数学

思想

把0-1下面积分为n个小矩形，再每个处理器上处理一部分面积，最后加起来
比较重要的是for (i = myid + 1; i <= n; i += numprocs)来分配每个处理器计算的矩形id，很巧妙

代码

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

double f(double);

double f(double a) {
    return 4.0 / (1.0 + a * a);
}

int main(int argc, char* argv[])
{
    int n, myid, numproc, i;
    double PI25DT = 3.141592653589793238462643;
    double mypi, pi, h, sum, x;
    double startwtime = 0.0, endwtime;

    MPI_Init(&argc, &argv);
    MPI_Comm_size(MPI_COMM_WORLD, &numproc);
    MPI_Comm_rank(MPI_COMM_WORLD, &myid);

    n = 100000000;
    
    startwtime = MPI_Wtime();
    h = 1.0 / double(n);
    sum = 0.0;

    for (i = myid + 1; i <= n; i += numproc) {
        x = h * (double(i) - 0.5);
        sum += f(x);
    }
    mypi = h * sum;
    MPI_Reduce(&mypi, &pi, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
    if (myid == 0) {
        endwtime = MPI_Wtime();
        printf("pi is approximately %.16f, Error is %.16f\n", pi, fabs(pi - PI25DT));
        printf("wall clock time = %f\n", endwtime);
        fflush(stdout);
    }

    MPI_Finalize();
    return 0;
}

performance