mirror of https://gitlab.com/rnger/amath
107 lines
3.2 KiB
C
107 lines
3.2 KiB
C
/*-
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* Copyright (c) 2014-2017 Carsten Sonne Larsen <cs@innolan.net>
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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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* Project homepage:
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* https://amath.innolan.net
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*
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* The original 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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* 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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* @file atanh.c
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* @brief Inverse hyperbolic tangent function
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*/
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#include "prim.h"
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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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* @details
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* <pre>
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* Method
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*
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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
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* atanh(NaN) is that NaN
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* atanh(+-1) is +-INF
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* </pre>
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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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int32_t hx, ix;
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uint32_t 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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// |x| > 1
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if ((ix | ((lx | (-lx)) >> 31)) > 0x3FF00000)
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{
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return NAN;
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}
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if (ix == 0x3FF00000)
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return x / zero;
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if (ix < 0x3E300000 && (huge + x) > zero)
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return x; /* x<2**-28 */
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SET_HIGH_WORD(x, ix); /* x <- |x| */
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if (ix < 0x3FE00000)
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{ /* 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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}
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else
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t = 0.5 * log1p((x + x) / (one - x));
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if (hx >= 0)
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{
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return t;
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}
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return -t;
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}
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