lgammacor.cpp

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000-2001 The R Core Team
 *
 *  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, a copy is available at
 *  https://www.R-project.org/Licenses/
 *
 *  SYNOPSIS
 *
 *    #include <Rmath.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.
 *
 *  SEE ALSO
 *
 *    Loader(1999)'s stirlerr() {in ./stirlerr.c} is *very* similar in spirit,
 *    is faster and cleaner, but is only defined "fast" for half integers.
 */

template<class Float>
Float attribute_hidden lgammacor(Float x)
{
    const 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
    };

    Float tmp;

/* For IEEE double precision DBL_EPSILON = 2^-52 = 2.220446049250313e-16 :
 *   xbig = 2 ^ 26.5
 *   xmax = DBL_MAX / 48 =  2^1020 / 3 */
#define nalgm 5
#define xbig  94906265.62425156
#define xmax  3.745194030963158e306

    if (x < 10)
        ML_ERR_return_NAN
    else if (x >= xmax) {
        ML_ERROR(ME_UNDERFLOW, "lgammacor");
        /* allow to underflow below */
    }
    else if (x < xbig) {
        tmp = 10 / x;
        return chebyshev_eval(tmp * tmp * 2 - 1, algmcs, nalgm) / x;
    }
    return 1 / (x * 12);
}