1 /* Complex tangent function for double.
2 Copyright (C) 1997-2015 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>
27 __ctan (__complex__
double x
)
29 __complex__
double res
;
31 if (__glibc_unlikely (!isfinite (__real__ x
) || !isfinite (__imag__ x
)))
33 if (__isinf_ns (__imag__ x
))
35 __real__ res
= __copysign (0.0, __real__ x
);
36 __imag__ res
= __copysign (1.0, __imag__ x
);
38 else if (__real__ x
== 0.0)
44 __real__ res
= __nan ("");
45 __imag__ res
= __nan ("");
47 if (__isinf_ns (__real__ x
))
48 feraiseexcept (FE_INVALID
);
55 const int t
= (int) ((DBL_MAX_EXP
- 1) * M_LN2
/ 2);
57 /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
58 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
60 if (__glibc_likely (fabs (__real__ x
) > DBL_MIN
))
62 __sincos (__real__ x
, &sinrx
, &cosrx
);
70 if (fabs (__imag__ x
) > t
)
72 /* Avoid intermediate overflow when the real part of the
73 result may be subnormal. Ignoring negligible terms, the
74 imaginary part is +/- 1, the real part is
75 sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
76 double exp_2t
= __ieee754_exp (2 * t
);
78 __imag__ res
= __copysign (1.0, __imag__ x
);
79 __real__ res
= 4 * sinrx
* cosrx
;
80 __imag__ x
= fabs (__imag__ x
);
82 __real__ res
/= exp_2t
;
85 /* Underflow (original imaginary part of x has absolute
87 __real__ res
/= exp_2t
;
90 __real__ res
/= __ieee754_exp (2 * __imag__ x
);
94 double sinhix
, coshix
;
95 if (fabs (__imag__ x
) > DBL_MIN
)
97 sinhix
= __ieee754_sinh (__imag__ x
);
98 coshix
= __ieee754_cosh (__imag__ x
);
106 if (fabs (sinhix
) > fabs (cosrx
) * DBL_EPSILON
)
107 den
= cosrx
* cosrx
+ sinhix
* sinhix
;
110 __real__ res
= sinrx
* cosrx
/ den
;
111 __imag__ res
= sinhix
* coshix
/ den
;
117 weak_alias (__ctan
, ctan
)
118 #ifdef NO_LONG_DOUBLE
119 strong_alias (__ctan
, __ctanl
)
120 weak_alias (__ctan
, ctanl
)