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 /* atanh(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  *	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
19  *                  2             1 - x                      1 - x
20  *
21  * 	For x<0.5
22  *	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
23  *
24  * Special cases:
25  *	atanh(x) is NaN if |x| > 1 with signal;
26  *	atanh(NaN) is that NaN with no signal;
27  *	atanh(+-1) is +-INF with signal.
28  *
29  */
30 
31 #include <float.h>
32 #include <math.h>
33 
34 #include "math_private.h"
35 
36 static const double one = 1.0, huge = 1e300;
37 static const double zero = 0.0;
38 
39 double
40 atanh(double x)
41 {
42 	double t;
43 	int32_t hx,ix;
44 	u_int32_t lx;
45 	EXTRACT_WORDS(hx,lx,x);
46 	ix = hx&0x7fffffff;
47 	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
48 	    return (x-x)/(x-x);
49 	if(ix==0x3ff00000)
50 	    return x/zero;
51 	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
52 	SET_HIGH_WORD(x,ix);
53 	if(ix<0x3fe00000) {		/* x < 0.5 */
54 	    t = x+x;
55 	    t = 0.5*log1p(t+t*x/(one-x));
56 	} else
57 	    t = 0.5*log1p((x+x)/(one-x));
58 	if(hx>=0) return t; else return -t;
59 }
60 
61 #if	LDBL_MANT_DIG == DBL_MANT_DIG
62 __strong_alias(atanhl, atanh);
63 #endif	/* LDBL_MANT_DIG == DBL_MANT_DIG */
64