mirror of https://gitlab.com/rnger/amath
124 lines
3.8 KiB
C
124 lines
3.8 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_sinh.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 sinh.c
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* @brief Hyperbolic sine function
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*/
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#include "prim.h"
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#if __GNUC__ > 2
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#pragma GCC diagnostic ignored "-Wstrict-aliasing"
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#endif
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static const double
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one = 1.0,
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shuge = 1.0e307;
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/**
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* @brief Hyperbolic sine function
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* @details
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* <pre>
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* Method
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* mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2
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* 1. Replace x by |x| (sinh(-x) = -sinh(x)).
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* 2.
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* E + E/(E+1)
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* 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x)
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* 2
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*
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* 22 <= x <= lnovft : sinh(x) := exp(x)/2
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* lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2)
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* ln2ovft < x : sinh(x) := x*shuge (overflow)
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*
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* Special cases
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* sinh(x) is |x| if x is +INF, -INF, or NaN.
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* only sinh(0)=0 is exact for finite x.
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* </pre>
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*/
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double sinh(double x)
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{
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double t, w, h;
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int32_t ix, jx;
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uint32_t lx;
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// High word of |x|
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GET_HIGH_WORD(jx, x);
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ix = jx & 0x7FFFFFFF;
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// x is INF or NaN
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if (ix >= 0x7FF00000)
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{
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return NAN;
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}
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h = 0.5;
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if (jx < 0)
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h = -h;
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/* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
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if (ix < 0x40360000)
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{ /* |x|<22 */
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if (ix < 0x3E300000) /* |x|<2**-28 */
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if (shuge + x > one)
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return x; /* sinh(tiny) = tiny with inexact */
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t = expm1(fabs(x));
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if (ix < 0x3FF00000)
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return h * (2.0 * t - t * t / (t + one));
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return h * (t + t / (t + one));
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}
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/* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */
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if (ix < 0x40862E42)
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return h * exp(fabs(x));
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/* |x| in [log(maxdouble), overflowthresold] */
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lx = *((((*(uint32_t *)&one) >> 29)) + (uint32_t *)&x);
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if (ix < 0x408633CE || ((ix == 0x408633CE) && (lx <= (uint32_t)0X8FB9F87D)))
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{
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w = exp(0.5 * fabs(x));
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t = h * w;
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return t * w;
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}
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/* |x| > overflowthresold, sinh(x) overflow */
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return x * shuge;
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}
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