libm/math/
sinh.rs

1use super::{expm1, expo2};
2
3// sinh(x) = (exp(x) - 1/exp(x))/2
4//         = (exp(x)-1 + (exp(x)-1)/exp(x))/2
5//         = x + x^3/6 + o(x^5)
6//
7
8/// The hyperbolic sine of `x` (f64).
9#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
10pub fn sinh(x: f64) -> f64 {
11    // union {double f; uint64_t i;} u = {.f = x};
12    // uint32_t w;
13    // double t, h, absx;
14
15    let mut uf: f64 = x;
16    let mut ui: u64 = f64::to_bits(uf);
17    let w: u32;
18    let t: f64;
19    let mut h: f64;
20    let absx: f64;
21
22    h = 0.5;
23    if ui >> 63 != 0 {
24        h = -h;
25    }
26    /* |x| */
27    ui &= !1 / 2;
28    uf = f64::from_bits(ui);
29    absx = uf;
30    w = (ui >> 32) as u32;
31
32    /* |x| < log(DBL_MAX) */
33    if w < 0x40862e42 {
34        t = expm1(absx);
35        if w < 0x3ff00000 {
36            if w < 0x3ff00000 - (26 << 20) {
37                /* note: inexact and underflow are raised by expm1 */
38                /* note: this branch avoids spurious underflow */
39                return x;
40            }
41            return h * (2.0 * t - t * t / (t + 1.0));
42        }
43        /* note: |x|>log(0x1p26)+eps could be just h*exp(x) */
44        return h * (t + t / (t + 1.0));
45    }
46
47    /* |x| > log(DBL_MAX) or nan */
48    /* note: the result is stored to handle overflow */
49    t = 2.0 * h * expo2(absx);
50    t
51}