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
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