1 | /* Return arc tangent of complex float 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__ float |
26 | __catanf (__complex__ float x) |
27 | { |
28 | __complex__ float 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 = __copysignf (M_PI_2, __real__ x); |
37 | __imag__ res = __copysignf (0.0, __imag__ x); |
38 | } |
39 | else if (icls == FP_INFINITE) |
40 | { |
41 | if (rcls >= FP_ZERO) |
42 | __real__ res = __copysignf (M_PI_2, __real__ x); |
43 | else |
44 | __real__ res = __nanf ("" ); |
45 | __imag__ res = __copysignf (0.0, __imag__ x); |
46 | } |
47 | else if (icls == FP_ZERO || icls == FP_INFINITE) |
48 | { |
49 | __real__ res = __nanf ("" ); |
50 | __imag__ res = __copysignf (0.0, __imag__ x); |
51 | } |
52 | else |
53 | { |
54 | __real__ res = __nanf ("" ); |
55 | __imag__ res = __nanf ("" ); |
56 | } |
57 | } |
58 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
59 | { |
60 | res = x; |
61 | } |
62 | else |
63 | { |
64 | if (fabsf (__real__ x) >= 16.0f / FLT_EPSILON |
65 | || fabsf (__imag__ x) >= 16.0f / FLT_EPSILON) |
66 | { |
67 | __real__ res = __copysignf ((float) M_PI_2, __real__ x); |
68 | if (fabsf (__real__ x) <= 1.0f) |
69 | __imag__ res = 1.0f / __imag__ x; |
70 | else if (fabsf (__imag__ x) <= 1.0f) |
71 | __imag__ res = __imag__ x / __real__ x / __real__ x; |
72 | else |
73 | { |
74 | float h = __ieee754_hypotf (__real__ x / 2.0f, |
75 | __imag__ x / 2.0f); |
76 | __imag__ res = __imag__ x / h / h / 4.0f; |
77 | } |
78 | } |
79 | else |
80 | { |
81 | float den, absx, absy; |
82 | |
83 | absx = fabsf (__real__ x); |
84 | absy = fabsf (__imag__ x); |
85 | if (absx < absy) |
86 | { |
87 | float t = absx; |
88 | absx = absy; |
89 | absy = t; |
90 | } |
91 | |
92 | if (absy < FLT_EPSILON / 2.0f) |
93 | { |
94 | den = (1.0f - absx) * (1.0f + absx); |
95 | if (den == -0.0f) |
96 | den = 0.0f; |
97 | } |
98 | else if (absx >= 1.0f) |
99 | den = (1.0f - absx) * (1.0f + absx) - absy * absy; |
100 | else if (absx >= 0.75f || absy >= 0.5f) |
101 | den = -__x2y2m1f (absx, absy); |
102 | else |
103 | den = (1.0f - absx) * (1.0f + absx) - absy * absy; |
104 | |
105 | __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den); |
106 | |
107 | if (fabsf (__imag__ x) == 1.0f |
108 | && fabsf (__real__ x) < FLT_EPSILON * FLT_EPSILON) |
109 | __imag__ res = (__copysignf (0.5f, __imag__ x) |
110 | * ((float) M_LN2 |
111 | - __ieee754_logf (fabsf (__real__ x)))); |
112 | else |
113 | { |
114 | float r2 = 0.0f, num, f; |
115 | |
116 | if (fabsf (__real__ x) >= FLT_EPSILON * FLT_EPSILON) |
117 | r2 = __real__ x * __real__ x; |
118 | |
119 | num = __imag__ x + 1.0f; |
120 | num = r2 + num * num; |
121 | |
122 | den = __imag__ x - 1.0f; |
123 | den = r2 + den * den; |
124 | |
125 | f = num / den; |
126 | if (f < 0.5f) |
127 | __imag__ res = 0.25f * __ieee754_logf (f); |
128 | else |
129 | { |
130 | num = 4.0f * __imag__ x; |
131 | __imag__ res = 0.25f * __log1pf (num / den); |
132 | } |
133 | } |
134 | } |
135 | |
136 | math_check_force_underflow_complex (res); |
137 | } |
138 | |
139 | return res; |
140 | } |
141 | #ifndef __catanf |
142 | weak_alias (__catanf, catanf) |
143 | #endif |
144 | |