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 pub fn atanh(x: f64) -> f64 {
9     let u = x.to_bits();
10     let e = ((u >> 52) as usize) & 0x7ff;
11     let sign = (u >> 63) != 0;
12 
13     /* |x| */
14     let mut y = f64::from_bits(u & 0x7fff_ffff_ffff_ffff);
15 
16     if e < 0x3ff - 1 {
17         if e < 0x3ff - 32 {
18             /* handle underflow */
19             if e == 0 {
20                 force_eval!(y as f32);
21             }
22         } else {
23             /* |x| < 0.5, up to 1.7ulp error */
24             y = 0.5 * log1p(2.0 * y + 2.0 * y * y / (1.0 - y));
25         }
26     } else {
27         /* avoid overflow */
28         y = 0.5 * log1p(2.0 * (y / (1.0 - y)));
atan2f(y: f32, x: f32) -> f3229     }
30 
31     if sign {
32         -y
33     } else {
34         y
35     }
36 }
37