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);
}