trig_const/
atanh.rs

1use crate::log1p::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`.
8pub const 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        } else {
19            /* |x| < 0.5, up to 1.7ulp error */
20            y = 0.5 * log1p(2.0 * y + 2.0 * y * y / (1.0 - y));
21        }
22    } else {
23        /* avoid overflow */
24        y = 0.5 * log1p(2.0 * (y / (1.0 - y)));
25    }
26
27    if sign {
28        -y
29    } else {
30        y
31    }
32}