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 /* atanhl(x)
14  * Method :
15  *    1.Reduced x to positive by atanh(-x) = -atanh(x)
16  *    2.For x>=0.5
17  *                   1              2x                          x
18  *	atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
19  *                   2             1 - x                      1 - x
20  *
21  * 	For x<0.5
22  *	atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
23  *
24  * Special cases:
25  *	atanhl(x) is NaN if |x| > 1 with signal;
26  *	atanhl(NaN) is that NaN with no signal;
27  *	atanhl(+-1) is +-INF with signal.
28  *
29  */
30 
31 #include <math.h>
32 
33 #include "math_private.h"
34 
35 static const long double one = 1.0, huge = 1e4900L;
36 
37 static const long double zero = 0.0;
38 
39 long double
40 atanhl(long double x)
41 {
42 	long double t;
43 	int32_t ix;
44 	u_int32_t se,i0,i1;
45 	GET_LDOUBLE_WORDS(se,i0,i1,x);
46 	ix = se&0x7fff;
47 	if ((ix+((((i0&0x7fffffff)|i1)|(-((i0&0x7fffffff)|i1)))>>31))>0x3fff)
48 	  /* |x|>1 */
49 	    return (x-x)/(x-x);
50 	if(ix==0x3fff)
51 	    return x/zero;
52 	if(ix<0x3fe3&&(huge+x)>zero) return x;	/* x<2**-28 */
53 	SET_LDOUBLE_EXP(x,ix);
54 	if(ix<0x3ffe) {		/* x < 0.5 */
55 	    t = x+x;
56 	    t = 0.5*log1pl(t+t*x/(one-x));
57 	} else
58 	    t = 0.5*log1pl((x+x)/(one-x));
59 	if(se<=0x7fff) return t; else return -t;
60 }
61