1 | /* Return arc tangent of complex 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 | __complex__ double |
26 | __catan (__complex__ double x) |
27 | { |
28 | __complex__ double res; |
29 | int rcls = fpclassify (__real__ x); |
30 | int icls = fpclassify (__imag__ x); |
31 | |
32 | if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) |
33 | { |
34 | if (rcls == FP_INFINITE) |
35 | { |
36 | __real__ res = __copysign (M_PI_2, __real__ x); |
37 | __imag__ res = __copysign (0.0, __imag__ x); |
38 | } |
39 | else if (icls == FP_INFINITE) |
40 | { |
41 | if (rcls >= FP_ZERO) |
42 | __real__ res = __copysign (M_PI_2, __real__ x); |
43 | else |
44 | __real__ res = __nan ("" ); |
45 | __imag__ res = __copysign (0.0, __imag__ x); |
46 | } |
47 | else if (icls == FP_ZERO || icls == FP_INFINITE) |
48 | { |
49 | __real__ res = __nan ("" ); |
50 | __imag__ res = __copysign (0.0, __imag__ x); |
51 | } |
52 | else |
53 | { |
54 | __real__ res = __nan ("" ); |
55 | __imag__ res = __nan ("" ); |
56 | } |
57 | } |
58 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
59 | { |
60 | res = x; |
61 | } |
62 | else |
63 | { |
64 | if (fabs (__real__ x) >= 16.0 / DBL_EPSILON |
65 | || fabs (__imag__ x) >= 16.0 / DBL_EPSILON) |
66 | { |
67 | __real__ res = __copysign (M_PI_2, __real__ x); |
68 | if (fabs (__real__ x) <= 1.0) |
69 | __imag__ res = 1.0 / __imag__ x; |
70 | else if (fabs (__imag__ x) <= 1.0) |
71 | __imag__ res = __imag__ x / __real__ x / __real__ x; |
72 | else |
73 | { |
74 | double h = __ieee754_hypot (__real__ x / 2.0, __imag__ x / 2.0); |
75 | __imag__ res = __imag__ x / h / h / 4.0; |
76 | } |
77 | } |
78 | else |
79 | { |
80 | double den, absx, absy; |
81 | |
82 | absx = fabs (__real__ x); |
83 | absy = fabs (__imag__ x); |
84 | if (absx < absy) |
85 | { |
86 | double t = absx; |
87 | absx = absy; |
88 | absy = t; |
89 | } |
90 | |
91 | if (absy < DBL_EPSILON / 2.0) |
92 | { |
93 | den = (1.0 - absx) * (1.0 + absx); |
94 | if (den == -0.0) |
95 | den = 0.0; |
96 | } |
97 | else if (absx >= 1.0) |
98 | den = (1.0 - absx) * (1.0 + absx) - absy * absy; |
99 | else if (absx >= 0.75 || absy >= 0.5) |
100 | den = -__x2y2m1 (absx, absy); |
101 | else |
102 | den = (1.0 - absx) * (1.0 + absx) - absy * absy; |
103 | |
104 | __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den); |
105 | |
106 | if (fabs (__imag__ x) == 1.0 |
107 | && fabs (__real__ x) < DBL_EPSILON * DBL_EPSILON) |
108 | __imag__ res = (__copysign (0.5, __imag__ x) |
109 | * (M_LN2 - __ieee754_log (fabs (__real__ x)))); |
110 | else |
111 | { |
112 | double r2 = 0.0, num, f; |
113 | |
114 | if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON) |
115 | r2 = __real__ x * __real__ x; |
116 | |
117 | num = __imag__ x + 1.0; |
118 | num = r2 + num * num; |
119 | |
120 | den = __imag__ x - 1.0; |
121 | den = r2 + den * den; |
122 | |
123 | f = num / den; |
124 | if (f < 0.5) |
125 | __imag__ res = 0.25 * __ieee754_log (f); |
126 | else |
127 | { |
128 | num = 4.0 * __imag__ x; |
129 | __imag__ res = 0.25 * __log1p (num / den); |
130 | } |
131 | } |
132 | } |
133 | |
134 | math_check_force_underflow_complex (res); |
135 | } |
136 | |
137 | return res; |
138 | } |
139 | weak_alias (__catan, catan) |
140 | #ifdef NO_LONG_DOUBLE |
141 | strong_alias (__catan, __catanl) |
142 | weak_alias (__catan, catanl) |
143 | #endif |
144 | |