/* Copyright (C) 1997-2001 Ken Turkowski. <turk@computer.org>
 *
 * All rights reserved.
 *
 * Warranty Information
 *  Even though I have reviewed this software, I make no warranty
 *  or representation, either express or implied, with respect to this
 *  software, its quality, accuracy, merchantability, or fitness for a
 *  particular purpose.  As a result, this software is provided "as is,"
 *  and you, its user, are assuming the entire risk as to its quality
 *  and accuracy.
 *
 * This code may be used and freely distributed as long as it includes
 * this copyright notice and the above warranty information.
 */

#include <math.h>


#ifdef DOUBLE_PRECISION
# define FLOAT double
# define PARAMFLOAT double_t
#else   /* DOUBLE_PRECISION */
# define FLOAT float
# define PARAMFLOAT float_t
#endif  /* DOUBLE_PRECISION */


/*******************************************************************************
 * FindCubicRoots
 *
 *  Solve:
 *      coeff[3] * x^3 + coeff[2] * x^2 + coeff[1] * x + coeff[0] = 0
 *
 *  returns:
 *      3 - 3 real roots
 *      1 - 1 real root (2 complex conjugate)
 *******************************************************************************/

int
FindCubicRoots(const FLOAT coeff[4], FLOAT x[3])
{
    FLOAT a1 = coeff[2] / coeff[3];
    FLOAT a2 = coeff[1] / coeff[3];
    FLOAT a3 = coeff[0] / coeff[3];

    double_t Q = (a1 * a1 - 3 * a2) / 9;
    double_t R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) / 54;
    double_t Qcubed = Q * Q * Q;
    double_t d = Qcubed - R * R;

    /* Three real roots */
    if (d >= 0) {
        double_t theta = acos(R / sqrt(Qcubed));
        double_t sqrtQ = sqrt(Q);
        x[0] = -2 * sqrtQ * cos( theta             / 3) - a1 / 3;
        x[1] = -2 * sqrtQ * cos((theta + 2 * M_PI) / 3) - a1 / 3;
        x[2] = -2 * sqrtQ * cos((theta + 4 * M_PI) / 3) - a1 / 3;
        return (3);
    }

    /* One real root */
    else {
        double_t e = pow(sqrt(-d) + fabs(R), 1. / 3.);
        if (R > 0)
            e = -e;
        x[0] = (e + Q / e) - a1 / 3.;
        return (1);
    }
}