欧拉-黎曼函数的K阶近似（OpenMP实现和MPI实现）

问题描述

OpenMP代码实现

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <omp.h>

#include<time.h>
#include <windows.h>        //window环境下调用Sleep()函数包含此头文件

double zeta_approximation(int s, int k)
{
    double result = 0.0;

#pragma omp parallel for reduction(+:result)
    for (int i = 1; i <= k; i++) {
        for (int j = 1; j <= k; j++)
        {
            //result += 1.0 / (pow(n, k) * pow(k, n));
            result += pow(-1, i+1) / pow(i+j, s);
        }
    }

    return result * pow(2, s);
}

int main()
{
    int s = 20;
    int k = 3000;

	clock_t start = 0;
	clock_t end   = 0;
    double approximation = 0.0;

    start = clock();
    for (int i = 1; i <= k; i++) {
        for (int j = 1; j <= k; j++)
        {
            //result += 1.0 / (pow(n, k) * pow(k, n));
            approximation += pow(-1, i + 1) / pow(i + j, s);
        }
    }
    approximation = approximation * pow(2, s);
    end = clock();
    printf("zeta(%d, %d) ≈ %f\n", s, k, approximation);
    printf("总的cpU时间 = %f\n", (end - start) / (double)CLOCKS_PER_SEC);


    omp_set_num_threads(4);  // 设置线程数量
    approximation = 0.0;
    start = 0;
    end = 0;

	start = clock();
    approximation = zeta_approximation(s, k);
	end = clock();
    printf("Zetaop(%d, %d) ≈ %f\n", s, k, approximation);
    printf("总的CPU时间 = %f\n", (end - start) / (double)CLOCKS_PER_SEC);

    return 0;
}

MPI代码实现

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <mpi.h>

double zeta_approximation(int s, int k, int rank, int num_procs)
{
    double result = 0.0;
    int start = rank * (k / num_procs) + 1;
    int end = (rank + 1) * (k / num_procs);

    if (rank == num_procs - 1) {
        end = k;
    }

    for (int i = start; i <= end; i++) {
        for (int j = 1; j <= k; j++) {
            result += pow(-1, i + 1) / pow(i + j, s);
        }
    }

    return result;
}

int main(int argc, char** argv)
{
    int s = 20;
    int k = 800;
    double approximation = 0.0;
    double total_approximation = 0.0;
    int rank, num_procs;

    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &num_procs);

    double start_time = MPI_Wtime();

    approximation = zeta_approximation(s, k, rank, num_procs);

    MPI_Reduce(&approximation, &total_approximation, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);

    double end_time = MPI_Wtime();

    if (rank == 0) {
        printf("Zetaop(%d, %d) ≈ %f\n", s, k, total_approximation * pow(2, s));
        printf("总的CPU时间 = %f\n", end_time - start_time);
    }

    MPI_Finalize();

    return 0;
}

注意事项

关于运行多线程，因为vs2019中只能显示一个线程的程序，所以我们要到cmd中实现多线程程序。

保存一下你的代码，到项目中找到exe程序，如下图。（一定是项目目录x64下的Debug中）

在路径栏中输入cmd打开dos窗口，输入下面这句话

mpiexec -n 8 demo.exe

8代表8个线程，后面是我的文件名，需要替换为你自己的文件名，回车运行即可。

运行

win10 + vs2019

参考资料

[1] OpenMP和MPI环境配置
[2]
[3]