1 /* Complex tangent function for long double.
2 Copyright (C) 1997-2013 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>
26 __complex__
long double
27 __ctanl (__complex__
long double x
)
29 __complex__
long double res
;
31 if (__builtin_expect (!isfinite (__real__ x
) || !isfinite (__imag__ x
), 0))
33 if (__isinf_nsl (__imag__ x
))
35 __real__ res
= __copysignl (0.0, __real__ x
);
36 __imag__ res
= __copysignl (1.0, __imag__ x
);
38 else if (__real__ x
== 0.0)
44 __real__ res
= __nanl ("");
45 __imag__ res
= __nanl ("");
47 if (__isinf_nsl (__real__ x
))
48 feraiseexcept (FE_INVALID
);
53 long double sinrx
, cosrx
;
55 const int t
= (int) ((LDBL_MAX_EXP
- 1) * M_LN2l
/ 2);
56 int rcls
= fpclassify (__real__ x
);
58 /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
59 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
61 if (__builtin_expect (rcls
!= FP_SUBNORMAL
, 1))
63 __sincosl (__real__ x
, &sinrx
, &cosrx
);
71 if (fabsl (__imag__ x
) > t
)
73 /* Avoid intermediate overflow when the real part of the
74 result may be subnormal. Ignoring negligible terms, the
75 imaginary part is +/- 1, the real part is
76 sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
77 long double exp_2t
= __ieee754_expl (2 * t
);
79 __imag__ res
= __copysignl (1.0, __imag__ x
);
80 __real__ res
= 4 * sinrx
* cosrx
;
81 __imag__ x
= fabsl (__imag__ x
);
83 __real__ res
/= exp_2t
;
86 /* Underflow (original imaginary part of x has absolute
88 __real__ res
/= exp_2t
;
91 __real__ res
/= __ieee754_expl (2 * __imag__ x
);
95 long double sinhix
, coshix
;
96 if (fabsl (__imag__ x
) > LDBL_MIN
)
98 sinhix
= __ieee754_sinhl (__imag__ x
);
99 coshix
= __ieee754_coshl (__imag__ x
);
107 if (fabsl (sinhix
) > fabsl (cosrx
) * LDBL_EPSILON
)
108 den
= cosrx
* cosrx
+ sinhix
* sinhix
;
111 __real__ res
= sinrx
* cosrx
/ den
;
112 __imag__ res
= sinhix
* coshix
/ den
;
118 weak_alias (__ctanl
, ctanl
)