1 /* @(#)e_atanh.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
15 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
18 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
22 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
25 * atanh(x) is NaN if |x| > 1 with signal;
26 * atanh(NaN) is that NaN with no signal;
27 * atanh(+-1) is +-INF with signal.
32 #include <math_private.h>
34 static const long double one
= 1.0L, huge
= 1e300L
;
36 static const long double zero
= 0.0L;
39 __ieee754_atanhl(long double x
)
46 EXTRACT_WORDS64 (hx
, xhi
);
47 ix
= hx
&0x7fffffffffffffffLL
;
48 if (ix
>= 0x3ff0000000000000LL
) { /* |x|>=1 */
49 if (ix
> 0x3ff0000000000000LL
)
57 if(ix
<0x3e20000000000000LL
&&(huge
+x
)>zero
) return x
; /* x<2**-29 */
59 if(ix
<0x3fe0000000000000LL
) { /* x < 0.5 */
61 t
= 0.5*__log1pl(t
+t
*x
/(one
-x
));
63 t
= 0.5*__log1pl((x
+x
)/(one
-x
));
64 if(hx
>=0) return t
; else return -t
;
66 strong_alias (__ieee754_atanhl
, __atanhl_finite
)