1use super::{log, log1p, sqrt};
2
3const LN2: f64 = 0.693147180559945309417232121458176568; /* 0x3fe62e42, 0xfefa39ef*/
4
5/// Inverse hyperbolic cosine (f64)
6///
7/// Calculates the inverse hyperbolic cosine of `x`.
8/// Is defined as `log(x + sqrt(x*x-1))`.
9/// `x` must be a number greater than or equal to 1.
10#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
11pub fn acosh(x: f64) -> f64 {
12 let u: u64 = x.to_bits();
13 let e: usize = ((u >> 52) as usize) & 0x7ff;
14
15 /* x < 1 domain error is handled in the called functions */
16
17 if e < 0x3ff + 1 {
18 /* |x| < 2, up to 2ulp error in [1,1.125] */
19 return log1p(x - 1.0 + sqrt((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));
20 }
21 if e < 0x3ff + 26 {
22 /* |x| < 0x1p26 */
23 return log(2.0 * x - 1.0 / (x + sqrt(x * x - 1.0)));
24 }
25 /* |x| >= 0x1p26 or nan */
26 return log(x) + LN2;
27}
28