1 | use super::{log1pf, logf, sqrtf}; |
2 | |
3 | const LN2: f32 = 0.693147180559945309417232121458176568; |
4 | |
5 | /* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ |
6 | /// Inverse hyperbolic sine (f32) |
7 | /// |
8 | /// Calculates the inverse hyperbolic sine of `x`. |
9 | /// Is defined as `sgn(x)*log(|x|+sqrt(x*x+1))`. |
10 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
11 | pub fn asinhf(mut x: f32) -> f32 { |
12 | let u = x.to_bits(); |
13 | let i = u & 0x7fffffff; |
14 | let sign = (u >> 31) != 0; |
15 | |
16 | /* |x| */ |
17 | x = f32::from_bits(i); |
18 | |
19 | if i >= 0x3f800000 + (12 << 23) { |
20 | /* |x| >= 0x1p12 or inf or nan */ |
21 | x = logf(x) + LN2; |
22 | } else if i >= 0x3f800000 + (1 << 23) { |
23 | /* |x| >= 2 */ |
24 | x = logf(2.0 * x + 1.0 / (sqrtf(x * x + 1.0) + x)); |
25 | } else if i >= 0x3f800000 - (12 << 23) { |
26 | /* |x| >= 0x1p-12, up to 1.6ulp error in [0.125,0.5] */ |
27 | x = log1pf(x + x * x / (sqrtf(x * x + 1.0) + 1.0)); |
28 | } else { |
29 | /* |x| < 0x1p-12, raise inexact if x!=0 */ |
30 | let x1p120 = f32::from_bits(0x7b800000); |
31 | force_eval!(x + x1p120); |
32 | } |
33 | |
34 | if sign { |
35 | -x |
36 | } else { |
37 | x |
38 | } |
39 | } |
40 | |