/*
 * Newton.c: Newton Method ニュートン法
 */
#include <stdio.h>
#include <math.h>
/*
  f(x) = x^2-a = 0
  x = sqrt(a)
*/
int main()
{
    double a, x, x0, err;
    double epsa = 1e-70, epsr = 1e-10;
    char s[128];

    printf(" a = "); gets(s); sscanf(s,"%lf",&a);

    x = (a+1)/2;
    do {
        x0 = x;
        x = 0.5*(x0+a/x0);
        err = fabs(x-x0)/(epsa+epsr*(fabs(x0)+fabs(x)));
        printf(" x =  %e err =  %e\n",x,err);
    } while (err >= 1);
    putchar('\n');
    printf(" sqrt(%e) =  %e\n", a,x);
    return 0;
}
/*   ---------   実行例: 教科書 p.42 例題3.1   ---------   */
/*
Z:\src\C>Newton
 a = 2
 x =  1.416667e+00 err =  2.857143e+08
 x =  1.414216e+00 err =  8.658009e+06
 x =  1.414214e+00 err =  7.509114e+03
 x =  1.414214e+00 err =  5.638202e-03

 sqrt(2.000000e+00) =  1.414214e+00
*/