/* poly/solve_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.

 */

/* solve_quadratic.c - finds the real roots of a x^2 + b x + c = 0 */

#include <config.h>

#include <math.h>

#include <gsl/gsl_poly.h>

int 

gsl_poly_solve_quadratic (double a, double b, double c, 

                          double *x0, double *x1)

{

  if (a == 0) /* Handle linear case */

    {

      if (b == 0)

        {

          return 0;

        }

      else

        {

          *x0 = -c / b;

          return 1;

        };

    }

  {

    double disc = b * b - 4 * a * c;

    if (disc > 0)

      {

        if (b == 0)

          {

            double r = sqrt (-c / a);

            *x0 = -r;

            *x1 =  r;

          }

        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) 

              {

                *x0 = r1 ;

                *x1 = r2 ;

              } 

            else 

              {

                *x0 = r2 ;

                  *x1 = r1 ;

              }

          }

        return 2;

      }

    else if (disc == 0) 

      {

        *x0 = -0.5 * b / a ;

        *x1 = -0.5 * b / a ;

        return 2 ;

      }

    else

      {

        return 0;

      }

  }

}