1 /* s_atanhl.c -- long double version of s_atan.c.
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
12 * ====================================================
15 /* __ieee754_atanhl(x)
17 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
20 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
24 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
27 * atanhl(x) is NaN if |x| > 1 with signal;
28 * atanhl(NaN) is that NaN with no signal;
29 * atanhl(+-1) is +-INF with signal.
35 #include <math_private.h>
36 #include <math-underflow.h>
37 #include <libm-alias-finite.h>
39 static const _Float128 one
= 1, huge
= L(1e4900
);
41 static const _Float128 zero
= 0;
44 __ieee754_atanhl(_Float128 x
)
48 ieee854_long_double_shape_type u
;
54 if (ix
>= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
61 if(ix
<0x3fc60000 && (huge
+x
)>zero
) /* x < 2^-57 */
63 math_check_force_underflow (x
);
67 if(ix
<0x3ffe0000) { /* x < 0.5 */
69 t
= 0.5*__log1pl(t
+t
*u
.value
/(one
-u
.value
));
71 t
= 0.5*__log1pl((u
.value
+u
.value
)/(one
-u
.value
));
72 if(jx
& 0x80000000) return -t
; else return t
;
74 libm_alias_finite (__ieee754_atanhl
, __atanhl
)