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log1p.c
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log1p.c
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/*
* Mathlib : A C Library of Special Functions
* Copyright (C) 1998 Ross Ihaka
* Copyright (C) 2000, 2003, 2011 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
* http://www.r-project.org/Licenses/
*
* 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.
*/
/* Every currently known platform has log1p (which is C99),
but NetBSD/OpenBSD were at least at one time inaccurate */
#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 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,
};
#ifdef NOMORE_FOR_THREADS
static int nlnrel = 0;
static double xmin = 0.0;
if (xmin == 0.0) xmin = -1 + sqrt(DBL_EPSILON);/*was sqrt(d1mach(4)); */
if (nlnrel == 0) /* initialize chebychev coefficients */
nlnrel = chebyshev_init(alnrcs, 43, DBL_EPSILON/20);/*was .1*d1mach(3)*/
#else
# define nlnrel 22
const static double xmin = -0.999999985;
/* 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, "log1p");
}
return log(1 + x);
}
#endif
#ifndef HAVE_HYPOT
/* Used as a substitute for the C99 function hypot, which all currently
known platforms have */
/* hypot(a,b) finds sqrt(a^2 + b^2)
* without overflow or destructive underflow.
*/
double hypot(double a, double b)
{
double p, r, s, t, tmp, u;
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;
}
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;
/* This was a test of 4.0 + r == 4.0, but optimizing
compilers nowadays infinite loop on that. */
if(fabs(r) < 2*DBL_EPSILON) break;
s = r / t;
u = 1. + 2. * s;
p *= u ;
/* r = (s / u)^2 * r */
tmp = s / u;
r *= tmp * tmp;
}
}
return p;
}
#endif