#include "erfa.h"

void eraLtpequ(double epj, double veq[3])
/*
**  - - - - - - - - - -
**   e r a L t p e q u
**  - - - - - - - - - -
**
**  Long-term precession of the equator.
**
**  Given:
**     epj     double         Julian epoch (TT)
**
**  Returned:
**     veq     double[3]      equator pole unit vector
**
**  Notes:
**
**  1) The returned vector is with respect to the J2000.0 mean equator
**     and equinox.
**
**  2) The Vondrak et al. (2011, 2012) 400 millennia precession model
**     agrees with the IAU 2006 precession at J2000.0 and stays within
**     100 microarcseconds during the 20th and 21st centuries.  It is
**     accurate to a few arcseconds throughout the historical period,
**     worsening to a few tenths of a degree at the end of the
**     +/- 200,000 year time span.
**
**  References:
**
**    Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
**    expressions, valid for long time intervals, Astron.Astrophys. 534,
**    A22
**
**    Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
**    expressions, valid for long time intervals (Corrigendum),
**    Astron.Astrophys. 541, C1
**
**  Copyright (C) 2013-2020, NumFOCUS Foundation.
**  Derived, with permission, from the SOFA library.  See notes at end of file.
*/
{
/* Polynomial coefficients */
   enum { NPOL = 4 };
   static const double xypol[2][NPOL] = {
      {  5453.282155,
            0.4252841,
           -0.00037173,
           -0.000000152},
      {-73750.930350,
           -0.7675452,
           -0.00018725,
            0.000000231}
   };

/* Periodic coefficients */
   static const double xyper[][5] = {
      { 256.75, -819.940624,75004.344875,81491.287984, 1558.515853},
      { 708.15,-8444.676815,  624.033993,  787.163481, 7774.939698},
      { 274.20, 2600.009459, 1251.136893, 1251.296102,-2219.534038},
      { 241.45, 2755.175630,-1102.212834,-1257.950837,-2523.969396},
      {2309.00, -167.659835,-2660.664980,-2966.799730,  247.850422},
      { 492.20,  871.855056,  699.291817,  639.744522, -846.485643},
      { 396.10,   44.769698,  153.167220,  131.600209,-1393.124055},
      { 288.90, -512.313065, -950.865637, -445.040117,  368.526116},
      { 231.10, -819.415595,  499.754645,  584.522874,  749.045012},
      {1610.00, -538.071099, -145.188210,  -89.756563,  444.704518},
      { 620.00, -189.793622,  558.116553,  524.429630,  235.934465},
      { 157.87, -402.922932,  -23.923029,  -13.549067,  374.049623},
      { 220.30,  179.516345, -165.405086, -210.157124, -171.330180},
      {1200.00,   -9.814756,    9.344131,  -44.919798,  -22.899655}
   };
   static const int NPER = (int) ( sizeof xyper / 5 / sizeof (double) );

/* Miscellaneous */
   int i;
   double t, x, y, w, a, s, c;


/* Centuries since J2000. */
   t  = ( epj - 2000.0 ) / 100.0;

/* Initialize X and Y accumulators. */
   x = 0.0;
   y = 0.0;

/* Periodic terms. */
   w = ERFA_D2PI * t;
   for ( i = 0; i < NPER; i++ ) {
      a = w / xyper[i][0];
      s = sin(a);
      c = cos(a);
      x += c*xyper[i][1] + s*xyper[i][3];
      y += c*xyper[i][2] + s*xyper[i][4];
   }

/* Polynomial terms. */
   w = 1.0;
   for ( i = 0; i < NPOL; i++ ) {
      x += xypol[0][i]*w;
      y += xypol[1][i]*w;
      w *= t;
   }

/* X and Y (direction cosines). */
   x *= ERFA_DAS2R;
   y *= ERFA_DAS2R;

/* Form the equator pole vector. */
   veq[0] = x;
   veq[1] = y;
   w = 1.0 - x*x - y*y;
   veq[2] = w < 0.0 ? 0.0 : sqrt(w);

}
/*----------------------------------------------------------------------
**  
**  
**  Copyright (C) 2013-2020, NumFOCUS Foundation.
**  All rights reserved.
**  
**  This library is derived, with permission, from the International
**  Astronomical Union's "Standards of Fundamental Astronomy" library,
**  available from http://www.iausofa.org.
**  
**  The ERFA version is intended to retain identical functionality to
**  the SOFA library, but made distinct through different function and
**  file names, as set out in the SOFA license conditions.  The SOFA
**  original has a role as a reference standard for the IAU and IERS,
**  and consequently redistribution is permitted only in its unaltered
**  state.  The ERFA version is not subject to this restriction and
**  therefore can be included in distributions which do not support the
**  concept of "read only" software.
**  
**  Although the intent is to replicate the SOFA API (other than
**  replacement of prefix names) and results (with the exception of
**  bugs;  any that are discovered will be fixed), SOFA is not
**  responsible for any errors found in this version of the library.
**  
**  If you wish to acknowledge the SOFA heritage, please acknowledge
**  that you are using a library derived from SOFA, rather than SOFA
**  itself.
**  
**  
**  TERMS AND CONDITIONS
**  
**  Redistribution and use in source and binary forms, with or without
**  modification, are permitted provided that the following conditions
**  are met:
**  
**  1 Redistributions of source code must retain the above copyright
**    notice, this list of conditions and the following disclaimer.
**  
**  2 Redistributions in binary form must reproduce the above copyright
**    notice, this list of conditions and the following disclaimer in
**    the documentation and/or other materials provided with the
**    distribution.
**  
**  3 Neither the name of the Standards Of Fundamental Astronomy Board,
**    the International Astronomical Union nor the names of its
**    contributors may be used to endorse or promote products derived
**    from this software without specific prior written permission.
**  
**  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
**  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
**  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
**  FOR A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE
**  COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
**  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
**  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
**  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
**  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
**  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
**  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
**  POSSIBILITY OF SUCH DAMAGE.
**  
*/
