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

double iauEect00(double date1, double date2)
/*
**  - - - - - - - - - -
**   i a u E e c t 0 0
**  - - - - - - - - - -
**
**  Equation of the equinoxes complementary terms, consistent with
**  IAU 2000 resolutions.
**
**  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 (function value):
**                  double   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:
**     iauFal03     mean anomaly of the Moon
**     iauFalp03    mean anomaly of the Sun
**     iauFaf03     mean argument of the latitude of the Moon
**     iauFad03     mean elongation of the Moon from the Sun
**     iauFaom03    mean longitude of the Moon's ascending node
**     iauFave03    mean longitude of Venus
**     iauFae03     mean longitude of Earth
**     iauFapa03    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
**
**  SOFA release 2023-10-11
**
**  Copyright (C) 2023 IAU SOFA Board.  See notes at end.
*/
{
/* Time since J2000.0, in Julian centuries */
   double t;

/* Miscellaneous */
   int i, j;
   double a, s0, s1;

/* Fundamental arguments */
   double fa[14];

/* Returned value. */
   double eect;

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

   typedef struct {
      int nfa[8];      /* coefficients of l,l',F,D,Om,LVe,LE,pA */
      double s, c;     /* sine and cosine coefficients */
   } TERM;

/* Terms of order t^0 */
   static const TERM e0[] = {

   /* 1-10 */
      {{ 0,  0,  0,  0,  1,  0,  0,  0}, 2640.96e-6, -0.39e-6 },
      {{ 0,  0,  0,  0,  2,  0,  0,  0},   63.52e-6, -0.02e-6 },
      {{ 0,  0,  2, -2,  3,  0,  0,  0},   11.75e-6,  0.01e-6 },
      {{ 0,  0,  2, -2,  1,  0,  0,  0},   11.21e-6,  0.01e-6 },
      {{ 0,  0,  2, -2,  2,  0,  0,  0},   -4.55e-6,  0.00e-6 },
      {{ 0,  0,  2,  0,  3,  0,  0,  0},    2.02e-6,  0.00e-6 },
      {{ 0,  0,  2,  0,  1,  0,  0,  0},    1.98e-6,  0.00e-6 },
      {{ 0,  0,  0,  0,  3,  0,  0,  0},   -1.72e-6,  0.00e-6 },
      {{ 0,  1,  0,  0,  1,  0,  0,  0},   -1.41e-6, -0.01e-6 },
      {{ 0,  1,  0,  0, -1,  0,  0,  0},   -1.26e-6, -0.01e-6 },

   /* 11-20 */
      {{ 1,  0,  0,  0, -1,  0,  0,  0},   -0.63e-6,  0.00e-6 },
      {{ 1,  0,  0,  0,  1,  0,  0,  0},   -0.63e-6,  0.00e-6 },
      {{ 0,  1,  2, -2,  3,  0,  0,  0},    0.46e-6,  0.00e-6 },
      {{ 0,  1,  2, -2,  1,  0,  0,  0},    0.45e-6,  0.00e-6 },
      {{ 0,  0,  4, -4,  4,  0,  0,  0},    0.36e-6,  0.00e-6 },
      {{ 0,  0,  1, -1,  1, -8, 12,  0},   -0.24e-6, -0.12e-6 },
      {{ 0,  0,  2,  0,  0,  0,  0,  0},    0.32e-6,  0.00e-6 },
      {{ 0,  0,  2,  0,  2,  0,  0,  0},    0.28e-6,  0.00e-6 },
      {{ 1,  0,  2,  0,  3,  0,  0,  0},    0.27e-6,  0.00e-6 },
      {{ 1,  0,  2,  0,  1,  0,  0,  0},    0.26e-6,  0.00e-6 },

   /* 21-30 */
      {{ 0,  0,  2, -2,  0,  0,  0,  0},   -0.21e-6,  0.00e-6 },
      {{ 0,  1, -2,  2, -3,  0,  0,  0},    0.19e-6,  0.00e-6 },
      {{ 0,  1, -2,  2, -1,  0,  0,  0},    0.18e-6,  0.00e-6 },
      {{ 0,  0,  0,  0,  0,  8,-13, -1},   -0.10e-6,  0.05e-6 },
      {{ 0,  0,  0,  2,  0,  0,  0,  0},    0.15e-6,  0.00e-6 },
      {{ 2,  0, -2,  0, -1,  0,  0,  0},   -0.14e-6,  0.00e-6 },
      {{ 1,  0,  0, -2,  1,  0,  0,  0},    0.14e-6,  0.00e-6 },
      {{ 0,  1,  2, -2,  2,  0,  0,  0},   -0.14e-6,  0.00e-6 },
      {{ 1,  0,  0, -2, -1,  0,  0,  0},    0.14e-6,  0.00e-6 },
      {{ 0,  0,  4, -2,  4,  0,  0,  0},    0.13e-6,  0.00e-6 },

   /* 31-33 */
      {{ 0,  0,  2, -2,  4,  0,  0,  0},   -0.11e-6,  0.00e-6 },
      {{ 1,  0, -2,  0, -3,  0,  0,  0},    0.11e-6,  0.00e-6 },
      {{ 1,  0, -2,  0, -1,  0,  0,  0},    0.11e-6,  0.00e-6 }
   };

/* Terms of order t^1 */
   static const TERM e1[] = {
      {{ 0,  0,  0,  0,  1,  0,  0,  0},    -0.87e-6,  0.00e-6 }
   };

/* Number of terms in the series */
   const int NE0 = (int) (sizeof e0 / sizeof (TERM));
   const int NE1 = (int) (sizeof e1 / sizeof (TERM));

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

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

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

/* Mean anomaly of the Moon. */
   fa[0] = iauFal03(t);

/* Mean anomaly of the Sun. */
   fa[1] = iauFalp03(t);

/* Mean longitude of the Moon minus that of the ascending node. */
   fa[2] = iauFaf03(t);

/* Mean elongation of the Moon from the Sun. */
   fa[3] = iauFad03(t);

/* Mean longitude of the ascending node of the Moon. */
   fa[4] = iauFaom03(t);

/* Mean longitude of Venus. */
   fa[5] = iauFave03(t);

/* Mean longitude of Earth. */
   fa[6] = iauFae03(t);

/* General precession in longitude. */
   fa[7] = iauFapa03(t);

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

   for (i = NE0-1; i >= 0; i--) {
      a = 0.0;
      for (j = 0; j < 8; j++) {
         a += (double)(e0[i].nfa[j]) * fa[j];
      }
      s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
   }

   for (i = NE1-1; i >= 0; i--) {
      a = 0.0;
      for (j = 0; j < 8; j++) {
         a += (double)(e1[i].nfa[j]) * fa[j];
      }
      s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
   }

   eect = (s0 + s1 * t ) * DAS2R;

   return eect;

/* 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
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**     SOFA software.  SOFA makes no warranties, express or implied, as
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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
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*
**  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
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**
**--------------------------------------------------------------------*/
}
