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#ifndef lint |
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static const char RCSid[] = "$Id$"; |
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#endif |
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/* |
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* zeroes.c - compute roots for various equations. |
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* |
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* External symbols declared in standard.h |
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*/ |
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|
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/* ==================================================================== |
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* The Radiance Software License, Version 1.0 |
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* |
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* Copyright (c) 1990 - 2002 The Regents of the University of California, |
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* through Lawrence Berkeley National Laboratory. All rights reserved. |
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* |
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* Redistribution and use in source and binary forms, with or without |
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* modification, are permitted provided that the following conditions |
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* are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in |
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* the documentation and/or other materials provided with the |
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* distribution. |
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* |
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* 3. The end-user documentation included with the redistribution, |
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* if any, must include the following acknowledgment: |
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* "This product includes Radiance software |
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* (http://radsite.lbl.gov/) |
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* developed by the Lawrence Berkeley National Laboratory |
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* (http://www.lbl.gov/)." |
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* Alternately, this acknowledgment may appear in the software itself, |
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* if and wherever such third-party acknowledgments normally appear. |
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* |
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* 4. The names "Radiance," "Lawrence Berkeley National Laboratory" |
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* and "The Regents of the University of California" must |
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* not be used to endorse or promote products derived from this |
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* software without prior written permission. For written |
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* permission, please contact [email protected]. |
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* |
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* 5. Products derived from this software may not be called "Radiance", |
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* nor may "Radiance" appear in their name, without prior written |
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* permission of Lawrence Berkeley National Laboratory. |
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* |
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND ANY EXPRESSED OR IMPLIED |
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* WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES |
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE |
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* DISCLAIMED. IN NO EVENT SHALL Lawrence Berkeley National Laboratory OR |
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* ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
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* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
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* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF |
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* USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND |
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* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, |
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT |
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* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
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* SUCH DAMAGE. |
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* ==================================================================== |
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* |
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* This software consists of voluntary contributions made by many |
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* individuals on behalf of Lawrence Berkeley National Laboratory. For more |
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* information on Lawrence Berkeley National Laboratory, please see |
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* <http://www.lbl.gov/>. |
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*/ |
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|
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|
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#include <math.h> |
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|
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#include "fvect.h" |
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|
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|
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int |
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quadratic(r, a, b, c) /* find real roots of quadratic equation */ |
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double *r; /* roots in ascending order */ |
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double a, b, c; |
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{ |
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double disc; |
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int first; |
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|
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if (a < -FTINY) |
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first = 1; |
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else if (a > FTINY) |
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first = 0; |
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else if (fabs(b) > FTINY) { /* solve linearly */ |
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r[0] = -c/b; |
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return(1); |
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} else |
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return(0); /* equation is c == 0 ! */ |
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|
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b *= 0.5; /* simplifies formula */ |
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|
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disc = b*b - a*c; /* discriminant */ |
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|
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if (disc < -FTINY*FTINY) /* no real roots */ |
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return(0); |
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|
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if (disc <= FTINY*FTINY) { /* double root */ |
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r[0] = -b/a; |
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return(1); |
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} |
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|
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disc = sqrt(disc); |
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|
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r[first] = (-b - disc)/a; |
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r[1-first] = (-b + disc)/a; |
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|
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return(2); |
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} |