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/* s_asinhl.c -- long double version of s_asinh.c.
* Conversion to long double by Ulrich Drepper,
* Cygnus Support, drepper@cygnus.com.
*/
/*
* ====================================================
* 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.
* ====================================================
*/
/* asinhl(x)
* Method :
* Based on
* asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
* we have
* asinhl(x) := x if 1+x*x=1,
* := signl(x)*(logl(x)+ln2)) for large |x|, else
* := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
* := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
*/
#include "quadmath-imp.h"
static const __float128
one = 1.0Q,
ln2 = 6.931471805599453094172321214581765681e-1Q,
huge = 1.0e+4900Q;
__float128
asinhq (__float128 x)
{
__float128 t, w;
int32_t ix, sign;
ieee854_float128 u;
u.value = x;
sign = u.words32.w0;
ix = sign & 0x7fffffff;
if (ix == 0x7fff0000)
return x + x; /* x is inf or NaN */
if (ix < 0x3fc70000)
{ /* |x| < 2^ -56 */
if (huge + x > one)
return x; /* return x inexact except 0 */
}
u.words32.w0 = ix;
if (ix > 0x40350000)
{ /* |x| > 2 ^ 54 */
w = logq (u.value) + ln2;
}
else if (ix >0x40000000)
{ /* 2^ 54 > |x| > 2.0 */
t = u.value;
w = logq (2.0 * t + one / (sqrtq (x * x + one) + t));
}
else
{ /* 2.0 > |x| > 2 ^ -56 */
t = x * x;
w = log1pq (u.value + t / (one + sqrtq (one + t)));
}
if (sign & 0x80000000)
return -w;
else
return w;
}
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