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
#	User	Rev	Content
1	greg	1.1	#ifndef lint
2	greg	2.3	static const char RCSid[] = "$Id$";
3	greg	1.1	#endif
4			/*
5			* zeroes.c - compute roots for various equations.
6			*
7	greg	2.3	* 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	greg	1.1	*/
66
67
68	greg	2.2	#include <math.h>
69	greg	1.1
70	greg	2.2	#include "fvect.h"
71
72
73	greg	1.1	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			}