1/* Complex tangent function for a complex float type.
2 Copyright (C) 1997-2020 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 <https://www.gnu.org/licenses/>. */
19
20#include <complex.h>
21#include <fenv.h>
22#include <math.h>
23#include <math_private.h>
24#include <math-underflow.h>
25#include <float.h>
26
27CFLOAT
28M_DECL_FUNC (__ctan) (CFLOAT x)
29{
30 CFLOAT res;
31
32 if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
33 {
34 if (isinf (__imag__ x))
35 {
36 if (isfinite (__real__ x) && M_FABS (__real__ x) > 1)
37 {
38 FLOAT sinrx, cosrx;
39 M_SINCOS (__real__ x, &sinrx, &cosrx);
40 __real__ res = M_COPYSIGN (0, sinrx * cosrx);
41 }
42 else
43 __real__ res = M_COPYSIGN (0, __real__ x);
44 __imag__ res = M_COPYSIGN (1, __imag__ x);
45 }
46 else if (__real__ x == 0)
47 {
48 res = x;
49 }
50 else
51 {
52 __real__ res = M_NAN;
53 if (__imag__ x == 0)
54 __imag__ res = __imag__ x;
55 else
56 __imag__ res = M_NAN;
57
58 if (isinf (__real__ x))
59 feraiseexcept (FE_INVALID);
60 }
61 }
62 else
63 {
64 FLOAT sinrx, cosrx;
65 FLOAT den;
66 const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
67
68 /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
69 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
70
71 if (__glibc_likely (M_FABS (__real__ x) > M_MIN))
72 {
73 M_SINCOS (__real__ x, &sinrx, &cosrx);
74 }
75 else
76 {
77 sinrx = __real__ x;
78 cosrx = 1;
79 }
80
81 if (M_FABS (__imag__ x) > t)
82 {
83 /* Avoid intermediate overflow when the real part of the
84 result may be subnormal. Ignoring negligible terms, the
85 imaginary part is +/- 1, the real part is
86 sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
87 FLOAT exp_2t = M_EXP (2 * t);
88
89 __imag__ res = M_COPYSIGN (1, __imag__ x);
90 __real__ res = 4 * sinrx * cosrx;
91 __imag__ x = M_FABS (__imag__ x);
92 __imag__ x -= t;
93 __real__ res /= exp_2t;
94 if (__imag__ x > t)
95 {
96 /* Underflow (original imaginary part of x has absolute
97 value > 2t). */
98 __real__ res /= exp_2t;
99 }
100 else
101 __real__ res /= M_EXP (2 * __imag__ x);
102 }
103 else
104 {
105 FLOAT sinhix, coshix;
106 if (M_FABS (__imag__ x) > M_MIN)
107 {
108 sinhix = M_SINH (__imag__ x);
109 coshix = M_COSH (__imag__ x);
110 }
111 else
112 {
113 sinhix = __imag__ x;
114 coshix = 1;
115 }
116
117 if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON)
118 den = cosrx * cosrx + sinhix * sinhix;
119 else
120 den = cosrx * cosrx;
121 __real__ res = sinrx * cosrx / den;
122 __imag__ res = sinhix * coshix / den;
123 }
124 math_check_force_underflow_complex (res);
125 }
126
127 return res;
128}
129
130declare_mgen_alias (__ctan, ctan)
131