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use obl06;
use crate;
/// Precession angles, IAU 2006, equinox based.
///
/// This function is part of the International Astronomical Union's
/// SOFA (Standards of Fundamental Astronomy) software collection.
///
/// Status: canonical models.
///
/// Given:
/// date1,date2 f64 TT as a 2-part Julian Date (Note 1)
///
/// Returned (see Note 2):
/// eps0 f64 epsilon_0
/// psia f64 psi_A
/// oma f64 omega_A
/// bpa f64 P_A
/// bqa f64 Q_A
/// pia f64 pi_A
/// bpia f64 Pi_A
/// epsa f64 obliquity epsilon_A
/// chia f64 chi_A
/// za f64 z_A
/// zetaa f64 zeta_A
/// thetaa f64 theta_A
/// pa f64 p_A
/// gam f64 F-W angle gamma_J2000
/// phi f64 F-W angle phi_J2000
/// psi f64 F-W angle psi_J2000
///
/// 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:
///
/// ```text
/// 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) This function returns the set of equinox based angles for the
/// Capitaine et al. "P03" precession theory, adopted by the IAU in
/// 2006. The angles are set out in Table 1 of Hilton et al. (2006):
///
/// eps0 epsilon_0 obliquity at J2000.0
/// psia psi_A luni-solar precession
/// oma omega_A inclination of equator wrt J2000.0 ecliptic
/// bpa P_A ecliptic pole x, J2000.0 ecliptic triad
/// bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
/// pia pi_A angle between moving and J2000.0 ecliptics
/// bpia Pi_A longitude of ascending node of the ecliptic
/// epsa epsilon_A obliquity of the ecliptic
/// chia chi_A planetary precession
/// za z_A equatorial precession: -3rd 323 Euler angle
/// zetaa zeta_A equatorial precession: -1st 323 Euler angle
/// thetaa theta_A equatorial precession: 2nd 323 Euler angle
/// pa p_A general precession (n.b. see below)
/// gam gamma_J2000 J2000.0 RA difference of ecliptic poles
/// phi phi_J2000 J2000.0 codeclination of ecliptic pole
/// psi psi_J2000 longitude difference of equator poles, J2000.0
///
/// The returned values are all radians.
///
/// Note that the t^5 coefficient in the series for p_A from
/// Capitaine et al. (2003) is incorrectly signed in Hilton et al.
/// (2006).
///
/// 3) Hilton et al. (2006) Table 1 also contains angles that depend on
/// models distinct from the P03 precession theory itself, namely the
/// IAU 2000A frame bias and nutation. The quoted polynomials are
/// used in other SOFA functions:
///
/// . iauXy06 contains the polynomial parts of the X and Y series.
///
/// . iauS06 contains the polynomial part of the s+XY/2 series.
///
/// . iauPfw06 implements the series for the Fukushima-Williams
/// angles that are with respect to the GCRS pole (i.e. the variants
/// that include frame bias).
///
/// 4) The IAU resolution stipulated that the choice of parameterization
/// was left to the user, and so an IAU compliant precession
/// implementation can be constructed using various combinations of
/// the angles returned by the present function.
///
/// 5) The parameterization used by SOFA is the version of the Fukushima-
/// Williams angles that refers directly to the GCRS pole. These
/// angles may be calculated by calling the function iauPfw06. SOFA
/// also supports the direct computation of the CIP GCRS X,Y by
/// series, available by calling iauXy06.
///
/// 6) The agreement between the different parameterizations is at the
/// 1 microarcsecond level in the present era.
///
/// 7) When constructing a precession formulation that refers to the GCRS
/// pole rather than the dynamical pole, it may (depending on the
/// choice of angles) be necessary to introduce the frame bias
/// explicitly.
///
/// References:
///
/// Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
/// Astron.Astrophys., 412, 567
///
/// Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351