update for ANSI C from Alex Zliu and John Gilmore

[unix-history] / usr / src / lib / libm / common_source / atanh.c

/*
* Copyright (c) 1985 Regents of the University of California.
* All rights reserved.
*
* Redistribution and use in source and binary forms are permitted
* provided that the above copyright notice and this paragraph are
* duplicated in all such forms and that any documentation,
* advertising materials, and other materials related to such
* distribution and use acknowledge that the software was developed
* by the University of California, Berkeley.  The name of the
* University may not be used to endorse or promote products derived
* from this software without specific prior written permission.
* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
*
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
*/

#ifndef lint
static char sccsid[] = "@(#)atanh.c     5.4 (Berkeley) %G%";
#endif /* not lint */

/* 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 "mathimpl.h"

#if defined(vax)||defined(tahoe)
#include <errno.h>
#endif  /* defined(vax)||defined(tahoe) */

double atanh(x)
double x;
{
       double z;
       z = copysign(0.5,x);
       x = copysign(x,1.0);
#if defined(vax)||defined(tahoe)
       if (x == 1.0) {
           return(copysign(1.0,z)*infnan(ERANGE));     /* sign(x)*INF */
       }
#endif  /* defined(vax)||defined(tahoe) */
       x = x/(1.0-x);
       return( z*log1p(x+x) );
}