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e_cosh.c
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e_cosh.c
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/* @(#)e_cosh.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
/* __ieee754_cosh(x)
* Method :
* mathematically ieee_cosh(x) if defined to be (ieee_exp(x)+ieee_exp(-x))/2
* 1. Replace x by |x| (ieee_cosh(x) = ieee_cosh(-x)).
* 2.
* [ ieee_exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : ieee_cosh(x) := 1 + -------------------
* 2*ieee_exp(x)
*
* ieee_exp(x) + 1/ieee_exp(x)
* ln2/2 <= x <= 22 : ieee_cosh(x) := -------------------
* 2
* 22 <= x <= lnovft : ieee_cosh(x) := ieee_exp(x)/2
* lnovft <= x <= ln2ovft: ieee_cosh(x) := ieee_exp(x/2)/2 * ieee_exp(x/2)
* ln2ovft < x : ieee_cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only ieee_cosh(0)=1 is exact for finite x.
*/
#include "fdlibm.h"
#ifdef __STDC__
static const double one = 1.0, half=0.5, huge = 1.0e300;
#else
static double one = 1.0, half=0.5, huge = 1.0e300;
#endif
#ifdef __STDC__
double __ieee754_cosh(double x)
#else
double __ieee754_cosh(x)
double x;
#endif
{
double t,w;
int ix;
unsigned lx;
/* High word of |x|. */
ix = __HI(x);
ix &= 0x7fffffff;
/* x is INF or NaN */
if(ix>=0x7ff00000) return x*x;
/* |x| in [0,0.5*ln2], return 1+ieee_expm1(|x|)^2/(2*ieee_exp(|x|)) */
if(ix<0x3fd62e43) {
t = ieee_expm1(ieee_fabs(x));
w = one+t;
if (ix<0x3c800000) return w; /* ieee_cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (ieee_exp(|x|)+1/ieee_exp(|x|)/2; */
if (ix < 0x40360000) {
t = __ieee754_exp(ieee_fabs(x));
return half*t+half/t;
}
/* |x| in [22, ieee_log(maxdouble)] return half*ieee_exp(|x|) */
if (ix < 0x40862E42) return half*__ieee754_exp(ieee_fabs(x));
/* |x| in [log(maxdouble), overflowthresold] */
lx = *( (((*(unsigned*)&one)>>29)) + (unsigned*)&x);
if (ix<0x408633CE ||
(ix==0x408633ce)&&(lx<=(unsigned)0x8fb9f87d)) {
w = __ieee754_exp(half*ieee_fabs(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, ieee_cosh(x) overflow */
return huge*huge;
}