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4239f144 JM |
1 | /* Return arc hyperbolic tangent for a complex float type. |
2 | Copyright (C) 1997-2018 Free Software Foundation, Inc. | |
fa23b182 JJ |
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 | |
4239f144 JM |
17 | License along with the GNU C Library; if not, see |
18 | <http://www.gnu.org/licenses/>. */ | |
fa23b182 JJ |
19 | |
20 | #include "quadmath-imp.h" | |
21 | ||
fa23b182 JJ |
22 | __complex128 |
23 | catanhq (__complex128 x) | |
24 | { | |
25 | __complex128 res; | |
26 | int rcls = fpclassifyq (__real__ x); | |
27 | int icls = fpclassifyq (__imag__ x); | |
28 | ||
4239f144 | 29 | if (__glibc_unlikely (rcls <= QUADFP_INFINITE || icls <= QUADFP_INFINITE)) |
fa23b182 JJ |
30 | { |
31 | if (icls == QUADFP_INFINITE) | |
32 | { | |
4239f144 | 33 | __real__ res = copysignq (0, __real__ x); |
fa23b182 JJ |
34 | __imag__ res = copysignq (M_PI_2q, __imag__ x); |
35 | } | |
36 | else if (rcls == QUADFP_INFINITE || rcls == QUADFP_ZERO) | |
37 | { | |
4239f144 | 38 | __real__ res = copysignq (0, __real__ x); |
fa23b182 JJ |
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 | } | |
4239f144 | 50 | else if (__glibc_unlikely (rcls == QUADFP_ZERO && icls == QUADFP_ZERO)) |
fa23b182 JJ |
51 | { |
52 | res = x; | |
53 | } | |
54 | else | |
55 | { | |
4239f144 JM |
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; | |
fa23b182 | 85 | |
4239f144 JM |
86 | __float128 den = 1 - __real__ x; |
87 | den = i2 + den * den; | |
fa23b182 | 88 | |
4239f144 JM |
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 | } | |
fa23b182 | 98 | |
4239f144 | 99 | __float128 absx, absy, den; |
fa23b182 | 100 | |
4239f144 JM |
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 | } | |
fa23b182 | 109 | |
4239f144 JM |
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 | } | |
fa23b182 | 125 | |
4239f144 | 126 | math_check_force_underflow_complex (res); |
fa23b182 JJ |
127 | } |
128 | ||
129 | return res; | |
130 | } |