mirror of https://gitlab.com/rnger/amath
103 lines
3.4 KiB
C
103 lines
3.4 KiB
C
/* @(#)e_atanh.c 1.3 95/01/18 */
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/*
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* Copyright (c) 2015 Carsten Larsen
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* 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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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*
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* The origin source code can be obtained from:
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* http://www.netlib.org/fdlibm/e_atanh.c
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*
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunSoft, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*
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*/
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#include "prim.h"
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#include "math.h"
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#ifdef _WIN32
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#pragma warning( disable : 4146 )
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#endif
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static const double one = 1.0, huge = 1e300;
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static double zero = 0.0;
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/**
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* @brief Inverse hyperbolic tangent function.
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* @version 1.3
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* @date 95/01/18
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* @details
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* <pre>
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* Method :
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* 1.Reduced x to positive by atanh(-x) = -atanh(x)
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* 2.For x>=0.5
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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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* For x<0.5
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* atanh(x) = 0.5*log1p(2x+2x*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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* </pre>
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* @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission
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* to use, copy, modify, and distribute this software is freely granted,
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* provided that this notice is preserved.
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*/
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double atanh(double x)
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{
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double t;
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sword hx,ix;
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uword lx;
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GET_HIGH_WORD(hx,x);
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GET_LOW_WORD(lx,x);
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ix = hx&0x7fffffff;
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if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
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return (x-x)/(x-x);
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if(ix==0x3ff00000)
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return x/zero;
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if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
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SET_HIGH_WORD(x, ix); /* x <- |x| */
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if(ix<0x3fe00000) { /* x < 0.5 */
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t = x+x;
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t = 0.5*log1p(t+t*x/(one-x));
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} else
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t = 0.5*log1p((x+x)/(one-x));
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if(hx>=0) return t;
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else return -t;
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}
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