#include <library.h>

using namespace std;

bool close(const double a, const double b)
{ return fabs(a - b) < 0.000001; } 


// The Newton-Raphson method, N is what you want the square root of,
// and g is just a rough guess at what that square root might be.
// and doesn't matter much how bad the guess is, this procedure
// improves the first guess very quickly.

double nr(const double N, const double g)
{ cout << g << " squared " << setprecision(15) << g * g << "\n";
  if (close(N, g * g))
    return g;
  else
    return nr(N, (g + N / g) / 2); }

int main()
{ cout << "number: ";
  const double n = read_double();
                   // see the note below
  const double s = nr(n, combine_mant_exp(0.9, exponent(n) / 2));
  cout << setprecision(16) << s << " squared is " << s * s << "\n"; }

  // the original version of this function call was:
  //   const double s = nr(n, n / 2);
  // n / 2 is a really bad guess at sqrt(n) but it still works really
  // well. This next version stars with a really good initial guess
  // and gets to an accurate answer even faster. Do not be worried if
  // you don't see exactly how that expression works, that isn't the
  // point today and you'll learn about this sort of thing before
  // verl long