TheAlgorithms-C-Plus-Plus/math/sqrt_double.cpp

#include <iostream>
#include <cassert>

/* Calculate the square root of any 
number in O(logn) time, 
with precision fixed */

double Sqrt(double x)
{
    double l = 0, r = x;
    /* Epsilon is the precision. 
    A great precision is 
    between 1e-7 and 1e-12.
    double epsilon = 1e-12;
    */
    while( l <= r )
    {
        double mid = (l + r) / 2;
        if( mid * mid > x )
        {
            r = mid;
        } 
        else 
        {
            if( x - mid * mid < epsilon )
            {
                return mid;
            }
            l = mid;
        }
    }
    return -1;
}

int main()
{
  double n{};
  std::cin >> n;
  assert(n >= 0);
  //Change this line for a better precision
  std::cout.precision(12);
  std::cout << std::fixed << Sqrt(n);
}