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nutation.cpp
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nutation.cpp
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/*
As part of the ccal program by Zhuo Meng, this version is
distributed under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2 of the
License, or (at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
The whole package can be obtained from
http://aa.usno.navy.mil/software/novas/novas_c/novasc_info.php
Adapted from:
Naval Observatory Vector Astrometry Software (NOVAS)
C Edition, Version 3.1
nutation.c: Nutation models
U. S. Naval Observatory
Astronomical Applications Dept.
Washington, DC
http://www.usno.navy.mil/USNO/astronomical-applications
*/
#ifndef _NOVAS_
#include "novas.h"
#endif
/********iau2000a */
void iau2000a (double jd_high, double jd_low,
double *dpsi, double *deps)
/*
------------------------------------------------------------------------
PURPOSE:
To compute the forced nutation of the non-rigid Earth based on
the IAU 2000A nutation model.
REFERENCES:
IERS Conventions (2003), Chapter 5.
Simon et al. (1994) Astronomy and Astrophysics 282, 663-683,
esp. Sections 3.4-3.5.
INPUT
ARGUMENTS:
jd_high (double)
High-order part of TT Julian date.
jd_low (double)
Low-order part of TT Julian date.
OUTPUT
ARGUMENTS:
*dpsi (double)
Nutation (luni-solar + planetary) in longitude, in radians.
*deps (double)
Nutation (luni-solar + planetary) in obliquity, in radians.
RETURNED
VALUE:
None.
GLOBALS
USED:
T0, ASEC2RAD, TWOPI
FUNCTIONS
CALLED:
fund_args novas.c
fmod math.h
sin math.h
cos math.h
VER./DATE/
PROGRAMMER:
V1.0/03-04/JAB (USNO/AA)
V1.1/12-10/JAB (USNO/AA): Implement static storage class for const
arrays.
V1.2/03-11/WKP (USNO/AA): Added braces to 2-D array initialization
to quiet gcc warnings.
NOTES:
1. The IAU 2000A nutation model is MHB_2000 without the free core
nutation and without the corrections to Lieske precession.
2. This function is the "C" version of NOVAS Fortran routine
'nu2000a'.
------------------------------------------------------------------------
*/
{
short int i;
double t, a[5], dp, de, arg, sarg, carg, factor, dpsils, depsls,
al, alsu, af, ad, aom, alme, alve, alea, alma, alju, alsa, alur,
alne, apa, dpsipl, depspl;
/*
Luni-Solar argument multipliers:
L L' F D Om
*/
static const short int nals_t[678][5] = {
{ 0, 0, 0, 0, 1},
{ 0, 0, 2, -2, 2},
{ 0, 0, 2, 0, 2},
{ 0, 0, 0, 0, 2},
{ 0, 1, 0, 0, 0},
{ 0, 1, 2, -2, 2},
{ 1, 0, 0, 0, 0},
{ 0, 0, 2, 0, 1},
{ 1, 0, 2, 0, 2},
{ 0, -1, 2, -2, 2},
{ 0, 0, 2, -2, 1},
{-1, 0, 2, 0, 2},
{-1, 0, 0, 2, 0},
{ 1, 0, 0, 0, 1},
{-1, 0, 0, 0, 1},
{-1, 0, 2, 2, 2},
{ 1, 0, 2, 0, 1},
{-2, 0, 2, 0, 1},
{ 0, 0, 0, 2, 0},
{ 0, 0, 2, 2, 2},
{ 0, -2, 2, -2, 2},
{-2, 0, 0, 2, 0},
{ 2, 0, 2, 0, 2},
{ 1, 0, 2, -2, 2},
{-1, 0, 2, 0, 1},
{ 2, 0, 0, 0, 0},
{ 0, 0, 2, 0, 0},
{ 0, 1, 0, 0, 1},
{-1, 0, 0, 2, 1},
{ 0, 2, 2, -2, 2},
{ 0, 0, -2, 2, 0},
{ 1, 0, 0, -2, 1},
{ 0, -1, 0, 0, 1},
{-1, 0, 2, 2, 1},
{ 0, 2, 0, 0, 0},
{ 1, 0, 2, 2, 2},
{-2, 0, 2, 0, 0},
{ 0, 1, 2, 0, 2},
{ 0, 0, 2, 2, 1},
{ 0, -1, 2, 0, 2},
{ 0, 0, 0, 2, 1},
{ 1, 0, 2, -2, 1},
{ 2, 0, 2, -2, 2},
{-2, 0, 0, 2, 1},
{ 2, 0, 2, 0, 1},
{ 0, -1, 2, -2, 1},
{ 0, 0, 0, -2, 1},
{-1, -1, 0, 2, 0},
{ 2, 0, 0, -2, 1},
{ 1, 0, 0, 2, 0},
{ 0, 1, 2, -2, 1},
{ 1, -1, 0, 0, 0},
{-2, 0, 2, 0, 2},
{ 3, 0, 2, 0, 2},
{ 0, -1, 0, 2, 0},
{ 1, -1, 2, 0, 2},
{ 0, 0, 0, 1, 0},
{-1, -1, 2, 2, 2},
{-1, 0, 2, 0, 0},
{ 0, -1, 2, 2, 2},
{-2, 0, 0, 0, 1},
{ 1, 1, 2, 0, 2},
{ 2, 0, 0, 0, 1},
{-1, 1, 0, 1, 0},
{ 1, 1, 0, 0, 0},
{ 1, 0, 2, 0, 0},
{-1, 0, 2, -2, 1},
{ 1, 0, 0, 0, 2},
{-1, 0, 0, 1, 0},
{ 0, 0, 2, 1, 2},
{-1, 0, 2, 4, 2},
{-1, 1, 0, 1, 1},
{ 0, -2, 2, -2, 1},
{ 1, 0, 2, 2, 1},
{-2, 0, 2, 2, 2},
{-1, 0, 0, 0, 2},
{ 1, 1, 2, -2, 2},
{-2, 0, 2, 4, 2},
{-1, 0, 4, 0, 2},
{ 2, 0, 2, -2, 1},
{ 2, 0, 2, 2, 2},
{ 1, 0, 0, 2, 1},
{ 3, 0, 0, 0, 0},
{ 3, 0, 2, -2, 2},
{ 0, 0, 4, -2, 2},
{ 0, 1, 2, 0, 1},
{ 0, 0, -2, 2, 1},
{ 0, 0, 2, -2, 3},
{-1, 0, 0, 4, 0},
{ 2, 0, -2, 0, 1},
{-2, 0, 0, 4, 0},
{-1, -1, 0, 2, 1},
{-1, 0, 0, 1, 1},
{ 0, 1, 0, 0, 2},
{ 0, 0, -2, 0, 1},
{ 0, -1, 2, 0, 1},
{ 0, 0, 2, -1, 2},
{ 0, 0, 2, 4, 2},
{-2, -1, 0, 2, 0},
{ 1, 1, 0, -2, 1},
{-1, 1, 0, 2, 0},
{-1, 1, 0, 1, 2},
{ 1, -1, 0, 0, 1},
{ 1, -1, 2, 2, 2},
{-1, 1, 2, 2, 2},
{ 3, 0, 2, 0, 1},
{ 0, 1, -2, 2, 0},
{-1, 0, 0, -2, 1},
{ 0, 1, 2, 2, 2},
{-1, -1, 2, 2, 1},
{ 0, -1, 0, 0, 2},
{ 1, 0, 2, -4, 1},
{-1, 0, -2, 2, 0},
{ 0, -1, 2, 2, 1},
{ 2, -1, 2, 0, 2},
{ 0, 0, 0, 2, 2},
{ 1, -1, 2, 0, 1},
{-1, 1, 2, 0, 2},
{ 0, 1, 0, 2, 0},
{ 0, -1, -2, 2, 0},
{ 0, 3, 2, -2, 2},
{ 0, 0, 0, 1, 1},
{-1, 0, 2, 2, 0},
{ 2, 1, 2, 0, 2},
{ 1, 1, 0, 0, 1},
{ 1, 1, 2, 0, 1},
{ 2, 0, 0, 2, 0},
{ 1, 0, -2, 2, 0},
{-1, 0, 0, 2, 2},
{ 0, 1, 0, 1, 0},
{ 0, 1, 0, -2, 1},
{-1, 0, 2, -2, 2},
{ 0, 0, 0, -1, 1},
{-1, 1, 0, 0, 1},
{ 1, 0, 2, -1, 2},
{ 1, -1, 0, 2, 0},
{ 0, 0, 0, 4, 0},
{ 1, 0, 2, 1, 2},
{ 0, 0, 2, 1, 1},
{ 1, 0, 0, -2, 2},
{-1, 0, 2, 4, 1},
{ 1, 0, -2, 0, 1},
{ 1, 1, 2, -2, 1},
{ 0, 0, 2, 2, 0},
{-1, 0, 2, -1, 1},
{-2, 0, 2, 2, 1},
{ 4, 0, 2, 0, 2},
{ 2, -1, 0, 0, 0},
{ 2, 1, 2, -2, 2},
{ 0, 1, 2, 1, 2},
{ 1, 0, 4, -2, 2},
{-1, -1, 0, 0, 1},
{ 0, 1, 0, 2, 1},
{-2, 0, 2, 4, 1},
{ 2, 0, 2, 0, 0},
{ 1, 0, 0, 1, 0},
{-1, 0, 0, 4, 1},
{-1, 0, 4, 0, 1},
{ 2, 0, 2, 2, 1},
{ 0, 0, 2, -3, 2},
{-1, -2, 0, 2, 0},
{ 2, 1, 0, 0, 0},
{ 0, 0, 4, 0, 2},
{ 0, 0, 0, 0, 3},
{ 0, 3, 0, 0, 0},
{ 0, 0, 2, -4, 1},
{ 0, -1, 0, 2, 1},
{ 0, 0, 0, 4, 1},
{-1, -1, 2, 4, 2},
{ 1, 0, 2, 4, 2},
{-2, 2, 0, 2, 0},
{-2, -1, 2, 0, 1},
{-2, 0, 0, 2, 2},
{-1, -1, 2, 0, 2},
{ 0, 0, 4, -2, 1},
{ 3, 0, 2, -2, 1},
{-2, -1, 0, 2, 1},
{ 1, 0, 0, -1, 1},
{ 0, -2, 0, 2, 0},
{-2, 0, 0, 4, 1},
{-3, 0, 0, 0, 1},
{ 1, 1, 2, 2, 2},
{ 0, 0, 2, 4, 1},
{ 3, 0, 2, 2, 2},
{-1, 1, 2, -2, 1},
{ 2, 0, 0, -4, 1},
{ 0, 0, 0, -2, 2},
{ 2, 0, 2, -4, 1},
{-1, 1, 0, 2, 1},
{ 0, 0, 2, -1, 1},
{ 0, -2, 2, 2, 2},
{ 2, 0, 0, 2, 1},
{ 4, 0, 2, -2, 2},
{ 2, 0, 0, -2, 2},
{ 0, 2, 0, 0, 1},
{ 1, 0, 0, -4, 1},
{ 0, 2, 2, -2, 1},
{-3, 0, 0, 4, 0},
{-1, 1, 2, 0, 1},
{-1, -1, 0, 4, 0},
{-1, -2, 2, 2, 2},
{-2, -1, 2, 4, 2},
{ 1, -1, 2, 2, 1},
{-2, 1, 0, 2, 0},
{-2, 1, 2, 0, 1},
{ 2, 1, 0, -2, 1},
{-3, 0, 2, 0, 1},
{-2, 0, 2, -2, 1},
{-1, 1, 0, 2, 2},
{ 0, -1, 2, -1, 2},
{-1, 0, 4, -2, 2},
{ 0, -2, 2, 0, 2},
{-1, 0, 2, 1, 2},
{ 2, 0, 0, 0, 2},
{ 0, 0, 2, 0, 3},
{-2, 0, 4, 0, 2},
{-1, 0, -2, 0, 1},
{-1, 1, 2, 2, 1},
{ 3, 0, 0, 0, 1},
{-1, 0, 2, 3, 2},
{ 2, -1, 2, 0, 1},
{ 0, 1, 2, 2, 1},
{ 0, -1, 2, 4, 2},
{ 2, -1, 2, 2, 2},
{ 0, 2, -2, 2, 0},
{-1, -1, 2, -1, 1},
{ 0, -2, 0, 0, 1},
{ 1, 0, 2, -4, 2},
{ 1, -1, 0, -2, 1},
{-1, -1, 2, 0, 1},
{ 1, -1, 2, -2, 2},
{-2, -1, 0, 4, 0},
{-1, 0, 0, 3, 0},
{-2, -1, 2, 2, 2},
{ 0, 2, 2, 0, 2},
{ 1, 1, 0, 2, 0},
{ 2, 0, 2, -1, 2},
{ 1, 0, 2, 1, 1},
{ 4, 0, 0, 0, 0},
{ 2, 1, 2, 0, 1},
{ 3, -1, 2, 0, 2},
{-2, 2, 0, 2, 1},
{ 1, 0, 2, -3, 1},
{ 1, 1, 2, -4, 1},
{-1, -1, 2, -2, 1},
{ 0, -1, 0, -1, 1},
{ 0, -1, 0, -2, 1},
{-2, 0, 0, 0, 2},
{-2, 0, -2, 2, 0},
{-1, 0, -2, 4, 0},
{ 1, -2, 0, 0, 0},
{ 0, 1, 0, 1, 1},
{-1, 2, 0, 2, 0},
{ 1, -1, 2, -2, 1},
{ 1, 2, 2, -2, 2},
{ 2, -1, 2, -2, 2},
{ 1, 0, 2, -1, 1},
{ 2, 1, 2, -2, 1},
{-2, 0, 0, -2, 1},
{ 1, -2, 2, 0, 2},
{ 0, 1, 2, 1, 1},
{ 1, 0, 4, -2, 1},
{-2, 0, 4, 2, 2},
{ 1, 1, 2, 1, 2},
{ 1, 0, 0, 4, 0},
{ 1, 0, 2, 2, 0},
{ 2, 0, 2, 1, 2},
{ 3, 1, 2, 0, 2},
{ 4, 0, 2, 0, 1},
{-2, -1, 2, 0, 0},
{ 0, 1, -2, 2, 1},
{ 1, 0, -2, 1, 0},
{ 0, -1, -2, 2, 1},
{ 2, -1, 0, -2, 1},
{-1, 0, 2, -1, 2},
{ 1, 0, 2, -3, 2},
{ 0, 1, 2, -2, 3},
{ 0, 0, 2, -3, 1},
{-1, 0, -2, 2, 1},
{ 0, 0, 2, -4, 2},
{-2, 1, 0, 0, 1},
{-1, 0, 0, -1, 1},
{ 2, 0, 2, -4, 2},
{ 0, 0, 4, -4, 4},
{ 0, 0, 4, -4, 2},
{-1, -2, 0, 2, 1},
{-2, 0, 0, 3, 0},
{ 1, 0, -2, 2, 1},
{-3, 0, 2, 2, 2},
{-3, 0, 2, 2, 1},
{-2, 0, 2, 2, 0},
{ 2, -1, 0, 0, 1},
{-2, 1, 2, 2, 2},
{ 1, 1, 0, 1, 0},
{ 0, 1, 4, -2, 2},
{-1, 1, 0, -2, 1},
{ 0, 0, 0, -4, 1},
{ 1, -1, 0, 2, 1},
{ 1, 1, 0, 2, 1},
{-1, 2, 2, 2, 2},
{ 3, 1, 2, -2, 2},
{ 0, -1, 0, 4, 0},
{ 2, -1, 0, 2, 0},
{ 0, 0, 4, 0, 1},
{ 2, 0, 4, -2, 2},
{-1, -1, 2, 4, 1},
{ 1, 0, 0, 4, 1},
{ 1, -2, 2, 2, 2},
{ 0, 0, 2, 3, 2},
{-1, 1, 2, 4, 2},
{ 3, 0, 0, 2, 0},
{-1, 0, 4, 2, 2},
{ 1, 1, 2, 2, 1},
{-2, 0, 2, 6, 2},
{ 2, 1, 2, 2, 2},
{-1, 0, 2, 6, 2},
{ 1, 0, 2, 4, 1},
{ 2, 0, 2, 4, 2},
{ 1, 1, -2, 1, 0},
{-3, 1, 2, 1, 2},
{ 2, 0, -2, 0, 2},
{-1, 0, 0, 1, 2},
{-4, 0, 2, 2, 1},
{-1, -1, 0, 1, 0},
{ 0, 0, -2, 2, 2},
{ 1, 0, 0, -1, 2},
{ 0, -1, 2, -2, 3},
{-2, 1, 2, 0, 0},
{ 0, 0, 2, -2, 4},
{-2, -2, 0, 2, 0},
{-2, 0, -2, 4, 0},
{ 0, -2, -2, 2, 0},
{ 1, 2, 0, -2, 1},
{ 3, 0, 0, -4, 1},
{-1, 1, 2, -2, 2},
{ 1, -1, 2, -4, 1},
{ 1, 1, 0, -2, 2},
{-3, 0, 2, 0, 0},
{-3, 0, 2, 0, 2},
{-2, 0, 0, 1, 0},
{ 0, 0, -2, 1, 0},
{-3, 0, 0, 2, 1},
{-1, -1, -2, 2, 0},
{ 0, 1, 2, -4, 1},
{ 2, 1, 0, -4, 1},
{ 0, 2, 0, -2, 1},
{ 1, 0, 0, -3, 1},
{-2, 0, 2, -2, 2},
{-2, -1, 0, 0, 1},
{-4, 0, 0, 2, 0},
{ 1, 1, 0, -4, 1},
{-1, 0, 2, -4, 1},
{ 0, 0, 4, -4, 1},
{ 0, 3, 2, -2, 2},
{-3, -1, 0, 4, 0},
{-3, 0, 0, 4, 1},
{ 1, -1, -2, 2, 0},
{-1, -1, 0, 2, 2},
{ 1, -2, 0, 0, 1},
{ 1, -1, 0, 0, 2},
{ 0, 0, 0, 1, 2},
{-1, -1, 2, 0, 0},
{ 1, -2, 2, -2, 2},
{ 0, -1, 2, -1, 1},
{-1, 0, 2, 0, 3},
{ 1, 1, 0, 0, 2},
{-1, 1, 2, 0, 0},
{ 1, 2, 0, 0, 0},
{-1, 2, 2, 0, 2},
{-1, 0, 4, -2, 1},
{ 3, 0, 2, -4, 2},
{ 1, 2, 2, -2, 1},
{ 1, 0, 4, -4, 2},
{-2, -1, 0, 4, 1},
{ 0, -1, 0, 2, 2},
{-2, 1, 0, 4, 0},
{-2, -1, 2, 2, 1},
{ 2, 0, -2, 2, 0},
{ 1, 0, 0, 1, 1},
{ 0, 1, 0, 2, 2},
{ 1, -1, 2, -1, 2},
{-2, 0, 4, 0, 1},
{ 2, 1, 0, 0, 1},
{ 0, 1, 2, 0, 0},
{ 0, -1, 4, -2, 2},
{ 0, 0, 4, -2, 4},
{ 0, 2, 2, 0, 1},
{-3, 0, 0, 6, 0},
{-1, -1, 0, 4, 1},
{ 1, -2, 0, 2, 0},
{-1, 0, 0, 4, 2},
{-1, -2, 2, 2, 1},
{-1, 0, 0, -2, 2},
{ 1, 0, -2, -2, 1},
{ 0, 0, -2, -2, 1},
{-2, 0, -2, 0, 1},
{ 0, 0, 0, 3, 1},
{ 0, 0, 0, 3, 0},
{-1, 1, 0, 4, 0},
{-1, -1, 2, 2, 0},
{-2, 0, 2, 3, 2},
{ 1, 0, 0, 2, 2},
{ 0, -1, 2, 1, 2},
{ 3, -1, 0, 0, 0},
{ 2, 0, 0, 1, 0},
{ 1, -1, 2, 0, 0},
{ 0, 0, 2, 1, 0},
{ 1, 0, 2, 0, 3},
{ 3, 1, 0, 0, 0},
{ 3, -1, 2, -2, 2},
{ 2, 0, 2, -1, 1},
{ 1, 1, 2, 0, 0},
{ 0, 0, 4, -1, 2},
{ 1, 2, 2, 0, 2},
{-2, 0, 0, 6, 0},
{ 0, -1, 0, 4, 1},
{-2, -1, 2, 4, 1},
{ 0, -2, 2, 2, 1},
{ 0, -1, 2, 2, 0},
{-1, 0, 2, 3, 1},
{-2, 1, 2, 4, 2},
{ 2, 0, 0, 2, 2},
{ 2, -2, 2, 0, 2},
{-1, 1, 2, 3, 2},
{ 3, 0, 2, -1, 2},
{ 4, 0, 2, -2, 1},
{-1, 0, 0, 6, 0},
{-1, -2, 2, 4, 2},
{-3, 0, 2, 6, 2},
{-1, 0, 2, 4, 0},
{ 3, 0, 0, 2, 1},
{ 3, -1, 2, 0, 1},
{ 3, 0, 2, 0, 0},
{ 1, 0, 4, 0, 2},
{ 5, 0, 2, -2, 2},
{ 0, -1, 2, 4, 1},
{ 2, -1, 2, 2, 1},
{ 0, 1, 2, 4, 2},
{ 1, -1, 2, 4, 2},
{ 3, -1, 2, 2, 2},
{ 3, 0, 2, 2, 1},
{ 5, 0, 2, 0, 2},
{ 0, 0, 2, 6, 2},
{ 4, 0, 2, 2, 2},
{ 0, -1, 1, -1, 1},
{-1, 0, 1, 0, 3},
{ 0, -2, 2, -2, 3},
{ 1, 0, -1, 0, 1},
{ 2, -2, 0, -2, 1},
{-1, 0, 1, 0, 2},
{-1, 0, 1, 0, 1},
{-1, -1, 2, -1, 2},
{-2, 2, 0, 2, 2},
{-1, 0, 1, 0, 0},
{-4, 1, 2, 2, 2},
{-3, 0, 2, 1, 1},
{-2, -1, 2, 0, 2},
{ 1, 0, -2, 1, 1},
{ 2, -1, -2, 0, 1},
{-4, 0, 2, 2, 0},
{-3, 1, 0, 3, 0},
{-1, 0, -1, 2, 0},
{ 0, -2, 0, 0, 2},
{ 0, -2, 0, 0, 2},
{-3, 0, 0, 3, 0},
{-2, -1, 0, 2, 2},
{-1, 0, -2, 3, 0},
{-4, 0, 0, 4, 0},
{ 2, 1, -2, 0, 1},
{ 2, -1, 0, -2, 2},
{ 0, 0, 1, -1, 0},
{-1, 2, 0, 1, 0},
{-2, 1, 2, 0, 2},
{ 1, 1, 0, -1, 1},
{ 1, 0, 1, -2, 1},
{ 0, 2, 0, 0, 2},
{ 1, -1, 2, -3, 1},
{-1, 1, 2, -1, 1},
{-2, 0, 4, -2, 2},
{-2, 0, 4, -2, 1},
{-2, -2, 0, 2, 1},
{-2, 0, -2, 4, 0},
{ 1, 2, 2, -4, 1},
{ 1, 1, 2, -4, 2},
{-1, 2, 2, -2, 1},
{ 2, 0, 0, -3, 1},
{-1, 2, 0, 0, 1},
{ 0, 0, 0, -2, 0},
{-1, -1, 2, -2, 2},
{-1, 1, 0, 0, 2},
{ 0, 0, 0, -1, 2},
{-2, 1, 0, 1, 0},
{ 1, -2, 0, -2, 1},
{ 1, 0, -2, 0, 2},
{-3, 1, 0, 2, 0},
{-1, 1, -2, 2, 0},
{-1, -1, 0, 0, 2},
{-3, 0, 0, 2, 0},
{-3, -1, 0, 2, 0},
{ 2, 0, 2, -6, 1},
{ 0, 1, 2, -4, 2},
{ 2, 0, 0, -4, 2},
{-2, 1, 2, -2, 1},
{ 0, -1, 2, -4, 1},
{ 0, 1, 0, -2, 2},
{-1, 0, 0, -2, 0},
{ 2, 0, -2, -2, 1},
{-4, 0, 2, 0, 1},
{-1, -1, 0, -1, 1},
{ 0, 0, -2, 0, 2},
{-3, 0, 0, 1, 0},
{-1, 0, -2, 1, 0},
{-2, 0, -2, 2, 1},
{ 0, 0, -4, 2, 0},
{-2, -1, -2, 2, 0},
{ 1, 0, 2, -6, 1},
{-1, 0, 2, -4, 2},
{ 1, 0, 0, -4, 2},
{ 2, 1, 2, -4, 2},
{ 2, 1, 2, -4, 1},
{ 0, 1, 4, -4, 4},
{ 0, 1, 4, -4, 2},
{-1, -1, -2, 4, 0},
{-1, -3, 0, 2, 0},
{-1, 0, -2, 4, 1},
{-2, -1, 0, 3, 0},
{ 0, 0, -2, 3, 0},
{-2, 0, 0, 3, 1},
{ 0, -1, 0, 1, 0},
{-3, 0, 2, 2, 0},
{ 1, 1, -2, 2, 0},
{-1, 1, 0, 2, 2},
{ 1, -2, 2, -2, 1},
{ 0, 0, 1, 0, 2},
{ 0, 0, 1, 0, 1},
{ 0, 0, 1, 0, 0},
{-1, 2, 0, 2, 1},
{ 0, 0, 2, 0, 2},
{-2, 0, 2, 0, 2},
{ 2, 0, 0, -1, 1},
{ 3, 0, 0, -2, 1},
{ 1, 0, 2, -2, 3},
{ 1, 2, 0, 0, 1},
{ 2, 0, 2, -3, 2},
{-1, 1, 4, -2, 2},
{-2, -2, 0, 4, 0},
{ 0, -3, 0, 2, 0},
{ 0, 0, -2, 4, 0},
{-1, -1, 0, 3, 0},
{-2, 0, 0, 4, 2},
{-1, 0, 0, 3, 1},
{ 2, -2, 0, 0, 0},
{ 1, -1, 0, 1, 0},
{-1, 0, 0, 2, 0},
{ 0, -2, 2, 0, 1},
{-1, 0, 1, 2, 1},
{-1, 1, 0, 3, 0},
{-1, -1, 2, 1, 2},
{ 0, -1, 2, 0, 0},
{-2, 1, 2, 2, 1},
{ 2, -2, 2, -2, 2},
{ 1, 1, 0, 1, 1},
{ 1, 0, 1, 0, 1},
{ 1, 0, 1, 0, 0},
{ 0, 2, 0, 2, 0},
{ 2, -1, 2, -2, 1},
{ 0, -1, 4, -2, 1},
{ 0, 0, 4, -2, 3},
{ 0, 1, 4, -2, 1},
{ 4, 0, 2, -4, 2},
{ 2, 2, 2, -2, 2},
{ 2, 0, 4, -4, 2},
{-1, -2, 0, 4, 0},
{-1, -3, 2, 2, 2},
{-3, 0, 2, 4, 2},
{-3, 0, 2, -2, 1},
{-1, -1, 0, -2, 1},
{-3, 0, 0, 0, 2},
{-3, 0, -2, 2, 0},
{ 0, 1, 0, -4, 1},
{-2, 1, 0, -2, 1},
{-4, 0, 0, 0, 1},
{-1, 0, 0, -4, 1},
{-3, 0, 0, -2, 1},
{ 0, 0, 0, 3, 2},
{-1, 1, 0, 4, 1},
{ 1, -2, 2, 0, 1},
{ 0, 1, 0, 3, 0},
{-1, 0, 2, 2, 3},
{ 0, 0, 2, 2, 2},
{-2, 0, 2, 2, 2},
{-1, 1, 2, 2, 0},
{ 3, 0, 0, 0, 2},
{ 2, 1, 0, 1, 0},
{ 2, -1, 2, -1, 2},
{ 0, 0, 2, 0, 1},
{ 0, 0, 3, 0, 3},
{ 0, 0, 3, 0, 2},
{-1, 2, 2, 2, 1},
{-1, 0, 4, 0, 0},
{ 1, 2, 2, 0, 1},
{ 3, 1, 2, -2, 1},
{ 1, 1, 4, -2, 2},
{-2, -1, 0, 6, 0},
{ 0, -2, 0, 4, 0},
{-2, 0, 0, 6, 1},
{-2, -2, 2, 4, 2},
{ 0, -3, 2, 2, 2},
{ 0, 0, 0, 4, 2},
{-1, -1, 2, 3, 2},
{-2, 0, 2, 4, 0},
{ 2, -1, 0, 2, 1},
{ 1, 0, 0, 3, 0},
{ 0, 1, 0, 4, 1},
{ 0, 1, 0, 4, 0},
{ 1, -1, 2, 1, 2},
{ 0, 0, 2, 2, 3},
{ 1, 0, 2, 2, 2},
{-1, 0, 2, 2, 2},
{-2, 0, 4, 2, 1},
{ 2, 1, 0, 2, 1},
{ 2, 1, 0, 2, 0},
{ 2, -1, 2, 0, 0},
{ 1, 0, 2, 1, 0},
{ 0, 1, 2, 2, 0},
{ 2, 0, 2, 0, 3},
{ 3, 0, 2, 0, 2},
{ 1, 0, 2, 0, 2},
{ 1, 0, 3, 0, 3},
{ 1, 1, 2, 1, 1},
{ 0, 2, 2, 2, 2},
{ 2, 1, 2, 0, 0},
{ 2, 0, 4, -2, 1},
{ 4, 1, 2, -2, 2},
{-1, -1, 0, 6, 0},
{-3, -1, 2, 6, 2},
{-1, 0, 0, 6, 1},
{-3, 0, 2, 6, 1},
{ 1, -1, 0, 4, 1},
{ 1, -1, 0, 4, 0},
{-2, 0, 2, 5, 2},
{ 1, -2, 2, 2, 1},
{ 3, -1, 0, 2, 0},
{ 1, -1, 2, 2, 0},
{ 0, 0, 2, 3, 1},
{-1, 1, 2, 4, 1},
{ 0, 1, 2, 3, 2},
{-1, 0, 4, 2, 1},
{ 2, 0, 2, 1, 1},
{ 5, 0, 0, 0, 0},
{ 2, 1, 2, 1, 2},
{ 1, 0, 4, 0, 1},
{ 3, 1, 2, 0, 1},
{ 3, 0, 4, -2, 2},
{-2, -1, 2, 6, 2},
{ 0, 0, 0, 6, 0},
{ 0, -2, 2, 4, 2},
{-2, 0, 2, 6, 1},
{ 2, 0, 0, 4, 1},
{ 2, 0, 0, 4, 0},
{ 2, -2, 2, 2, 2},
{ 0, 0, 2, 4, 0},
{ 1, 0, 2, 3, 2},
{ 4, 0, 0, 2, 0},
{ 2, 0, 2, 2, 0},
{ 0, 0, 4, 2, 2},
{ 4, -1, 2, 0, 2},
{ 3, 0, 2, 1, 2},
{ 2, 1, 2, 2, 1},
{ 4, 1, 2, 0, 2},
{-1, -1, 2, 6, 2},
{-1, 0, 2, 6, 1},
{ 1, -1, 2, 4, 1},
{ 1, 1, 2, 4, 2},
{ 3, 1, 2, 2, 2},
{ 5, 0, 2, 0, 1},
{ 2, -1, 2, 4, 2},
{ 2, 0, 2, 4, 1}};
/*
Luni-Solar nutation coefficients, unit 1e-7 arcsec:
longitude (sin, t*sin, cos), obliquity (cos, t*cos, sin)
Each row of coefficients in 'cls_t' belongs with the corresponding
row of fundamental-argument multipliers in 'nals_t'.
*/
static const double cls_t[678][6] = {
{-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0},
{ -13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0},
{ -2276413.0, -234.0, 2796.0, 978459.0, -485.0, 1374.0},
{ 2074554.0, 207.0, -698.0, -897492.0, 470.0, -291.0},
{ 1475877.0, -3633.0, 11817.0, 73871.0, -184.0, -1924.0},
{ -516821.0, 1226.0, -524.0, 224386.0, -677.0, -174.0},
{ 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0},
{ -387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0},
{ -301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0},
{ 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0},
{ 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0},
{ 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0},
{ 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0},
{ 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0},
{ -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0},
{ -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0},
{ -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0},
{ 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0},
{ 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0},
{ -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0},
{ 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0},
{ -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0},
{ -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0},
{ 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0},
{ 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0},
{ 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0},
{ 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0},
{ -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0},
{ 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0},
{ -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0},
{ 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0},
{ -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0},
{ -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0},
{ -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0},
{ 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0},
{ -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0},
{ -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0},
{ 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0},
{ -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0},
{ -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0},
{ -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0},
{ 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0},
{ 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0},
{ -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0},
{ -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0},
{ -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0},
{ -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0},
{ 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0},
{ 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0},
{ 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0},
{ 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0},
{ 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0},
{ -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0},
{ -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0},
{ 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0},
{ -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0},
{ -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0},
{ -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0},
{ -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0},
{ -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0},
{ -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0},
{ 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0},
{ 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0},
{ 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0},
{ -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0},
{ 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0},
{ -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0},
{ -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0},
{ 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0},
{ 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0},
{ -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0},
{ 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0},
{ -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0},
{ -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0},
{ 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0},
{ 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0},
{ 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0},
{ -1214.0, 0.0, 5.0, 518.0, 0.0, 2.0},
{ 1146.0, 0.0, -3.0, -490.0, 0.0, -1.0},
{ 1019.0, 0.0, -1.0, -527.0, 0.0, -1.0},
{ -1100.0, 0.0, 9.0, 465.0, 0.0, 4.0},
{ -970.0, 0.0, 2.0, 496.0, 0.0, 1.0},
{ 1575.0, 0.0, -6.0, -50.0, 0.0, 0.0},
{ 934.0, 0.0, -3.0, -399.0, 0.0, -1.0},
{ 922.0, 0.0, -1.0, -395.0, 0.0, -1.0},
{ 815.0, 0.0, -1.0, -422.0, 0.0, -1.0},
{ 834.0, 0.0, 2.0, -440.0, 0.0, 1.0},
{ 1248.0, 0.0, 0.0, -170.0, 0.0, 1.0},
{ 1338.0, 0.0, -5.0, -39.0, 0.0, 0.0},
{ 716.0, 0.0, -2.0, -389.0, 0.0, -1.0},
{ 1282.0, 0.0, -3.0, -23.0, 0.0, 1.0},
{ 742.0, 0.0, 1.0, -391.0, 0.0, 0.0},
{ 1020.0, 0.0, -25.0, -495.0, 0.0, -10.0},
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