1 | /* Complex tangent function for a complex float type. |
2 | Copyright (C) 1997-2022 Free Software Foundation, Inc. |
3 | This file is part of the GNU C Library. |
4 | |
5 | The GNU C Library is free software; you can redistribute it and/or |
6 | modify it under the terms of the GNU Lesser General Public |
7 | License as published by the Free Software Foundation; either |
8 | version 2.1 of the License, or (at your option) any later version. |
9 | |
10 | The GNU C Library is distributed in the hope that it will be useful, |
11 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
13 | Lesser General Public License for more details. |
14 | |
15 | You should have received a copy of the GNU Lesser General Public |
16 | License along with the GNU C Library; if not, see |
17 | <https://www.gnu.org/licenses/>. */ |
18 | |
19 | #include <complex.h> |
20 | #include <fenv.h> |
21 | #include <math.h> |
22 | #include <math_private.h> |
23 | #include <math-underflow.h> |
24 | #include <float.h> |
25 | |
26 | CFLOAT |
27 | M_DECL_FUNC (__ctan) (CFLOAT x) |
28 | { |
29 | CFLOAT res; |
30 | |
31 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) |
32 | { |
33 | if (isinf (__imag__ x)) |
34 | { |
35 | if (isfinite (__real__ x) && M_FABS (__real__ x) > 1) |
36 | { |
37 | FLOAT sinrx, cosrx; |
38 | M_SINCOS (__real__ x, &sinrx, &cosrx); |
39 | __real__ res = M_COPYSIGN (0, sinrx * cosrx); |
40 | } |
41 | else |
42 | __real__ res = M_COPYSIGN (0, __real__ x); |
43 | __imag__ res = M_COPYSIGN (1, __imag__ x); |
44 | } |
45 | else if (__real__ x == 0) |
46 | { |
47 | res = x; |
48 | } |
49 | else |
50 | { |
51 | __real__ res = M_NAN; |
52 | if (__imag__ x == 0) |
53 | __imag__ res = __imag__ x; |
54 | else |
55 | __imag__ res = M_NAN; |
56 | |
57 | if (isinf (__real__ x)) |
58 | feraiseexcept (FE_INVALID); |
59 | } |
60 | } |
61 | else |
62 | { |
63 | FLOAT sinrx, cosrx; |
64 | FLOAT den; |
65 | const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2); |
66 | |
67 | /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) |
68 | = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ |
69 | |
70 | if (__glibc_likely (M_FABS (__real__ x) > M_MIN)) |
71 | { |
72 | M_SINCOS (__real__ x, &sinrx, &cosrx); |
73 | } |
74 | else |
75 | { |
76 | sinrx = __real__ x; |
77 | cosrx = 1; |
78 | } |
79 | |
80 | if (M_FABS (__imag__ x) > t) |
81 | { |
82 | /* Avoid intermediate overflow when the real part of the |
83 | result may be subnormal. Ignoring negligible terms, the |
84 | imaginary part is +/- 1, the real part is |
85 | sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ |
86 | FLOAT exp_2t = M_EXP (2 * t); |
87 | |
88 | __imag__ res = M_COPYSIGN (1, __imag__ x); |
89 | __real__ res = 4 * sinrx * cosrx; |
90 | __imag__ x = M_FABS (__imag__ x); |
91 | __imag__ x -= t; |
92 | __real__ res /= exp_2t; |
93 | if (__imag__ x > t) |
94 | { |
95 | /* Underflow (original imaginary part of x has absolute |
96 | value > 2t). */ |
97 | __real__ res /= exp_2t; |
98 | } |
99 | else |
100 | __real__ res /= M_EXP (2 * __imag__ x); |
101 | } |
102 | else |
103 | { |
104 | FLOAT sinhix, coshix; |
105 | if (M_FABS (__imag__ x) > M_MIN) |
106 | { |
107 | sinhix = M_SINH (__imag__ x); |
108 | coshix = M_COSH (__imag__ x); |
109 | } |
110 | else |
111 | { |
112 | sinhix = __imag__ x; |
113 | coshix = 1; |
114 | } |
115 | |
116 | if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON) |
117 | den = cosrx * cosrx + sinhix * sinhix; |
118 | else |
119 | den = cosrx * cosrx; |
120 | __real__ res = sinrx * cosrx / den; |
121 | __imag__ res = sinhix * coshix / den; |
122 | } |
123 | math_check_force_underflow_complex (res); |
124 | } |
125 | |
126 | return res; |
127 | } |
128 | |
129 | declare_mgen_alias (__ctan, ctan) |
130 | |