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/*
* ====================================================
* 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.
* ====================================================
*/
#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_cosh.c,v 1.7 1995/05/10 20:44:58 jtc Exp $";
#endif
/* __ieee754_coshl(x)
* Method :
* mathematically coshl(x) if defined to be (exp(x)+exp(-x))/2
* 1. Replace x by |x| (coshl(x) = coshl(-x)).
* 2.
* [ exp(x) - 1 ]^2
* 0 <= x <= ln2/2 : coshl(x) := 1 + -------------------
* 2*exp(x)
*
* exp(x) + 1/exp(x)
* ln2/2 <= x <= 22 : coshl(x) := -------------------
* 2
* 22 <= x <= lnovft : coshl(x) := expl(x)/2
* lnovft <= x <= ln2ovft: coshl(x) := expl(x/2)/2 * expl(x/2)
* ln2ovft < x : coshl(x) := huge*huge (overflow)
*
* Special cases:
* coshl(x) is |x| if x is +INF, -INF, or NaN.
* only coshl(0)=1 is exact for finite x.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const long double one = 1.0, half=0.5, huge = 1.0e4900L;
#else
static long double one = 1.0, half=0.5, huge = 1.0e4900L;
#endif
#ifdef __STDC__
long double __ieee754_coshl(long double x)
#else
long double __ieee754_coshl(x)
long double x;
#endif
{
long double t,w;
int32_t ex;
u_int32_t mx,lx;
/* High word of |x|. */
GET_LDOUBLE_WORDS(ex,mx,lx,x);
ex &= 0x7fff;
/* x is INF or NaN */
if(ex==0x7fff) return x*x;
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
if(ex < 0x3ffd || (ex == 0x3ffd && mx < 0xb17217f7u)) {
t = __expm1l(fabsl(x));
w = one+t;
if (ex<0x3fbc) return w; /* cosh(tiny) = 1 */
return one+(t*t)/(w+w);
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ex < 0x4003 || (ex == 0x4003 && mx < 0xb0000000u)) {
t = __ieee754_expl(fabsl(x));
return half*t+half/t;
}
/* |x| in [22, ln(maxdouble)] return half*exp(|x|) */
if (ex < 0x400c || (ex == 0x400c && mx < 0xb1700000u))
return half*__ieee754_expl(fabsl(x));
/* |x| in [log(maxdouble), overflowthresold] */
if (ex < 0x400d
|| (ex == 0x400d && (mx < 0xb170b513u
|| (mx == 0xb170b513u && lx < 0xa1dfd60cu))))
{
w = __ieee754_expl(half*fabsl(x));
t = half*w;
return t*w;
}
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
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