1 /* Complex tangent function for a complex float type.
2 Copyright (C) 1997-2019 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/>. */
23 #include <math_private.h>
24 #include <math-underflow.h>
28 M_DECL_FUNC (__ctan
) (CFLOAT x
)
32 if (__glibc_unlikely (!isfinite (__real__ x
) || !isfinite (__imag__ x
)))
34 if (isinf (__imag__ x
))
36 if (isfinite (__real__ x
) && M_FABS (__real__ x
) > 1)
39 M_SINCOS (__real__ x
, &sinrx
, &cosrx
);
40 __real__ res
= M_COPYSIGN (0, sinrx
* cosrx
);
43 __real__ res
= M_COPYSIGN (0, __real__ x
);
44 __imag__ res
= M_COPYSIGN (1, __imag__ x
);
46 else if (__real__ x
== 0)
54 __imag__ res
= __imag__ x
;
58 if (isinf (__real__ x
))
59 feraiseexcept (FE_INVALID
);
66 const int t
= (int) ((M_MAX_EXP
- 1) * M_MLIT (M_LN2
) / 2);
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). */
71 if (__glibc_likely (M_FABS (__real__ x
) > M_MIN
))
73 M_SINCOS (__real__ x
, &sinrx
, &cosrx
);
81 if (M_FABS (__imag__ x
) > t
)
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
);
89 __imag__ res
= M_COPYSIGN (1, __imag__ x
);
90 __real__ res
= 4 * sinrx
* cosrx
;
91 __imag__ x
= M_FABS (__imag__ x
);
93 __real__ res
/= exp_2t
;
96 /* Underflow (original imaginary part of x has absolute
98 __real__ res
/= exp_2t
;
101 __real__ res
/= M_EXP (2 * __imag__ x
);
105 FLOAT sinhix
, coshix
;
106 if (M_FABS (__imag__ x
) > M_MIN
)
108 sinhix
= M_SINH (__imag__ x
);
109 coshix
= M_COSH (__imag__ x
);
117 if (M_FABS (sinhix
) > M_FABS (cosrx
) * M_EPSILON
)
118 den
= cosrx
* cosrx
+ sinhix
* sinhix
;
121 __real__ res
= sinrx
* cosrx
/ den
;
122 __imag__ res
= sinhix
* coshix
/ den
;
124 math_check_force_underflow_complex (res
);
130 declare_mgen_alias (__ctan
, ctan
)