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      1 /*      $NetBSD: n_atanh.c,v 1.7 2003/08/07 16:44:50 agc 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. Neither the name of the University nor the names of its contributors
     15  *    may be used to endorse or promote products derived from this software
     16  *    without specific prior written permission.
     17  *
     18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
     19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
     20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
     21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
     22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
     24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     28  * SUCH DAMAGE.
     29  */
     30 
     31 #ifndef lint
     32 #if 0
     33 static char sccsid[] = "@(#)atanh.c	8.1 (Berkeley) 6/4/93";
     34 #endif
     35 #endif /* not lint */
     36 
     37 /* ATANH(X)
     38  * RETURN THE HYPERBOLIC ARC TANGENT OF X
     39  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
     40  * CODED IN C BY K.C. NG, 1/8/85;
     41  * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
     42  *
     43  * Required kernel function:
     44  *	log1p(x) 	...return log(1+x)
     45  *
     46  * Method :
     47  *	Return
     48  *                          1              2x                          x
     49  *		atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
     50  *                          2             1 - x                      1 - x
     51  *
     52  * Special cases:
     53  *	atanh(x) is NaN if |x| > 1 with signal;
     54  *	atanh(NaN) is that NaN with no signal;
     55  *	atanh(+-1) is +-INF with signal.
     56  *
     57  * Accuracy:
     58  *	atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
     59  *	In a test run with 512,000 random arguments on a VAX, the maximum
     60  *	observed error was 1.87 ulps (units in the last place) at
     61  *	x= -3.8962076028810414000e-03.
     62  */
     63 #include "mathimpl.h"
     64 
     65 #if defined(__vax__)||defined(tahoe)
     66 #include <errno.h>
     67 #endif	/* defined(__vax__)||defined(tahoe) */
     68 
     69 double
     70 atanh(double x)
     71 {
     72 	double z;
     73 	z = copysign(0.5,x);
     74 	x = copysign(x,1.0);
     75 #if defined(__vax__)||defined(tahoe)
     76 	if (x == 1.0) {
     77 	    return(copysign(1.0,z)*infnan(ERANGE));	/* sign(x)*INF */
     78 	}
     79 #endif	/* defined(__vax__)||defined(tahoe) */
     80 	x = x/(1.0-x);
     81 	return( z*log1p(x+x) );
     82 }
     83