mirror of https://gitlab.com/rnger/amath
126 lines
4.1 KiB
C
126 lines
4.1 KiB
C
/* @(#)e_cosh.c 1.3 95/01/18 */
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/*
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* Copyright (c) 2015 Carsten Larsen
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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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* The origin 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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/*
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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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#include "prim.h"
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#include "math.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 one = 1.0, half=0.5, huge = 1.0e300;
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/**
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* @brief Hyperbolic cosine function.
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* @version 1.3
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* @date 95/01/18
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* @details
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* <pre>
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* Method :
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* mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2
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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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* 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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* @copyright Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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* @license Developed at SunSoft, a Sun Microsystems, Inc. business. Permission
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* to use, copy, modify, and distribute this software is freely granted,
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* provided that this notice is preserved.
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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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sword ix;
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uword 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) return x*x;
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/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
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if(ix<0x3fd62e43) {
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t = expm1(fabs(x));
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w = one+t;
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if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */
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return one+(t*t)/(w+w);
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}
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/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
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if (ix < 0x40360000) {
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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)] return half*exp(|x|) */
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if (ix < 0x40862E42) return half*exp(fabs(x));
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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 ||
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((ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d))) {
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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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