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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_coshl.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* 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) := inf (overflow)
*
* Special cases:
* coshl(x) is |x| if x is +INF, -INF, or NaN.
* only coshl(0)=1 is exact for finite x.
*/
#include "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double coshl(long double x)
{
return cosh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
long double coshl(long double x)
{
union {
long double f;
struct{uint64_t m; uint16_t se; uint16_t pad;} i;
} u = {.f = x};
unsigned ex = u.i.se & 0x7fff;
long double t;
uint32_t mx,lx;
/* |x| */
u.i.se = ex;
x = u.f;
mx = u.i.m >> 32;
lx = u.i.m;
/* |x| in [0,0.5*ln2], return 1+expm1l(|x|)^2/(2*expl(|x|)) */
if (ex < 0x3fff-2 || (ex == 0x3fff-2 && mx < 0xb17217f7)) {
t = expm1l(x);
if (ex < 0x3fff-64)
return 1;
return 1 + t*t/(2*(1+t));
}
/* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */
if (ex < 0x3fff+4 || (ex == 0x3fff+4 && mx < 0xb0000000)) {
t = expl(x);
return 0.5*t + 0.5/t;
}
/* |x| in [22, ln(maxdouble)] return 0.5*exp(|x|) */
if (ex < 0x3fff+13 || (ex == 0x3fff+13 && mx < 0xb1700000))
return 0.5*expl(x);
/* |x| in [log(maxdouble), log(2*maxdouble)) */
if (ex == 0x3fff+13 && (mx < 0xb174ddc0 ||
(mx == 0xb174ddc0 && lx < 0x31aec0eb))) {
t = expl(0.5*x);
return 0.5*t*t;
}
/* |x| >= log(2*maxdouble) or nan */
return x*0x1p16383L;
}
#endif
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