1 /*- 2 * Copyright (c) 1985 The Regents of the University of California. 3 * All rights reserved. 4 * 5 * %sccs.include.proprietary.c% 6 */ 7 8 #ifndef lint 9 static char sccsid[] = "@(#)erf.c 5.3 (Berkeley) 04/20/91"; 10 #endif /* not lint */ 11 12 /* 13 C program for floating point error function 14 15 erf(x) returns the error function of its argument 16 erfc(x) returns 1.0-erf(x) 17 18 erf(x) is defined by 19 ${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$ 20 21 the entry for erfc is provided because of the 22 extreme loss of relative accuracy if erf(x) is 23 called for large x and the result subtracted 24 from 1. (e.g. for x= 10, 12 places are lost). 25 26 There are no error returns. 27 28 Calls exp. 29 30 Coefficients for large x are #5667 from Hart & Cheney (18.72D). 31 */ 32 33 #define M 7 34 #define N 9 35 static double torp = 1.1283791670955125738961589031; 36 static double p1[] = { 37 0.804373630960840172832162e5, 38 0.740407142710151470082064e4, 39 0.301782788536507577809226e4, 40 0.380140318123903008244444e2, 41 0.143383842191748205576712e2, 42 -.288805137207594084924010e0, 43 0.007547728033418631287834e0, 44 }; 45 static double q1[] = { 46 0.804373630960840172826266e5, 47 0.342165257924628539769006e5, 48 0.637960017324428279487120e4, 49 0.658070155459240506326937e3, 50 0.380190713951939403753468e2, 51 0.100000000000000000000000e1, 52 0.0, 53 }; 54 static double p2[] = { 55 0.18263348842295112592168999e4, 56 0.28980293292167655611275846e4, 57 0.2320439590251635247384768711e4, 58 0.1143262070703886173606073338e4, 59 0.3685196154710010637133875746e3, 60 0.7708161730368428609781633646e2, 61 0.9675807882987265400604202961e1, 62 0.5641877825507397413087057563e0, 63 0.0, 64 }; 65 static double q2[] = { 66 0.18263348842295112595576438e4, 67 0.495882756472114071495438422e4, 68 0.60895424232724435504633068e4, 69 0.4429612803883682726711528526e4, 70 0.2094384367789539593790281779e4, 71 0.6617361207107653469211984771e3, 72 0.1371255960500622202878443578e3, 73 0.1714980943627607849376131193e2, 74 1.0, 75 }; 76 77 double 78 erf(arg) double arg;{ 79 double erfc(); 80 int sign; 81 double argsq; 82 double d, n; 83 int i; 84 85 sign = 1; 86 if(arg < 0.){ 87 arg = -arg; 88 sign = -1; 89 } 90 if(arg < 0.5){ 91 argsq = arg*arg; 92 for(n=0,d=0,i=M-1; i>=0; i--){ 93 n = n*argsq + p1[i]; 94 d = d*argsq + q1[i]; 95 } 96 return(sign*torp*arg*n/d); 97 } 98 if(arg >= 10.) 99 return(sign*1.); 100 return(sign*(1. - erfc(arg))); 101 } 102 103 double 104 erfc(arg) double arg;{ 105 double erf(); 106 double exp(); 107 double n, d; 108 int i; 109 110 if(arg < 0.) 111 return(2. - erfc(-arg)); 112 /* 113 if(arg < 0.5) 114 return(1. - erf(arg)); 115 */ 116 if(arg >= 10.) 117 return(0.); 118 119 for(n=0,d=0,i=N-1; i>=0; i--){ 120 n = n*arg + p2[i]; 121 d = d*arg + q2[i]; 122 } 123 return(exp(-arg*arg)*n/d); 124 } 125