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Annotation of researchv9/libc/math/gamma.c, revision 1.1.1.1

1.1       root        1: /*
                      2:        C program for floating point log gamma function
                      3: 
                      4:        gamma(x) computes the log of the absolute
                      5:        value of the gamma function.
                      6:        The sign of the gamma function is returned in the
                      7:        external quantity signgam.
                      8: 
                      9:        The coefficients for expansion around zero
                     10:        are #5243 from Hart & Cheney; for expansion
                     11:        around infinity they are #5404.
                     12: 
                     13:        Calls log and sin.
                     14: */
                     15: 
                     16: #include <errno.h>
                     17: #include <math.h>
                     18: 
                     19: int    errno;
                     20: int    signgam = 0;
                     21: static double goobie   = 0.9189385332046727417803297;
                     22: static double pi       = 3.1415926535897932384626434;
                     23: 
                     24: #define M 6
                     25: #define N 8
                     26: static double p1[] = {
                     27:        0.83333333333333101837e-1,
                     28:        -.277777777735865004e-2,
                     29:        0.793650576493454e-3,
                     30:        -.5951896861197e-3,
                     31:        0.83645878922e-3,
                     32:        -.1633436431e-2,
                     33: };
                     34: static double p2[] = {
                     35:        -.42353689509744089647e5,
                     36:        -.20886861789269887364e5,
                     37:        -.87627102978521489560e4,
                     38:        -.20085274013072791214e4,
                     39:        -.43933044406002567613e3,
                     40:        -.50108693752970953015e2,
                     41:        -.67449507245925289918e1,
                     42:        0.0,
                     43: };
                     44: static double q2[] = {
                     45:        -.42353689509744090010e5,
                     46:        -.29803853309256649932e4,
                     47:        0.99403074150827709015e4,
                     48:        -.15286072737795220248e4,
                     49:        -.49902852662143904834e3,
                     50:        0.18949823415702801641e3,
                     51:        -.23081551524580124562e2,
                     52:        0.10000000000000000000e1,
                     53: };
                     54: 
                     55: double
                     56: gamma(arg)
                     57: double arg;
                     58: {
                     59:        double log(), pos(), neg(), asym();
                     60: 
                     61:        signgam = 1.;
                     62:        if(arg <= 0.) return(neg(arg));
                     63:        if(arg > 8.) return(asym(arg));
                     64:        return(log(pos(arg)));
                     65: }
                     66: 
                     67: static double
                     68: asym(arg)
                     69: double arg;
                     70: {
                     71:        double log();
                     72:        double n, argsq;
                     73:        int i;
                     74: 
                     75:        argsq = 1./(arg*arg);
                     76:        for(n=0,i=M-1; i>=0; i--){
                     77:                n = n*argsq + p1[i];
                     78:        }
                     79:        return((arg-.5)*log(arg) - arg + goobie + n/arg);
                     80: }
                     81: 
                     82: static double
                     83: neg(arg)
                     84: double arg;
                     85: {
                     86:        double temp;
                     87:        double log(), sin(), pos();
                     88: 
                     89:        arg = -arg;
                     90:        temp = sin(pi*arg);
                     91:        if(temp == 0.) {
                     92:                errno = EDOM;
                     93:                return(HUGE);
                     94:        }
                     95:        if(temp < 0.) temp = -temp;
                     96:        else signgam = -1;
                     97:        return(-log(arg*pos(arg)*temp/pi));
                     98: }
                     99: 
                    100: static double
                    101: pos(arg)
                    102: double arg;
                    103: {
                    104:        double n, d, s;
                    105:        register i;
                    106: 
                    107:        if(arg < 2.) return(pos(arg+1.)/arg);
                    108:        if(arg > 3.) return((arg-1.)*pos(arg-1.));
                    109: 
                    110:        s = arg - 2.;
                    111:        for(n=0,d=0,i=N-1; i>=0; i--){
                    112:                n = n*s + p2[i];
                    113:                d = d*s + q2[i];
                    114:        }
                    115:        return(n/d);
                    116: }

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