1/* s_atanhl.c -- long double version of s_atan.c.
2 * Conversion to long double by Ulrich Drepper,
3 * Cygnus Support, drepper@cygnus.com.
4 */
5
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17/* __ieee754_atanhl(x)
18 * Method :
19 * 1.Reduced x to positive by atanh(-x) = -atanh(x)
20 * 2.For x>=0.5
21 * 1 2x x
22 * atanhl(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
23 * 2 1 - x 1 - x
24 *
25 * For x<0.5
26 * atanhl(x) = 0.5*log1pl(2x+2x*x/(1-x))
27 *
28 * Special cases:
29 * atanhl(x) is NaN if |x| > 1 with signal;
30 * atanhl(NaN) is that NaN with no signal;
31 * atanhl(+-1) is +-INF with signal.
32 *
33 */
34
35#include <float.h>
36#include <math.h>
37#include <math_private.h>
38#include <math-underflow.h>
39#include <libm-alias-finite.h>
40
41static const _Float128 one = 1, huge = L(1e4900);
42
43static const _Float128 zero = 0;
44
45_Float128
46__ieee754_atanhl(_Float128 x)
47{
48 _Float128 t;
49 uint32_t jx, ix;
50 ieee854_long_double_shape_type u;
51
52 u.value = x;
53 jx = u.parts32.w0;
54 ix = jx & 0x7fffffff;
55 u.parts32.w0 = ix;
56 if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */
57 {
58 if (u.value == one)
59 return x/zero;
60 else
61 return (x-x)/(x-x);
62 }
63 if(ix<0x3fc60000 && (huge+x)>zero) /* x < 2^-57 */
64 {
65 math_check_force_underflow (x);
66 return x;
67 }
68
69 if(ix<0x3ffe0000) { /* x < 0.5 */
70 t = u.value+u.value;
71 t = 0.5*__log1pl(t+t*u.value/(one-u.value));
72 } else
73 t = 0.5*__log1pl((u.value+u.value)/(one-u.value));
74 if(jx & 0x80000000) return -t; else return t;
75}
76libm_alias_finite (__ieee754_atanhl, __atanhl)
77