libm/math/
tanh.rs

1use super::expm1;
2
3/* tanh(x) = (exp(x) - exp(-x))/(exp(x) + exp(-x))
4 *         = (exp(2*x) - 1)/(exp(2*x) - 1 + 2)
5 *         = (1 - exp(-2*x))/(exp(-2*x) - 1 + 2)
6 */
7
8/// The hyperbolic tangent of `x` (f64).
9///
10/// `x` is specified in radians.
11#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
12pub fn tanh(mut x: f64) -> f64 {
13    let mut uf: f64 = x;
14    let mut ui: u64 = f64::to_bits(uf);
15
16    let w: u32;
17    let sign: bool;
18    let mut t: f64;
19
20    /* x = |x| */
21    sign = ui >> 63 != 0;
22    ui &= !1 / 2;
23    uf = f64::from_bits(ui);
24    x = uf;
25    w = (ui >> 32) as u32;
26
27    if w > 0x3fe193ea {
28        /* |x| > log(3)/2 ~= 0.5493 or nan */
29        if w > 0x40340000 {
30            /* |x| > 20 or nan */
31            /* note: this branch avoids raising overflow */
32            t = 1.0 - 0.0 / x;
33        } else {
34            t = expm1(2.0 * x);
35            t = 1.0 - 2.0 / (t + 2.0);
36        }
37    } else if w > 0x3fd058ae {
38        /* |x| > log(5/3)/2 ~= 0.2554 */
39        t = expm1(2.0 * x);
40        t = t / (t + 2.0);
41    } else if w >= 0x00100000 {
42        /* |x| >= 0x1p-1022, up to 2ulp error in [0.1,0.2554] */
43        t = expm1(-2.0 * x);
44        t = -t / (t + 2.0);
45    } else {
46        /* |x| is subnormal */
47        /* note: the branch above would not raise underflow in [0x1p-1023,0x1p-1022) */
48        force_eval!(x as f32);
49        t = x;
50    }
51
52    if sign { -t } else { t }
53}