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63551311 | 1 | /* Return arc tangent of complex float value. |
f7a9f785 | 2 | Copyright (C) 1997-2016 Free Software Foundation, Inc. |
63551311 UD |
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 | |
41bdb6e2 AJ |
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. | |
63551311 UD |
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 | |
41bdb6e2 | 14 | Lesser General Public License for more details. |
63551311 | 15 | |
41bdb6e2 | 16 | You should have received a copy of the GNU Lesser General Public |
59ba27a6 PE |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
63551311 UD |
19 | |
20 | #include <complex.h> | |
21 | #include <math.h> | |
9277c064 | 22 | #include <math_private.h> |
9457fd95 | 23 | #include <float.h> |
63551311 UD |
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 | ||
a1ffb40e | 32 | if (__glibc_unlikely (rcls <= FP_INFINITE || icls <= FP_INFINITE)) |
63551311 UD |
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 | } | |
a1ffb40e | 58 | else if (__glibc_unlikely (rcls == FP_ZERO && icls == FP_ZERO)) |
63551311 UD |
59 | { |
60 | res = x; | |
61 | } | |
62 | else | |
63 | { | |
5b4217d7 JM |
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 | { | |
10de07f5 | 81 | float den, absx, absy; |
63551311 | 82 | |
caf84319 JM |
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 | } | |
63551311 | 91 | |
10de07f5 | 92 | if (absy < FLT_EPSILON / 2.0f) |
a84e78c8 JM |
93 | { |
94 | den = (1.0f - absx) * (1.0f + absx); | |
95 | if (den == -0.0f) | |
96 | den = 0.0f; | |
97 | } | |
10de07f5 JM |
98 | else if (absx >= 1.0f) |
99 | den = (1.0f - absx) * (1.0f + absx) - absy * absy; | |
caf84319 JM |
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; | |
63551311 | 104 | |
5b4217d7 | 105 | __real__ res = 0.5f * __ieee754_atan2f (2.0f * __real__ x, den); |
63551311 | 106 | |
10de07f5 JM |
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; | |
caf84319 | 115 | |
10de07f5 JM |
116 | if (fabsf (__real__ x) >= FLT_EPSILON * FLT_EPSILON) |
117 | r2 = __real__ x * __real__ x; | |
63551311 | 118 | |
10de07f5 JM |
119 | num = __imag__ x + 1.0f; |
120 | num = r2 + num * num; | |
63551311 | 121 | |
10de07f5 JM |
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 | } | |
5b4217d7 | 133 | } |
2f38fbfe | 134 | } |
9457fd95 | 135 | |
d96164c3 | 136 | math_check_force_underflow_complex (res); |
63551311 UD |
137 | } |
138 | ||
139 | return res; | |
140 | } | |
1705f0a3 | 141 | #ifndef __catanf |
63551311 | 142 | weak_alias (__catanf, catanf) |
1705f0a3 | 143 | #endif |