mirror of https://gitlab.com/rnger/amath
113 lines
3.1 KiB
C
113 lines
3.1 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_acosh.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 acosh.c
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* @brief Inverse hyperbolic cosine function
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*/
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#include "prim.h"
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static const double
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one = 1.0,
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ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */
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/**
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* @brief Inverse hyperbolic cosine function
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* @details
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* <pre>
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* Based on
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* acosh(x) = log [ x + sqrt(x*x-1) ]
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*
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* we have
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* acosh(x) = log(x)+ln2, if x is large; else
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* acosh(x) = log(2x-1/(sqrt(x*x-1)+x)) if x>2; else
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* acosh(x) = log1p(t+sqrt(2.0*t+t*t)); where t=x-1
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*
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* Special cases
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* acosh(x) is NaN if x<1
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* acosh(NaN) is NaN
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* </pre>
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*/
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double acosh(double x)
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{
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double t;
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int32_t hx, lx;
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GET_HIGH_WORD(hx, x);
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GET_LOW_WORD(lx, x);
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// x < 1
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if (hx < 0x3FF00000)
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{
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return NAN;
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}
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// x > 2**28
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if (hx >= 0x41B00000)
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{
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// x is inf or NaN
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if (hx >= 0x7FF00000)
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{
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return NAN;
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}
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// acosh(huge) = log(2x)
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return log(x) + ln2;
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}
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// acosh(1) = 0
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if (((hx - 0x3FF00000) | lx) == 0)
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{
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return 0.0;
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}
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// 2**28 > x > 2
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if (hx > 0x40000000)
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{
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t = x * x;
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return log(2.0 * x - one / (x + sqrt(t - one)));
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}
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// 1 < x < 2
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t = x - one;
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return log1p(t + sqrt(2.0 * t + t * t));
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}
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