1 /* @(#)e_atanh.c 5.1 93/09/24 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
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
9 * is preserved.
10 * ====================================================
11 */
12
13 #include <sys/cdefs.h>
14 #if defined(LIBM_SCCS) && !defined(lint)
15 __RCSID("$NetBSD: e_atanh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
16 #endif
17
18 /* __ieee754_atanh(x)
19 * Method :
20 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
21 * 2.For x>=0.5
22 * 1 2x x
23 * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
24 * 2 1 - x 1 - x
25 *
26 * For x<0.5
27 * atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
28 *
29 * Special cases:
30 * atanh(x) is NaN if |x| > 1 with signal;
31 * atanh(NaN) is that NaN with no signal;
32 * atanh(+-1) is +-INF with signal.
33 *
34 */
35
36 #include "math.h"
37 #include "math_private.h"
38
39 static const double one = 1.0, huge = 1e300;
40
41 static const double zero = 0.0;
42
43 double
__ieee754_atanh(double x)44 __ieee754_atanh(double x)
45 {
46 double t;
47 int32_t hx,ix;
48 u_int32_t lx;
49 EXTRACT_WORDS(hx,lx,x);
50 ix = hx&0x7fffffff;
51 if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
52 return (x-x)/(x-x);
53 if(ix==0x3ff00000)
54 return x/zero;
55 if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */
56 SET_HIGH_WORD(x,ix);
57 if(ix<0x3fe00000) { /* x < 0.5 */
58 t = x+x;
59 t = 0.5*log1p(t+t*x/(one-x));
60 } else
61 t = 0.5*log1p((x+x)/(one-x));
62 if(hx>=0) return t; else return -t;
63 }
64