atanh.c

<B>Digital的Unix操作系统VAX 4.2源码</B>

#ifndef lint
static char	*sccsid = "@(#)atanh.c	4.1	ULTRIX	7/17/90";
#endif lint

/************************************************************************
 *									*
 *			Copyright (c) 1986 by				*
 *		Digital Equipment Corporation, Maynard, MA		*
 *			All rights reserved.				*
 *									*
 *   This software is furnished under a license and may be used and	*
 *   copied  only  in accordance with the terms of such license and	*
 *   with the  inclusion  of  the  above  copyright  notice.   This	*
 *   software  or  any  other copies thereof may not be provided or	*
 *   otherwise made available to any other person.  No title to and	*
 *   ownership of the software is hereby transferred.			*
 *									*
 *   This software is  derived  from  software  received  from  the	*
 *   University    of   California,   Berkeley,   and   from   Bell	*
 *   Laboratories.  Use, duplication, or disclosure is  subject  to	*
 *   restrictions  under  license  agreements  with  University  of	*
 *   California and with AT&T.						*
 *									*
 *   The information in this software is subject to change  without	*
 *   notice  and should not be construed as a commitment by Digital	*
 *   Equipment Corporation.						*
 *									*
 *   Digital assumes no responsibility for the use  or  reliability	*
 *   of its software on equipment which is not supplied by Digital.	*
 *									*
 ************************************************************************/

/************************************************************************
*
*			Modification History
*
*		David Metsky		13-Jan-86
*
* 001	Added from BSD 4.3 version as part of upgrade
*
*	Based on:	atanh.c		1.2		8/21/85
*
*************************************************************************/

/* ATANH(X)
 * RETURN THE HYPERBOLIC ARC TANGENT OF X
 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
 * CODED IN C BY K.C. NG, 1/8/85; 
 * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
 *
 * Required kernel function:
 *	log1p(x) 	...return log(1+x)
 *
 * Method :
 *	Return 
 *                          1              2x                          x
 *		atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
 *                          2             1 - x                      1 - x
 *
 * Special cases:
 *	atanh(x) is NaN if |x| > 1 with signal;
 *	atanh(NaN) is that NaN with no signal;
 *	atanh(+-1) is +-INF with signal.
 *
 * Accuracy:
 *	atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
 *	In a test run with 512,000 random arguments on a VAX, the maximum
 *	observed error was 1.87 ulps (units in the last place) at
 *	x= -3.8962076028810414000e-03.
 */
#include <math.h>
#include <errno.h>

double atanh(x)
double x;
{
	double copysign(),log1p(),z;
	z = copysign(0.5,x);
	x = copysign(x,1.0);
	if (x >= 1.0) {
	    errno = ERANGE;
	    return(copysign(1.0,z)*(HUGE_VAL));	/* sign(x)*HUGE */
	}
	x = x/(1.0-x);
	return( z*log1p(x+x) );
}