src/common/erf.c

#ifndef lint
static const char       RCSid[] = "$Id$";
#endif
#ifndef lint
static  char sccsid[] = "@(#)erf.c 1.1 87/12/21 SMI"; /* from UCB 4.1 12/25/82 */
#endif

/*
        C program for floating point error function

        erf(x) returns the error function of its argument
        erfc(x) returns 1.0-erf(x)

        erf(x) is defined by
        ${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$

        the entry for erfc is provided because of the
        extreme loss of relative accuracy if erf(x) is
        called for large x and the result subtracted
        from 1. (e.g. for x= 10, 12 places are lost).

        There are no error returns.

        Calls exp.

        Coefficients for large x are #5667 from Hart & Cheney (18.72D).
*/

#define M 7
#define N 9
static double torp = 1.1283791670955125738961589031;
static double p1[] = {
        0.804373630960840172832162e5,
        0.740407142710151470082064e4,
        0.301782788536507577809226e4,
        0.380140318123903008244444e2,
        0.143383842191748205576712e2,
        -.288805137207594084924010e0,
        0.007547728033418631287834e0,
};
static double q1[]  = {
        0.804373630960840172826266e5,
        0.342165257924628539769006e5,
        0.637960017324428279487120e4,
        0.658070155459240506326937e3,
        0.380190713951939403753468e2,
        0.100000000000000000000000e1,
        0.0,
};
static double p2[]  = {
        0.18263348842295112592168999e4,
        0.28980293292167655611275846e4,
        0.2320439590251635247384768711e4,
        0.1143262070703886173606073338e4,
        0.3685196154710010637133875746e3,
        0.7708161730368428609781633646e2,
        0.9675807882987265400604202961e1,
        0.5641877825507397413087057563e0,
        0.0,
};
static double q2[]  = {
        0.18263348842295112595576438e4,
        0.495882756472114071495438422e4,
        0.60895424232724435504633068e4,
        0.4429612803883682726711528526e4,
        0.2094384367789539593790281779e4,
        0.6617361207107653469211984771e3,
        0.1371255960500622202878443578e3,
        0.1714980943627607849376131193e2,
        1.0,
};

double
erf(arg) double arg;{
        double erfc();
        int sign;
        double argsq;
        double d, n;
        int i;

        sign = 1;
        if(arg < 0.){
                arg = -arg;
                sign = -1;
        }
        if(arg < 0.5){
                argsq = arg*arg;
                for(n=0,d=0,i=M-1; i>=0; i--){
                        n = n*argsq + p1[i];
                        d = d*argsq + q1[i];
                }
                return(sign*torp*arg*n/d);
        }
        if(arg >= 10.)
                return(sign*1.);
        return(sign*(1. - erfc(arg)));
}

double
erfc(arg) double arg;{
        double erf();
        double exp();
        double n, d;
        int i;

        if(arg < 0.)
                return(2. - erfc(-arg));
/*
        if(arg < 0.5)
                return(1. - erf(arg));
*/
        if(arg >= 10.)
                return(0.);

        for(n=0,d=0,i=N-1; i>=0; i--){
                n = n*arg + p2[i];
                d = d*arg + q2[i];
        }
        return(exp(-arg*arg)*n/d);
}
Revision:	3.1
Committed:	Sat Feb 22 02:07:22 2003 UTC (21 years, 8 months ago) by greg
Content type:	text/plain
Branch:	MAIN
CVS Tags:	rad3R7P2, rad3R7P1, rad4R1, rad4R0, rad3R5, rad3R6, rad3R6P1, rad3R8, rad3R9
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	3.1	#ifndef lint
2			static const char RCSid[] = "$Id$";
3			#endif
4			#ifndef lint
5			static char sccsid[] = "@(#)erf.c 1.1 87/12/21 SMI"; /* from UCB 4.1 12/25/82 */
6			#endif
7
8			/*
9			C program for floating point error function
10
11			erf(x) returns the error function of its argument
12			erfc(x) returns 1.0-erf(x)
13
14			erf(x) is defined by
15			${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$
16
17			the entry for erfc is provided because of the
18			extreme loss of relative accuracy if erf(x) is
19			called for large x and the result subtracted
20			from 1. (e.g. for x= 10, 12 places are lost).
21
22			There are no error returns.
23
24			Calls exp.
25
26			Coefficients for large x are #5667 from Hart & Cheney (18.72D).
27			*/
28
29			#define M 7
30			#define N 9
31			static double torp = 1.1283791670955125738961589031;
32			static double p1[] = {
33			0.804373630960840172832162e5,
34			0.740407142710151470082064e4,
35			0.301782788536507577809226e4,
36			0.380140318123903008244444e2,
37			0.143383842191748205576712e2,
38			-.288805137207594084924010e0,
39			0.007547728033418631287834e0,
40			};
41			static double q1[] = {
42			0.804373630960840172826266e5,
43			0.342165257924628539769006e5,
44			0.637960017324428279487120e4,
45			0.658070155459240506326937e3,
46			0.380190713951939403753468e2,
47			0.100000000000000000000000e1,
48			0.0,
49			};
50			static double p2[] = {
51			0.18263348842295112592168999e4,
52			0.28980293292167655611275846e4,
53			0.2320439590251635247384768711e4,
54			0.1143262070703886173606073338e4,
55			0.3685196154710010637133875746e3,
56			0.7708161730368428609781633646e2,
57			0.9675807882987265400604202961e1,
58			0.5641877825507397413087057563e0,
59			0.0,
60			};
61			static double q2[] = {
62			0.18263348842295112595576438e4,
63			0.495882756472114071495438422e4,
64			0.60895424232724435504633068e4,
65			0.4429612803883682726711528526e4,
66			0.2094384367789539593790281779e4,
67			0.6617361207107653469211984771e3,
68			0.1371255960500622202878443578e3,
69			0.1714980943627607849376131193e2,
70			1.0,
71			};
72
73			double
74			erf(arg) double arg;{
75			double erfc();
76			int sign;
77			double argsq;
78			double d, n;
79			int i;
80
81			sign = 1;
82			if(arg < 0.){
83			arg = -arg;
84			sign = -1;
85			}
86			if(arg < 0.5){
87			argsq = arg*arg;
88			for(n=0,d=0,i=M-1; i>=0; i--){
89			n = n*argsq + p1[i];
90			d = d*argsq + q1[i];
91			}
92			return(signtorparg*n/d);
93			}
94			if(arg >= 10.)
95			return(sign*1.);
96			return(sign*(1. - erfc(arg)));
97			}
98
99			double
100			erfc(arg) double arg;{
101			double erf();
102			double exp();
103			double n, d;
104			int i;
105
106			if(arg < 0.)
107			return(2. - erfc(-arg));
108			/*
109			if(arg < 0.5)
110			return(1. - erf(arg));
111			*/
112			if(arg >= 10.)
113			return(0.);
114
115			for(n=0,d=0,i=N-1; i>=0; i--){
116			n = n*arg + p2[i];
117			d = d*arg + q2[i];
118			}
119			return(exp(-argarg)n/d);
120			}