src/common/zeroes.c

#ifndef lint
static const char       RCSid[] = "$Id$";
#endif
/*
 *  zeroes.c - compute roots for various equations.
 *
 *  External symbols declared in standard.h
 */

/* ====================================================================
 * The Radiance Software License, Version 1.0
 *
 * Copyright (c) 1990 - 2002 The Regents of the University of California,
 * through Lawrence Berkeley National Laboratory.   All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *         notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *       notice, this list of conditions and the following disclaimer in
 *       the documentation and/or other materials provided with the
 *       distribution.
 *
 * 3. The end-user documentation included with the redistribution,
 *           if any, must include the following acknowledgment:
 *             "This product includes Radiance software
 *                 (http://radsite.lbl.gov/)
 *                 developed by the Lawrence Berkeley National Laboratory
 *               (http://www.lbl.gov/)."
 *       Alternately, this acknowledgment may appear in the software itself,
 *       if and wherever such third-party acknowledgments normally appear.
 *
 * 4. The names "Radiance," "Lawrence Berkeley National Laboratory"
 *       and "The Regents of the University of California" must
 *       not be used to endorse or promote products derived from this
 *       software without prior written permission. For written
 *       permission, please contact [email protected].
 *
 * 5. Products derived from this software may not be called "Radiance",
 *       nor may "Radiance" appear in their name, without prior written
 *       permission of Lawrence Berkeley National Laboratory.
 *
 * THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
 * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED.   IN NO EVENT SHALL Lawrence Berkeley National Laboratory OR
 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
 * USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
 * OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
 * OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 * ====================================================================
 *
 * This software consists of voluntary contributions made by many
 * individuals on behalf of Lawrence Berkeley National Laboratory.   For more
 * information on Lawrence Berkeley National Laboratory, please see
 * <http://www.lbl.gov/>.
 */


#include  <math.h>

#include  "fvect.h"


int
quadratic(r, a, b, c)           /* find real roots of quadratic equation */
double  *r;                     /* roots in ascending order */
double  a, b, c; 
{
        double  disc;
        int  first;

        if (a < -FTINY)
                first = 1;
        else if (a > FTINY)
                first = 0;
        else if (fabs(b) > FTINY) {     /* solve linearly */
                r[0] = -c/b;
                return(1);
        } else
                return(0);              /* equation is c == 0 ! */
                
        b *= 0.5;                       /* simplifies formula */
        
        disc = b*b - a*c;               /* discriminant */

        if (disc < -FTINY*FTINY)        /* no real roots */
                return(0);

        if (disc <= FTINY*FTINY) {      /* double root */
                r[0] = -b/a;
                return(1);
        }
        
        disc = sqrt(disc);

        r[first] = (-b - disc)/a;
        r[1-first] = (-b + disc)/a;

        return(2);
}
Revision:	2.3
Committed:	Sat Feb 22 02:07:23 2003 UTC (22 years, 8 months ago) by greg
Content type:	text/plain
Branch:	MAIN
Changes since 2.2:	+59 -5 lines
Log Message:	Changes and check-in for 3.5 release Includes new source files and modifications not recorded for many years See ray/doc/notes/ReleaseNotes for notes between 3.1 and 3.5 release
#	Content
1	#ifndef lint
2	static const char RCSid[] = "$Id$";
3	#endif
4	/*
5	* zeroes.c - compute roots for various equations.
6	*
7	* External symbols declared in standard.h
8	*/
9
10	/* ====================================================================
11	* The Radiance Software License, Version 1.0
12	*
13	* Copyright (c) 1990 - 2002 The Regents of the University of California,
14	* through Lawrence Berkeley National Laboratory. All rights reserved.
15	*
16	* Redistribution and use in source and binary forms, with or without
17	* modification, are permitted provided that the following conditions
18	* are met:
19	*
20	* 1. Redistributions of source code must retain the above copyright
21	* notice, this list of conditions and the following disclaimer.
22	*
23	* 2. Redistributions in binary form must reproduce the above copyright
24	* notice, this list of conditions and the following disclaimer in
25	* the documentation and/or other materials provided with the
26	* distribution.
27	*
28	* 3. The end-user documentation included with the redistribution,
29	* if any, must include the following acknowledgment:
30	* "This product includes Radiance software
31	* (http://radsite.lbl.gov/)
32	* developed by the Lawrence Berkeley National Laboratory
33	* (http://www.lbl.gov/)."
34	* Alternately, this acknowledgment may appear in the software itself,
35	* if and wherever such third-party acknowledgments normally appear.
36	*
37	* 4. The names "Radiance," "Lawrence Berkeley National Laboratory"
38	* and "The Regents of the University of California" must
39	* not be used to endorse or promote products derived from this
40	* software without prior written permission. For written
41	* permission, please contact [email protected].
42	*
43	* 5. Products derived from this software may not be called "Radiance",
44	* nor may "Radiance" appear in their name, without prior written
45	* permission of Lawrence Berkeley National Laboratory.
46	*
47	* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED
48	* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
49	* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
50	* DISCLAIMED. IN NO EVENT SHALL Lawrence Berkeley National Laboratory OR
51	* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
52	* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
53	* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF
54	* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
55	* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
56	* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
57	* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
58	* SUCH DAMAGE.
59	* ====================================================================
60	*
61	* This software consists of voluntary contributions made by many
62	* individuals on behalf of Lawrence Berkeley National Laboratory. For more
63	* information on Lawrence Berkeley National Laboratory, please see
64	* <http://www.lbl.gov/>.
65	*/
66
67
68	#include <math.h>
69
70	#include "fvect.h"
71
72
73	int
74	quadratic(r, a, b, c) /* find real roots of quadratic equation */
75	double r; / roots in ascending order */
76	double a, b, c;
77	{
78	double disc;
79	int first;
80
81	if (a < -FTINY)
82	first = 1;
83	else if (a > FTINY)
84	first = 0;
85	else if (fabs(b) > FTINY) { /* solve linearly */
86	r[0] = -c/b;
87	return(1);
88	} else
89	return(0); /* equation is c == 0 ! */
90
91	b = 0.5; / simplifies formula */
92
93	disc = bb - ac; /* discriminant */
94
95	if (disc < -FTINYFTINY) / no real roots */
96	return(0);
97
98	if (disc <= FTINYFTINY) { / double root */
99	r[0] = -b/a;
100	return(1);
101	}
102
103	disc = sqrt(disc);
104
105	r[first] = (-b - disc)/a;
106	r[1-first] = (-b + disc)/a;
107
108	return(2);
109	}