1 /**
2 * This file has no copyright assigned and is placed in the Public Domain.
3 * This file is part of the mingw-w64 runtime package.
4 * No warranty is given; refer to the file DISCLAIMER.PD within this package.
5 */
6 #include <math.h>
7 #include <errno.h>
8 #include "fastmath.h"
9
10 /* atanh (x) = 0.5 * log ((1.0 + x)/(1.0 - x)) */
atanhl(long double x)11 long double atanhl (long double x)
12 {
13 long double z;
14 if (isnan (x))
15 return x;
16 z = fabsl (x);
17 if (z == 1.0L)
18 {
19 errno = ERANGE;
20 return (x > 0 ? INFINITY : -INFINITY);
21 }
22 if ( z > 1.0L)
23 {
24 errno = EDOM;
25 return nanl("");
26 }
27 /* Rearrange formula to avoid precision loss for small x.
28 atanh(x) = 0.5 * log ((1.0 + x)/(1.0 - x))
29 = 0.5 * log1p ((1.0 + x)/(1.0 - x) - 1.0)
30 = 0.5 * log1p ((1.0 + x - 1.0 + x) /(1.0 - x))
31 = 0.5 * log1p ((2.0 * x ) / (1.0 - x)) */
32 z = 0.5L * __fast_log1pl ((z + z) / (1.0L - z));
33 return x >= 0 ? z : -z;
34 }
35