BSD 4_1c_2 release

[unix-history] / usr / src / usr.lib / libm / erf.c

/*      @(#)erf.c       4.1     12/25/82        */

/*
       C program for floating point error function

       erf(x) returns the error function of its argument
       erfc(x) returns 1.0-erf(x)

       erf(x) is defined by
       ${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$

       the entry for erfc is provided because of the
       extreme loss of relative accuracy if erf(x) is
       called for large x and the result subtracted
       from 1. (e.g. for x= 10, 12 places are lost).

       There are no error returns.

       Calls exp.

       Coefficients for large x are #5667 from Hart & Cheney (18.72D).
*/

#define M 7
#define N 9
int errno;
static double torp = 1.1283791670955125738961589031;
static double p1[] = {
       0.804373630960840172832162e5,
       0.740407142710151470082064e4,
       0.301782788536507577809226e4,
       0.380140318123903008244444e2,
       0.143383842191748205576712e2,
       -.288805137207594084924010e0,
       0.007547728033418631287834e0,
};
static double q1[]  = {
       0.804373630960840172826266e5,
       0.342165257924628539769006e5,
       0.637960017324428279487120e4,
       0.658070155459240506326937e3,
       0.380190713951939403753468e2,
       0.100000000000000000000000e1,
       0.0,
};
static double p2[]  = {
       0.18263348842295112592168999e4,
       0.28980293292167655611275846e4,
       0.2320439590251635247384768711e4,
       0.1143262070703886173606073338e4,
       0.3685196154710010637133875746e3,
       0.7708161730368428609781633646e2,
       0.9675807882987265400604202961e1,
       0.5641877825507397413087057563e0,
       0.0,
};
static double q2[]  = {
       0.18263348842295112595576438e4,
       0.495882756472114071495438422e4,
       0.60895424232724435504633068e4,
       0.4429612803883682726711528526e4,
       0.2094384367789539593790281779e4,
       0.6617361207107653469211984771e3,
       0.1371255960500622202878443578e3,
       0.1714980943627607849376131193e2,
       1.0,
};

double
erf(arg) double arg;{
       double erfc();
       int sign;
       double argsq;
       double d, n;
       int i;

       errno = 0;
       sign = 1;
       if(arg < 0.){
               arg = -arg;
               sign = -1;
       }
       if(arg < 0.5){
               argsq = arg*arg;
               for(n=0,d=0,i=M-1; i>=0; i--){
                       n = n*argsq + p1[i];
                       d = d*argsq + q1[i];
               }
               return(sign*torp*arg*n/d);
       }
       if(arg >= 10.)
               return(sign*1.);
       return(sign*(1. - erfc(arg)));
}

double
erfc(arg) double arg;{
       double erf();
       double exp();
       double n, d;
       int i;

       errno = 0;
       if(arg < 0.)
               return(2. - erfc(-arg));
/*
       if(arg < 0.5)
               return(1. - erf(arg));
*/
       if(arg >= 10.)
               return(0.);

       for(n=0,d=0,i=N-1; i>=0; i--){
               n = n*arg + p2[i];
               d = d*arg + q2[i];
       }
       return(exp(-arg*arg)*n/d);
}