1 /* Copyright (C) 2011-2022 Free Software Foundation, Inc.
2    This file is part of the GNU C Library.
3 
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.
8 
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.
13 
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/>.  */
17 
18 
19 /* __ieee754_atanh(x)
20    Method :
21       1.Reduced x to positive by atanh(-x) = -atanh(x)
22       2.For x>=0.5
23 		    1              2x                          x
24 	atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------)
25 		    2             1 - x                      1 - x
26 
27 	For x<0.5
28 	atanh(x) = 0.5*log1p(2x+2x*x/(1-x))
29 
30    Special cases:
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.
34 
35  */
36 
37 #include <float.h>
38 #include <inttypes.h>
39 #include <math.h>
40 #include <math-barriers.h>
41 #include <math_private.h>
42 #include <math-underflow.h>
43 #include <libm-alias-finite.h>
44 
45 static const double huge = 1e300;
46 
47 double
__ieee754_atanh(double x)48 __ieee754_atanh (double x)
49 {
50   double xa = fabs (x);
51   double t;
52   if (isless (xa, 0.5))
53     {
54       if (__glibc_unlikely (xa < 0x1.0p-28))
55 	{
56 	  math_force_eval (huge + x);
57 	  math_check_force_underflow (x);
58 	  return x;
59 	}
60 
61       t = xa + xa;
62       t = 0.5 * __log1p (t + t * xa / (1.0 - xa));
63     }
64   else if (__glibc_likely (isless (xa, 1.0)))
65     t = 0.5 * __log1p ((xa + xa) / (1.0 - xa));
66   else
67     {
68       if (isgreater (xa, 1.0))
69 	return (x - x) / (x - x);
70 
71       return x / 0.0;
72     }
73 
74   return copysign (t, x);
75 }
76 libm_alias_finite (__ieee754_atanh, __atanh)
77