/// Convert RA/Dec to Altitude/Azimuth.
/// All inputs and outputs in degrees.
pub fn radec_to_altaz(
    ra_deg: f64,
    dec_deg: f64,
    lst_deg: f64,
    lat_deg: f64,
) -> (f64, f64) {
    let ha = (lst_deg - ra_deg).rem_euclid(360.0);
    let ha_rad = ha.to_radians();
    let dec_rad = dec_deg.to_radians();
    let lat_rad = lat_deg.to_radians();

    let sin_alt = dec_rad.sin() * lat_rad.sin()
        + dec_rad.cos() * lat_rad.cos() * ha_rad.cos();
    let alt_rad = sin_alt.asin();

    let cos_az = (dec_rad.sin() - lat_rad.sin() * sin_alt)
        / (lat_rad.cos() * alt_rad.cos());
    let cos_az = cos_az.clamp(-1.0, 1.0);
    let az_rad = cos_az.acos();

    let az_deg = if ha_rad.sin() < 0.0 {
        az_rad.to_degrees()
    } else {
        360.0 - az_rad.to_degrees()
    };

    (alt_rad.to_degrees(), az_deg)
}

/// Rozenberg airmass formula — valid to horizon.
pub fn airmass(alt_deg: f64) -> f64 {
    if alt_deg <= 0.0 {
        return 40.0; // clamp at horizon
    }
    let z_rad = (90.0 - alt_deg).to_radians();
    1.0 / (z_rad.cos() + 0.025 * (-11.0 * z_rad.cos()).exp())
}

/// Extinction in magnitudes. k = 0.20 mag/airmass (Bortle 5 site).
pub fn extinction_mag(alt_deg: f64) -> f64 {
    airmass(alt_deg) * 0.20
}