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