1 | /* Return arc tangent of complex 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 | __catanl (__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 (rcls == FP_INFINITE) |
42 | { |
43 | __real__ res = __copysignl (M_PI_2l, __real__ x); |
44 | __imag__ res = __copysignl (0.0, __imag__ x); |
45 | } |
46 | else if (icls == FP_INFINITE) |
47 | { |
48 | if (rcls >= FP_ZERO) |
49 | __real__ res = __copysignl (M_PI_2l, __real__ x); |
50 | else |
51 | __real__ res = __nanl ("" ); |
52 | __imag__ res = __copysignl (0.0, __imag__ x); |
53 | } |
54 | else if (icls == FP_ZERO || icls == FP_INFINITE) |
55 | { |
56 | __real__ res = __nanl ("" ); |
57 | __imag__ res = __copysignl (0.0, __imag__ x); |
58 | } |
59 | else |
60 | { |
61 | __real__ res = __nanl ("" ); |
62 | __imag__ res = __nanl ("" ); |
63 | } |
64 | } |
65 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
66 | { |
67 | res = x; |
68 | } |
69 | else |
70 | { |
71 | if (fabsl (__real__ x) >= 16.0L / LDBL_EPSILON |
72 | || fabsl (__imag__ x) >= 16.0L / LDBL_EPSILON) |
73 | { |
74 | __real__ res = __copysignl (M_PI_2l, __real__ x); |
75 | if (fabsl (__real__ x) <= 1.0L) |
76 | __imag__ res = 1.0L / __imag__ x; |
77 | else if (fabsl (__imag__ x) <= 1.0L) |
78 | __imag__ res = __imag__ x / __real__ x / __real__ x; |
79 | else |
80 | { |
81 | long double h = __ieee754_hypotl (__real__ x / 2.0L, |
82 | __imag__ x / 2.0L); |
83 | __imag__ res = __imag__ x / h / h / 4.0L; |
84 | } |
85 | } |
86 | else |
87 | { |
88 | long double den, absx, absy; |
89 | |
90 | absx = fabsl (__real__ x); |
91 | absy = fabsl (__imag__ x); |
92 | if (absx < absy) |
93 | { |
94 | long double t = absx; |
95 | absx = absy; |
96 | absy = t; |
97 | } |
98 | |
99 | if (absy < LDBL_EPSILON / 2.0L) |
100 | { |
101 | den = (1.0L - absx) * (1.0L + absx); |
102 | if (den == -0.0L) |
103 | den = 0.0L; |
104 | } |
105 | else if (absx >= 1.0L) |
106 | den = (1.0L - absx) * (1.0L + absx) - absy * absy; |
107 | else if (absx >= 0.75L || absy >= 0.5L) |
108 | den = -__x2y2m1l (absx, absy); |
109 | else |
110 | den = (1.0L - absx) * (1.0L + absx) - absy * absy; |
111 | |
112 | __real__ res = 0.5L * __ieee754_atan2l (2.0L * __real__ x, den); |
113 | |
114 | if (fabsl (__imag__ x) == 1.0L |
115 | && fabsl (__real__ x) < LDBL_EPSILON * LDBL_EPSILON) |
116 | __imag__ res = (__copysignl (0.5L, __imag__ x) |
117 | * (M_LN2l - __ieee754_logl (fabsl (__real__ x)))); |
118 | else |
119 | { |
120 | long double r2 = 0.0L, num, f; |
121 | |
122 | if (fabsl (__real__ x) >= LDBL_EPSILON * LDBL_EPSILON) |
123 | r2 = __real__ x * __real__ x; |
124 | |
125 | num = __imag__ x + 1.0L; |
126 | num = r2 + num * num; |
127 | |
128 | den = __imag__ x - 1.0L; |
129 | den = r2 + den * den; |
130 | |
131 | f = num / den; |
132 | if (f < 0.5L) |
133 | __imag__ res = 0.25L * __ieee754_logl (f); |
134 | else |
135 | { |
136 | num = 4.0L * __imag__ x; |
137 | __imag__ res = 0.25L * __log1pl (num / den); |
138 | } |
139 | } |
140 | } |
141 | |
142 | math_check_force_underflow_complex (res); |
143 | } |
144 | |
145 | return res; |
146 | } |
147 | weak_alias (__catanl, catanl) |
148 | |