70 lines
2.4 KiB
C
70 lines
2.4 KiB
C
/*
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted provided
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* that: (1) source distributions retain this entire copyright notice and
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* comment, and (2) distributions including binaries display the following
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* acknowledgement: ``This product includes software developed by the
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* University of California, Berkeley and its contributors'' in the
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* documentation or other materials provided with the distribution and in
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* all advertising materials mentioning features or use of this software.
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* Neither the name of the University nor the names of its contributors may
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* be used to endorse or promote products derived from this software without
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* specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*/
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#ifndef lint
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static char sccsid[] = "@(#)atanh.c 5.6 (Berkeley) 10/9/90";
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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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* CODED IN C BY K.C. NG, 1/8/85;
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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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* Return
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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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