目录
1. 使用一个二维网格和二维块的矩阵加法
1.1 关键代码
1.2 完整代码
1.3 运行时间
2. 使用一维网格和一维块的矩阵加法
2.1 关键代码
2.2 完整代码
2.3 运行时间
3. 使用二维网格和一维块的矩阵矩阵加法
3.1 关键代码
3.2 完整代码
3.3 运行时间
1. 使用一个二维网格和二维块的矩阵加法
这里建立二维网格(2,3)+二维块(4,2)为例，使用其块和线程索引映射矩阵索引。
（1）第一步，可以用以下公式把线程和块索引映射到矩阵坐标上；
（2）第二步，可以用以下公式把矩阵坐标映射到全局内存中的索引/存储单元上；
比如要获取矩阵元素(col,row) = (2,4) ,其全局索引是34，映射到矩阵坐标上，
ix = 2 + 0*3=2； iy = 0 + 2*2=4. 然后再映射到全局内存idx = 4*8 + 2 = 34.
1.1 关键代码
(1) 先固定二维线程块尺寸，再利用矩阵尺寸结合被分块尺寸，推导出二维网格尺寸。
// config
int dimx = 32;
int dimy = 32;
dim3 block(dimx, dimy); // 二维线程块(x,y)=(4,2)
dim3 grid((nx + block.x - 1) / block.x, (ny + block.y - 1) / block.y); // 二维网格(2,3)
// 直接nx/block.x = 8/4=2. (8+4-1)/4=2. (9+4-1)/4=3(2) 前面建立好了二维网格和二维线程块，根据公式去求矩阵索引。
// 去掉了循环
// 利用公式，使用二维网格、二维线程块映射矩阵索引。
__global__ void sumMatrixOnDevice2D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
// 二维网格和二维块，映射到矩阵坐标
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
unsigned int iy = threadIdx.y + blockIdx.y * blockDim.y;
// 由矩阵坐标, 映射到全局坐标(都是线性存储的)
unsigned int idx = iy * nx + ix; // 坐标(ix, iy),前面由iy行，每行有nx个元素
// 相加
if (ix < nx && iy < ny) // 配置线程的可能过多，这里防止越界。
{
d_c[idx] = d_a[idx] + d_b[idx];
}
}
1.2 完整代码
#include "cuda_runtime.h"
#include "device_launch_parameters.h" // threadIdx
#include <stdio.h> // io
#include <time.h> // time_t clock_t
#include <stdlib.h> // rand
#include <memory.h> //memset
#define CHECK(call) \
{ \
const cudaError_t error_code = call; \
if (error_code != cudaSuccess) \
{ \
printf("CUDA Error:\n"); \
printf(" File: %s\n", __FILE__); \
printf(" Line: %d\n", __LINE__); \
printf(" Error code: %d\n", error_code); \
printf(" Error text: %s\n", \
cudaGetErrorString(error_code)); \
exit(1); \
} \
}
/// <summary>
/// 矩阵相加，线性存储的二维矩阵
/// </summary>
/// <param name="h_a"></param>
/// <param name="h_b"></param>
/// <param name="h_c"></param>
/// <param name="nx"></param>
/// <param name="ny"></param>
void sumMatrixOnHost(float* h_a, float* h_b, float* h_c, const int nx, const int ny)
{
float* ia = h_a;
float* ib = h_b;
float* ic = h_c;
for (int iy = 0; iy < ny; iy++)
{
for (int ix = 0; ix < nx; ix++) // 处理当前行
{
ic[ix] = ia[ix] + ib[ix];
}
ia += nx; ib += nx; ic += nx; // 移动到下一行，ia下一行的第一个索引变成了0.
}
}
// 去掉循环
__global__ void sumMatrixOnDevice2D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
// 二维网格和二维块，映射到矩阵坐标
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
unsigned int iy = threadIdx.y + blockIdx.y * blockDim.y;
// 由矩阵坐标, 映射到全局坐标(都是线性存储的)
unsigned int idx = iy * nx + ix; // 坐标(ix, iy),前面由iy行，每行有nx个元素
// 相加
if (ix < nx && iy < ny) // 配置线程的可能过多，这里防止越界。
{
d_c[idx] = d_a[idx] + d_b[idx];
}
}
void initialData(float* p, const int N)
{
//generate different seed from random number
time_t t;
srand((unsigned int)time(&t)); // 生成种子
for (int i = 0; i < N; i++)
{
p[i] = (float)(rand() & 0xFF) / 10.0f; // 随机数
}
}
void checkResult(float* hostRef, float* deviceRef, const int N)
{
double eps = 1.0E-8;
int match = 1;
for (int i = 0; i < N; i++)
{
if (hostRef[i] - deviceRef[i] > eps)
{
match = 0;
printf("\nArrays do not match\n");
printf("host %5.2f gpu %5.2f at current %d\n", hostRef[i], deviceRef[i], i);
break;
}
}
if (match)
printf("\nArrays match!\n");
}
int main(void)
{
// get device info
int device = 0;
cudaDeviceProp deviceProp;
CHECK(cudaGetDeviceProperties(&deviceProp, device));
printf("Using device: %d %s", device, deviceProp.name); // 卡号0的显卡名称。
CHECK(cudaSetDevice(device)); // 设置显卡号
// set matrix dimension. 2^14 = 16384行列数
int nx = 1 << 13, ny = 1 << 13, nxy = nx * ny;
int nBytes = nxy * sizeof(float);
// malloc host memory
float* h_a, * h_b, * hostRef, * gpuRef;
h_a = (float*)malloc(nBytes);
h_b = (float*)malloc(nBytes);
hostRef = (float*)malloc(nBytes); // 主机端求得的结果
gpuRef = (float*)malloc(nBytes); // 设备端拷回的数据
// init data
initialData(h_a, nxy);
initialData(h_b, nxy);
memset(hostRef, 0, nBytes);
memset(gpuRef, 0, nBytes);
clock_t begin = clock();
// add matrix on host side for result checks.
sumMatrixOnHost(h_a, h_b, hostRef, nx, ny);
printf("\ncpu: %f s\n", (double)(clock() - begin) / CLOCKS_PER_SEC);
// malloc device memory
float* d_mat_a, * d_mat_b, * d_mat_c;
cudaMalloc((void**)&d_mat_a, nBytes);
cudaMalloc((void**)&d_mat_b, nBytes);
cudaMalloc((void**)&d_mat_c, nBytes);
// transfer data from host to device
cudaMemcpy(d_mat_a, h_a, nBytes, cudaMemcpyHostToDevice);
cudaMemcpy(d_mat_b, h_b, nBytes, cudaMemcpyHostToDevice);
// config
int dimx = 32;
int dimy = 32;
dim3 block(dimx, dimy); // 二维线程块(x,y)=(4,2)
dim3 grid((nx + block.x - 1) / block.x, (ny + block.y - 1) / block.y); // 二维网格(2,3)
// 直接nx/block.x = 8/4=2. (8+4-1)/4=2.
// invoke kernel
begin = clock();
sumMatrixOnDevice2D << <grid, block >> > (d_mat_a, d_mat_b, d_mat_c, nx, ny);
CHECK(cudaDeviceSynchronize());
printf("\ngpu: %f s\n", (double)(clock() - begin) / CLOCKS_PER_SEC);
// check kernel error
CHECK(cudaGetLastError());
// copy kernel result back to host side
cudaMemcpy(gpuRef, d_mat_c, nBytes, cudaMemcpyDeviceToHost);
// check result
checkResult(hostRef, gpuRef, nxy);
// free memory
cudaFree(d_mat_a);
cudaFree(d_mat_b);
cudaFree(d_mat_c);
free(h_a);
free(h_b);
free(hostRef);
free(gpuRef);
// reset device
cudaDeviceReset();
return 0;
}1.3 运行时间
加法运行速度提高了8倍。数据量越大，提升越明显。
2. 使用一维网格和一维块的矩阵加法
为了使用一维网格和一维块，需要写一个新的核函数，其中每个线程处理ny个数据元素。如上图，一维网格是水平方向的一维，一维块是水平方向的一维。
2.1 关键代码
(1) 建立垂直方向的一维块，再是水平方向一维网格
// config
int dimx = 32;
int dimy = 1;
dim3 block(dimx, dimy); // 一维线程块(x,y)=(32,1)，其中每一个线程都处理ny个元素。
// 一维网格((nx+block.x-1)/block.x,1)
dim3 grid((nx + block.x - 1) / block.x, 1);
(2) 前面建立好了一维网格和一维线程块，根据公式去求矩阵索引。
假设blockDim = (32,1). gridDim = (1024,1). 比如当前的threadIdx.x = 10, 由于前面有一个块，当前的位置映射矩阵索引
ix = threadIdx.x + blockIdx.x * blockDim.x = 10 + 1 * 32 = 42
由于一个线程处理ny个元素（所以这里有一个循环，ix不变，iy从第一行开始到ny行）。
__global__ void sumMatrixOnDevice1D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
// 一个线程处理ny个数据
if (ix < nx)
{
for (int iy = 0; iy < ny; iy++) // 处理ix这一列元素。
{
int idx = iy * nx + ix; // 第iy行前面有iy*nx个元素，再加上当前行第ix个
d_c[idx] = d_a[idx] + d_b[idx];
}
}
}2.2 完整代码
#include "cuda_runtime.h"
#include "device_launch_parameters.h" // threadIdx
#include <stdio.h> // io
#include <time.h> // time_t clock_t
#include <stdlib.h> // rand
#include <memory.h> //memset
#define CHECK(call) \
{ \
const cudaError_t error_code = call; \
if (error_code != cudaSuccess) \
{ \
printf("CUDA Error:\n"); \
printf(" File: %s\n", __FILE__); \
printf(" Line: %d\n", __LINE__); \
printf(" Error code: %d\n", error_code); \
printf(" Error text: %s\n", \
cudaGetErrorString(error_code)); \
exit(1); \
} \
}
/// <summary>
/// 矩阵相加，线性存储的二维矩阵
/// </summary>
/// <param name="h_a"></param>
/// <param name="h_b"></param>
/// <param name="h_c"></param>
/// <param name="nx"></param>
/// <param name="ny"></param>
void sumMatrixOnHost(float* h_a, float* h_b, float* h_c, const int nx, const int ny)
{
float* ia = h_a;
float* ib = h_b;
float* ic = h_c;
for (int iy = 0; iy < ny; iy++)
{
for (int ix = 0; ix < nx; ix++) // 处理当前行
{
ic[ix] = ia[ix] + ib[ix];
}
ia += nx; ib += nx; ic += nx; // 移动到下一行，ia下一行的第一个索引变成了0.
}
}
// 去掉了循环
__global__ void sumMatrixOnDevice2D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
// 二维网格和二维块，映射到矩阵坐标
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
unsigned int iy = threadIdx.y + blockIdx.y * blockDim.y;
// 由矩阵坐标, 映射到全局坐标(都是线性存储的)
unsigned int idx = iy * nx + ix; // 坐标(ix, iy),前面由iy行，每行有nx个元素
// 相加
if (ix < nx && iy < ny) // 配置线程的可能过多，这里防止越界。
{
d_c[idx] = d_a[idx] + d_b[idx];
}
}
__global__ void sumMatrixOnDevice1D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
// 一个线程处理ny个数据
if (ix < nx)
{
for (int iy = 0; iy < ny; iy++)
{
int idx = iy * nx + ix; // 第iy行前面有iy*nx个元素，再加上当前行第ix个
d_c[idx] = d_a[idx] + d_b[idx];
}
}
}
void initialData(float* p, const int N)
{
//generate different seed from random number
time_t t;
srand((unsigned int)time(&t)); // 生成种子
for (int i = 0; i < N; i++)
{
p[i] = (float)(rand() & 0xFF) / 10.0f; // 随机数
}
}
void checkResult(float* hostRef, float* deviceRef, const int N)
{
double eps = 1.0E-8;
int match = 1;
for (int i = 0; i < N; i++)
{
if (hostRef[i] - deviceRef[i] > eps)
{
match = 0;
printf("\nArrays do not match\n");
printf("host %5.2f gpu %5.2f at current %d\n", hostRef[i], deviceRef[i], i);
break;
}
}
if (match)
printf("\nArrays match!\n");
}
int main(void)
{
// get device info
int device = 0;
cudaDeviceProp deviceProp;
CHECK(cudaGetDeviceProperties(&deviceProp, device));
printf("Using device: %d %s", device, deviceProp.name); // 卡号0的显卡名称。
CHECK(cudaSetDevice(device)); // 设置显卡号
// set matrix dimension. 2^14 = 16384行列数
int nx = 1 << 13, ny = 1 << 13, nxy = nx * ny;
int nBytes = nxy * sizeof(float);
// malloc host memory
float* h_a, * h_b, * hostRef, * gpuRef;
h_a = (float*)malloc(nBytes);
h_b = (float*)malloc(nBytes);
hostRef = (float*)malloc(nBytes); // 主机端求得的结果
gpuRef = (float*)malloc(nBytes); // 设备端拷回的数据
// init data
initialData(h_a, nxy);
initialData(h_b, nxy);
memset(hostRef, 0, nBytes);
memset(gpuRef, 0, nBytes);
clock_t begin = clock();
// add matrix on host side for result checks.
sumMatrixOnHost(h_a, h_b, hostRef, nx, ny);
printf("\ncpu: %f s\n", (double)(clock() - begin) / CLOCKS_PER_SEC);
// malloc device memory
float* d_mat_a, * d_mat_b, * d_mat_c;
cudaMalloc((void**)&d_mat_a, nBytes);
cudaMalloc((void**)&d_mat_b, nBytes);
cudaMalloc((void**)&d_mat_c, nBytes);
// transfer data from host to device
cudaMemcpy(d_mat_a, h_a, nBytes, cudaMemcpyHostToDevice);
cudaMemcpy(d_mat_b, h_b, nBytes, cudaMemcpyHostToDevice);
// config
int dimx = 32;
int dimy = 1;
dim3 block(dimx, dimy); // 一维线程块(x,y)=(32,1)，其中每一个线程都处理ny个元素。
dim3 grid((nx + block.x - 1) / block.x, 1); // 一维网格((nx+block.x-1)/block.x,1)
// invoke kernel
begin = clock();
//sumMatrixOnDevice2D << <grid, block >> > (d_mat_a, d_mat_b, d_mat_c, nx, ny);
sumMatrixOnDevice1D << <grid, block >> > (d_mat_a, d_mat_b, d_mat_c, nx, ny);
CHECK(cudaDeviceSynchronize());
printf("\ngpu: %f s\n", (double)(clock() - begin) / CLOCKS_PER_SEC);
// check kernel error
CHECK(cudaGetLastError());
// copy kernel result back to host side
cudaMemcpy(gpuRef, d_mat_c, nBytes, cudaMemcpyDeviceToHost);
// check result
checkResult(hostRef, gpuRef, nxy);
// free memory
cudaFree(d_mat_a);
cudaFree(d_mat_b);
cudaFree(d_mat_c);
free(h_a);
free(h_b);
free(hostRef);
free(gpuRef);
// reset device
cudaDeviceReset();
return 0;
}2.3 运行时间
3. 使用二维网格和一维块的矩阵矩阵加法
当使用一个包含一维块的二维网格时，每个线程都只关注一个数据元素并且网格的第二个维数等于ny。比如块的维度是(32,1)，网格的维度是((nx+32-1)/32, (ny+1-1)/1) = ((nx+32-1)/32, ny).
这可以看作是含有一个二维块的二维网格的特殊情况，其中块的第二个维数是1.
利用块和网格索引，映射矩阵索引，如上图，blockIdx.y等于矩阵索引iy：
ix = threadIdx.x + blockIdx.x * blockDim.x;
iy = threadIdx.y + blockIdx.y * blockDim.y = threadIdx.y + 0 * 1 = threadIdx.y
再利用矩阵索引，映射全局内存索引:
idx = iy * nx + ix; // 当前行iy，块外的前面有iy * nx个元素，块内索引是ix
3.1 关键代码
(1) 建立一维线程块和二维网格
// config
int dimx = 32;
int dimy = 1;
dim3 block(dimx, dimy); // 一维线程块(x,y)=(32,1)，其中每一个线程都处理一个元素。
// ((nx+32-1)/32, (ny+1-1)/1) = ((nx+32-1)/32, ny)
dim3 grid((nx + block.x - 1) / block.x, ny);（2）利用块和网格索引，映射矩阵索引，再映射全局内存索引
__global__ void sumMatrixOnDevice2DGrid1DBlock(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
unsigned int iy = blockIdx.y; // threadIdx.y + blockIdx.y * blockDim.y = threadIdx.y + 0 * 1
unsigned int idx = iy * nx + ix;
if (ix < nx && iy < ny)
{
d_c[idx] = d_a[idx] + d_b[idx];
}
}3.2 完整代码
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#include "cuda_runtime.h"
#include "device_launch_parameters.h" // threadIdx
#include <stdio.h> // io
#include <time.h> // time_t clock_t
#include <stdlib.h> // rand
#include <memory.h> //memset
#define CHECK(call) \
{ \
const cudaError_t error_code = call; \
if (error_code != cudaSuccess) \
{ \
printf("CUDA Error:\n"); \
printf(" File: %s\n", __FILE__); \
printf(" Line: %d\n", __LINE__); \
printf(" Error code: %d\n", error_code); \
printf(" Error text: %s\n", \
cudaGetErrorString(error_code)); \
exit(1); \
} \
}
/// <summary>
/// 矩阵相加，线性存储的二维矩阵
/// </summary>
/// <param name="h_a"></param>
/// <param name="h_b"></param>
/// <param name="h_c"></param>
/// <param name="nx"></param>
/// <param name="ny"></param>
void sumMatrixOnHost(float* h_a, float* h_b, float* h_c, const int nx, const int ny)
{
float* ia = h_a;
float* ib = h_b;
float* ic = h_c;
for (int iy = 0; iy < ny; iy++)
{
for (int ix = 0; ix < nx; ix++) // 处理当前行
{
ic[ix] = ia[ix] + ib[ix];
}
ia += nx; ib += nx; ic += nx; // 移动到下一行，ia下一行的第一个索引变成了0.
}
}
// 去掉了循环
__global__ void sumMatrixOnDevice2D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
// 二维网格和二维块，映射到矩阵坐标
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
unsigned int iy = threadIdx.y + blockIdx.y * blockDim.y;
// 由矩阵坐标, 映射到全局坐标(都是线性存储的)
unsigned int idx = iy * nx + ix; // 坐标(ix, iy),前面由iy行，每行有nx个元素
// 相加
if (ix < nx && iy < ny) // 配置线程的可能过多，这里防止越界。
{
d_c[idx] = d_a[idx] + d_b[idx];
}
}
__global__ void sumMatrixOnDevice1D(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
// 一个线程处理ny个数据
if (ix < nx)
{
for (int iy = 0; iy < ny; iy++)
{
int idx = iy * nx + ix; // 第iy行前面有iy*nx个元素，再加上当前行第ix个
d_c[idx] = d_a[idx] + d_b[idx];
}
}
}
__global__ void sumMatrixOnDevice2DGrid1DBlock(float* d_a, float* d_b, float* d_c, const int nx, const int ny)
{
unsigned int ix = threadIdx.x + blockIdx.x * blockDim.x;
unsigned int iy = blockIdx.y; // threadIdx.y + blockIdx.y * blockDim.y = threadIdx.y + 0 * 1
unsigned int idx = iy * nx + ix;
if (ix < nx && iy < ny)
{
d_c[idx] = d_a[idx] + d_b[idx];
}
}
void initialData(float* p, const int N)
{
//generate different seed from random number
time_t t;
srand((unsigned int)time(&t)); // 生成种子
for (int i = 0; i < N; i++)
{
p[i] = (float)(rand() & 0xFF) / 10.0f; // 随机数
}
}
void checkResult(float* hostRef, float* deviceRef, const int N)
{
double eps = 1.0E-8;
int match = 1;
for (int i = 0; i < N; i++)
{
if (hostRef[i] - deviceRef[i] > eps)
{
match = 0;
printf("\nArrays do not match\n");
printf("host %5.2f gpu %5.2f at current %d\n", hostRef[i], deviceRef[i], i);
break;
}
}
if (match)
printf("\nArrays match!\n");
}
int main(void)
{
// get device info
int device = 0;
cudaDeviceProp deviceProp;
CHECK(cudaGetDeviceProperties(&deviceProp, device));
printf("Using device: %d %s", device, deviceProp.name); // 卡号0的显卡名称。
CHECK(cudaSetDevice(device)); // 设置显卡号
// set matrix dimension. 2^14 = 16384行列数
int nx = 1 << 13, ny = 1 << 13, nxy = nx * ny;
int nBytes = nxy * sizeof(float);
// malloc host memory
float* h_a, * h_b, * hostRef, * gpuRef;
h_a = (float*)malloc(nBytes);
h_b = (float*)malloc(nBytes);
hostRef = (float*)malloc(nBytes); // 主机端求得的结果
gpuRef = (float*)malloc(nBytes); // 设备端拷回的数据
// init data
initialData(h_a, nxy);
initialData(h_b, nxy);
memset(hostRef, 0, nBytes);
memset(gpuRef, 0, nBytes);
clock_t begin = clock();
// add matrix on host side for result checks.
sumMatrixOnHost(h_a, h_b, hostRef, nx, ny);
printf("\ncpu: %f s\n", (double)(clock() - begin) / CLOCKS_PER_SEC);
// malloc device memory
float* d_mat_a, * d_mat_b, * d_mat_c;
cudaMalloc((void**)&d_mat_a, nBytes);
cudaMalloc((void**)&d_mat_b, nBytes);
cudaMalloc((void**)&d_mat_c, nBytes);
// transfer data from host to device
cudaMemcpy(d_mat_a, h_a, nBytes, cudaMemcpyHostToDevice);
cudaMemcpy(d_mat_b, h_b, nBytes, cudaMemcpyHostToDevice);
// config
int dimx = 32;
int dimy = 1;
dim3 block(dimx, dimy); // 一维线程块(x,y)=(32,1)，其中每一个线程都处理一个元素。
// ((nx+32-1)/32, (ny+1-1)/1) = ((nx+32-1)/32, ny)
dim3 grid((nx + block.x - 1) / block.x, ny);
// invoke kernel
begin = clock();
//sumMatrixOnDevice2D << <grid, block >> > (d_mat_a, d_mat_b, d_mat_c, nx, ny);
//sumMatrixOnDevice1D << <grid, block >> > (d_mat_a, d_mat_b, d_mat_c, nx, ny);
sumMatrixOnDevice2DGrid1DBlock << <grid, block >> > (d_mat_a, d_mat_b, d_mat_c, nx, ny);
CHECK(cudaDeviceSynchronize());
printf("\ngpu: %f s\n", (double)(clock() - begin) / CLOCKS_PER_SEC);
// check kernel error
CHECK(cudaGetLastError());
// copy kernel result back to host side
cudaMemcpy(gpuRef, d_mat_c, nBytes, cudaMemcpyDeviceToHost);
// check result
checkResult(hostRef, gpuRef, nxy);
// free memory
cudaFree(d_mat_a);
cudaFree(d_mat_b);
cudaFree(d_mat_c);
free(h_a);
free(h_b);
free(hostRef);
free(gpuRef);
// reset device
cudaDeviceReset();
return 0;
}3.3 运行时间
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