The R Project SVN R

/*
 *  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 dlnrel(double x);
 *
 *  DESCRIPTION
 *
 *    Compute the relative error logarithm.
 *
 *                      log(1 + x)
 *
 *  NOTES
 *
 *    This code is a translation of a Fortran subroutine of the
 *    same name written by W. Fullerton of Los Alamos Scientific
 *    Laboratory.
 */

#include "Mathlib.h"

double logrelerr(double x)
{
    /* series for alnr on the interval -3.75000e-01 to  3.75000e-01 */
    /*                               with weighted error   6.35e-32 */
    /*                                log weighted error  31.20     */
    /*                      significant figures required  30.93     */
    /*                           decimal places required  32.01     */
    static double alnrcs[43] = {
    +.10378693562743769800686267719098e+1,
    -.13364301504908918098766041553133e+0,
    +.19408249135520563357926199374750e-1,
    -.30107551127535777690376537776592e-2,
    +.48694614797154850090456366509137e-3,
    -.81054881893175356066809943008622e-4,
    +.13778847799559524782938251496059e-4,
    -.23802210894358970251369992914935e-5,
    +.41640416213865183476391859901989e-6,
    -.73595828378075994984266837031998e-7,
    +.13117611876241674949152294345011e-7,
    -.23546709317742425136696092330175e-8,
    +.42522773276034997775638052962567e-9,
    -.77190894134840796826108107493300e-10,
    +.14075746481359069909215356472191e-10,
    -.25769072058024680627537078627584e-11,
    +.47342406666294421849154395005938e-12,
    -.87249012674742641745301263292675e-13,
    +.16124614902740551465739833119115e-13,
    -.29875652015665773006710792416815e-14,
    +.55480701209082887983041321697279e-15,
    -.10324619158271569595141333961932e-15,
    +.19250239203049851177878503244868e-16,
    -.35955073465265150011189707844266e-17,
    +.67264542537876857892194574226773e-18,
    -.12602624168735219252082425637546e-18,
    +.23644884408606210044916158955519e-19,
    -.44419377050807936898878389179733e-20,
    +.83546594464034259016241293994666e-21,
    -.15731559416479562574899253521066e-21,
    +.29653128740247422686154369706666e-22,
    -.55949583481815947292156013226666e-23,
    +.10566354268835681048187284138666e-23,
    -.19972483680670204548314999466666e-24,
    +.37782977818839361421049855999999e-25,
    -.71531586889081740345038165333333e-26,
    +.13552488463674213646502024533333e-26,
    -.25694673048487567430079829333333e-27,
    +.48747756066216949076459519999999e-28,
    -.92542112530849715321132373333333e-29,
    +.17578597841760239233269760000000e-29,
    -.33410026677731010351377066666666e-30,
    +.63533936180236187354180266666666e-31,
    };
    static int nlnrel = 0;
    static double xmin = 0.;

    if (nlnrel == 0) {
        nlnrel = chebyshev_init(alnrcs, 43, 0.1 * d1mach(3));
        xmin = -1.0 + sqrt(d1mach(4));
    }

    if (x <= -1) {
    ML_ERROR(ME_DOMAIN);
    return ML_NAN;
    }

    if (x < xmin) {
    /* answer less than half precision because x too near -1 */
    ML_ERROR(ME_PRECISION);
    }

    if (fabs(x) <= .375)
    return x * (1 - x * chebyshev_eval(x / .375, alnrcs, nlnrel));
    else
    return log(x + 1);
}