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/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with this program; if not, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA.
 *
 *  SYNOPSIS
 *
 *    #include "Mathlib.h"
 *    double lgammacor(double x);
 *
 *  DESCRIPTION
 *
 *    Compute the log gamma correction factor for x >= 10 so that
 *
 *    log(gamma(x)) = .5*log(2*pi) + (x-.5)*log(x) -x + lgammacor(x)
 *
 *    [ lgammacor(x) is called  Del(x)  in other contexts (e.g. dcdflib)]
 *
 *  NOTES
 *
 *    This routine is a translation into C of a Fortran subroutine
 *    written by W. Fullerton of Los Alamos Scientific Laboratory.
 */

#include "Mathlib.h"

double lgammacor(double x)
{
    static double algmcs[15] = {
    +.1666389480451863247205729650822e+0,
    -.1384948176067563840732986059135e-4,
    +.9810825646924729426157171547487e-8,
    -.1809129475572494194263306266719e-10,
    +.6221098041892605227126015543416e-13,
    -.3399615005417721944303330599666e-15,
    +.2683181998482698748957538846666e-17,
    -.2868042435334643284144622399999e-19,
    +.3962837061046434803679306666666e-21,
    -.6831888753985766870111999999999e-23,
    +.1429227355942498147573333333333e-24,
    -.3547598158101070547199999999999e-26,
    +.1025680058010470912000000000000e-27,
    -.3401102254316748799999999999999e-29,
    +.1276642195630062933333333333333e-30
    };
    static int nalgm = 0;
    static double xbig = 0;
    static double xmax = 0;
    double tmp;

    if (nalgm == 0) {/* initialize machine dependent constants _ONCE_ */
    nalgm = chebyshev_init(algmcs, 15, d1mach(3));
    xbig = 1 / sqrt(d1mach(3)); /* ~ 94906265.6 for IEEE double */
    xmax = exp(fmin2(log(d1mach(2) / 12), -log(12 * d1mach(1))));
        /* ~= 3.745 e306 for IEEE double */
    }

    if (x < 10) {
    ML_ERROR(ME_DOMAIN);
    return ML_NAN;
    }
    else if (x >= xmax) {
    ML_ERROR(ME_UNDERFLOW);
    return ML_UNDERFLOW;
    }
    else if (x < xbig) {
    tmp = 10 / x;
    return chebyshev_eval(tmp * tmp * 2 - 1, algmcs, nalgm) / x;
    }
    else return 1 / (x * 12);
}