1 /* Complex tangent function for long double. IBM extended format version.
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_ldbl_opt.h>
26 #include <math_private.h>
28 /* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */
29 static const long double ldbl_eps
= 0x1p
-106L;
31 __complex__
long double
32 __ctanl (__complex__
long double x
)
34 __complex__
long double res
;
36 if (!isfinite (__real__ x
) || !isfinite (__imag__ x
))
38 if (__isinfl (__imag__ x
))
40 __real__ res
= __copysignl (0.0, __real__ x
);
41 __imag__ res
= __copysignl (1.0, __imag__ x
);
43 else if (__real__ x
== 0.0)
49 __real__ res
= __nanl ("");
50 __imag__ res
= __nanl ("");
52 if (__isinf_nsl (__real__ x
))
53 feraiseexcept (FE_INVALID
);
58 long double sinrx
, cosrx
;
60 const int t
= (int) ((LDBL_MAX_EXP
- 1) * M_LN2l
/ 2.0L);
62 /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y))
63 = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */
65 __sincosl (__real__ x
, &sinrx
, &cosrx
);
67 if (fabsl (__imag__ x
) > t
)
69 /* Avoid intermediate overflow when the real part of the
70 result may be subnormal. Ignoring negligible terms, the
71 imaginary part is +/- 1, the real part is
72 sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */
73 long double exp_2t
= __ieee754_expl (2 * t
);
75 __imag__ res
= __copysignl (1.0L, __imag__ x
);
76 __real__ res
= 4 * sinrx
* cosrx
;
77 __imag__ x
= fabsl (__imag__ x
);
79 __real__ res
/= exp_2t
;
82 /* Underflow (original imaginary part of x has absolute
84 __real__ res
/= exp_2t
;
87 __real__ res
/= __ieee754_expl (2.0L * __imag__ x
);
91 long double sinhix
, coshix
;
92 if (fabsl (__imag__ x
) > LDBL_MIN
)
94 sinhix
= __ieee754_sinhl (__imag__ x
);
95 coshix
= __ieee754_coshl (__imag__ x
);
103 if (fabsl (sinhix
) > fabsl (cosrx
) * ldbl_eps
)
104 den
= cosrx
* cosrx
+ sinhix
* sinhix
;
107 __real__ res
= sinrx
* (cosrx
/ den
);
108 __imag__ res
= sinhix
* (coshix
/ den
);
111 /* __gcc_qmul does not respect -0.0 so we need the following fixup. */
112 if ((__real__ res
== 0.0L) && (__real__ x
== 0.0L))
113 __real__ res
= __real__ x
;
115 if ((__real__ res
== 0.0L) && (__imag__ x
== 0.0L))
116 __imag__ res
= __imag__ x
;
121 long_double_symbol (libm
, __ctanl
, ctanl
);