1 /* from: FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das */
2
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
17 #include "namespace.h"
18
19 #include <float.h>
20 #include <machine/ieee.h>
21
22 #include "math.h"
23 #include "math_private.h"
24
25 __weak_alias(atanhl, _atanhl)
26
27 #ifdef __HAVE_LONG_DOUBLE
28 /*
29 * See e_atanh.c for complete comments.
30 *
31 * Converted to long double by David Schultz <das@FreeBSD.ORG> and
32 * Bruce D. Evans.
33 */
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
51 static const double one = 1.0, huge = 1e300;
52 static const double zero = 0.0;
53
54 long double
atanhl(long double x)55 atanhl(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 #else
76 long double
77 atanhl(long double x)
78 {
79 return atanh(x);
80 }
81 #endif
82