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/* @(#)e_cosh.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, 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 cosh(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (cosh(x) = cosh(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : cosh(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 40 : cosh(x) := -------------------
* 2
* 40 <= x <= lnovft : cosh(x) := exp(x)/2
* lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2)
* ln2ovft < x : cosh(x) := huge*huge (overflow)
*
* Special cases:
* cosh(x) is |x| if x is +INF, -INF, or NaN.
* only cosh(0)=1 is exact for finite x.
*/
#include <math.h>
#include <math_private.h>
static const long double one = 1.0L, half=0.5L, huge = 1.0e300L;
long double
__ieee754_coshl (long double x)
{
long double t,w;
int64_t ix;
double xhi;
/* High word of |x|. */
xhi = ldbl_high (x);
EXTRACT_WORDS64 (ix, xhi);
ix &= 0x7fffffffffffffffLL;
/* x is INF or NaN */
if(ix>=0x7ff0000000000000LL) return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */
if(ix<0x3fd62e42fefa39efLL) {
if (ix<0x3c80000000000000LL) return one; /* cosh(tiny) = 1 */
t = __expm1l(fabsl(x));
w = one+t;
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,40], return (exp(|x|)+1/exp(|x|)/2; */
if (ix < 0x4044000000000000LL) {
t = __ieee754_expl(fabsl(x));
return half*t+half/t;
}
/* |x| in [40, log(maxdouble)] return half*exp(|x|) */
if (ix < 0x40862e42fefa39efLL) return half*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ix < 0x408633ce8fb9f87fLL) {
w = __ieee754_expl(half*fabsl(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
strong_alias (__ieee754_coshl, __coshl_finite)
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