1 /* @(#)erf.c 4.2 (Berkeley) 8/21/85; 5.1 (ucb.elefunt) 11/30/87 */ 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 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 69 erf(arg) double arg;{ 70 double erfc(); 71 int sign; 72 double argsq; 73 double d, n; 74 int i; 75 76 sign = 1; 77 if(arg < 0.){ 78 arg = -arg; 79 sign = -1; 80 } 81 if(arg < 0.5){ 82 argsq = arg*arg; 83 for(n=0,d=0,i=M-1; i>=0; i--){ 84 n = n*argsq + p1[i]; 85 d = d*argsq + q1[i]; 86 } 87 return(sign*torp*arg*n/d); 88 } 89 if(arg >= 10.) 90 return(sign*1.); 91 return(sign*(1. - erfc(arg))); 92 } 93 94 double 95 erfc(arg) double arg;{ 96 double erf(); 97 double exp(); 98 double n, d; 99 int i; 100 101 if(arg < 0.) 102 return(2. - erfc(-arg)); 103 /* 104 if(arg < 0.5) 105 return(1. - erf(arg)); 106 */ 107 if(arg >= 10.) 108 return(0.); 109 110 for(n=0,d=0,i=N-1; i>=0; i--){ 111 n = n*arg + p2[i]; 112 d = d*arg + q2[i]; 113 } 114 return(exp(-arg*arg)*n/d); 115 } 116