compiler_builtins/math/libm_math/
acosh.rs

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 = x.to_bits();
13    let e = ((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}