1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
|
/* Complex tangent function for complex __float128.
Copyright (C) 1997-2012 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
#include "quadmath-imp.h"
#ifdef HAVE_FENV_H
# include <fenv.h>
#endif
__complex128
ctanq (__complex128 x)
{
__complex128 res;
if (__builtin_expect (!finiteq (__real__ x) || !finiteq (__imag__ x), 0))
{
if (__quadmath_isinf_nsq (__imag__ x))
{
__real__ res = copysignq (0.0Q, __real__ x);
__imag__ res = copysignq (1.0Q, __imag__ x);
}
else if (__real__ x == 0.0Q)
{
res = x;
}
else
{
__real__ res = nanq ("");
__imag__ res = nanq ("");
#ifdef HAVE_FENV_H
if (__quadmath_isinf_nsq (__real__ x))
feraiseexcept (FE_INVALID);
#endif
}
}
else
{
__float128 sinrx, cosrx;
__float128 den;
const int t = (int) ((FLT128_MAX_EXP - 1) * M_LN2q / 2.0Q);
int rcls = fpclassifyq (__real__ x);
/* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
= (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
if (__builtin_expect (rcls != QUADFP_SUBNORMAL, 1))
{
sincosq (__real__ x, &sinrx, &cosrx);
}
else
{
sinrx = __real__ x;
cosrx = 1.0Q;
}
if (fabsq (__imag__ x) > t)
{
/* Avoid intermediate overflow when the real part of the
result may be subnormal. Ignoring negligible terms, the
imaginary part is +/- 1, the real part is
sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
__float128 exp_2t = expq (2 * t);
__imag__ res = copysignq (1.0Q, __imag__ x);
__real__ res = 4 * sinrx * cosrx;
__imag__ x = fabsq (__imag__ x);
__imag__ x -= t;
__real__ res /= exp_2t;
if (__imag__ x > t)
{
/* Underflow (original imaginary part of x has absolute
value > 2t). */
__real__ res /= exp_2t;
}
else
__real__ res /= expq (2 * __imag__ x);
}
else
{
__float128 sinhix, coshix;
if (fabsq (__imag__ x) > FLT128_MIN)
{
sinhix = sinhq (__imag__ x);
coshix = coshq (__imag__ x);
}
else
{
sinhix = __imag__ x;
coshix = 1.0Q;
}
if (fabsq (sinhix) > fabsq (cosrx) * FLT128_EPSILON)
den = cosrx * cosrx + sinhix * sinhix;
else
den = cosrx * cosrx;
__real__ res = sinrx * cosrx / den;
__imag__ res = sinhix * coshix / den;
}
}
return res;
}
|
