c++ - 我怎样才能优化我的程序？

Question

我编写了实现这个公式的程序:

Pi = 1/n * summ( 4/( 1 + ((i-0.5)/n)^2)

程序代码:

#include <iostream>
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <sys/time.h>
using namespace std;

const long double PI = double(M_PI);

int main(int argc, char* argv[])
{
    typedef struct timeval tm;
    tm start, end;
    int  timer = 0;
    int n;

    if (argc == 2) n = atoi(argv[1]);
    else n = 8000;

    long double pi1 = 0;
    gettimeofday ( &start, NULL );

    for(int i = 1; i <= n; i++) {
        pi1 += 4 / ( 1 + (i-0.5) * (i-0.5) / (n*n) );
    }

    pi1/=n;
    gettimeofday ( &end, NULL );
    timer = ( end.tv_usec - start.tv_usec ); 
    long double delta = pi1 - PI;
    printf("pi = %.12Lf\n",pi1);
    printf("delta = %.12Lf\n", delta);

    cout << "time = " << timer << endl;
    return 0;
}

如何以最佳方式呈现？当这部分浮点运算较少时:

for(int i = 1; i <= n; i++) {
            pi1 += 4 / ( 1 + (i-0.5) * (i-0.5) / (n*n) );
        }

谢谢

Answer 1

一个想法是:

double nn = n*n;
for(double i = 0.5; i < n; i += 1) {
    pi1 += 4 / ( 1 + i * i / nn );
}

但你需要测试一下它与当前代码是否有任何差异。