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