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/*
** CUBIC.C - Solve a cubic polynomial
** public domain by Ross Cottrell
*/
#include <math.h>
#include <stdlib.h>
void SolveCubic(double a,
double b,
double c,
double d,
int *solutions,
double *x)
{
long double a1 = b/a, a2 = c/a, a3 = d/a;
long double Q = (a1*a1 - 3.0*a2)/9.0;
long double R = (2.0*a1*a1*a1 - 9.0*a1*a2 + 27.0*a3)/54.0;
double R2_Q3 = R*R - Q*Q*Q;
double theta;
if (R2_Q3 <= 0)
{
*solutions = 3;
theta = acos(R/sqrt(Q*Q*Q));
x[0] = -2.0*sqrt(Q)*cos(theta/3.0) - a1/3.0;
x[1] = -2.0*sqrt(Q)*cos((theta+2.0*M_PI)/3.0) - a1/3.0;
x[2] = -2.0*sqrt(Q)*cos((theta+4.0*M_PI)/3.0) - a1/3.0;
}
else
{
*solutions = 1;
x[0] = pow(sqrt(R2_Q3)+fabs(R), 1/3.0);
x[0] += Q/x[0];
x[0] *= (R < 0.0) ? 1 : -1;
x[0] -= a1/3.0;
}
}
#ifdef TEST
int main(void)
{
double a1 = 1.0, b1 = -10.5, c1 = 32.0, d1 = -30.0;
double a2 = 1.0, b2 = -4.5, c2 = 17.0, d2 = -30.0;
double x[3];
int solutions;
SolveCubic(a1, b1, c1, d1, &solutions, x);
/* should get 3 solutions: 2, 6 & 2.5 */
SolveCubic(a2, b2, c2, d2, &solutions, x);
/* should get 1 solution: 2.5 */
return 0;
}
#endif /* TEST */
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