1 /* Return arc hyperbolic tangent for a 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
catanhq(__complex128 x)23 catanhq (__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 (icls == QUADFP_INFINITE)
32 {
33 __real__ res = copysignq (0, __real__ x);
34 __imag__ res = copysignq (M_PI_2q, __imag__ x);
35 }
36 else if (rcls == QUADFP_INFINITE || rcls == QUADFP_ZERO)
37 {
38 __real__ res = copysignq (0, __real__ x);
39 if (icls >= QUADFP_ZERO)
40 __imag__ res = copysignq (M_PI_2q, __imag__ x);
41 else
42 __imag__ res = nanq ("");
43 }
44 else
45 {
46 __real__ res = nanq ("");
47 __imag__ res = nanq ("");
48 }
49 }
50 else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO))
51 {
52 res = x;
53 }
54 else
55 {
56 if (fabsq (__real__ x) >= 16 / FLT128_EPSILON
57 || fabsq (__imag__ x) >= 16 / FLT128_EPSILON)
58 {
59 __imag__ res = copysignq (M_PI_2q, __imag__ x);
60 if (fabsq (__imag__ x) <= 1)
61 __real__ res = 1 / __real__ x;
62 else if (fabsq (__real__ x) <= 1)
63 __real__ res = __real__ x / __imag__ x / __imag__ x;
64 else
65 {
66 __float128 h = hypotq (__real__ x / 2, __imag__ x / 2);
67 __real__ res = __real__ x / h / h / 4;
68 }
69 }
70 else
71 {
72 if (fabsq (__real__ x) == 1
73 && fabsq (__imag__ x) < FLT128_EPSILON * FLT128_EPSILON)
74 __real__ res = (copysignq (0.5Q, __real__ x)
75 * ((__float128) M_LN2q
76 - logq (fabsq (__imag__ x))));
77 else
78 {
79 __float128 i2 = 0;
80 if (fabsq (__imag__ x) >= FLT128_EPSILON * FLT128_EPSILON)
81 i2 = __imag__ x * __imag__ x;
82
83 __float128 num = 1 + __real__ x;
84 num = i2 + num * num;
85
86 __float128 den = 1 - __real__ x;
87 den = i2 + den * den;
88
89 __float128 f = num / den;
90 if (f < 0.5Q)
91 __real__ res = 0.25Q * logq (f);
92 else
93 {
94 num = 4 * __real__ x;
95 __real__ res = 0.25Q * log1pq (num / den);
96 }
97 }
98
99 __float128 absx, absy, den;
100
101 absx = fabsq (__real__ x);
102 absy = fabsq (__imag__ x);
103 if (absx < absy)
104 {
105 __float128 t = absx;
106 absx = absy;
107 absy = t;
108 }
109
110 if (absy < FLT128_EPSILON / 2)
111 {
112 den = (1 - absx) * (1 + absx);
113 if (den == 0)
114 den = 0;
115 }
116 else if (absx >= 1)
117 den = (1 - absx) * (1 + absx) - absy * absy;
118 else if (absx >= 0.75Q || absy >= 0.5Q)
119 den = -__quadmath_x2y2m1q (absx, absy);
120 else
121 den = (1 - absx) * (1 + absx) - absy * absy;
122
123 __imag__ res = 0.5Q * atan2q (2 * __imag__ x, den);
124 }
125
126 math_check_force_underflow_complex (res);
127 }
128
129 return res;
130 }
131