// Code by Hale F. Trotter to fractionalize a decimal value
// Converted to C by Alex Kontorovich, 4/20/02

int fractionestimate (double x, int *num, int *den, double tol)
/*{given a double  x , computes  longints  num  and  den  and}
{returns true if  num/den  is a rational number in lowest}
{terms that is a good rational approximation to  x .}
*/ 
{
	double //tol = 1e-9,    //{ x  is treated as  0  if  |x|  < tol }
		acc = 0.9e-3,  //{returns false if  |x|  > maxlongint/2 or }
                   //{                  |x - num/den| > acc*abs(x) + tol}
	crit = 1.0/tol,  //    {limit on how large numbers are allowed to get}
//		halfmaxlong = 1073741823.5, //; {half of maxlongint}
		w, y, qr, tr;
    int qi, ti;

	*num = 1;
	*den = 0;
	w = fabs(x);

	qr = (int)(w);  //{rounds  a double to int}
	y = 1.0;
	while (qr * abs(*den) < crit) //{don't let things get out of hand}
	{
		qi = (int)(qr);
		tr = y;
		y = w - qi * y;
		w = tr;
		ti = *den;
		*den = *num - qi * (*den);
		*num = ti;
		if (fabs(y) < tol)
			qr = crit;
		else
			qr = w / y;
	}
	*den = abs(*den);
	*num = (int)(*den * x);
	return (fabs(x - (*num) / (*den)) <= acc * fabs(x) + tol);
}