1 /* Complex tangent function 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
ctanq(__complex128 x)23 ctanq (__complex128 x)
24 {
25 __complex128 res;
26
27 if (__glibc_unlikely (!finiteq (__real__ x) || !finiteq (__imag__ x)))
28 {
29 if (isinfq (__imag__ x))
30 {
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);
40 }
41 else if (__real__ x == 0)
42 {
43 res = x;
44 }
45 else
46 {
47 __real__ res = nanq ("");
48 if (__imag__ x == 0)
49 __imag__ res = __imag__ x;
50 else
51 __imag__ res = nanq ("");
52
53 if (isinfq (__real__ x))
54 feraiseexcept (FE_INVALID);
55 }
56 }
57 else
58 {
59 __float128 sinrx, cosrx;
60 __float128 den;
61 const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2);
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
66 if (__glibc_likely (fabsq (__real__ x) > FLT128_MIN))
67 {
68 sincosq (__real__ x, &sinrx, &cosrx);
69 }
70 else
71 {
72 sinrx = __real__ x;
73 cosrx = 1;
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
84 __imag__ res = copysignq (1, __imag__ x);
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;
109 coshix = 1;
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 }
119 math_check_force_underflow_complex (res);
120 }
121
122 return res;
123 }
124