1/* from: FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das */
2
3/* @(#)e_atanh.c 1.3 95/01/18 */
4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 *
14 */
15
16#include <sys/cdefs.h>
17__FBSDID("$FreeBSD$");
18
19/*
20 * See e_atanh.c for complete comments.
21 *
22 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
23 * Bruce D. Evans.
24 */
25
26#include <float.h>
27#ifdef __i386__
28#include <ieeefp.h>
29#endif
30
31#include "fpmath.h"
32#include "math.h"
33#include "math_private.h"
34
35/* EXP_TINY is the threshold below which we use atanh(x) ~= x. */
36#if LDBL_MANT_DIG == 64
37#define	EXP_TINY	-34
38#elif LDBL_MANT_DIG == 113
39#define	EXP_TINY	-58
40#else
41#error "Unsupported long double format"
42#endif
43
44#if LDBL_MAX_EXP != 0x4000
45/* We also require the usual expsign encoding. */
46#error "Unsupported long double format"
47#endif
48
49#define	BIAS	(LDBL_MAX_EXP - 1)
50
51static const double one = 1.0, huge = 1e300;
52static const double zero = 0.0;
53
54long double
55atanhl(long double x)
56{
57	long double t;
58	uint16_t hx, ix;
59
60	ENTERI();
61	GET_LDBL_EXPSIGN(hx, x);
62	ix = hx & 0x7fff;
63	if (ix >= 0x3fff)		/* |x| >= 1, or NaN or misnormal */
64	    RETURNI(fabsl(x) == 1 ? x / zero : (x - x) / (x - x));
65	if (ix < BIAS + EXP_TINY && (huge + x) > zero)
66	    RETURNI(x);			/* x is tiny */
67	SET_LDBL_EXPSIGN(x, ix);
68	if (ix < 0x3ffe) {		/* |x| < 0.5, or misnormal */
69	    t = x+x;
70	    t = 0.5*log1pl(t+t*x/(one-x));
71	} else
72	    t = 0.5*log1pl((x+x)/(one-x));
73	RETURNI((hx & 0x8000) == 0 ? t : -t);
74}
75