xref: /netbsd-src/lib/libm/src/e_atanh.c (revision 2a399c6883d870daece976daec6ffa7bb7f934ce)
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 1.9 1997/10/09 11:28:44 lukem 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 #ifdef __STDC__
40 static const double one = 1.0, huge = 1e300;
41 #else
42 static double one = 1.0, huge = 1e300;
43 #endif
44 
45 #ifdef __STDC__
46 static const double zero = 0.0;
47 #else
48 static double zero = 0.0;
49 #endif
50 
51 #ifdef __STDC__
52 	double __ieee754_atanh(double x)
53 #else
54 	double __ieee754_atanh(x)
55 	double x;
56 #endif
57 {
58 	double t;
59 	int32_t hx,ix;
60 	u_int32_t lx;
61 	EXTRACT_WORDS(hx,lx,x);
62 	ix = hx&0x7fffffff;
63 	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
64 	    return (x-x)/(x-x);
65 	if(ix==0x3ff00000)
66 	    return x/zero;
67 	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
68 	SET_HIGH_WORD(x,ix);
69 	if(ix<0x3fe00000) {		/* x < 0.5 */
70 	    t = x+x;
71 	    t = 0.5*log1p(t+t*x/(one-x));
72 	} else
73 	    t = 0.5*log1p((x+x)/(one-x));
74 	if(hx>=0) return t; else return -t;
75 }
76