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 | |
40 | static const _Float128 one = 1, huge = L(1e4900); |
41 | |
42 | static const _Float128 zero = 0; |
43 | |
44 | _Float128 |
45 | __ieee754_atanhl(_Float128 x) |
46 | { |
47 | _Float128 t; |
48 | uint32_t jx, ix; |
49 | ieee854_long_double_shape_type u; |
50 | |
51 | u.value = x; |
52 | jx = u.parts32.w0; |
53 | ix = jx & 0x7fffffff; |
54 | u.parts32.w0 = ix; |
55 | if (ix >= 0x3fff0000) /* |x| >= 1.0 or infinity or NaN */ |
56 | { |
57 | if (u.value == one) |
58 | return x/zero; |
59 | else |
60 | return (x-x)/(x-x); |
61 | } |
62 | if(ix<0x3fc60000 && (huge+x)>zero) /* x < 2^-57 */ |
63 | { |
64 | math_check_force_underflow (x); |
65 | return x; |
66 | } |
67 | |
68 | if(ix<0x3ffe0000) { /* x < 0.5 */ |
69 | t = u.value+u.value; |
70 | t = 0.5*__log1pl(t+t*u.value/(one-u.value)); |
71 | } else |
72 | t = 0.5*__log1pl((u.value+u.value)/(one-u.value)); |
73 | if(jx & 0x80000000) return -t; else return t; |
74 | } |
75 | strong_alias (__ieee754_atanhl, __atanhl_finite) |
76 | |