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