1 /* Complex tangent function for a complex float type.
2 Copyright (C) 1997-2021 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
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.
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.
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/>. */
22 #include <math_private.h>
23 #include <math-underflow.h>
27 M_DECL_FUNC (__ctan) (CFLOAT x)
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)
38 M_SINCOS (__real__ x, &sinrx, &cosrx);
39 __real__ res = M_COPYSIGN (0, sinrx * cosrx);
42 __real__ res = M_COPYSIGN (0, __real__ x);
43 __imag__ res = M_COPYSIGN (1, __imag__ x);
45 else if (__real__ x == 0)
53 __imag__ res = __imag__ x;
57 if (isinf (__real__ x))
58 feraiseexcept (FE_INVALID);
65 const int t = (int) ((M_MAX_EXP - 1) * M_MLIT (M_LN2) / 2);
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). */
70 if (__glibc_likely (M_FABS (__real__ x) > M_MIN))
72 M_SINCOS (__real__ x, &sinrx, &cosrx);
80 if (M_FABS (__imag__ x) > t)
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);
88 __imag__ res = M_COPYSIGN (1, __imag__ x);
89 __real__ res = 4 * sinrx * cosrx;
90 __imag__ x = M_FABS (__imag__ x);
92 __real__ res /= exp_2t;
95 /* Underflow (original imaginary part of x has absolute
97 __real__ res /= exp_2t;
100 __real__ res /= M_EXP (2 * __imag__ x);
104 FLOAT sinhix, coshix;
105 if (M_FABS (__imag__ x) > M_MIN)
107 sinhix = M_SINH (__imag__ x);
108 coshix = M_COSH (__imag__ x);
116 if (M_FABS (sinhix) > M_FABS (cosrx) * M_EPSILON)
117 den = cosrx * cosrx + sinhix * sinhix;
120 __real__ res = sinrx * cosrx / den;
121 __imag__ res = sinhix * coshix / den;
123 math_check_force_underflow_complex (res);
129 declare_mgen_alias (__ctan, ctan)