col = blockIdx.x*blockDim.x + threadIdx.x;
if(row < numCRows && col < numCColumns){
for (int i = 0; i < numAColumns; ++i)
{
sum += A[row*numAColumns + i] * B[i*numBColumns + col];
}
C[row*numBColumns + col] = sum;
}
printf("C = %f\n",C[row*numBColumns + col]);
}
int main(int argc, char **argv) {
wbArg_t args;
float *hostA; // The A matrix
float *hostB; // The B matrix
float *hostC; // The output C matrix
float *deviceA;
float *deviceB;
float *deviceC;
int numARows; // number of rows in the matrix A
int numAColumns; // number of columns in the matrix A
int numBRows; // number of rows in the matrix B
int numBColumns; // number of columns in the matrix B
int numCRows; // number of rows in the matrix C (you have to set this)
int numCColumns; // number of columns in the matrix C (you have to set this)
args = wbArg_read(argc, argv);
wbTime_start(Generic, "Importing data and creating memory on host");
hostA =
( float * )wbImport(wbArg_getInputFile(args, 0), &numARows, &numAColumns);
hostB =
( float * )wbImport(wbArg_getInputFile(args, 1), &numBRows, &numBColumns);
//@@ Set numCRows and numCColumns
numCRows = 0;
numCColumns = 0;
if(numAColumns != numBRows){
wbLog(TRACE, "numAColumns != numBRows, Break ");
return 1;
}
numCRows = numARows;
numCColumns = numBColumns;
unsigned int A_size = numARows * numAColumns * sizeof(float);
unsigned int B_size = numBRows * numBColumns * sizeof(float);
unsigned int C_size = numCRows * numCColumns * sizeof(float);
//@@ Allocate the hostC matrix
hostC = ( float * )malloc(C_size);
wbTime_stop(Generic, "Importing data and creating memory on host");
wbLog(TRACE, "The dimensions of A are ", numARows, " x ", numAColumns);
wbLog(TRACE, "The dimensions of B are ", numBRows, " x ", numBColumns);
wbTime_start(GPU, "Allocating GPU memory.");
//@@ Allocate GPU memory here
wbCheck(cudaMalloc((void**)&deviceA, A_size));
wbCheck(cudaMalloc((void**)&deviceB, B_size));
wbCheck(cudaMalloc((void**)&deviceC, C_size));
wbTime_stop(GPU, "Allocating GPU memory.");
wbTime_start(GPU, "Copying input memory to the GPU.");
//@@ Copy memory to the GPU here
wbCheck(cudaMemcpy(deviceA, hostA, A_size, cudaMemcpyHostToDevice));
wbCheck(cudaMemcpy(deviceB, hostB, B_size, cudaMemcpyHostToDevice));
wbCheck(cudaMemcpy(deviceC, hostC, C_size, cudaMemcpyHostToDevice));
wbTime_stop(GPU, "Copying input memory to the GPU.");
//@@ Initialize the grid and block dimensions here
dim3 DimGrid((numCColumns-1)/16+1, (numCRows-1)/16+1, 1);
dim3 DimBlock(16, 16, 1);
wbTime_start(Compute, "Performing CUDA computation");
//@@ Launch the GPU Kernel here
matrixMultiply<<< DimGrid, DimBlock >>>(deviceA, deviceB, deviceC, numARows, numAColumns, numBRows, numBColumns, numCRows, numCColumns);
cudaDeviceSynchronize();
wbTime_stop(Compute, "Performing CUDA computation");
wbTime_start(Copy, "Copying output memory to the CPU");
//@@ Copy the GPU memory back to the CPU here
//@@ Copy the GPU memory back to the CPU here
wbCheck(cudaMemcpy(hostC, deviceC, C_size, cudaMemcpyDeviceToHost));
wbTime_stop(Copy, "Copying output memory to the CPU");
wbTime_start(GPU, "Freeing GPU Memory");
//@@ Free the GPU memory here
wbCheck(cudaFree(deviceA));
wbCheck(cudaFree(deviceB));
wbCheck(cudaFree(deviceC));
wbTime_stop(GPU, "Freeing GPU Memory");
wbSolution(args, hostC, numCRows, numCColumns);
free(hostA);
free(hostB);
free(hostC);
return 0;
}
使用tile来划分矩阵乘法
另外一种思路，我们不让每一个线程完整计算一个C(i,j)，通过C(i,j) = sum { A(i,k)*B(k,j) }发现，我们还可以再细度划分：
Csub(i,j) = sum{A(i,ksub+offsetA)*B(ksub+offsetB,j)} 0<=ksub < blockSize
C(i,j) = sum{Csub(i,j)}
就是把矩阵分成n*n个大的子块，然后每一个block负责计算子块i 和 子块j的子乘积，计算完毕后加起来则可。这里主要引入shared Memory来提高程序效率．
__global__ void matrix_kernel_1(float* _C,const float* _A,const float *_B,int _wa,int _wb)
{
int bx = blockIdx.x; //Block X的当前位置
int by = blockIdx.y; //Block y的当前位置
int tx = threadIdx.x;
int ty = threadIdx.y;
//该block要处理的A
int aBegin = _wa*(by*BLOCK_SIZE);//A(0,by)
int aEnd = aBegin + _wa - 1;
int aStep = BLOCK_SIZE;//offsetA
int bBegin = BLOCK_SIZE*bx;//B(bx,0)
int bStep = BLOCK_SIZE*_wb;//offsetB
float cSub = 0;
for (int a = aBegin,b = bBegin; a <= aEnd; a += aStep,b += bStep)
{
__shared__ float As[BLOCK_SIZE][BLOCK_SIZE];
__shared__ float Bs[BLOCK_SIZE][BLOCK_SIZE];
//每个线程负责一个元素拷贝
As[ty][tx] = _A[a + _wa*ty + tx];
Bs[ty][tx] = _B[b + _wb*ty + tx];
__syncthreads();
//每个线程负责计算一个子块i 和 子块j的子乘积
for (int k = 0; k < BLOCK_SIZE; ++k)
{
cSub += As[ty][k]*Bs[k][tx];
}
__syncthreads();
}
//全局地址，向全局寄存器写回去
//一个线程负责一个元素，一个block负责一个子块
int cIndex = (by*BLOCK_SIZE + ty)*_wb + (bx*BLOCK_SIZE + tx);
_C[cIndex] = cSub;
}
时间： 2024-11-09 06:18:22