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use crate*;
/// IAU 1976 precession model.
///
/// This function forms the three Euler angles which implement general
/// precession between two dates, using the IAU 1976 model (as for the
/// FK5 catalog).
///
/// Given:
/// * date01,date02 TDB starting date (Note 1)
/// * date11,date12 TDB ending date (Note 1)
///
/// Returned:
/// * zeta 1st rotation: radians cw around z
/// * z 3rd rotation: radians cw around z
/// * theta 2nd rotation: radians ccw around y
///
/// # Notes:
///
/// 1) The dates date01+date02 and date11+date12 are Julian Dates,
/// apportioned in any convenient way between the arguments daten1
/// and daten2. For example, JD(TDB)=2450123.7 could be expressed in
/// any of these ways, among others:
///
/// | daten1 | daten2 | |
/// |-------------|--------------|----------------------|
/// |2450123.7 | 0.0 | (JD method) |
/// |2451545.0 | -1421.3 | (J2000 method) |
/// |2400000.5 | 50123.2 | (MJD method) |
/// |2450123.5 | 0.2 | (date & time method) |
///
/// The JD method is the most natural and convenient to use in cases
/// where the loss of several decimal digits of resolution is
/// acceptable. The J2000 method is best matched to the way the
/// argument is handled internally and will deliver the optimum
/// optimum resolution. The MJD method and the date & time methods
/// are both good compromises between resolution and convenience.
/// The two dates may be expressed using different methods, but at
/// the risk of losing some resolution.
///
/// 2) The accumulated precession angles zeta, z, theta are expressed
/// through canonical polynomials which are valid only for a limited
/// time span. In addition, the IAU 1976 precession rate is known to
/// be imperfect. The absolute accuracy of the present formulation
/// is better than 0.1 arcsec from 1960AD to 2040AD, better than
/// 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
/// the whole of the period 500BC to 3000AD. The errors exceed
/// 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
/// outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
/// 8200AD.
///
/// 3) The three angles are returned in the conventional order, which
/// is not the same as the order of the corresponding Euler
/// rotations. The precession matrix is
/// R_3(-z) x R_2(+theta) x R_3(-zeta).
///
/// # Reference:
/// * Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations (6) & (7), p283.
///
/// This revision: 2021 May 11