xref: /minix3/lib/libm/src/e_atanh.c (revision 2fe8fb192fe7e8720e3e7a77f928da545e872a6a)
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