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n_atanh.c revision 1.1 
      1 /*      $NetBSD: n_atanh.c,v 1.1 1995/10/10 23:36:38 ragge Exp $ */
      2 /*
      3  * Copyright (c) 1985, 1993
      4  *	The Regents of the University of California.  All rights reserved.
      5  *
      6  * Redistribution and use in source and binary forms, with or without
      7  * modification, are permitted provided that the following conditions
      8  * are met:
      9  * 1. Redistributions of source code must retain the above copyright
     10  *    notice, this list of conditions and the following disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  * 3. All advertising materials mentioning features or use of this software
     15  *    must display the following acknowledgement:
     16  *	This product includes software developed by the University of
     17  *	California, Berkeley and its contributors.
     18  * 4. Neither the name of the University nor the names of its contributors
     19  *    may be used to endorse or promote products derived from this software
     20  *    without specific prior written permission.
     21  *
     22  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     23  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     24  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     25  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     26  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     27  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     28  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     29  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     30  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     31  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     32  * SUCH DAMAGE.
     33  */
     34 
     35 #ifndef lint
     36 static char sccsid[] = "@(#)atanh.c	8.1 (Berkeley) 6/4/93";
     37 #endif /* not lint */
     38 
     39 /* ATANH(X)
     40  * RETURN THE HYPERBOLIC ARC TANGENT OF X
     41  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
     42  * CODED IN C BY K.C. NG, 1/8/85;
     43  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
     44  *
     45  * Required kernel function:
     46  *	log1p(x) 	...return log(1+x)
     47  *
     48  * Method :
     49  *	Return
     50  *                          1              2x                          x
     51  *		atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
     52  *                          2             1 - x                      1 - x
     53  *
     54  * Special cases:
     55  *	atanh(x) is NaN if |x| > 1 with signal;
     56  *	atanh(NaN) is that NaN with no signal;
     57  *	atanh(+-1) is +-INF with signal.
     58  *
     59  * Accuracy:
     60  *	atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
     61  *	In a test run with 512,000 random arguments on a VAX, the maximum
     62  *	observed error was 1.87 ulps (units in the last place) at
     63  *	x= -3.8962076028810414000e-03.
     64  */
     65 #include "mathimpl.h"
     66 
     67 #if defined(vax)||defined(tahoe)
     68 #include <errno.h>
     69 #endif	/* defined(vax)||defined(tahoe) */
     70 
     71 double atanh(x)
     72 double x;
     73 {
     74 	double z;
     75 	z = copysign(0.5,x);
     76 	x = copysign(x,1.0);
     77 #if defined(vax)||defined(tahoe)
     78 	if (x == 1.0) {
     79 	    return(copysign(1.0,z)*infnan(ERANGE));	/* sign(x)*INF */
     80 	}
     81 #endif	/* defined(vax)||defined(tahoe) */
     82 	x = x/(1.0-x);
     83 	return( z*log1p(x+x) );
     84 }
     85