1
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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
14/* atanh(x)
15 * Method :
16 *    1.Reduced x to positive by atanh(-x) = -atanh(x)
17 *    2.For x>=0.5
18 *                  1              2x                          x
19 *	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
20 *                  2             1 - x                      1 - x
21 *
22 * 	For x<0.5
23 *	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
24 *
25 * Special cases:
26 *	atanh(x) is NaN if |x| > 1 with signal;
27 *	atanh(NaN) is that NaN with no signal;
28 *	atanh(+-1) is +-INF with signal.
29 *
30 */
31
32#include <float.h>
33
34#include "math.h"
35#include "math_private.h"
36
37static const double one = 1.0, huge = 1e300;
38static const double zero = 0.0;
39
40double
41atanh(double x)
42{
43	double t;
44	int32_t hx,ix;
45	u_int32_t lx;
46	EXTRACT_WORDS(hx,lx,x);
47	ix = hx&0x7fffffff;
48	if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */
49	    return (x-x)/(x-x);
50	if(ix==0x3ff00000)
51	    return x/zero;
52	if(ix<0x3e300000&&(huge+x)>zero) return x;	/* x<2**-28 */
53	SET_HIGH_WORD(x,ix);
54	if(ix<0x3fe00000) {		/* x < 0.5 */
55	    t = x+x;
56	    t = 0.5*log1p(t+t*x/(one-x));
57	} else
58	    t = 0.5*log1p((x+x)/(one-x));
59	if(hx>=0) return t; else return -t;
60}
61
62#if LDBL_MANT_DIG == 53
63__weak_reference(atanh, atanhl);
64#endif
65