libm/math/
atanhf.rs

1use super::log1pf;
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 (f32)
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)]
9pub fn atanhf(mut x: f32) -> f32 {
10    let mut u = x.to_bits();
11    let sign = (u >> 31) != 0;
12
13    /* |x| */
14    u &= 0x7fffffff;
15    x = f32::from_bits(u);
16
17    if u < 0x3f800000 - (1 << 23) {
18        if u < 0x3f800000 - (32 << 23) {
19            /* handle underflow */
20            if u < (1 << 23) {
21                force_eval!((x * x) as f32);
22            }
23        } else {
24            /* |x| < 0.5, up to 1.7ulp error */
25            x = 0.5 * log1pf(2.0 * x + 2.0 * x * x / (1.0 - x));
26        }
27    } else {
28        /* avoid overflow */
29        x = 0.5 * log1pf(2.0 * (x / (1.0 - x)));
30    }
31
32    if sign { -x } else { x }
33}