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 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 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