#include "sofa.h"

void iauAe2hd (double az, double el, double phi,
               double *ha, double *dec)
/*
**  - - - - - - - - -
**   i a u A e 2 h d
**  - - - - - - - - -
**
**  Horizon to equatorial coordinates:  transform azimuth and altitude
**  to hour angle and declination.
**
**  Given:
**     az       double       azimuth
**     el       double       altitude (informally, elevation)
**     phi      double       site latitude
**
**  Returned:
**     ha       double       hour angle (local)
**     dec      double       declination
**
**  Notes:
**
**  1)  All the arguments are angles in radians.
**
**  2)  The sign convention for azimuth is north zero, east +pi/2.
**
**  3)  HA is returned in the range +/-pi.  Declination is returned in
**      the range +/-pi/2.
**
**  4)  The latitude phi is pi/2 minus the angle between the Earth's
**      rotation axis and the adopted zenith.  In many applications it
**      will be sufficient to use the published geodetic latitude of the
**      site.  In very precise (sub-arcsecond) applications, phi can be
**      corrected for polar motion.
**
**  5)  The azimuth az must be with respect to the rotational north pole,
**      as opposed to the ITRS pole, and an azimuth with respect to north
**      on a map of the Earth's surface will need to be adjusted for
**      polar motion if sub-arcsecond accuracy is required.
**
**  6)  Should the user wish to work with respect to the astronomical
**      zenith rather than the geodetic zenith, phi will need to be
**      adjusted for deflection of the vertical (often tens of
**      arcseconds), and the zero point of ha will also be affected.
**
**  7)  The transformation is the same as Ve = Ry(phi-pi/2)*Rz(pi)*Vh,
**      where Ve and Vh are lefthanded unit vectors in the (ha,dec) and
**      (az,el) systems respectively and Rz and Ry are rotations about
**      first the z-axis and then the y-axis.  (n.b. Rz(pi) simply
**      reverses the signs of the x and y components.)  For efficiency,
**      the algorithm is written out rather than calling other utility
**      functions.  For applications that require even greater
**      efficiency, additional savings are possible if constant terms
**      such as functions of latitude are computed once and for all.
**
**  8)  Again for efficiency, no range checking of arguments is carried
**      out.
**
**  Last revision:   2017 September 12
**
**  SOFA release 2020-07-21
**
**  Copyright (C) 2020 IAU SOFA Board.  See notes at end.
*/
{
   double sa, ca, se, ce, sp, cp, x, y, z, r;


/* Useful trig functions. */
   sa = sin(az);
   ca = cos(az);
   se = sin(el);
   ce = cos(el);
   sp = sin(phi);
   cp = cos(phi);

/* HA,Dec unit vector. */
   x = - ca*ce*sp + se*cp;
   y = - sa*ce;
   z = ca*ce*cp + se*sp;

/* To spherical. */
   r = sqrt(x*x + y*y);
   *ha = (r != 0.0) ? atan2(y,x) : 0.0;
   *dec = atan2(z,r);

/* Finished. */

/*----------------------------------------------------------------------
**
**  Copyright (C) 2020
**  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
**     fitness for any particular purpose.  In no event will SOFA be
**     liable to the user for any consequential, incidental, or special
**     damages, including any lost profits or lost savings, even if a
**     SOFA representative has been advised of such damages, or for any
**     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
**                 Admiralty Way, Taunton
**                 Somerset, TA1 2DN
**                 United Kingdom
**
**--------------------------------------------------------------------*/
}
