libm/math/
asinh.rs

1use super::{log, 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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
11pub fn asinh(mut x: f64) -> f64 {
12    let mut u = x.to_bits();
13    let e = ((u >> 52) as usize) & 0x7ff;
14    let sign = (u >> 63) != 0;
15
16    /* |x| */
17    u &= (!0) >> 1;
18    x = f64::from_bits(u);
19
20    if e >= 0x3ff + 26 {
21        /* |x| >= 0x1p26 or inf or nan */
22        x = log(x) + LN2;
23    } else if e >= 0x3ff + 1 {
24        /* |x| >= 2 */
25        x = log(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x));
26    } else if e >= 0x3ff - 26 {
27        /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
28        x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0));
29    } else {
30        /* |x| < 0x1p-26, raise inexact if x != 0 */
31        let x1p120 = f64::from_bits(0x4770000000000000);
32        force_eval!(x + x1p120);
33    }
34
35    if sign { -x } else { x }
36}
libm/math/asinh.rs

libm/math/
asinh.rs
