rfa 0.5.9

A port ERFA to Rust.
Documentation 
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use crate::{rfam::*, utils::*,};
use crate::fundamental_args::{fal03::*, falp03::*, fapa03::*, faf03::*, fad03::*, faom03::*, fave03::*, fae03::*};
///  Equation of the equinoxes complementary terms, consistent with
///  IAU 2000 resolutions.
///
///  Given:
///   * date1,date2 TT as a 2-part Julian Date (Note 1)
///
///  Returned (function value):
///   * complementary terms (Note 2)
///
/// # 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) The "complementary terms" are part of the equation of the
///     equinoxes (EE), classically the difference between apparent and
///     mean Sidereal Time:
///
///        GAST = GMST + EE
///
///     with:
///
///        EE = dpsi * cos(eps)
///
///     where dpsi is the nutation in longitude and eps is the obliquity
///     of date.  However, if the rotation of the Earth were constant in
///     an inertial frame the classical formulation would lead to
///     apparent irregularities in the UT1 timescale traceable to side-
///     effects of precession-nutation.  In order to eliminate these
///     effects from UT1, "complementary terms" were introduced in 1994
///     (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
///     1993):
///
///        GAST = GMST + CT + EE
///
///     By convention, the complementary terms are included as part of
///     the equation of the equinoxes rather than as part of the mean
///     Sidereal Time.  This slightly compromises the "geometrical"
///     interpretation of mean sidereal time but is otherwise
///     inconsequential.
///
///     The present function computes CT in the above expression,
///     compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
///     IERS Conventions 2003).
///
///  Called:
///   * fal03     mean anomaly of the Moon
///   * falp03    mean anomaly of the Sun
///   * faf03     mean argument of the latitude of the Moon
///   * fad03     mean elongation of the Moon from the Sun
///   * faom03    mean longitude of the Moon's ascending node
///   * fave03    mean longitude of Venus
///   * fae03     mean longitude of Earth
///   * fapa03    general accumulated precession in longitude
///
///  References:
///   * Capitaine, N. & Gontier, A.-M., Astron.Astrophys., 275,
///     645-650 (1993)
///   * Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
///     implement the IAU 2000 definition of UT1", Astron.Astrophys., 406,
///     1135-1149 (2003)
///   * IAU Resolution C7, Recommendation 3 (1994)
///   * McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
///     IERS Technical Note No. 32, BKG (2004)
///
///  This revision:  2021 May 11
pub fn eect00(date1: f64, date2: f64)->f64
{
    /* Fundamental arguments */
        let mut fa = [0.0; 14];

    /* ----------------------------------------- */
    /* The series for the EE complementary terms */
    /* ----------------------------------------- */

        struct TERM {
            nfa: [i32; 8],      /* coefficients of l,l',F,D,Om,LVe,LE,pA */
            s: f64, c: f64,     /* sine and cosine coefficients */
        } 
        impl TERM {
            pub const fn new (nfa: [i32; 8], s: f64, c: f64,)->Self{
                TERM { nfa: nfa, s: s, c: c }    
            }
        } 

    /* Terms of order t^0 */
        const E0: [TERM; 33] = [

        /* 1-10 */
TERM::new([ 0,  0,  0,  0,  1,  0,  0,  0], 2640.96e-6, -0.39e-6 ),
TERM::new([ 0,  0,  0,  0,  2,  0,  0,  0],  63.52e-6, -0.02e-6 ),
TERM::new([ 0,  0,  2, -2,  3,  0,  0,  0],  11.75e-6,  0.01e-6 ),
TERM::new([ 0,  0,  2, -2,  1,  0,  0,  0],  11.21e-6,  0.01e-6 ),
TERM::new([ 0,  0,  2, -2,  2,  0,  0,  0],  -4.55e-6,  0.00e-6 ),
TERM::new([ 0,  0,  2,  0,  3,  0,  0,  0],   2.02e-6,  0.00e-6 ),
TERM::new([ 0,  0,  2,  0,  1,  0,  0,  0],   1.98e-6,  0.00e-6 ),
TERM::new([ 0,  0,  0,  0,  3,  0,  0,  0],  -1.72e-6,  0.00e-6 ),
TERM::new([ 0,  1,  0,  0,  1,  0,  0,  0],  -1.41e-6, -0.01e-6 ),
TERM::new([ 0,  1,  0,  0, -1,  0,  0,  0],  -1.26e-6, -0.01e-6 ),

        /* 11-20 */
TERM::new([ 1,  0,  0,  0, -1,  0,  0,  0],  -0.63e-6,  0.00e-6 ),
TERM::new([ 1,  0,  0,  0,  1,  0,  0,  0],  -0.63e-6,  0.00e-6 ),
TERM::new([ 0,  1,  2, -2,  3,  0,  0,  0],   0.46e-6,  0.00e-6 ),
TERM::new([ 0,  1,  2, -2,  1,  0,  0,  0],   0.45e-6,  0.00e-6 ),
TERM::new([ 0,  0,  4, -4,  4,  0,  0,  0],   0.36e-6,  0.00e-6 ),
TERM::new([ 0,  0,  1, -1,  1, -8, 12,  0],  -0.24e-6, -0.12e-6 ),
TERM::new([ 0,  0,  2,  0,  0,  0,  0,  0],   0.32e-6,  0.00e-6 ),
TERM::new([ 0,  0,  2,  0,  2,  0,  0,  0],   0.28e-6,  0.00e-6 ),
TERM::new([ 1,  0,  2,  0,  3,  0,  0,  0],   0.27e-6,  0.00e-6 ),
TERM::new([ 1,  0,  2,  0,  1,  0,  0,  0],   0.26e-6,  0.00e-6 ),

        /* 21-30 */
TERM::new([ 0,  0,  2, -2,  0,  0,  0,  0],  -0.21e-6,  0.00e-6 ),
TERM::new([ 0,  1, -2,  2, -3,  0,  0,  0],   0.19e-6,  0.00e-6 ),
TERM::new([ 0,  1, -2,  2, -1,  0,  0,  0],   0.18e-6,  0.00e-6 ),
TERM::new([ 0,  0,  0,  0,  0,  8,-13, -1],  -0.10e-6,  0.05e-6 ),
TERM::new([ 0,  0,  0,  2,  0,  0,  0,  0],   0.15e-6,  0.00e-6 ),
TERM::new([ 2,  0, -2,  0, -1,  0,  0,  0],  -0.14e-6,  0.00e-6 ),
TERM::new([ 1,  0,  0, -2,  1,  0,  0,  0],   0.14e-6,  0.00e-6 ),
TERM::new([ 0,  1,  2, -2,  2,  0,  0,  0],  -0.14e-6,  0.00e-6 ),
TERM::new([ 1,  0,  0, -2, -1,  0,  0,  0],   0.14e-6,  0.00e-6 ),
TERM::new([ 0,  0,  4, -2,  4,  0,  0,  0],   0.13e-6,  0.00e-6 ),

        /* 31-33 */
TERM::new([ 0,  0,  2, -2,  4,  0,  0,  0],  -0.11e-6,  0.00e-6 ),
TERM::new([ 1,  0, -2,  0, -3,  0,  0,  0],   0.11e-6,  0.00e-6 ),
TERM::new([ 1,  0, -2,  0, -1,  0,  0,  0],   0.11e-6,  0.00e-6 )
        ];

    /* Terms of order t^1 */
        const  E1: [TERM; 1] = [
TERM::new([ 0,  0,  0,  0,  1,  0,  0,  0],   -0.87e-6,  0.00e-6 )
        ];

    /* ------------------------------------------------------------------ */

    /* Interval between fundamental epoch J2000.0 and current date (JC). */
        let t = ((date1 - URSA_DJ00) + date2) / URSA_DJC;

    /* Fundamental Arguments (from IERS Conventions 2003) */

    /* Mean anomaly of the Moon. */
        fa[0] = fal03(t);

    /* Mean anomaly of the Sun. */
        fa[1] = falp03(t);

    /* Mean longitude of the Moon minus that of the ascending node. */
        fa[2] = faf03(t);

    /* Mean elongation of the Moon from the Sun. */
        fa[3] = fad03(t);

    /* Mean longitude of the ascending node of the Moon. */
        fa[4] = faom03(t);

    /* Mean longitude of Venus. */
        fa[5] = fave03(t);

    /* Mean longitude of Earth. */
        fa[6] = fae03(t);

    /* General precession in longitude. */
        fa[7] = fapa03(t);

    /* Evaluate the EE complementary terms. */
        let mut s0 = 0.0;
        let mut s1 = 0.0;

        for e0_i in E0.iter() {
            let mut a = 0.0;
            for j in 0..8 {
                a += (e0_i.nfa[j]) as f64 * fa[j];
            }
            s0 += e0_i.s * sin(a) + e0_i.c * cos(a);
        }

        for e1_i in E1.iter() {
            let mut a = 0.0;
            for j in 0..8 {
                a += (e1_i.nfa[j]) as f64 * fa[j];
            }
            s1 += e1_i.s * sin(a) + e1_i.c * cos(a);
        }

        (s0 + s1 * t ) * URSA_DAS2R


    /* Finished. */
    
}