The R Project SVN R

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 1998 Ross Ihaka
 *  Copyright (C) 2000, 2003 The R Development 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, write to the Free Software
 *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307 USA.
 *
 *  SYNOPSIS
 *
 *  #include <Rmath.h>
 *  double log1p(double x);
 *
 *  DESCRIPTION
 *
 *  Compute the relative error logarithm.
 *
 *          log(1 + x)
 *
 *  NOTES
 *
 *  This code is a translation of the Fortran subroutine `dlnrel'
 *  written by W. Fullerton of Los Alamos Scientific Laboratory.
 */

#ifdef HAVE_CONFIG_H
# include <config.h>
#endif
#include "nmath.h"

/* want to compile log1p as Rlog1p if HAVE_LOG1P && !HAVE_WORKING_LOG1P */
#if defined(HAVE_LOG1P) && !defined(HAVE_WORKING_LOG1P)
#undef HAVE_LOG1P
#endif

#ifndef HAVE_LOG1P
double log1p(double x)
{
    /* series for log1p on the interval -.375 to .375
     *                   with weighted error   6.35e-32
     *                    log weighted error  31.20
     *              significant figures required  30.93
     *               decimal places required  32.01
     */
    const 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,
    };
    const double xmin = -1 + sqrt(1/DBL_EPSILON);/*was sqrt(d1mach(4)); */

#ifdef NOMORE_FOR_THREADS
    static int nlnrel = 0;

    if (nlnrel == 0) {/* initialize chebychev coefficients */
    nlnrel = chebyshev_init(alnrcs, 43, DBL_EPSILON/20);/*was .1*d1mach(3)*/
    }
#else
# define nlnrel 22
/* 22: for IEEE double precision where DBL_EPSILON =  2.22044604925031e-16 */
#endif

    if (x == 0.) return 0.;/* speed */
    if (x == -1) return(ML_NEGINF);
    if (x  < -1) ML_ERR_return_NAN;

    if (fabs(x) <= .375) {
        /* Improve on speed (only);
       again give result accurate to IEEE double precision: */
    if(fabs(x) < .5 * DBL_EPSILON)
        return x;

    if( (0 < x && x < 1e-8) || (-1e-9 < x && x < 0))
        return x * (1 - .5 * x);
    /* else */
    return x * (1 - x * chebyshev_eval(x / .375, alnrcs, nlnrel));
    }
    /* else */
    if (x < xmin) {
    /* answer less than half precision because x too near -1 */
    ML_ERROR(ME_PRECISION);
    }
    return log(1 + x);
}
#endif



/* pythag(a,b)  finds sqrt(a^2 + b^2)
 *      without overflow or destructive underflow.
 */

double pythag(double a, double b)
{
#ifndef HAVE_HYPOT
    double p, r, s, t, tmp, u;
#endif

    if(ISNAN(a) || ISNAN(b)) /* propagate Na(N)s: */
        return
#ifdef IEEE_754
      a + b;
#else
          ML_NAN;
#endif
    if (!R_FINITE(a) || !R_FINITE(b)) {
        return ML_POSINF;
    }
#ifdef HAVE_HYPOT
    return hypot(a, b);
#else
    p = fmax2(fabs(a), fabs(b));
    if (p != 0.0) {

    /* r = (min(|a|,|b|) / p) ^2 */
    tmp = fmin2(fabs(a), fabs(b))/p;
    r = tmp * tmp;
    for(;;) {
        t = 4.0 + r;
        if (t == 4.0)
        break;
        s = r / t;
        u = 1. + 2. * s;
        p *= u ;

        /* r = (s / u)^2 * r */
        tmp = s / u;
        r *= tmp * tmp;
    }
    }
    return p;
#endif
}