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 * ====================================================
12 * $NetBSD: e_atanh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $
13 * $DragonFly: src/lib/libm/src/e_atanh.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
18 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
21 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
25 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
28 * atanh(x) is NaN if |x| > 1 with signal;
29 * atanh(NaN) is that NaN with no signal;
30 * atanh(+-1) is +-INF with signal.
35 #include "math_private.h"
37 static const double one
= 1.0, huge
= 1e300
;
39 static const double zero
= 0.0;
47 EXTRACT_WORDS(hx
,lx
,x
);
49 if ((ix
|((lx
|(-lx
))>>31))>0x3ff00000) /* |x|>1 */
53 if(ix
<0x3e300000&&(huge
+x
)>zero
) return x
; /* x<2**-28 */
55 if(ix
<0x3fe00000) { /* x < 0.5 */
57 t
= 0.5*log1p(t
+t
*x
/(one
-x
));
59 t
= 0.5*log1p((x
+x
)/(one
-x
));
60 if(hx
>=0) return t
; else return -t
;