1 | use super::log1p; |
2 | |
3 | /* atanh(x) = log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2 ~= x + x^3/3 + o(x^5) */ |
4 | /// Inverse hyperbolic tangent (f64) |
5 | /// |
6 | /// Calculates the inverse hyperbolic tangent of `x`. |
7 | /// Is defined as `log((1+x)/(1-x))/2 = log1p(2x/(1-x))/2`. |
8 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
9 | pub fn atanh(x: f64) -> f64 { |
10 | let u = x.to_bits(); |
11 | let e = ((u >> 52) as usize) & 0x7ff; |
12 | let sign = (u >> 63) != 0; |
13 | |
14 | /* |x| */ |
15 | let mut y = f64::from_bits(u & 0x7fff_ffff_ffff_ffff); |
16 | |
17 | if e < 0x3ff - 1 { |
18 | if e < 0x3ff - 32 { |
19 | /* handle underflow */ |
20 | if e == 0 { |
21 | force_eval!(y as f32); |
22 | } |
23 | } else { |
24 | /* |x| < 0.5, up to 1.7ulp error */ |
25 | y = 0.5 * log1p(2.0 * y + 2.0 * y * y / (1.0 - y)); |
26 | } |
27 | } else { |
28 | /* avoid overflow */ |
29 | y = 0.5 * log1p(2.0 * (y / (1.0 - y))); |
30 | } |
31 | |
32 | if sign { |
33 | -y |
34 | } else { |
35 | y |
36 | } |
37 | } |
38 | |