xref: /csrg-svn/lib/libm/common_source/lgamma.c (revision 48402)

/*-
 * Copyright (c) 1985 The Regents of the University of California.
 * All rights reserved.
 *
 * %sccs.include.proprietary.c%
 */

#ifndef lint
static char sccsid[] = "@(#)lgamma.c	5.4 (Berkeley) 04/20/91";
#endif /* not lint */

/*
	C program for floating point log Gamma function

	lgamma(x) computes the log of the absolute
	value of the Gamma function.
	The sign of the Gamma function is returned in the
	external quantity signgam.

	The coefficients for expansion around zero
	are #5243 from Hart & Cheney; for expansion
	around infinity they are #5404.

	Calls log, floor and sin.
*/

#include "mathimpl.h"
#if defined(vax)||defined(tahoe)
#include <errno.h>
#endif	/* defined(vax)||defined(tahoe) */

int	signgam = 0;
static const double goobie = 0.9189385332046727417803297;  /* log(2*pi)/2 */
static const double pi	   = 3.1415926535897932384626434;

#define M 6
#define N 8
static const double p1[] = {
	0.83333333333333101837e-1,
	-.277777777735865004e-2,
	0.793650576493454e-3,
	-.5951896861197e-3,
	0.83645878922e-3,
	-.1633436431e-2,
};
static const double p2[] = {
	-.42353689509744089647e5,
	-.20886861789269887364e5,
	-.87627102978521489560e4,
	-.20085274013072791214e4,
	-.43933044406002567613e3,
	-.50108693752970953015e2,
	-.67449507245925289918e1,
	0.0,
};
static const double q2[] = {
	-.42353689509744090010e5,
	-.29803853309256649932e4,
	0.99403074150827709015e4,
	-.15286072737795220248e4,
	-.49902852662143904834e3,
	0.18949823415702801641e3,
	-.23081551524580124562e2,
	0.10000000000000000000e1,
};

static double pos(), neg(), asym();

double
lgamma(arg)
double arg;
{

	signgam = 1.;
	if(arg <= 0.) return(neg(arg));
	if(arg > 8.) return(asym(arg));
	return(log(pos(arg)));
}

static double
asym(arg)
double arg;
{
	double n, argsq;
	int i;

	argsq = 1./(arg*arg);
	for(n=0,i=M-1; i>=0; i--){
		n = n*argsq + p1[i];
	}
	return((arg-.5)*log(arg) - arg + goobie + n/arg);
}

static double
neg(arg)
double arg;
{
	double t;

	arg = -arg;
     /*
      * to see if arg were a true integer, the old code used the
      * mathematically correct observation:
      * sin(n*pi) = 0 <=> n is an integer.
      * but in finite precision arithmetic, sin(n*PI) will NEVER
      * be zero simply because n*PI is a rational number.  hence
      *	it failed to work with our newer, more accurate sin()
      * which uses true pi to do the argument reduction...
      *	temp = sin(pi*arg);
      */
	t = floor(arg);
	if (arg - t  > 0.5e0)
	    t += 1.e0;				/* t := integer nearest arg */
#if defined(vax)||defined(tahoe)
	if (arg == t) {
	    return(infnan(ERANGE));		/* +INF */
	}
#endif	/* defined(vax)||defined(tahoe) */
	signgam = (int) (t - 2*floor(t/2));	/* signgam =  1 if t was odd, */
						/*            0 if t was even */
	signgam = signgam - 1 + signgam;	/* signgam =  1 if t was odd, */
						/*           -1 if t was even */
	t = arg - t;				/*  -0.5 <= t <= 0.5 */
	if (t < 0.e0) {
	    t = -t;
	    signgam = -signgam;
	}
	return(-log(arg*pos(arg)*sin(pi*t)/pi));
}

static double
pos(arg)
double arg;
{
	double n, d, s;
	register i;

	if(arg < 2.) return(pos(arg+1.)/arg);
	if(arg > 3.) return((arg-1.)*pos(arg-1.));

	s = arg - 2.;
	for(n=0,d=0,i=N-1; i>=0; i--){
		n = n*s + p2[i];
		d = d*s + q2[i];
	}
	return(n/d);
}