1 /* Copyright (C) 2011-2023 Free Software Foundation, Inc.
2 This file is part of the GNU C Library.
4 The GNU C Library is free software; you can redistribute it and/or
5 modify it under the terms of the GNU Lesser General Public
6 License as published by the Free Software Foundation; either
7 version 2.1 of the License, or (at your option) any later version.
9 The GNU C Library is distributed in the hope that it will be useful,
10 but WITHOUT ANY WARRANTY; without even the implied warranty of
11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
12 Lesser General Public License for more details.
14 You should have received a copy of the GNU Lesser General Public
15 License along with the GNU C Library; if not, see
16 <https://www.gnu.org/licenses/>. */
21 1.Reduced x to positive by atanh(-x) = -atanh(x)
24 atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
28 atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
31 atanh(x) is NaN if |x| > 1 with signal;
32 atanh(NaN) is that NaN with no signal;
33 atanh(+-1) is +-INF with signal.
40 #include <math-barriers.h>
41 #include <math_private.h>
42 #include <math-underflow.h>
43 #include <libm-alias-finite.h>
45 static const double huge
= 1e300
;
48 __ieee754_atanh (double x
)
54 if (__glibc_unlikely (xa
< 0x1.0p
-28))
56 math_force_eval (huge
+ x
);
57 math_check_force_underflow (x
);
62 t
= 0.5 * __log1p (t
+ t
* xa
/ (1.0 - xa
));
64 else if (__glibc_likely (isless (xa
, 1.0)))
65 t
= 0.5 * __log1p ((xa
+ xa
) / (1.0 - xa
));
68 if (isgreater (xa
, 1.0))
69 return (x
- x
) / (x
- x
);
74 return copysign (t
, x
);
76 libm_alias_finite (__ieee754_atanh
, __atanh
)