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/* origin: OpenBSD /usr/src/lib/libm/src/ld80/s_asinhl.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.
* ====================================================
*/
/* 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 "libm.h"
#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double asinhl(long double x)
{
return asinh(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384
static const long double
one = 1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
ln2 = 6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
huge = 1.000000000000000000e+4900L;
long double asinhl(long double x)
{
long double t,w;
int32_t hx,ix;
GET_LDOUBLE_EXP(hx, x);
ix = hx & 0x7fff;
if (ix == 0x7fff)
return x + x; /* x is inf or NaN */
if (ix < 0x3fde) { /* |x| < 2**-34 */
/* return x, raise inexact if x != 0 */
if (huge+x > one)
return x;
}
if (ix > 0x4020) { /* |x| > 2**34 */
w = logl(fabsl(x)) + ln2;
} else if (ix > 0x4000) { /* 2**34 > |x| > 2.0 */
t = fabsl(x);
w = logl(2.0*t + one/(sqrtl(x*x + one) + t));
} else { /* 2.0 > |x| > 2**-28 */
t = x*x;
w =log1pl(fabsl(x) + t/(one + sqrtl(one + t)));
}
if (hx & 0x8000)
return -w;
return w;
}
#endif
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