mirror of https://gitlab.com/rnger/amath
100 lines
3.3 KiB
C
100 lines
3.3 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/s_asinh.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 asinh.c
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* @brief Inverse hyperbolic sine function
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*/
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#include "prim.h"
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static const double
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one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
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huge = 1.00000000000000000000e+300;
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/**
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* @brief Inverse hyperbolic sine function
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* @details
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* <pre>
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* Method
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* Based on
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* asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
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*
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* we have
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* asinh(x) = x if 1+x*x=1,
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* = sign(x)*(log(x)+ln2)) for large |x|, else
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* = sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
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* = sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
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* </pre>
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*/
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double asinh(double x)
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{
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double t, w;
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int32_t hx, ix;
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GET_HIGH_WORD(hx, x);
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ix = hx & 0x7fffffff;
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if (ix >= 0x7ff00000)
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return x + x; /* x is inf or NaN */
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if (ix < 0x3e300000)
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{ /* |x|<2**-28 */
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if (huge + x > one)
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return x; /* return x inexact except 0 */
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}
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if (ix > 0x41b00000)
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{ /* |x| > 2**28 */
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w = log(fabs(x)) + ln2;
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}
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else if (ix > 0x40000000)
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{ /* 2**28 > |x| > 2.0 */
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t = fabs(x);
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w = log(2.0 * t + one / (sqrt(x * x + one) + t));
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}
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else
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{ /* 2.0 > |x| > 2**-28 */
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t = x * x;
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w = log1p(fabs(x) + t / (one + sqrt(one + t)));
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}
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if (hx > 0)
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return w;
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else
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return -w;
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}
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