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)]
atanh(x: f64) -> f649 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