1 /* @(#)erf.c 4.1 12/25/82 */
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
erf(arg)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
erfc(arg)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 }
119