mirror of https://gitlab.com/rnger/amath
138 lines
4.0 KiB
C
138 lines
4.0 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_cosh.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 cosh.c
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* @brief Hyperbolic cosine 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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half = 0.5,
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huge = 1.0e300;
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/**
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* @brief Hyperbolic cosine function
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* @details
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* Mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
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* <pre>
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* Method
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*
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* 1. Replace x by |x| (cosh(x) = cosh(-x))
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* 2.
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* [ exp(x) - 1 ]^2
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* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
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* 2*exp(x)
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*
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* exp(x) + 1/exp(x)
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* ln2/2 <= x <= 22 : cosh(x) := -------------------
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* 2
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* 22 <= x <= lnovft : cosh(x) := exp(x)/2
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* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
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* ln2ovft < x : cosh(x) := huge*huge (overflow)
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*
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* Special cases:
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*
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* cosh(x) is |x| if x is +INF, -INF, or NaN
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* only cosh(0)=1 is exact for finite x
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* </pre>
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*/
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double cosh(double x)
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{
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double t, w;
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int32_t ix;
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uint32_t lx;
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// High word of |x|
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GET_HIGH_WORD(ix, x);
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ix &= 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 x * x;
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}
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// |x| in [0,0.5*ln2]
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if (ix < 0x3FD62E43)
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{
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t = expm1(fabs(x));
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w = one + t;
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if (ix < 0x3C800000)
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{
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// cosh(tiny) = 1
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return w;
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}
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return one + (t * t) / (w + w);
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}
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// |x| in [0.5*ln2,22]
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if (ix < 0x40360000)
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{
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t = exp(fabs(x));
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return half * t + half / t;
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}
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// |x| in [22, log(maxdouble)]
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if (ix < 0x40862E42)
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{
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return half * exp(fabs(x));
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}
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// |x| in [log(maxdouble), overflowthresold]
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lx = *((((*(unsigned *)&one) >> 29)) + (unsigned *)&x);
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if (ix < 0x408633CE || ((ix == 0x408633CE) && (lx <= (unsigned)0x8FB9F87D)))
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{
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w = exp(half * fabs(x));
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t = half * w;
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return t * w;
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}
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// |x| > overflowthresold, cosh(x) overflow
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return huge * huge;
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}
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