1 use super::{log, log1p, sqrt};
2
3 const 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.
acosh(x: f64) -> f6410 pub fn acosh(x: f64) -> f64 {
11 let u = x.to_bits();
12 let e = ((u >> 52) as usize) & 0x7ff;
13
14 /* x < 1 domain error is handled in the called functions */
15
16 if e < 0x3ff + 1 {
17 /* |x| < 2, up to 2ulp error in [1,1.125] */
18 return log1p(x - 1.0 + sqrt((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0)));
19 }
20 if e < 0x3ff + 26 {
21 /* |x| < 0x1p26 */
22 return log(2.0 * x - 1.0 / (x + sqrt(x * x - 1.0)));
23 }
24 /* |x| >= 0x1p26 or nan */
25 return log(x) + LN2;
26 }
27