expm1.c

/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 2002 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 expm1(double x);
 *
 *  DESCRIPTION
 *
 *	Compute the Exponential minus 1
 *
 *			exp(x) - 1
 *
 *      accurately also when x is close to zero, i.e. |x| << 1
 *
 *  NOTES
 *
 *	As log1p(), this is a standard function in some C libraries,
 *	particularly GNU and BSD (but is neither ISO/ANSI C nor POSIX).
 *
 *  We supply a substitute for the case when there is no system one.
 */

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


#ifndef HAVE_EXPM1
double expm1(double x)
{
    double y, a = fabs(x);

    if (a < DBL_EPSILON) return x;
    if (a > 0.697) return exp(x) - 1;  /* negligible cancellation */

    if (a > 1e-8)
	y = exp(x) - 1;
    else /* Taylor expansion, more accurate in this range */
	y = (x / 2 + 1) * x;

    /* Newton step for solving   log(1 + y) = x   for y : */
    /* WARNING: does not work for y ~ -1: bug in 1.5.0 */
    y -= (1 + y) * (log1p (y) - x);
    return y;
}
#endif