/* Copyright (C) 1997-2001 Ken Turkowski.
*
* 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
#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);
}
}