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 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 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