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/* $Id: solvers.c,v 1.1.1.1 2004/12/23 04:04:04 ellson Exp $ $Revision: 1.1.1.1 $ */
/* vim:set shiftwidth=4 ts=8: */
/**********************************************************
* This software is part of the graphviz package *
* http://www.graphviz.org/ *
* *
* Copyright (c) 1994-2004 AT&T Corp. *
* and is licensed under the *
* Common Public License, Version 1.0 *
* by AT&T Corp. *
* *
* Information and Software Systems Research *
* AT&T Research, Florham Park NJ *
**********************************************************/
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <math.h>
#include "solvers.h"
#ifdef DMALLOC
#include "dmalloc.h"
#endif
#ifndef HAVE_CBRT
#define cbrt(x) ((x < 0) ? (-1*pow(-x, 1.0/3.0)) : pow (x, 1.0/3.0))
#endif
#ifndef M_PI
#define M_PI 3.14159265358979323846
#endif
#define EPS 1E-7
#define AEQ0(x) (((x) < EPS) && ((x) > -EPS))
int solve3(double *coeff, double *roots)
{
double a, b, c, d;
int rootn, i;
double p, q, disc, b_over_3a, c_over_a, d_over_a;
double r, theta, temp, alpha, beta;
a = coeff[3], b = coeff[2], c = coeff[1], d = coeff[0];
if (AEQ0(a))
return solve2(coeff, roots);
b_over_3a = b / (3 * a);
c_over_a = c / a;
d_over_a = d / a;
p = b_over_3a * b_over_3a;
q = 2 * b_over_3a * p - b_over_3a * c_over_a + d_over_a;
p = c_over_a / 3 - p;
disc = q * q + 4 * p * p * p;
if (disc < 0) {
r = .5 * sqrt(-disc + q * q);
theta = atan2(sqrt(-disc), -q);
temp = 2 * cbrt(r);
roots[0] = temp * cos(theta / 3);
roots[1] = temp * cos((theta + M_PI + M_PI) / 3);
roots[2] = temp * cos((theta - M_PI - M_PI) / 3);
rootn = 3;
} else {
alpha = .5 * (sqrt(disc) - q);
beta = -q - alpha;
roots[0] = cbrt(alpha) + cbrt(beta);
if (disc > 0)
rootn = 1;
else
roots[1] = roots[2] = -.5 * roots[0], rootn = 3;
}
for (i = 0; i < rootn; i++)
roots[i] -= b_over_3a;
return rootn;
}
int solve2(double *coeff, double *roots)
{
double a, b, c;
double disc, b_over_2a, c_over_a;
a = coeff[2], b = coeff[1], c = coeff[0];
if (AEQ0(a))
return solve1(coeff, roots);
b_over_2a = b / (2 * a);
c_over_a = c / a;
disc = b_over_2a * b_over_2a - c_over_a;
if (disc < 0)
return 0;
else if (disc == 0) {
roots[0] = -b_over_2a;
return 1;
} else {
roots[0] = -b_over_2a + sqrt(disc);
roots[1] = -2 * b_over_2a - roots[0];
return 2;
}
}
int solve1(double *coeff, double *roots)
{
double a, b;
a = coeff[1], b = coeff[0];
if (AEQ0(a)) {
if (AEQ0(b))
return 4;
else
return 0;
}
roots[0] = -b / a;
return 1;
}
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