sofars 0.6.0

Pure Rust implementation of the IAU SOFA library
Documentation 
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use super::era00;
use crate::pnp::{bpn2xy, eors, s06};
use crate::vm::anp;

///  Greenwich apparent ST, IAU 2006, given NPB matrix
///
///  Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.
///
///  This function is part of the International Astronomical Union's
///  SOFA (Standards of Fundamental Astronomy) software collection.
///
///  Status:  support function.
///
///  Given:
///  ```
///     uta,utb  double        UT1 as a 2-part Julian Date (Notes 1,2)
///     tta,ttb  double        TT as a 2-part Julian Date (Notes 1,2)
///     rnpb     double[3][3]  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:
///  ```
///     iauBpn2xy    extract CIP X,Y coordinates from NPB matrix
///     iauS06       the CIO locator s, given X,Y, IAU 2006
///     iauAnp       normalize angle into range 0 to 2pi
///     iauEra00     Earth rotation angle, IAU 2000
///     iauEors      equation of the origins, given NPB matrix and s
///  ```
///  Reference:
///
///     Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
///
pub fn gst06(uta: f64, utb: f64, tta: f64, ttb: f64, rnpb: &[[f64; 3]; 3]) -> f64 {
    let (x, y) = bpn2xy(rnpb);

    // The CIO locator, s.
    let s = s06(tta, ttb, x, y);

    // Greenwich apparent sidereal time.
    let era = era00(uta, utb);
    let eors = eors(rnpb, s);
    let gst = anp(era - eors);

    gst
}