1 /* Return arc tangent of complex float type.
2 Copyright (C) 1997-2021 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 <https://www.gnu.org/licenses/>. */
22 #include <math_private.h>
23 #include <math-underflow.h>
27 M_DECL_FUNC (__catan
) (CFLOAT x
)
30 int rcls
= fpclassify (__real__ x
);
31 int icls
= fpclassify (__imag__ x
);
33 if (__glibc_unlikely (rcls
<= FP_INFINITE
|| icls
<= FP_INFINITE
))
35 if (rcls
== FP_INFINITE
)
37 __real__ res
= M_COPYSIGN (M_MLIT (M_PI_2
), __real__ x
);
38 __imag__ res
= M_COPYSIGN (0, __imag__ x
);
40 else if (icls
== FP_INFINITE
)
43 __real__ res
= M_COPYSIGN (M_MLIT (M_PI_2
), __real__ x
);
46 __imag__ res
= M_COPYSIGN (0, __imag__ x
);
48 else if (icls
== FP_ZERO
|| icls
== FP_INFINITE
)
51 __imag__ res
= M_COPYSIGN (0, __imag__ x
);
59 else if (__glibc_unlikely (rcls
== FP_ZERO
&& icls
== FP_ZERO
))
65 if (M_FABS (__real__ x
) >= 16 / M_EPSILON
66 || M_FABS (__imag__ x
) >= 16 / M_EPSILON
)
68 __real__ res
= M_COPYSIGN (M_MLIT (M_PI_2
), __real__ x
);
69 if (M_FABS (__real__ x
) <= 1)
70 __imag__ res
= 1 / __imag__ x
;
71 else if (M_FABS (__imag__ x
) <= 1)
72 __imag__ res
= __imag__ x
/ __real__ x
/ __real__ x
;
75 FLOAT h
= M_HYPOT (__real__ x
/ 2, __imag__ x
/ 2);
76 __imag__ res
= __imag__ x
/ h
/ h
/ 4;
81 FLOAT den
, absx
, absy
;
83 absx
= M_FABS (__real__ x
);
84 absy
= M_FABS (__imag__ x
);
92 if (absy
< M_EPSILON
/ 2)
94 den
= (1 - absx
) * (1 + absx
);
99 den
= (1 - absx
) * (1 + absx
) - absy
* absy
;
100 else if (absx
>= M_LIT (0.75) || absy
>= M_LIT (0.5))
101 den
= -M_SUF (__x2y2m1
) (absx
, absy
);
103 den
= (1 - absx
) * (1 + absx
) - absy
* absy
;
105 __real__ res
= M_LIT (0.5) * M_ATAN2 (2 * __real__ x
, den
);
107 if (M_FABS (__imag__ x
) == 1
108 && M_FABS (__real__ x
) < M_EPSILON
* M_EPSILON
)
109 __imag__ res
= (M_COPYSIGN (M_LIT (0.5), __imag__ x
)
110 * ((FLOAT
) M_MLIT (M_LN2
)
111 - M_LOG (M_FABS (__real__ x
))));
114 FLOAT r2
= 0, num
, f
;
116 if (M_FABS (__real__ x
) >= M_EPSILON
* M_EPSILON
)
117 r2
= __real__ x
* __real__ x
;
119 num
= __imag__ x
+ 1;
120 num
= r2
+ num
* num
;
122 den
= __imag__ x
- 1;
123 den
= r2
+ den
* den
;
127 __imag__ res
= M_LIT (0.25) * M_LOG (f
);
130 num
= 4 * __imag__ x
;
131 __imag__ res
= M_LIT (0.25) * M_LOG1P (num
/ den
);
136 math_check_force_underflow_complex (res
);
142 declare_mgen_alias (__catan
, catan
)