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}
37