/*

 *  Mathlib : A C Library of Special Functions

 *  Copyright (C) 1998 Ross Ihaka

 *  Copyright (C) 1999-2025  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>

 *    void gammalims(double *xmin, double *xmax);

 *

 *  DESCRIPTION

 *

 *    This function calculates the minimum and maximum legal bounds

 *    for x in gammafn(x).  These are not the only bounds, but they

 *    are the only non-trivial ones to calculate.

 *

 *  NOTES

 *

 *    This routine is a translation into C of a Fortran subroutine

 *    by W. Fullerton of Los Alamos Scientific Laboratory.

 */

#include "nmath.h"

attribute_hidden void gammalims(double *xmin, double *xmax)

{

/* FIXME: Even better: If IEEE, #define these in nmath.h

    and don't call gammalims() at all

*/

#ifdef IEEE_754

    *xmin = -170.5674972726612;

    *xmax =  171.61447887182298;/*(3 Intel/Sparc architectures)*/

#else

    double alnbig, alnsml, xln, xold;

    int i;

    alnsml = log(d1mach(1));

    *xmin = -alnsml;

    for (i=1; i<=10; ++i) {

  xold = *xmin;

  xln = log(*xmin);

  *xmin -= *xmin * ((*xmin + .5) * xln - *xmin - .2258 + alnsml) /

    (*xmin * xln + .5);

  if (fabs(*xmin - xold) < .005) {

      *xmin = -(*xmin) + .01;

      goto find_xmax;

  }

    }

    /* unable to find xmin */

    ML_WARNING(ME_NOCONV, "gammalims");

    *xmin = *xmax = ML_NAN;

find_xmax:

    alnbig = log(d1mach(2));

    *xmax = alnbig;

    for (i=1; i<=10; ++i) {

  xold = *xmax;

  xln = log(*xmax);

  *xmax -= *xmax * ((*xmax - .5) * xln - *xmax + .9189 - alnbig) /

    (*xmax * xln - .5);

  if (fabs(*xmax - xold) < .005) {

      *xmax += -.01;

      goto done;

  }

    }

    /* unable to find xmax */

    ML_WARNING(ME_NOCONV, "gammalims");

    *xmin = *xmax = ML_NAN;

done:

    *xmin = fmax2(*xmin, -(*xmax) + 1);

#endif

}