1 /* 2 * Copyright (c) 1985 Regents of the University of California. 3 * All rights reserved. The Berkeley software License Agreement 4 * specifies the terms and conditions for redistribution. 5 */ 6 7 #ifndef lint 8 static char sccsid[] = "@(#)erf.c 5.2 (Berkeley) 04/29/88"; 9 #endif /* not lint */ 10 11 /* 12 C program for floating point error function 13 14 erf(x) returns the error function of its argument 15 erfc(x) returns 1.0-erf(x) 16 17 erf(x) is defined by 18 ${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$ 19 20 the entry for erfc is provided because of the 21 extreme loss of relative accuracy if erf(x) is 22 called for large x and the result subtracted 23 from 1. (e.g. for x= 10, 12 places are lost). 24 25 There are no error returns. 26 27 Calls exp. 28 29 Coefficients for large x are #5667 from Hart & Cheney (18.72D). 30 */ 31 32 #define M 7 33 #define N 9 34 static double torp = 1.1283791670955125738961589031; 35 static double p1[] = { 36 0.804373630960840172832162e5, 37 0.740407142710151470082064e4, 38 0.301782788536507577809226e4, 39 0.380140318123903008244444e2, 40 0.143383842191748205576712e2, 41 -.288805137207594084924010e0, 42 0.007547728033418631287834e0, 43 }; 44 static double q1[] = { 45 0.804373630960840172826266e5, 46 0.342165257924628539769006e5, 47 0.637960017324428279487120e4, 48 0.658070155459240506326937e3, 49 0.380190713951939403753468e2, 50 0.100000000000000000000000e1, 51 0.0, 52 }; 53 static double p2[] = { 54 0.18263348842295112592168999e4, 55 0.28980293292167655611275846e4, 56 0.2320439590251635247384768711e4, 57 0.1143262070703886173606073338e4, 58 0.3685196154710010637133875746e3, 59 0.7708161730368428609781633646e2, 60 0.9675807882987265400604202961e1, 61 0.5641877825507397413087057563e0, 62 0.0, 63 }; 64 static double q2[] = { 65 0.18263348842295112595576438e4, 66 0.495882756472114071495438422e4, 67 0.60895424232724435504633068e4, 68 0.4429612803883682726711528526e4, 69 0.2094384367789539593790281779e4, 70 0.6617361207107653469211984771e3, 71 0.1371255960500622202878443578e3, 72 0.1714980943627607849376131193e2, 73 1.0, 74 }; 75 76 double 77 erf(arg) double arg;{ 78 double erfc(); 79 int sign; 80 double argsq; 81 double d, n; 82 int i; 83 84 sign = 1; 85 if(arg < 0.){ 86 arg = -arg; 87 sign = -1; 88 } 89 if(arg < 0.5){ 90 argsq = arg*arg; 91 for(n=0,d=0,i=M-1; i>=0; i--){ 92 n = n*argsq + p1[i]; 93 d = d*argsq + q1[i]; 94 } 95 return(sign*torp*arg*n/d); 96 } 97 if(arg >= 10.) 98 return(sign*1.); 99 return(sign*(1. - erfc(arg))); 100 } 101 102 double 103 erfc(arg) double arg;{ 104 double erf(); 105 double exp(); 106 double n, d; 107 int i; 108 109 if(arg < 0.) 110 return(2. - erfc(-arg)); 111 /* 112 if(arg < 0.5) 113 return(1. - erf(arg)); 114 */ 115 if(arg >= 10.) 116 return(0.); 117 118 for(n=0,d=0,i=N-1; i>=0; i--){ 119 n = n*arg + p2[i]; 120 d = d*arg + q2[i]; 121 } 122 return(exp(-arg*arg)*n/d); 123 } 124