/* poly/zsolve_quadratic.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough

 * 

 * This program is free software; you can redistribute it and/or modify

 * it under the terms of the GNU General Public License as published by

 * the Free Software Foundation; either version 3 of the License, or (at

 * your option) any later version.

 * 

 * This program is distributed in the hope that it will be useful, but

 * WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 * 

 * You should have received a copy of the GNU General Public License

 * along with this program; if not, write to the Free Software

 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

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

#include <config.h>

#include <math.h>

#include <gsl/gsl_complex.h>

#include <gsl/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 (a == 0) /* Handle linear case */

    {

      if (b == 0)

        {

          return 0;

        }

      else

        {

          GSL_REAL(*z0) = -c / b;

          GSL_IMAG(*z0) = 0;

          return 1;

        };

    }

  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;

    }

}