trig_const/
asinh.rs

1use crate::{ln, log1p::log1p, sqrt};
2
3const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42,  0xfefa39ef*/
4
5/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */
6/// Inverse hyperbolic sine (f64)
7///
8/// Calculates the inverse hyperbolic sine of `x`.
9/// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`.
10/// ```
11/// # use trig_const::asinh;
12/// const ASINH_1: f64 = asinh(0.0);
13/// assert_eq!(ASINH_1, 0.0);
14/// ```
15pub const fn asinh(mut x: f64) -> f64 {
16    let mut u = x.to_bits();
17    let e = ((u >> 52) as usize) & 0x7ff;
18    let sign = (u >> 63) != 0;
19
20    /* |x| */
21    u &= (!0) >> 1;
22    x = f64::from_bits(u);
23
24    if e >= 0x3ff + 26 {
25        /* |x| >= 0x1p26 or inf or nan */
26        x = ln(x) + LN2;
27    } else if e > 0x3ff {
28        /* |x| >= 2 */
29        x = ln(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x));
30    } else if e >= 0x3ff - 26 {
31        /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
32        x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0));
33    } else {
34        /* |x| < 0x1p-26, raise inexact if x != 0 */
35    }
36
37    if sign {
38        -x
39    } else {
40        x
41    }
42}
trig_const/asinh.rs

trig_const/
asinh.rs
