1 /* Return arc hyperbolic tangent for a complex float type.
2 Copyright (C) 1997-2019 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/>. */
22 #include <math_private.h>
23 #include <math-underflow.h>
27 M_DECL_FUNC (__catanh
) (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 (icls
== FP_INFINITE
)
37 __real__ res
= M_COPYSIGN (0, __real__ x
);
38 __imag__ res
= M_COPYSIGN (M_MLIT (M_PI_2
), __imag__ x
);
40 else if (rcls
== FP_INFINITE
|| rcls
== FP_ZERO
)
42 __real__ res
= M_COPYSIGN (0, __real__ x
);
44 __imag__ res
= M_COPYSIGN (M_MLIT (M_PI_2
), __imag__ x
);
54 else if (__glibc_unlikely (rcls
== FP_ZERO
&& icls
== FP_ZERO
))
60 if (M_FABS (__real__ x
) >= 16 / M_EPSILON
61 || M_FABS (__imag__ x
) >= 16 / M_EPSILON
)
63 __imag__ res
= M_COPYSIGN (M_MLIT (M_PI_2
), __imag__ x
);
64 if (M_FABS (__imag__ x
) <= 1)
65 __real__ res
= 1 / __real__ x
;
66 else if (M_FABS (__real__ x
) <= 1)
67 __real__ res
= __real__ x
/ __imag__ x
/ __imag__ x
;
70 FLOAT h
= M_HYPOT (__real__ x
/ 2, __imag__ x
/ 2);
71 __real__ res
= __real__ x
/ h
/ h
/ 4;
76 if (M_FABS (__real__ x
) == 1
77 && M_FABS (__imag__ x
) < M_EPSILON
* M_EPSILON
)
78 __real__ res
= (M_COPYSIGN (M_LIT (0.5), __real__ x
)
79 * ((FLOAT
) M_MLIT (M_LN2
)
80 - M_LOG (M_FABS (__imag__ x
))));
84 if (M_FABS (__imag__ x
) >= M_EPSILON
* M_EPSILON
)
85 i2
= __imag__ x
* __imag__ x
;
87 FLOAT num
= 1 + __real__ x
;
90 FLOAT den
= 1 - __real__ x
;
95 __real__ res
= M_LIT (0.25) * M_LOG (f
);
99 __real__ res
= M_LIT (0.25) * M_LOG1P (num
/ den
);
103 FLOAT absx
, absy
, den
;
105 absx
= M_FABS (__real__ x
);
106 absy
= M_FABS (__imag__ x
);
114 if (absy
< M_EPSILON
/ 2)
116 den
= (1 - absx
) * (1 + absx
);
121 den
= (1 - absx
) * (1 + absx
) - absy
* absy
;
122 else if (absx
>= M_LIT (0.75) || absy
>= M_LIT (0.5))
123 den
= -M_SUF (__x2y2m1
) (absx
, absy
);
125 den
= (1 - absx
) * (1 + absx
) - absy
* absy
;
127 __imag__ res
= M_LIT (0.5) * M_ATAN2 (2 * __imag__ x
, den
);
130 math_check_force_underflow_complex (res
);
136 declare_mgen_alias (__catanh
, catanh
)