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use crateanp;
use crate;
use *;
/// Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.
///
/// Given:
/// * uta,utb UT1 as a 2-part Julian Date (Notes 1,2)
/// * tta,ttb TT as a 2-part Julian Date (Notes 1,2)
/// * rnpb nutation x precession x bias matrix
///
/// Returned (function value):
/// double Greenwich apparent sidereal time (radians)
///
/// # Notes:
///
/// 1) The UT1 and TT dates uta+utb and tta+ttb respectively, are both
/// Julian Dates, apportioned in any convenient way between the
/// argument pairs. For example, JD(UT1)=2450123.7 could be
/// expressed in any of these ways, among others:
///
/// | uta | utb | |
/// |-------------|--------------|----------------------|
/// |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 (in the case of UT; the TT is not at all critical
/// in this respect). The J2000 and MJD methods are good compromises
/// between resolution and convenience. For UT, the date & time
/// method is best matched to the algorithm that is used by the Earth
/// rotation angle function, called internally: maximum precision is
/// delivered when the uta argument is for 0hrs UT1 on the day in
/// question and the utb argument lies in the range 0 to 1, or vice
/// versa.
///
/// 2) Both UT1 and TT are required, UT1 to predict the Earth rotation
/// and TT to predict the effects of precession-nutation. If UT1 is
/// used for both purposes, errors of order 100 microarcseconds
/// result.
///
/// 3) Although the function uses the IAU 2006 series for s+XY/2, it is
/// otherwise independent of the precession-nutation model and can in
/// practice be used with any equinox-based NPB matrix.
///
/// 4) The result is returned in the range 0 to 2pi.
///
/// # Called:
/// * bpn2xy extract CIP X,Y coordinates from NPB matrix
/// * s06 the CIO locator s, given X,Y, IAU 2006
/// * anp normalize angle into range 0 to 2pi
/// * era00 Earth rotation angle, IAU 2000
/// * eors equation of the origins, given NPB matrix and s
///
/// # Reference:
/// * Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
///
/// This revision: 2021 May 11