1 /* Return arc tangent of complex float type.
2 Copyright (C) 1997-2018 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/>. */
20 #include "quadmath-imp.h"
23 catanq (__complex128 x
)
26 int rcls
= fpclassifyq (__real__ x
);
27 int icls
= fpclassifyq (__imag__ x
);
29 if (__glibc_unlikely (rcls
<= QUADFP_INFINITE
|| icls
<= QUADFP_INFINITE
))
31 if (rcls
== QUADFP_INFINITE
)
33 __real__ res
= copysignq (M_PI_2q
, __real__ x
);
34 __imag__ res
= copysignq (0, __imag__ x
);
36 else if (icls
== QUADFP_INFINITE
)
38 if (rcls
>= QUADFP_ZERO
)
39 __real__ res
= copysignq (M_PI_2q
, __real__ x
);
41 __real__ res
= nanq ("");
42 __imag__ res
= copysignq (0, __imag__ x
);
44 else if (icls
== QUADFP_ZERO
|| icls
== QUADFP_INFINITE
)
46 __real__ res
= nanq ("");
47 __imag__ res
= copysignq (0, __imag__ x
);
51 __real__ res
= nanq ("");
52 __imag__ res
= nanq ("");
55 else if (__glibc_unlikely (rcls
== QUADFP_ZERO
&& icls
== QUADFP_ZERO
))
61 if (fabsq (__real__ x
) >= 16 / FLT128_EPSILON
62 || fabsq (__imag__ x
) >= 16 / FLT128_EPSILON
)
64 __real__ res
= copysignq (M_PI_2q
, __real__ x
);
65 if (fabsq (__real__ x
) <= 1)
66 __imag__ res
= 1 / __imag__ x
;
67 else if (fabsq (__imag__ x
) <= 1)
68 __imag__ res
= __imag__ x
/ __real__ x
/ __real__ x
;
71 __float128 h
= hypotq (__real__ x
/ 2, __imag__ x
/ 2);
72 __imag__ res
= __imag__ x
/ h
/ h
/ 4;
77 __float128 den
, absx
, absy
;
79 absx
= fabsq (__real__ x
);
80 absy
= fabsq (__imag__ x
);
88 if (absy
< FLT128_EPSILON
/ 2)
90 den
= (1 - absx
) * (1 + absx
);
95 den
= (1 - absx
) * (1 + absx
) - absy
* absy
;
96 else if (absx
>= 0.75Q
|| absy
>= 0.5Q
)
97 den
= -__quadmath_x2y2m1q (absx
, absy
);
99 den
= (1 - absx
) * (1 + absx
) - absy
* absy
;
101 __real__ res
= 0.5Q
* atan2q (2 * __real__ x
, den
);
103 if (fabsq (__imag__ x
) == 1
104 && fabsq (__real__ x
) < FLT128_EPSILON
* FLT128_EPSILON
)
105 __imag__ res
= (copysignq (0.5Q
, __imag__ x
)
106 * ((__float128
) M_LN2q
107 - logq (fabsq (__real__ x
))));
110 __float128 r2
= 0, num
, f
;
112 if (fabsq (__real__ x
) >= FLT128_EPSILON
* FLT128_EPSILON
)
113 r2
= __real__ x
* __real__ x
;
115 num
= __imag__ x
+ 1;
116 num
= r2
+ num
* num
;
118 den
= __imag__ x
- 1;
119 den
= r2
+ den
* den
;
123 __imag__ res
= 0.25Q
* logq (f
);
126 num
= 4 * __imag__ x
;
127 __imag__ res
= 0.25Q
* log1pq (num
/ den
);
132 math_check_force_underflow_complex (res
);