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/* s_atanhl.c -- long double version of s_atan.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.
* ====================================================
*/
/* __ieee754_atanhl(x)
* Method :
* 1.Reduced x to positive by atanh(-x) = -atanh(x)
* 2.For x>=0.5
* 1 2x x
* atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
* 2 1 - x 1 - x
*
* For x<0.5
* atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
*
* Special cases:
* atanhl(x) is NaN if |x| > 1 with signal;
* atanhl(NaN) is that NaN with no signal;
* atanhl(+-1) is +-INF with signal.
*
*/
#include <float.h>
#include <math.h>
#include <math_private.h>
#include <math-underflow.h>
#include <libm-alias-finite.h>
static const _Float128 one = 1, huge = L(1e4900);
static const _Float128 zero = 0;
_Float128
__ieee754_atanhl(_Float128 x)
{
_Float128 t;
uint32_t jx, ix;
ieee854_long_double_shape_type u;
u.value = x;
jx = u.parts32.w0;
ix = jx & 0x7fffffff;
u.parts32.w0 = ix;
if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
{
if (u.value == one)
return x/zero;
else
return (x-x)/(x-x);
}
if(ix<0x3fc60000 && (huge+x)>zero) /* x < 2^-57 */
{
math_check_force_underflow (x);
return x;
}
if(ix<0x3ffe0000) { /* x < 0.5 */
t = u.value+u.value;
t = 0.5*__log1pl(t+t*u.value/(one-u.value));
} else
t = 0.5*__log1pl((u.value+u.value)/(one-u.value));
if(jx & 0x80000000) return -t; else return t;
}
libm_alias_finite (__ieee754_atanhl, __atanhl)
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