text: #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) 2013-2016, 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) 2013-2016, 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.
  **  
  */
  