ldbl-128ibm: Automatic replacing of _Float128 and L()
[glibc.git] / math / s_ctan_template.c
blob723156eed42f96fcb23cc5fe710ac9be63ac593b
1 /* Complex tangent function for a complex float type.
2 Copyright (C) 1997-2017 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997.
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.
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.
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/>. */
20 #include <complex.h>
21 #include <fenv.h>
22 #include <math.h>
23 #include <math_private.h>
24 #include <float.h>
26 CFLOAT
27 M_DECL_FUNC (__ctan) (CFLOAT x)
29 CFLOAT res;
31 if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x)))
33 if (isinf (__imag__ x))
35 if (isfinite (__real__ x) && M_FABS (__real__ x) > 1)
37 FLOAT sinrx, cosrx;
38 M_SINCOS (__real__ x, &sinrx, &cosrx);
39 __real__ res = M_COPYSIGN (0, sinrx * cosrx);
41 else
42 __real__ res = M_COPYSIGN (0, __real__ x);
43 __imag__ res = M_COPYSIGN (1, __imag__ x);
45 else if (__real__ x == 0)
47 res = x;
49 else
51 __real__ res = M_NAN;
52 __imag__ res = M_NAN;
54 if (isinf (__real__ x))
55 feraiseexcept (FE_INVALID);
58 else
60 FLOAT sinrx, cosrx;
61 FLOAT den;
62 const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
64 /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
65 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
67 if (__glibc_likely (M_FABS (__real__ x) > M_MIN))
69 M_SINCOS (__real__ x, &sinrx, &cosrx);
71 else
73 sinrx = __real__ x;
74 cosrx = 1;
77 if (M_FABS (__imag__ x) > t)
79 /* Avoid intermediate overflow when the real part of the
80 result may be subnormal. Ignoring negligible terms, the
81 imaginary part is +/- 1, the real part is
82 sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
83 FLOAT exp_2t = M_EXP (2 * t);
85 __imag__ res = M_COPYSIGN (1, __imag__ x);
86 __real__ res = 4 * sinrx * cosrx;
87 __imag__ x = M_FABS (__imag__ x);
88 __imag__ x -= t;
89 __real__ res /= exp_2t;
90 if (__imag__ x > t)
92 /* Underflow (original imaginary part of x has absolute
93 value > 2t). */
94 __real__ res /= exp_2t;
96 else
97 __real__ res /= M_EXP (2 * __imag__ x);
99 else
101 FLOAT sinhix, coshix;
102 if (M_FABS (__imag__ x) > M_MIN)
104 sinhix = M_SINH (__imag__ x);
105 coshix = M_COSH (__imag__ x);
107 else
109 sinhix = __imag__ x;
110 coshix = 1;
113 if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON)
114 den = cosrx * cosrx + sinhix * sinhix;
115 else
116 den = cosrx * cosrx;
117 __real__ res = sinrx * cosrx / den;
118 __imag__ res = sinhix * coshix / den;
120 math_check_force_underflow_complex (res);
123 return res;
126 declare_mgen_alias (__ctan, ctan)