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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"
 *    extern int signgam;
 *    double lgammafn(double x);
 *
 *  DESCRIPTION
 *
 *    This function computes log|gamma(x)|.  At the same time
 *    the variable "signgam" is set to the sign of the gamma
 *    function.
 *
 *  NOTES
 *
 *    This routine is a translation into C of a Fortran subroutine
 *    by W. Fullerton of Los Alamos Scientific Laboratory.
 *
 *    The accuracy of this routine compares (very) favourably
 *    with those of the Sun Microsystems portable mathematical
 *    library.
 */

#include "nmath.h"

int signgam;

double lgammafn(double x)
{
    static double xmax = 0.;
    static double dxrel = 0.;
    double ans, y, sinpiy;

    if (xmax == 0) {/* initialize machine dependent constants _ONCE_ */
    xmax = d1mach(2)/log(d1mach(2));/* = 2.533 e305  for IEEE double */
    dxrel = sqrt (d1mach(4));/* sqrt(Eps) ~ 1.49 e-8  for IEEE double */
    }

    signgam = 1;

#ifdef IEEE_754
    if(ISNAN(x)) return x;
#endif

    if (x <= 0 && x == (int)x) { /* Negative integer argument */
    ML_ERROR(ME_RANGE);
    return ML_POSINF;/* +Inf, since lgamma(x) = log|gamma(x)| */
    }

    y = fabs(x);

    if (y <= 10)
    return log(fabs(gammafn(x)));
    /*
      ELSE  y = |x| > 10 ---------------------- */

    if (y > xmax) {
    ML_ERROR(ME_RANGE);
    return ML_POSINF;
    }

    if (x > 0) { /* i.e. y = x > 10 */
#ifdef IEEE_754
    if(x > 1e17)
        return(x*(log(x) - 1.));
    else if(x > 4934720.)
        return(M_LN_SQRT_2PI + (x - 0.5) * log(x) - x);
    else
#endif
        return M_LN_SQRT_2PI + (x - 0.5) * log(x) - x + lgammacor(x);
    }
    /* else: x < -10; y = -x */
    sinpiy = fabs(sin(M_PI * y));

    if (sinpiy == 0) { /* Negative integer argument ===
              Now UNNECESSARY: caught above */
    MATHLIB_WARNING(" ** should NEVER happen! *** [lgamma.c: Neg.int, y=%g]\n",y);
    ML_ERR_return_NAN;
    }

    ans = M_LN_SQRT_PId2 + (x - 0.5) * log(y) - x - log(sinpiy) - lgammacor(y);

    if(fabs((x - (int)(x - 0.5)) * ans / x) < dxrel) {

    /* The answer is less than half precision because
     * the argument is too near a negative integer. */

    ML_ERROR(ME_PRECISION);
    }

    if (x <= 0 && ((int)(-x))%2 == 0)
    signgam = -1;
    return ans;
}