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Annotation of 43BSD/usr.lib/libm/lgamma.c, revision 1.1.1.1

1.1       root        1: #ifndef lint
                      2: static char sccsid[] = "@(#)lgamma.c   4.4 (Berkeley) 9/11/85";
                      3: #endif not lint
                      4: 
                      5: /*
                      6:        C program for floating point log Gamma function
                      7: 
                      8:        lgamma(x) computes the log of the absolute
                      9:        value of the Gamma function.
                     10:        The sign of the Gamma function is returned in the
                     11:        external quantity signgam.
                     12: 
                     13:        The coefficients for expansion around zero
                     14:        are #5243 from Hart & Cheney; for expansion
                     15:        around infinity they are #5404.
                     16: 
                     17:        Calls log, floor and sin.
                     18: */
                     19: 
                     20: #include <math.h>
                     21: #ifdef VAX
                     22: #include <errno.h>
                     23: #endif
                     24: int    signgam = 0;
                     25: static double goobie   = 0.9189385332046727417803297;  /* log(2*pi)/2 */
                     26: static double pi       = 3.1415926535897932384626434;
                     27: 
                     28: #define M 6
                     29: #define N 8
                     30: static double p1[] = {
                     31:        0.83333333333333101837e-1,
                     32:        -.277777777735865004e-2,
                     33:        0.793650576493454e-3,
                     34:        -.5951896861197e-3,
                     35:        0.83645878922e-3,
                     36:        -.1633436431e-2,
                     37: };
                     38: static double p2[] = {
                     39:        -.42353689509744089647e5,
                     40:        -.20886861789269887364e5,
                     41:        -.87627102978521489560e4,
                     42:        -.20085274013072791214e4,
                     43:        -.43933044406002567613e3,
                     44:        -.50108693752970953015e2,
                     45:        -.67449507245925289918e1,
                     46:        0.0,
                     47: };
                     48: static double q2[] = {
                     49:        -.42353689509744090010e5,
                     50:        -.29803853309256649932e4,
                     51:        0.99403074150827709015e4,
                     52:        -.15286072737795220248e4,
                     53:        -.49902852662143904834e3,
                     54:        0.18949823415702801641e3,
                     55:        -.23081551524580124562e2,
                     56:        0.10000000000000000000e1,
                     57: };
                     58: 
                     59: double
                     60: lgamma(arg)
                     61: double arg;
                     62: {
                     63:        double log(), pos(), neg(), asym();
                     64: 
                     65:        signgam = 1.;
                     66:        if(arg <= 0.) return(neg(arg));
                     67:        if(arg > 8.) return(asym(arg));
                     68:        return(log(pos(arg)));
                     69: }
                     70: 
                     71: static double
                     72: asym(arg)
                     73: double arg;
                     74: {
                     75:        double log();
                     76:        double n, argsq;
                     77:        int i;
                     78: 
                     79:        argsq = 1./(arg*arg);
                     80:        for(n=0,i=M-1; i>=0; i--){
                     81:                n = n*argsq + p1[i];
                     82:        }
                     83:        return((arg-.5)*log(arg) - arg + goobie + n/arg);
                     84: }
                     85: 
                     86: static double
                     87: neg(arg)
                     88: double arg;
                     89: {
                     90:        double t;
                     91:        double log(), sin(), floor(), pos();
                     92: 
                     93:        arg = -arg;
                     94:      /*
                     95:       * to see if arg were a true integer, the old code used the
                     96:       * mathematically correct observation:
                     97:       * sin(n*pi) = 0 <=> n is an integer.
                     98:       * but in finite precision arithmetic, sin(n*PI) will NEVER
                     99:       * be zero simply because n*PI is a rational number.  hence
                    100:       *        it failed to work with our newer, more accurate sin()
                    101:       * which uses true pi to do the argument reduction...
                    102:       *        temp = sin(pi*arg);
                    103:       */
                    104:        t = floor(arg);
                    105:        if (arg - t  > 0.5e0)
                    106:            t += 1.e0;                          /* t := integer nearest arg */
                    107: #ifdef VAX
                    108:        if (arg == t) {
                    109:            extern double infnan();
                    110:            return(infnan(ERANGE));             /* +INF */
                    111:        }
                    112: #endif
                    113:        signgam = (int) (t - 2*floor(t/2));     /* signgam =  1 if t was odd, */
                    114:                                                /*            0 if t was even */
                    115:        signgam = signgam - 1 + signgam;        /* signgam =  1 if t was odd, */
                    116:                                                /*           -1 if t was even */
                    117:        t = arg - t;                            /*  -0.5 <= t <= 0.5 */
                    118:        if (t < 0.e0) {
                    119:            t = -t;
                    120:            signgam = -signgam;
                    121:        }
                    122:        return(-log(arg*pos(arg)*sin(pi*t)/pi));
                    123: }
                    124: 
                    125: static double
                    126: pos(arg)
                    127: double arg;
                    128: {
                    129:        double n, d, s;
                    130:        register i;
                    131: 
                    132:        if(arg < 2.) return(pos(arg+1.)/arg);
                    133:        if(arg > 3.) return((arg-1.)*pos(arg-1.));
                    134: 
                    135:        s = arg - 2.;
                    136:        for(n=0,d=0,i=N-1; i>=0; i--){
                    137:                n = n*s + p2[i];
                    138:                d = d*s + q2[i];
                    139:        }
                    140:        return(n/d);
                    141: }

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