great-circular distance and its derivative

main.rs

fn distance_on_sphere(lat1: f32, lon1: f32, lat2: f32, lon2: f32) -> f32 {
    let dlat = (lat2 - lat1).abs();
    let dlon = (lon2 - lon1).abs();
    let a = (dlat * 0.5).sin().powi(2) + lat1.cos() * lat2.cos() * (dlon * 0.5).sin().powi(2);
    2.0 * a.sqrt().asin()
}

fn differential_distance_on_sphere(lat1: f32, lon1: f32, lat2: f32, lon2: f32) -> [f32; 2] {
    let diff = 1.0;
    let dlat = (lat2 - lat1).abs();
    let dlon = (lon2 - lon1).abs();
    let dlatsign = (lat2 - lat1).signum();
    let dlonsign = (lon2 - lon1).signum();
    let cc = lat1.cos() * lat2.cos();
    let (dlatsin, dlatcos) = (dlat * 0.5).sin_cos();
    let (dlonsin, dloncos) = (dlon * 0.5).sin_cos();
    let a = dlatsin.powi(2) + cc * dlonsin.powi(2);
    let e = diff / ((1.0 - a.abs()).sqrt() * a.sqrt()).max(1e-8);
    let dlon1 = -(dlonsign * dlonsin * dloncos * cc * e);
    let d = dlatcos * dlatsin * e;
    let dlat1 = -lat1.sin() * lat2.cos() * e * dlonsin.powi(2) - dlatsign * d;
    [dlat1, dlon1]
}