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63551311 | 1 | /* Return arc tangent of complex double value. |
b168057a | 2 | Copyright (C) 1997-2015 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__ double | |
26 | __catan (__complex__ double x) | |
27 | { | |
28 | __complex__ double 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 = __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 | } | |
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 (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 | { | |
10de07f5 | 80 | double den, absx, absy; |
63551311 | 81 | |
caf84319 JM |
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 | } | |
63551311 | 90 | |
10de07f5 | 91 | if (absy < DBL_EPSILON / 2.0) |
a84e78c8 JM |
92 | { |
93 | den = (1.0 - absx) * (1.0 + absx); | |
94 | if (den == -0.0) | |
95 | den = 0.0; | |
96 | } | |
10de07f5 JM |
97 | else if (absx >= 1.0) |
98 | den = (1.0 - absx) * (1.0 + absx) - absy * absy; | |
caf84319 JM |
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; | |
63551311 | 103 | |
5b4217d7 | 104 | __real__ res = 0.5 * __ieee754_atan2 (2.0 * __real__ x, den); |
63551311 | 105 | |
10de07f5 JM |
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; | |
caf84319 | 113 | |
10de07f5 JM |
114 | if (fabs (__real__ x) >= DBL_EPSILON * DBL_EPSILON) |
115 | r2 = __real__ x * __real__ x; | |
63551311 | 116 | |
10de07f5 JM |
117 | num = __imag__ x + 1.0; |
118 | num = r2 + num * num; | |
63551311 | 119 | |
10de07f5 JM |
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 | } | |
5b4217d7 | 131 | } |
2f38fbfe | 132 | } |
9457fd95 JM |
133 | |
134 | if (fabs (__real__ res) < DBL_MIN) | |
135 | { | |
136 | volatile double force_underflow = __real__ res * __real__ res; | |
137 | (void) force_underflow; | |
138 | } | |
139 | if (fabs (__imag__ res) < DBL_MIN) | |
140 | { | |
141 | volatile double force_underflow = __imag__ res * __imag__ res; | |
142 | (void) force_underflow; | |
143 | } | |
63551311 UD |
144 | } |
145 | ||
146 | return res; | |
147 | } | |
148 | weak_alias (__catan, catan) | |
149 | #ifdef NO_LONG_DOUBLE | |
150 | strong_alias (__catan, __catanl) | |
151 | weak_alias (__catan, catanl) | |
152 | #endif |