#ifndef lint
static const char RCSid[] = "$Id: zeroes.c,v 2.3 2003/02/22 02:07:23 greg Exp $";
#endif
/*
* zeroes.c - compute roots for various equations.
*
* External symbols declared in standard.h
*/
/* ====================================================================
* The Radiance Software License, Version 1.0
*
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* through Lawrence Berkeley National Laboratory. All rights reserved.
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* Redistribution and use in source and binary forms, with or without
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* if any, must include the following acknowledgment:
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* (http://radsite.lbl.gov/)
* developed by the Lawrence Berkeley National Laboratory
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*/
#include
#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);
}