1 /*
2  *  AUTHOR
3  *	Catherine Loader, catherine@research.bell-labs.com.
4  *	October 23, 2000.
5  *
6  *  Merge in to R:
7  *	Copyright (C) 2000, The R Core Team
8  *
9  *  This program is free software; you can redistribute it and/or modify
10  *  it under the terms of the GNU General Public License as published by
11  *  the Free Software Foundation; either version 2 of the License, or
12  *  (at your option) any later version.
13  *
14  *  This program is distributed in the hope that it will be useful,
15  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
16  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
17  *  GNU General Public License for more details.
18  *
19  *  You should have received a copy of the GNU General Public License
20  *  along with this program; if not, a copy is available at
21  *  http://www.r-project.org/Licenses/
22  *
23  *
24  *  DESCRIPTION
25  *	Evaluates the "deviance part"
26  *	bd0(x,M) :=  M * D0(x/M) = M*[ x/M * log(x/M) + 1 - (x/M) ] =
27  *		  =  x * log(x/M) + M - x
28  *	where M = E[X] = n*p (or = lambda), for	  x, M > 0
29  *
30  *	in a manner that should be stable (with small relative error)
31  *	for all x and M=np. In particular for x/np close to 1, direct
32  *	evaluation fails, and evaluation is based on the Taylor series
33  *	of log((1+v)/(1-v)) with v = (x-np)/(x+np).
34  */
35 #include "nmath.h"
36 
bd0(double x,double np)37 double attribute_hidden bd0(double x, double np)
38 {
39     double ej, s, s1, v;
40     int j;
41 
42     if(!R_FINITE(x) || !R_FINITE(np) || np == 0.0) ML_ERR_return_NAN;
43 
44     if (fabs(x-np) < 0.1*(x+np)) {
45 	v = (x-np)/(x+np);
46 	s = (x-np)*v;/* s using v -- change by MM */
47 	ej = 2*x*v;
48 	v = v*v;
49 	for (j=1; ; j++) { /* Taylor series */
50 	    ej *= v;
51 	    s1 = s+ej/((j<<1)+1);
52 	    if (s1==s) /* last term was effectively 0 */
53 		return(s1);
54 	    s = s1;
55 	}
56     }
57     /* else:  | x - np |  is not too small */
58     return(x*log(x/np)+np-x);
59 }
60