1 | /* Return arc hyperbole tangent for long double value. |
2 | Copyright (C) 1997-2016 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. |
5 | |
6 | The GNU C Library is free software; you can redistribute it and/or |
7 | modify it under the terms of the GNU Lesser General Public |
8 | License as published by the Free Software Foundation; either |
9 | version 2.1 of the License, or (at your option) any later version. |
10 | |
11 | The GNU C Library is distributed in the hope that it will be useful, |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
14 | Lesser General Public License for more details. |
15 | |
16 | You should have received a copy of the GNU Lesser General Public |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ |
19 | |
20 | #include <complex.h> |
21 | #include <math.h> |
22 | #include <math_private.h> |
23 | #include <float.h> |
24 | |
25 | /* To avoid spurious overflows, use this definition to treat IBM long |
26 | double as approximating an IEEE-style format. */ |
27 | #if LDBL_MANT_DIG == 106 |
28 | # undef LDBL_EPSILON |
29 | # define LDBL_EPSILON 0x1p-106L |
30 | #endif |
31 | |
32 | __complex__ long double |
33 | __catanhl (__complex__ long double x) |
34 | { |
35 | __complex__ long double res; |
36 | int rcls = fpclassify (__real__ x); |
37 | int icls = fpclassify (__imag__ x); |
38 | |
39 | if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) |
40 | { |
41 | if (icls == FP_INFINITE) |
42 | { |
43 | __real__ res = __copysignl (0.0, __real__ x); |
44 | __imag__ res = __copysignl (M_PI_2l, __imag__ x); |
45 | } |
46 | else if (rcls == FP_INFINITE || rcls == FP_ZERO) |
47 | { |
48 | __real__ res = __copysignl (0.0, __real__ x); |
49 | if (icls >= FP_ZERO) |
50 | __imag__ res = __copysignl (M_PI_2l, __imag__ x); |
51 | else |
52 | __imag__ res = __nanl ("" ); |
53 | } |
54 | else |
55 | { |
56 | __real__ res = __nanl ("" ); |
57 | __imag__ res = __nanl ("" ); |
58 | } |
59 | } |
60 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
61 | { |
62 | res = x; |
63 | } |
64 | else |
65 | { |
66 | if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON |
67 | || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON) |
68 | { |
69 | __imag__ res = __copysignl (M_PI_2l, __imag__ x); |
70 | if (fabsl (__imag__ x) <= 1.0L) |
71 | __real__ res = 1.0L / __real__ x; |
72 | else if (fabsl (__real__ x) <= 1.0L) |
73 | __real__ res = __real__ x / __imag__ x / __imag__ x; |
74 | else |
75 | { |
76 | long double h = __ieee754_hypotl (__real__ x / 2.0L, |
77 | __imag__ x / 2.0L); |
78 | __real__ res = __real__ x / h / h / 4.0L; |
79 | } |
80 | } |
81 | else |
82 | { |
83 | if (fabsl (__real__ x) == 1.0L |
84 | && fabsl (__imag__ x) < LDBL_EPSILON * LDBL_EPSILON) |
85 | __real__ res = (__copysignl (0.5L, __real__ x) |
86 | * (M_LN2l - __ieee754_logl (fabsl (__imag__ x)))); |
87 | else |
88 | { |
89 | long double i2 = 0.0; |
90 | if (fabsl (__imag__ x) >= LDBL_EPSILON * LDBL_EPSILON) |
91 | i2 = __imag__ x * __imag__ x; |
92 | |
93 | long double num = 1.0L + __real__ x; |
94 | num = i2 + num * num; |
95 | |
96 | long double den = 1.0L - __real__ x; |
97 | den = i2 + den * den; |
98 | |
99 | long double f = num / den; |
100 | if (f < 0.5L) |
101 | __real__ res = 0.25L * __ieee754_logl (f); |
102 | else |
103 | { |
104 | num = 4.0L * __real__ x; |
105 | __real__ res = 0.25L * __log1pl (num / den); |
106 | } |
107 | } |
108 | |
109 | long double absx, absy, den; |
110 | |
111 | absx = fabsl (__real__ x); |
112 | absy = fabsl (__imag__ x); |
113 | if (absx < absy) |
114 | { |
115 | long double t = absx; |
116 | absx = absy; |
117 | absy = t; |
118 | } |
119 | |
120 | if (absy < LDBL_EPSILON / 2.0L) |
121 | { |
122 | den = (1.0L - absx) * (1.0L + absx); |
123 | if (den == -0.0L) |
124 | den = 0.0L; |
125 | } |
126 | else if (absx >= 1.0L) |
127 | den = (1.0L - absx) * (1.0L + absx) - absy * absy; |
128 | else if (absx >= 0.75L || absy >= 0.5L) |
129 | den = -__x2y2m1l (absx, absy); |
130 | else |
131 | den = (1.0L - absx) * (1.0L + absx) - absy * absy; |
132 | |
133 | __imag__ res = 0.5L * __ieee754_atan2l (2.0L * __imag__ x, den); |
134 | } |
135 | |
136 | math_check_force_underflow_complex (res); |
137 | } |
138 | |
139 | return res; |
140 | } |
141 | weak_alias (__catanhl, catanhl) |
142 | |