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}
52