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/* @(#)e_cosh.c 1.3 95/01/18 */
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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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/* __ieee754_cosh(x)
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* Method :
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* mathematically ieee_cosh(x) if defined to be (ieee_exp(x)+ieee_exp(-x))/2
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* 1. Replace x by |x| (ieee_cosh(x) = ieee_cosh(-x)).
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* 2.
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* [ ieee_exp(x) - 1 ]^2
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* 0 <= x <= ln2/2 : ieee_cosh(x) := 1 + -------------------
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* 2*ieee_exp(x)
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*
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* ieee_exp(x) + 1/ieee_exp(x)
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* ln2/2 <= x <= 22 : ieee_cosh(x) := -------------------
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* 2
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* 22 <= x <= lnovft : ieee_cosh(x) := ieee_exp(x)/2
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* lnovft <= x <= ln2ovft: ieee_cosh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2)
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* ln2ovft < x : ieee_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 ieee_cosh(0)=1 is exact for finite x.
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*/
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#include "fdlibm.h"
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#ifdef __STDC__
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static const double one = 1.0, half=0.5, huge = 1.0e300;
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#else
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static double one = 1.0, half=0.5, huge = 1.0e300;
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#endif
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#ifdef __STDC__
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double __ieee754_cosh(double x)
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#else
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double __ieee754_cosh(x)
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double x;
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#endif
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{
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double t,w;
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int ix;
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unsigned lx;
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/* High word of |x|. */
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ix = __HI(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+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */
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if(ix<0x3fd62e43) {
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t = ieee_expm1(ieee_fabs(x));
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w = one+t;
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if (ix<0x3c800000) return w; /* ieee_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 (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */
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if (ix < 0x40360000) {
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t = __ieee754_exp(ieee_fabs(x));
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return half*t+half/t;
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}
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/* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */
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if (ix < 0x40862E42) return half*__ieee754_exp(ieee_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 = __ieee754_exp(half*ieee_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, ieee_cosh(x) overflow */
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return huge*huge;
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}
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