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}
54