Commit | Line | Data |
---|---|---|
0da3b2cd TL |
1 | /* |
2 | C program for floating point error function | |
3 | ||
4 | erf(x) returns the error function of its argument | |
5 | erfc(x) returns 1.0-erf(x) | |
6 | ||
7 | erf(x) is defined by | |
8 | ${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$ | |
9 | ||
10 | the entry for erfc is provided because of the | |
11 | extreme loss of relative accuracy if erf(x) is | |
12 | called for large x and the result subtracted | |
13 | from 1. (e.g. for x= 10, 12 places are lost). | |
14 | ||
15 | There are no error returns. | |
16 | ||
17 | Calls exp. | |
18 | ||
19 | Coefficients for large x are #5667 from Hart & Cheney (18.72D). | |
20 | */ | |
21 | ||
22 | #define M 7 | |
23 | #define N 9 | |
24 | int errno; | |
25 | static double torp = 1.1283791670955125738961589031; | |
26 | static double p1[] = { | |
27 | 0.804373630960840172832162e5, | |
28 | 0.740407142710151470082064e4, | |
29 | 0.301782788536507577809226e4, | |
30 | 0.380140318123903008244444e2, | |
31 | 0.143383842191748205576712e2, | |
32 | -.288805137207594084924010e0, | |
33 | 0.007547728033418631287834e0, | |
34 | }; | |
35 | static double q1[] = { | |
36 | 0.804373630960840172826266e5, | |
37 | 0.342165257924628539769006e5, | |
38 | 0.637960017324428279487120e4, | |
39 | 0.658070155459240506326937e3, | |
40 | 0.380190713951939403753468e2, | |
41 | 0.100000000000000000000000e1, | |
42 | 0.0, | |
43 | }; | |
44 | static double p2[] = { | |
45 | 0.18263348842295112592168999e4, | |
46 | 0.28980293292167655611275846e4, | |
47 | 0.2320439590251635247384768711e4, | |
48 | 0.1143262070703886173606073338e4, | |
49 | 0.3685196154710010637133875746e3, | |
50 | 0.7708161730368428609781633646e2, | |
51 | 0.9675807882987265400604202961e1, | |
52 | 0.5641877825507397413087057563e0, | |
53 | 0.0, | |
54 | }; | |
55 | static double q2[] = { | |
56 | 0.18263348842295112595576438e4, | |
57 | 0.495882756472114071495438422e4, | |
58 | 0.60895424232724435504633068e4, | |
59 | 0.4429612803883682726711528526e4, | |
60 | 0.2094384367789539593790281779e4, | |
61 | 0.6617361207107653469211984771e3, | |
62 | 0.1371255960500622202878443578e3, | |
63 | 0.1714980943627607849376131193e2, | |
64 | 1.0, | |
65 | }; | |
66 | ||
67 | double | |
68 | erf(arg) double arg;{ | |
69 | double erfc(); | |
70 | int sign; | |
71 | double argsq; | |
72 | double d, n; | |
73 | int i; | |
74 | ||
75 | errno = 0; | |
76 | sign = 1; | |
77 | if(arg < 0.){ | |
78 | arg = -arg; | |
79 | sign = -1; | |
80 | } | |
81 | if(arg < 0.5){ | |
82 | argsq = arg*arg; | |
83 | for(n=0,d=0,i=M-1; i>=0; i--){ | |
84 | n = n*argsq + p1[i]; | |
85 | d = d*argsq + q1[i]; | |
86 | } | |
87 | return(sign*torp*arg*n/d); | |
88 | } | |
89 | if(arg >= 10.) | |
90 | return(sign*1.); | |
91 | return(sign*(1. - erfc(arg))); | |
92 | } | |
93 | ||
94 | double | |
95 | erfc(arg) double arg;{ | |
96 | double erf(); | |
97 | double exp(); | |
98 | double n, d; | |
99 | int i; | |
100 | ||
101 | errno = 0; | |
102 | if(arg < 0.) | |
103 | return(2. - erfc(-arg)); | |
104 | /* | |
105 | if(arg < 0.5) | |
106 | return(1. - erf(arg)); | |
107 | */ | |
108 | if(arg >= 10.) | |
109 | return(0.); | |
110 | ||
111 | for(n=0,d=0,i=N-1; i>=0; i--){ | |
112 | n = n*arg + p2[i]; | |
113 | d = d*arg + q2[i]; | |
114 | } | |
115 | return(exp(-arg*arg)*n/d); | |
116 | } |