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1 | /* Complex tangent function for a complex float type. |
2 | Copyright (C) 1997-2018 Free Software Foundation, Inc. | |
f029f4be TB |
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 | ||
f029f4be TB |
22 | __complex128 |
23 | ctanq (__complex128 x) | |
24 | { | |
25 | __complex128 res; | |
26 | ||
4239f144 | 27 | if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x))) |
f029f4be | 28 | { |
4239f144 | 29 | if (isinfq (__imag__ x)) |
f029f4be | 30 | { |
4239f144 JM |
31 | if (finiteq (__real__ x) && fabsq (__real__ x) > 1) |
32 | { | |
33 | __float128 sinrx, cosrx; | |
34 | sincosq (__real__ x, &sinrx, &cosrx); | |
35 | __real__ res = copysignq (0, sinrx * cosrx); | |
36 | } | |
37 | else | |
38 | __real__ res = copysignq (0, __real__ x); | |
39 | __imag__ res = copysignq (1, __imag__ x); | |
f029f4be | 40 | } |
4239f144 | 41 | else if (__real__ x == 0) |
f029f4be TB |
42 | { |
43 | res = x; | |
44 | } | |
45 | else | |
46 | { | |
47 | __real__ res = nanq (""); | |
4239f144 JM |
48 | if (__imag__ x == 0) |
49 | __imag__ res = __imag__ x; | |
50 | else | |
51 | __imag__ res = nanq (""); | |
f029f4be | 52 | |
4239f144 | 53 | if (isinfq (__real__ x)) |
f029f4be | 54 | feraiseexcept (FE_INVALID); |
f029f4be TB |
55 | } |
56 | } | |
57 | else | |
58 | { | |
59 | __float128 sinrx, cosrx; | |
60 | __float128 den; | |
4239f144 | 61 | const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2); |
f029f4be TB |
62 | |
63 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) | |
64 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ | |
65 | ||
4239f144 | 66 | if (__glibc_likely (fabsq (__real__ x) > FLT128_MIN)) |
f029f4be TB |
67 | { |
68 | sincosq (__real__ x, &sinrx, &cosrx); | |
69 | } | |
70 | else | |
71 | { | |
72 | sinrx = __real__ x; | |
4239f144 | 73 | cosrx = 1; |
f029f4be TB |
74 | } |
75 | ||
76 | if (fabsq (__imag__ x) > t) | |
77 | { | |
78 | /* Avoid intermediate overflow when the real part of the | |
79 | result may be subnormal. Ignoring negligible terms, the | |
80 | imaginary part is +/- 1, the real part is | |
81 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ | |
82 | __float128 exp_2t = expq (2 * t); | |
83 | ||
4239f144 | 84 | __imag__ res = copysignq (1, __imag__ x); |
f029f4be TB |
85 | __real__ res = 4 * sinrx * cosrx; |
86 | __imag__ x = fabsq (__imag__ x); | |
87 | __imag__ x -= t; | |
88 | __real__ res /= exp_2t; | |
89 | if (__imag__ x > t) | |
90 | { | |
91 | /* Underflow (original imaginary part of x has absolute | |
92 | value > 2t). */ | |
93 | __real__ res /= exp_2t; | |
94 | } | |
95 | else | |
96 | __real__ res /= expq (2 * __imag__ x); | |
97 | } | |
98 | else | |
99 | { | |
100 | __float128 sinhix, coshix; | |
101 | if (fabsq (__imag__ x) > FLT128_MIN) | |
102 | { | |
103 | sinhix = sinhq (__imag__ x); | |
104 | coshix = coshq (__imag__ x); | |
105 | } | |
106 | else | |
107 | { | |
108 | sinhix = __imag__ x; | |
4239f144 | 109 | coshix = 1; |
f029f4be TB |
110 | } |
111 | ||
112 | if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON) | |
113 | den = cosrx * cosrx + sinhix * sinhix; | |
114 | else | |
115 | den = cosrx * cosrx; | |
116 | __real__ res = sinrx * cosrx / den; | |
117 | __imag__ res = sinhix * coshix / den; | |
118 | } | |
4239f144 | 119 | math_check_force_underflow_complex (res); |
f029f4be TB |
120 | } |
121 | ||
122 | return res; | |
123 | } |