1994-05-27 05:00:24 +00:00
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/*
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* Copyright (c) 1985, 1993
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* The Regents of the University of California. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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* 3. All advertising materials mentioning features or use of this software
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* must display the following acknowledgement:
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* This product includes software developed by the University of
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* California, Berkeley and its contributors.
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* 4. Neither the name of the University nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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* SUCH DAMAGE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)atanh.c 8.1 (Berkeley) 6/4/93";
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#endif /* not lint */
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/* ATANH(X)
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* RETURN THE HYPERBOLIC ARC TANGENT OF X
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* DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
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1995-05-30 05:51:47 +00:00
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* CODED IN C BY K.C. NG, 1/8/85;
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1994-05-27 05:00:24 +00:00
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* REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85.
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*
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* Required kernel function:
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* log1p(x) ...return log(1+x)
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*
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* Method :
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1995-05-30 05:51:47 +00:00
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* Return
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1994-05-27 05:00:24 +00:00
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* 1 2x x
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* atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
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* 2 1 - x 1 - x
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*
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* Special cases:
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* atanh(x) is NaN if |x| > 1 with signal;
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* atanh(NaN) is that NaN with no signal;
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* atanh(+-1) is +-INF with signal.
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*
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* Accuracy:
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* atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded.
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* In a test run with 512,000 random arguments on a VAX, the maximum
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* observed error was 1.87 ulps (units in the last place) at
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* x= -3.8962076028810414000e-03.
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*/
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#include "mathimpl.h"
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#if defined(vax)||defined(tahoe)
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#include <errno.h>
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#endif /* defined(vax)||defined(tahoe) */
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double atanh(x)
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double x;
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{
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double z;
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z = copysign(0.5,x);
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x = copysign(x,1.0);
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#if defined(vax)||defined(tahoe)
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if (x == 1.0) {
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return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */
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}
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#endif /* defined(vax)||defined(tahoe) */
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x = x/(1.0-x);
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return( z*log1p(x+x) );
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}
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