/* complex_solve_quadratic.c - finds complex roots of a x^2 + b x + c = 0 */

#include <config.h>
#include <math.h>
#include <gsl_complex.h>
#include <gsl_poly.h>

int
gsl_poly_complex_solve_quadratic (double a, double b, double c,
				  gsl_complex *z0, gsl_complex *z1)
{
  double disc = b * b - 4 * a * c;

  if (disc > 0)
    {
      if (b == 0)
	{
	  double s = fabs (0.5 * sqrt (disc) / a);
	  GSL_REAL (*z0) = -s;
	  GSL_IMAG (*z0) = 0;
	  GSL_REAL (*z1) = s;
	  GSL_IMAG (*z1) = 0;
	}
      else
	{
	  double sgnb = (b > 0 ? 1 : -1);
	  double temp = -0.5 * (b + sgnb * sqrt (disc));
	  double r1 = temp / a;
	  double r2 = c / temp;

	  if (r1 < r2)
	    {
	      GSL_REAL (*z0) = r1;
	      GSL_IMAG (*z0) = 0;
	      GSL_REAL (*z1) = r2;
	      GSL_IMAG (*z1) = 0;
	    }
	  else
	    {
	      GSL_REAL (*z0) = r2;
	      GSL_IMAG (*z0) = 0;
	      GSL_REAL (*z1) = r1;
	      GSL_IMAG (*z1) = 0;
	    }
	}
      return 2;
    }
  else if (disc == 0)
    {
      GSL_REAL (*z0) = -0.5 * b / a;
      GSL_IMAG (*z0) = 0;

      GSL_REAL (*z1) = -0.5 * b / a;
      GSL_IMAG (*z1) = 0;

      return 2;
    }
  else
    {
      double s = fabs (0.5 * sqrt (-disc) / a);

      GSL_REAL (*z0) = -0.5 * b / a;
      GSL_IMAG (*z0) = -s;

      GSL_REAL (*z1) = -0.5 * b / a;
      GSL_IMAG (*z1) = s;

      return 2;
    }
}