1 
2 /* @(#)e_atanh.c 1.3 95/01/18 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunSoft, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice
10  * is preserved.
11  * ====================================================
12  *
13  */
14 
15 #include <sys/cdefs.h>
16 __FBSDID("$FreeBSD$");
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 <float.h>
37 
38 #include "math.h"
39 #include "math_private.h"
40 
41 static const double one = 1.0, huge = 1e300;
42 static const double zero = 0.0;
43 
44 double
__ieee754_atanh(double x)45 __ieee754_atanh(double x)
46 {
47 	double t;
48 	int32_t hx,ix;
49 	u_int32_t lx;
50 	EXTRACT_WORDS(hx,lx,x);
51 	ix = hx&0x7fffffff;
52 	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
53 	    return (x-x)/(x-x);
54 	if(ix==0x3ff00000)
55 	    return x/zero;
56 	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
57 	SET_HIGH_WORD(x,ix);
58 	if(ix<0x3fe00000) {		/* x < 0.5 */
59 	    t = x+x;
60 	    t = 0.5*log1p(t+t*x/(one-x));
61 	} else
62 	    t = 0.5*log1p((x+x)/(one-x));
63 	if(hx>=0) return t; else return -t;
64 }
65 
66 #if LDBL_MANT_DIG == 53
67 __weak_reference(atanh, atanhl);
68 #endif
69