Function hll_tau

datafusion/functions-aggregate/src/hyperloglog.rs:188–206

(x: f64)

/// Otmar Ertl, arXiv:1702.01284
#[inline]
fn hll_tau(x: f64) -> f64 {
    if x == 0.0 || x == 1.0 {
        0.0
    } else {
        let mut y = 1.0;
        let mut z = 1.0 - x;
        let mut x = x;
        loop {
            x = x.sqrt();
            let z_prime = z;
            y *= 0.5;
            z -= (1.0 - x).powi(2) * y;
            if z_prime == z {
                break;
            }
        }
        z / 3.0
    }
}

impl<T> AsRef<[u8]> for HyperLogLog<T>
where