1 #include <math.h>
2 #include <errno.h>
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 - 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 static double torp = 1.1283791670955125738961589031;
27 static double p1[] = {
28 0.804373630960840172832162e5,
29 0.740407142710151470082064e4,
30 0.301782788536507577809226e4,
31 0.380140318123903008244444e2,
32 0.143383842191748205576712e2,
33 -.288805137207594084924010e0,
34 0.007547728033418631287834e0,
35 };
36 static double q1[] = {
37 0.804373630960840172826266e5,
38 0.342165257924628539769006e5,
39 0.637960017324428279487120e4,
40 0.658070155459240506326937e3,
41 0.380190713951939403753468e2,
42 0.100000000000000000000000e1,
43 0.0,
44 };
45 static double p2[] = {
46 0.18263348842295112592168999e4,
47 0.28980293292167655611275846e4,
48 0.2320439590251635247384768711e4,
49 0.1143262070703886173606073338e4,
50 0.3685196154710010637133875746e3,
51 0.7708161730368428609781633646e2,
52 0.9675807882987265400604202961e1,
53 0.5641877825507397413087057563e0,
54 0.0,
55 };
56 static double q2[] = {
57 0.18263348842295112595576438e4,
58 0.495882756472114071495438422e4,
59 0.60895424232724435504633068e4,
60 0.4429612803883682726711528526e4,
61 0.2094384367789539593790281779e4,
62 0.6617361207107653469211984771e3,
63 0.1371255960500622202878443578e3,
64 0.1714980943627607849376131193e2,
65 1.0,
66 };
67
68 double erfc(double);
69
70 double
erf(double arg)71 erf(double arg)
72 {
73 int sign;
74 double argsq;
75 double d, n;
76 int i;
77
78 errno = 0;
79 sign = 1;
80 if(arg < 0) {
81 arg = -arg;
82 sign = -1;
83 }
84 if(arg < 0.5) {
85 argsq = arg*arg;
86 for(n=0,d=0,i=M-1; i>=0; i--) {
87 n = n*argsq + p1[i];
88 d = d*argsq + q1[i];
89 }
90 return sign*torp*arg*n/d;
91 }
92 if(arg >= 10)
93 return sign;
94 return sign*(1 - erfc(arg));
95 }
96
97 double
erfc(double arg)98 erfc(double arg)
99 {
100 double n, d;
101 int i;
102
103 errno = 0;
104 if(arg < 0)
105 return 2 - erfc(-arg);
106 if(arg < 0.5)
107 return 1 - erf(arg);
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 }
117