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

void squareroots(double y)
{ double min=0, max=y+1;       // for binary chop
  double g = y/2;              // g = guess for Newton-Raphson
  for (int i=0; i<100; i+=1)
  { double mid = (min+max)/2;
    if (mid*mid > y)
      max = mid;
    else
      min = mid;
    double correction = (g - y/g)/2;    // f(g) / derivative_of_f(g)
    g -= correction; 
    printf("%2d %25.17f %25.17f\n", i, mid, g); } }

void main(int argc, char * argv[])
                                   // type "a.out 123" to run the program
                                   // and calculate the square root of 123.
{ double v = atof(argv[1]);
  printf("         Binary Chop               Newton\n");
  printf("------------------------------------------------------\n");
  squareroots(v); }