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root/radiance/ray/src/common/erf.c
Revision: 3.1
Committed: Sat Feb 22 02:07:22 2003 UTC (21 years, 1 month 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

File Contents

# Content
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(sign*torp*arg*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(-arg*arg)*n/d);
120 }