sofars 0.6.0

Pure Rust implementation of the IAU SOFA library
Documentation 
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use crate::consts::{DAS2R, DJ00, DJC};

///  Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
///
///  This function is part of the International Astronomical Union's
///  SOFA (Standards of Fundamental Astronomy) software collection.
///
///  Status:  canonical model.
///
///  Given:
///     date1,date2  double   TT as a 2-part Julian Date (Note 1)
///
///  Returned:
///     gamb         double   F-W angle gamma_bar (radians)
///     phib         double   F-W angle phi_bar (radians)
///     psib         double   F-W angle psi_bar (radians)
///     epsa         double   F-W angle epsilon_A (radians)
///
///  Notes:
///
///  1) The TT date date1+date2 is a Julian Date, apportioned in any
///     convenient way between the two arguments.  For example,
///     JD(TT)=2450123.7 could be expressed in any of these ways,
///     among others:
///
///            date1          date2
///
///         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 resolution.  The MJD method and the date & time methods
///     are both good compromises between resolution and convenience.
///
///  2) Naming the following points:
///
///           e = J2000.0 ecliptic pole,
///           p = GCRS pole,
///           E = mean ecliptic pole of date,
///     and   P = mean pole of date,
///
///     the four Fukushima-Williams angles are as follows:
///
///        gamb = gamma_bar = epE
///        phib = phi_bar = pE
///        psib = psi_bar = pEP
///        epsa = epsilon_A = EP
///
///  3) The matrix representing the combined effects of frame bias and
///     precession is:
///
///        PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)
///
///  4) The matrix representing the combined effects of frame bias,
///     precession and nutation is simply:
///
///        NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)
///
///     where dP and dE are the nutation components with respect to the
///     ecliptic of date.
///
///  Reference:
///
///     Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
///
///  Called:
///     iauObl06     mean obliquity, IAU 2006
pub fn pfw06(date1: f64, date2: f64) -> (f64, f64, f64, f64) {
    let t;

    /* Interval between fundamental date J2000.0 and given date (JC). */
    t = ((date1 - DJ00) + date2) / DJC;

    /* P03 bias+precession angles. */
    let gamb = (-0.052928
        + (10.556378
            + (0.4932044 + (-0.00031238 + (-0.000002788 + (0.0000000260) * t) * t) * t) * t)
            * t)
        * DAS2R;

    let phib = (84381.412819
        + (-46.811016
            + (0.0511268 + (0.00053289 + (-0.000000440 + (-0.0000000176) * t) * t) * t) * t)
            * t)
        * DAS2R;

    let psib = (-0.041775
        + (5038.481484
            + (1.5584175 + (-0.00018522 + (-0.000026452 + (-0.0000000148) * t) * t) * t) * t)
            * t)
        * DAS2R;

    let epsa = super::obl06(date1, date2);

    (gamb, phib, psib, epsa)
}