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))`.
asinh(mut x: f64) -> f6410 pub fn asinh(mut x: f64) -> f64 {
11 let mut u = x.to_bits();
12 let e = ((u >> 52) as usize) & 0x7ff;
13 let sign = (u >> 63) != 0;
14
15 /* |x| */
16 u &= (!0) >> 1;
17 x = f64::from_bits(u);
18
19 if e >= 0x3ff + 26 {
20 /* |x| >= 0x1p26 or inf or nan */
21 x = log(x) + LN2;
22 } else if e >= 0x3ff + 1 {
23 /* |x| >= 2 */
24 x = log(2.0 * x + 1.0 / (sqrt(x * x + 1.0) + x));
25 } else if e >= 0x3ff - 26 {
26 /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */
27 x = log1p(x + x * x / (sqrt(x * x + 1.0) + 1.0));
28 } else {
29 /* |x| < 0x1p-26, raise inexact if x != 0 */
30 let x1p120 = f64::from_bits(0x4770000000000000);
31 force_eval!(x + x1p120);
32 }
33
34 if sign {
35 -x
36 } else {
37 x
38 }
39 }
40