1 use super::{log, log1p, sqrt};
2 
3 const 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)]
asinh(mut x: f64) -> f6411 pub 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 {
36         -x
37     } else {
38         x
39     }
40 }
41