1 | use super::{log1pf, logf, sqrtf}; |
2 | |
3 | const LN2: f32 = 0.693147180559945309417232121458176568; |
4 | |
5 | /// Inverse hyperbolic cosine (f32) |
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)] |
11 | pub fn acoshf(x: f32) -> f32 { |
12 | let u: u32 = x.to_bits(); |
13 | let a: u32 = u & 0x7fffffff; |
14 | |
15 | if a < 0x3f800000 + (1 << 23) { |
16 | /* |x| < 2, invalid if x < 1 or nan */ |
17 | /* up to 2ulp error in [1,1.125] */ |
18 | return log1pf(x - 1.0 + sqrtf((x - 1.0) * (x - 1.0) + 2.0 * (x - 1.0))); |
19 | } |
20 | if a < 0x3f800000 + (12 << 23) { |
21 | /* |x| < 0x1p12 */ |
22 | return logf(2.0 * x - 1.0 / (x + sqrtf(x * x - 1.0))); |
23 | } |
24 | /* x >= 0x1p12 */ |
25 | return logf(x) + LN2; |
26 | } |
27 | |