#include "sofa.h"
#include "sofam.h"

void iauPrec76(double date01, double date02, double date11, double date12,
               double *zeta, double *z, double *theta)
/*
**  - - - - - - - - - -
**   i a u P r e c 7 6
**  - - - - - - - - - -
**
**  IAU 1976 precession model.
**
**  This function forms the three Euler angles which implement general
**  precession between two dates, using the IAU 1976 model (as for the
**  FK5 catalog).
**
**  This function is part of the International Astronomical Union's
**  SOFA (Standards of Fundamental Astronomy) software collection.
**
**  Status:  canonical model.
**
**  Given:
**     date01,date02   double    TDB starting date (Note 1)
**     date11,date12   double    TDB ending date (Note 1)
**
**  Returned:
**     zeta            double    1st rotation: radians cw around z
**     z               double    3rd rotation: radians cw around z
**     theta           double    2nd rotation: radians ccw around y
**
**  Notes:
**
**  1) The dates date01+date02 and date11+date12 are Julian Dates,
**     apportioned in any convenient way between the arguments daten1
**     and daten2.  For example, JD(TDB)=2450123.7 could be expressed in
**     any of these ways, among others:
**
**           daten1        daten2
**
**         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
**     optimum resolution.  The MJD method and the date & time methods
**     are both good compromises between resolution and convenience.
**     The two dates may be expressed using different methods, but at
**     the risk of losing some resolution.
**
**  2) The accumulated precession angles zeta, z, theta are expressed
**     through canonical polynomials which are valid only for a limited
**     time span.  In addition, the IAU 1976 precession rate is known to
**     be imperfect.  The absolute accuracy of the present formulation
**     is better than 0.1 arcsec from 1960AD to 2040AD, better than
**     1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
**     the whole of the period 500BC to 3000AD.  The errors exceed
**     10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
**     outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
**     8200AD.
**
**  3) The three angles are returned in the conventional order, which
**     is not the same as the order of the corresponding Euler
**     rotations.  The precession matrix is
**     R_3(-z) x R_2(+theta) x R_3(-zeta).
**
**  Reference:
**
**     Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
**     (6) & (7), p283.
**
**  This revision:  2021 May 11
**
**  SOFA release 2023-10-11
**
**  Copyright (C) 2023 IAU SOFA Board.  See notes at end.
*/
{
   double t0, t, tas2r, w;


/* Interval between fundamental epoch J2000.0 and start date (JC). */
   t0 = ((date01 - DJ00) + date02) / DJC;

/* Interval over which precession required (JC). */
   t = ((date11 - date01) + (date12 - date02)) / DJC;

/* Euler angles. */
   tas2r = t * DAS2R;
   w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;

   *zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;

   *z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;

   *theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
          + ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2023
**  Standards of Fundamental Astronomy Board
**  of the International Astronomical Union.
**
**  =====================
**  SOFA Software License
**  =====================
**
**  NOTICE TO USER:
**
**  BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
**  CONDITIONS WHICH APPLY TO ITS USE.
**
**  1. The Software is owned by the IAU SOFA Board ("SOFA").
**
**  2. Permission is granted to anyone to use the SOFA software for any
**     purpose, including commercial applications, free of charge and
**     without payment of royalties, subject to the conditions and
**     restrictions listed below.
**
**  3. You (the user) may copy and distribute SOFA source code to others,
**     and use and adapt its code and algorithms in your own software,
**     on a world-wide, royalty-free basis.  That portion of your
**     distribution that does not consist of intact and unchanged copies
**     of SOFA source code files is a "derived work" that must comply
**     with the following requirements:
**
**     a) Your work shall be marked or carry a statement that it
**        (i) uses routines and computations derived by you from
**        software provided by SOFA under license to you; and
**        (ii) does not itself constitute software provided by and/or
**        endorsed by SOFA.
**
**     b) The source code of your derived work must contain descriptions
**        of how the derived work is based upon, contains and/or differs
**        from the original SOFA software.
**
**     c) The names of all routines in your derived work shall not
**        include the prefix "iau" or "sofa" or trivial modifications
**        thereof such as changes of case.
**
**     d) The origin of the SOFA components of your derived work must
**        not be misrepresented;  you must not claim that you wrote the
**        original software, nor file a patent application for SOFA
**        software or algorithms embedded in the SOFA software.
**
**     e) These requirements must be reproduced intact in any source
**        distribution and shall apply to anyone to whom you have
**        granted a further right to modify the source code of your
**        derived work.
**
**     Note that, as originally distributed, the SOFA software is
**     intended to be a definitive implementation of the IAU standards,
**     and consequently third-party modifications are discouraged.  All
**     variations, no matter how minor, must be explicitly marked as
**     such, as explained above.
**
**  4. You shall not cause the SOFA software to be brought into
**     disrepute, either by misuse, or use for inappropriate tasks, or
**     by inappropriate modification.
**
**  5. The SOFA software is provided "as is" and SOFA makes no warranty
**     as to its use or performance.   SOFA does not and cannot warrant
**     the performance or results which the user may obtain by using the
**     SOFA software.  SOFA makes no warranties, express or implied, as
**     to non-infringement of third party rights, merchantability, or
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**     claim by any third party.
**
**  6. The provision of any version of the SOFA software under the terms
**     and conditions specified herein does not imply that future
**     versions will also be made available under the same terms and
**     conditions.
*
**  In any published work or commercial product which uses the SOFA
**  software directly, acknowledgement (see www.iausofa.org) is
**  appreciated.
**
**  Correspondence concerning SOFA software should be addressed as
**  follows:
**
**      By email:  sofa@ukho.gov.uk
**      By post:   IAU SOFA Center
**                 HM Nautical Almanac Office
**                 UK Hydrographic Office
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**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}
