欧拉-黎曼函数的K阶近似（OpenMP实现和MPI实现）

问题描述

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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;
}