1 /* Return arc tangent of complex float type.
2 Copyright (C) 1997-2018 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 "quadmath-imp.h"
21
22 __complex128
catanq(__complex128 x)23 catanq (__complex128 x)
24 {
25 __complex128 res;
26 int rcls = fpclassifyq (__real__ x);
27 int icls = fpclassifyq (__imag__ x);
28
29 if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE))
30 {
31 if (rcls == QUADFP_INFINITE)
32 {
33 __real__ res = copysignq (M_PI_2q, __real__ x);
34 __imag__ res = copysignq (0, __imag__ x);
35 }
36 else if (icls == QUADFP_INFINITE)
37 {
38 if (rcls >= QUADFP_ZERO)
39 __real__ res = copysignq (M_PI_2q, __real__ x);
40 else
41 __real__ res = nanq ("");
42 __imag__ res = copysignq (0, __imag__ x);
43 }
44 else if (icls == QUADFP_ZERO || icls == QUADFP_INFINITE)
45 {
46 __real__ res = nanq ("");
47 __imag__ res = copysignq (0, __imag__ x);
48 }
49 else
50 {
51 __real__ res = nanq ("");
52 __imag__ res = nanq ("");
53 }
54 }
55 else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
56 {
57 res = x;
58 }
59 else
60 {
61 if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
62 || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
63 {
64 __real__ res = copysignq (M_PI_2q, __real__ x);
65 if (fabsq (__real__ x) <= 1)
66 __imag__ res = 1 / __imag__ x;
67 else if (fabsq (__imag__ x) <= 1)
68 __imag__ res = __imag__ x / __real__ x / __real__ x;
69 else
70 {
71 __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
72 __imag__ res = __imag__ x / h / h / 4;
73 }
74 }
75 else
76 {
77 __float128 den, absx, absy;
78
79 absx = fabsq (__real__ x);
80 absy = fabsq (__imag__ x);
81 if (absx < absy)
82 {
83 __float128 t = absx;
84 absx = absy;
85 absy = t;
86 }
87
88 if (absy < FLT128_EPSILON / 2)
89 {
90 den = (1 - absx) * (1 + absx);
91 if (den == 0)
92 den = 0;
93 }
94 else if (absx >= 1)
95 den = (1 - absx) * (1 + absx) - absy * absy;
96 else if (absx >= 0.75Q || absy >= 0.5Q)
97 den = -__quadmath_x2y2m1q (absx, absy);
98 else
99 den = (1 - absx) * (1 + absx) - absy * absy;
100
101 __real__ res = 0.5Q * atan2q (2 * __real__ x, den);
102
103 if (fabsq (__imag__ x) == 1
104 && fabsq (__real__ x) < FLT128_EPSILON * FLT128_EPSILON)
105 __imag__ res = (copysignq (0.5Q, __imag__ x)
106 * ((__float128) M_LN2q
107 - logq (fabsq (__real__ x))));
108 else
109 {
110 __float128 r2 = 0, num, f;
111
112 if (fabsq (__real__ x) >= FLT128_EPSILON * FLT128_EPSILON)
113 r2 = __real__ x * __real__ x;
114
115 num = __imag__ x + 1;
116 num = r2 + num * num;
117
118 den = __imag__ x - 1;
119 den = r2 + den * den;
120
121 f = num / den;
122 if (f < 0.5Q)
123 __imag__ res = 0.25Q * logq (f);
124 else
125 {
126 num = 4 * __imag__ x;
127 __imag__ res = 0.25Q * log1pq (num / den);
128 }
129 }
130 }
131
132 math_check_force_underflow_complex (res);
133 }
134
135 return res;
136 }
137