Commit | Line | Data |
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f5b69fb6 SL |
1 | /* @(#)erf.c 4.1 %G% */ |
2 | ||
3 | /* | |
4 | C program for floating point error function | |
5 | ||
6 | erf(x) returns the error function of its argument | |
7 | erfc(x) returns 1.0-erf(x) | |
8 | ||
9 | erf(x) is defined by | |
10 | ${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$ | |
11 | ||
12 | the entry for erfc is provided because of the | |
13 | extreme loss of relative accuracy if erf(x) is | |
14 | called for large x and the result subtracted | |
15 | from 1. (e.g. for x= 10, 12 places are lost). | |
16 | ||
17 | There are no error returns. | |
18 | ||
19 | Calls exp. | |
20 | ||
21 | Coefficients for large x are #5667 from Hart & Cheney (18.72D). | |
22 | */ | |
23 | ||
24 | #define M 7 | |
25 | #define N 9 | |
26 | int errno; | |
27 | static double torp = 1.1283791670955125738961589031; | |
28 | static double p1[] = { | |
29 | 0.804373630960840172832162e5, | |
30 | 0.740407142710151470082064e4, | |
31 | 0.301782788536507577809226e4, | |
32 | 0.380140318123903008244444e2, | |
33 | 0.143383842191748205576712e2, | |
34 | -.288805137207594084924010e0, | |
35 | 0.007547728033418631287834e0, | |
36 | }; | |
37 | static double q1[] = { | |
38 | 0.804373630960840172826266e5, | |
39 | 0.342165257924628539769006e5, | |
40 | 0.637960017324428279487120e4, | |
41 | 0.658070155459240506326937e3, | |
42 | 0.380190713951939403753468e2, | |
43 | 0.100000000000000000000000e1, | |
44 | 0.0, | |
45 | }; | |
46 | static double p2[] = { | |
47 | 0.18263348842295112592168999e4, | |
48 | 0.28980293292167655611275846e4, | |
49 | 0.2320439590251635247384768711e4, | |
50 | 0.1143262070703886173606073338e4, | |
51 | 0.3685196154710010637133875746e3, | |
52 | 0.7708161730368428609781633646e2, | |
53 | 0.9675807882987265400604202961e1, | |
54 | 0.5641877825507397413087057563e0, | |
55 | 0.0, | |
56 | }; | |
57 | static double q2[] = { | |
58 | 0.18263348842295112595576438e4, | |
59 | 0.495882756472114071495438422e4, | |
60 | 0.60895424232724435504633068e4, | |
61 | 0.4429612803883682726711528526e4, | |
62 | 0.2094384367789539593790281779e4, | |
63 | 0.6617361207107653469211984771e3, | |
64 | 0.1371255960500622202878443578e3, | |
65 | 0.1714980943627607849376131193e2, | |
66 | 1.0, | |
67 | }; | |
68 | ||
69 | double | |
70 | erf(arg) double arg;{ | |
71 | double erfc(); | |
72 | int sign; | |
73 | double argsq; | |
74 | double d, n; | |
75 | int i; | |
76 | ||
77 | errno = 0; | |
78 | sign = 1; | |
79 | if(arg < 0.){ | |
80 | arg = -arg; | |
81 | sign = -1; | |
82 | } | |
83 | if(arg < 0.5){ | |
84 | argsq = arg*arg; | |
85 | for(n=0,d=0,i=M-1; i>=0; i--){ | |
86 | n = n*argsq + p1[i]; | |
87 | d = d*argsq + q1[i]; | |
88 | } | |
89 | return(sign*torp*arg*n/d); | |
90 | } | |
91 | if(arg >= 10.) | |
92 | return(sign*1.); | |
93 | return(sign*(1. - erfc(arg))); | |
94 | } | |
95 | ||
96 | double | |
97 | erfc(arg) double arg;{ | |
98 | double erf(); | |
99 | double exp(); | |
100 | double n, d; | |
101 | int i; | |
102 | ||
103 | errno = 0; | |
104 | if(arg < 0.) | |
105 | return(2. - erfc(-arg)); | |
106 | /* | |
107 | if(arg < 0.5) | |
108 | return(1. - erf(arg)); | |
109 | */ | |
110 | if(arg >= 10.) | |
111 | return(0.); | |
112 | ||
113 | for(n=0,d=0,i=N-1; i>=0; i--){ | |
114 | n = n*arg + p2[i]; | |
115 | d = d*arg + q2[i]; | |
116 | } | |
117 | return(exp(-arg*arg)*n/d); | |
118 | } |