text: // © 2016 and later: Unicode, Inc. and others.
  // License & terms of use: http://www.unicode.org/copyright.html
  /************************************************************************
   * Copyright (C) 1996-2012, International Business Machines Corporation
   * and others. All Rights Reserved.
   ************************************************************************
   *  2003-nov-07   srl       Port from Java
   */
  
  #include "astro.h"
  
  #if !UCONFIG_NO_FORMATTING
  
  #include "unicode/calendar.h"
  #include <math.h>
  #include <float.h>
  #include "unicode/putil.h"
  #include "uhash.h"
  #include "umutex.h"
  #include "ucln_in.h"
  #include "putilimp.h"
  #include <stdio.h>  // for toString()
  
  #if defined (PI)
  #undef PI
  #endif
  
  #ifdef U_DEBUG_ASTRO
  # include "uresimp.h" // for debugging
  
  static void debug_astro_loc(const char *f, int32_t l)
  {
    fprintf(stderr, "%s:%d: ", f, l);
  }
  
  static void debug_astro_msg(const char *pat, ...)
  {
    va_list ap;
    va_start(ap, pat);
    vfprintf(stderr, pat, ap);
    fflush(stderr);
  }
  #include "unicode/datefmt.h"
  #include "unicode/ustring.h"
  static const char * debug_astro_date(UDate d) {
    static char gStrBuf[1024];
    static DateFormat *df = NULL;
    if(df == NULL) {
      df = DateFormat::createDateTimeInstance(DateFormat::MEDIUM, DateFormat::MEDIUM, Locale::getUS());
      df->adoptTimeZone(TimeZone::getGMT()->clone());
    }
    UnicodeString str;
    df->format(d,str);
    u_austrncpy(gStrBuf,str.getTerminatedBuffer(),sizeof(gStrBuf)-1);
    return gStrBuf;
  }
  
  // must use double parens, i.e.:  U_DEBUG_ASTRO_MSG(("four is: %d",4));
  #define U_DEBUG_ASTRO_MSG(x) {debug_astro_loc(__FILE__,__LINE__);debug_astro_msg x;}
  #else
  #define U_DEBUG_ASTRO_MSG(x)
  #endif
  
  static inline UBool isINVALID(double d) {
    return(uprv_isNaN(d));
  }
  
  static icu::UMutex ccLock;
  
  U_CDECL_BEGIN
  static UBool calendar_astro_cleanup(void) {
    return TRUE;
  }
  U_CDECL_END
  
  U_NAMESPACE_BEGIN
  
  /**
   * The number of standard hours in one sidereal day.
   * Approximately 24.93.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define SIDEREAL_DAY (23.93446960027)
  
  /**
   * The number of sidereal hours in one mean solar day.
   * Approximately 24.07.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define SOLAR_DAY  (24.065709816)
  
  /**
   * The average number of solar days from one new moon to the next.  This is the time
   * it takes for the moon to return the same ecliptic longitude as the sun.
   * It is longer than the sidereal month because the sun's longitude increases
   * during the year due to the revolution of the earth around the sun.
   * Approximately 29.53.
   *
   * @see #SIDEREAL_MONTH
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  const double CalendarAstronomer::SYNODIC_MONTH  = 29.530588853;
  
  /**
   * The average number of days it takes
   * for the moon to return to the same ecliptic longitude relative to the
   * stellar background.  This is referred to as the sidereal month.
   * It is shorter than the synodic month due to
   * the revolution of the earth around the sun.
   * Approximately 27.32.
   *
   * @see #SYNODIC_MONTH
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define SIDEREAL_MONTH  27.32166
  
  /**
   * The average number number of days between successive vernal equinoxes.
   * Due to the precession of the earth's
   * axis, this is not precisely the same as the sidereal year.
   * Approximately 365.24
   *
   * @see #SIDEREAL_YEAR
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define TROPICAL_YEAR  365.242191
  
  /**
   * The average number of days it takes
   * for the sun to return to the same position against the fixed stellar
   * background.  This is the duration of one orbit of the earth about the sun
   * as it would appear to an outside observer.
   * Due to the precession of the earth's
   * axis, this is not precisely the same as the tropical year.
   * Approximately 365.25.
   *
   * @see #TROPICAL_YEAR
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define SIDEREAL_YEAR  365.25636
  
  //-------------------------------------------------------------------------
  // Time-related constants
  //-------------------------------------------------------------------------
  
  /**
   * The number of milliseconds in one second.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define SECOND_MS  U_MILLIS_PER_SECOND
  
  /**
   * The number of milliseconds in one minute.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define MINUTE_MS  U_MILLIS_PER_MINUTE
  
  /**
   * The number of milliseconds in one hour.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define HOUR_MS   U_MILLIS_PER_HOUR
  
  /**
   * The number of milliseconds in one day.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define DAY_MS U_MILLIS_PER_DAY
  
  /**
   * The start of the julian day numbering scheme used by astronomers, which
   * is 1/1/4713 BC (Julian), 12:00 GMT.  This is given as the number of milliseconds
   * since 1/1/1970 AD (Gregorian), a negative number.
   * Note that julian day numbers and
   * the Julian calendar are <em>not</em> the same thing.  Also note that
   * julian days start at <em>noon</em>, not midnight.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  #define JULIAN_EPOCH_MS  -210866760000000.0
  
  
  /**
   * Milliseconds value for 0.0 January 2000 AD.
   */
  #define EPOCH_2000_MS  946598400000.0
  
  //-------------------------------------------------------------------------
  // Assorted private data used for conversions
  //-------------------------------------------------------------------------
  
  // My own copies of these so compilers are more likely to optimize them away
  const double CalendarAstronomer::PI = 3.14159265358979323846;
  
  #define CalendarAstronomer_PI2  (CalendarAstronomer::PI*2.0)
  #define RAD_HOUR  ( 12 / CalendarAstronomer::PI )     // radians -> hours
  #define DEG_RAD ( CalendarAstronomer::PI / 180 )      // degrees -> radians
  #define RAD_DEG  ( 180 / CalendarAstronomer::PI )     // radians -> degrees
  
  /***
   * Given 'value', add or subtract 'range' until 0 <= 'value' < range.
   * The modulus operator.
   */
  inline static double normalize(double value, double range)  {
      return value - range * ClockMath::floorDivide(value, range);
  }
  
  /**
   * Normalize an angle so that it's in the range 0 - 2pi.
   * For positive angles this is just (angle % 2pi), but the Java
   * mod operator doesn't work that way for negative numbers....
   */
  inline static double norm2PI(double angle)  {
      return normalize(angle, CalendarAstronomer::PI * 2.0);
  }
  
  /**
   * Normalize an angle into the range -PI - PI
   */
  inline static  double normPI(double angle)  {
      return normalize(angle + CalendarAstronomer::PI, CalendarAstronomer::PI * 2.0) - CalendarAstronomer::PI;
  }
  
  //-------------------------------------------------------------------------
  // Constructors
  //-------------------------------------------------------------------------
  
  /**
   * Construct a new <code>CalendarAstronomer</code> object that is initialized to
   * the current date and time.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::CalendarAstronomer():
    fTime(Calendar::getNow()), fLongitude(0.0), fLatitude(0.0), fGmtOffset(0.0), moonPosition(0,0), moonPositionSet(FALSE) {
    clearCache();
  }
  
  /**
   * Construct a new <code>CalendarAstronomer</code> object that is initialized to
   * the specified date and time.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::CalendarAstronomer(UDate d): fTime(d), fLongitude(0.0), fLatitude(0.0), fGmtOffset(0.0), moonPosition(0,0), moonPositionSet(FALSE) {
    clearCache();
  }
  
  /**
   * Construct a new <code>CalendarAstronomer</code> object with the given
   * latitude and longitude.  The object's time is set to the current
   * date and time.
   * <p>
   * @param longitude The desired longitude, in <em>degrees</em> east of
   *                  the Greenwich meridian.
   *
   * @param latitude  The desired latitude, in <em>degrees</em>.  Positive
   *                  values signify North, negative South.
   *
   * @see java.util.Date#getTime()
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::CalendarAstronomer(double longitude, double latitude) :
    fTime(Calendar::getNow()), moonPosition(0,0), moonPositionSet(FALSE) {
    fLongitude = normPI(longitude * (double)DEG_RAD);
    fLatitude  = normPI(latitude  * (double)DEG_RAD);
    fGmtOffset = (double)(fLongitude * 24. * (double)HOUR_MS / (double)CalendarAstronomer_PI2);
    clearCache();
  }
  
  CalendarAstronomer::~CalendarAstronomer()
  {
  }
  
  //-------------------------------------------------------------------------
  // Time and date getters and setters
  //-------------------------------------------------------------------------
  
  /**
   * Set the current date and time of this <code>CalendarAstronomer</code> object.  All
   * astronomical calculations are performed based on this time setting.
   *
   * @param aTime the date and time, expressed as the number of milliseconds since
   *              1/1/1970 0:00 GMT (Gregorian).
   *
   * @see #setDate
   * @see #getTime
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  void CalendarAstronomer::setTime(UDate aTime) {
      fTime = aTime;
      U_DEBUG_ASTRO_MSG(("setTime(%.1lf, %sL)\n", aTime, debug_astro_date(aTime+fGmtOffset)));
      clearCache();
  }
  
  /**
   * Set the current date and time of this <code>CalendarAstronomer</code> object.  All
   * astronomical calculations are performed based on this time setting.
   *
   * @param jdn   the desired time, expressed as a "julian day number",
   *              which is the number of elapsed days since
   *              1/1/4713 BC (Julian), 12:00 GMT.  Note that julian day
   *              numbers start at <em>noon</em>.  To get the jdn for
   *              the corresponding midnight, subtract 0.5.
   *
   * @see #getJulianDay
   * @see #JULIAN_EPOCH_MS
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  void CalendarAstronomer::setJulianDay(double jdn) {
      fTime = (double)(jdn * DAY_MS) + JULIAN_EPOCH_MS;
      clearCache();
      julianDay = jdn;
  }
  
  /**
   * Get the current time of this <code>CalendarAstronomer</code> object,
   * represented as the number of milliseconds since
   * 1/1/1970 AD 0:00 GMT (Gregorian).
   *
   * @see #setTime
   * @see #getDate
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  UDate CalendarAstronomer::getTime() {
      return fTime;
  }
  
  /**
   * Get the current time of this <code>CalendarAstronomer</code> object,
   * expressed as a "julian day number", which is the number of elapsed
   * days since 1/1/4713 BC (Julian), 12:00 GMT.
   *
   * @see #setJulianDay
   * @see #JULIAN_EPOCH_MS
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getJulianDay() {
      if (isINVALID(julianDay)) {
          julianDay = (fTime - (double)JULIAN_EPOCH_MS) / (double)DAY_MS;
      }
      return julianDay;
  }
  
  /**
   * Return this object's time expressed in julian centuries:
   * the number of centuries after 1/1/1900 AD, 12:00 GMT
   *
   * @see #getJulianDay
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getJulianCentury() {
      if (isINVALID(julianCentury)) {
          julianCentury = (getJulianDay() - 2415020.0) / 36525.0;
      }
      return julianCentury;
  }
  
  /**
   * Returns the current Greenwich sidereal time, measured in hours
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getGreenwichSidereal() {
      if (isINVALID(siderealTime)) {
          // See page 86 of "Practial Astronomy with your Calculator",
          // by Peter Duffet-Smith, for details on the algorithm.
  
          double UT = normalize(fTime/(double)HOUR_MS, 24.);
  
          siderealTime = normalize(getSiderealOffset() + UT*1.002737909, 24.);
      }
      return siderealTime;
  }
  
  double CalendarAstronomer::getSiderealOffset() {
      if (isINVALID(siderealT0)) {
          double JD  = uprv_floor(getJulianDay() - 0.5) + 0.5;
          double S   = JD - 2451545.0;
          double T   = S / 36525.0;
          siderealT0 = normalize(6.697374558 + 2400.051336*T + 0.000025862*T*T, 24);
      }
      return siderealT0;
  }
  
  /**
   * Returns the current local sidereal time, measured in hours
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getLocalSidereal() {
      return normalize(getGreenwichSidereal() + (fGmtOffset/(double)HOUR_MS), 24.);
  }
  
  /**
   * Converts local sidereal time to Universal Time.
   *
   * @param lst   The Local Sidereal Time, in hours since sidereal midnight
   *              on this object's current date.
   *
   * @return      The corresponding Universal Time, in milliseconds since
   *              1 Jan 1970, GMT.
   */
  double CalendarAstronomer::lstToUT(double lst) {
      // Convert to local mean time
      double lt = normalize((lst - getSiderealOffset()) * 0.9972695663, 24);
  
      // Then find local midnight on this day
      double base = (DAY_MS * ClockMath::floorDivide(fTime + fGmtOffset,(double)DAY_MS)) - fGmtOffset;
  
      //out("    lt  =" + lt + " hours");
      //out("    base=" + new Date(base));
  
      return base + (long)(lt * HOUR_MS);
  }
  
  
  //-------------------------------------------------------------------------
  // Coordinate transformations, all based on the current time of this object
  //-------------------------------------------------------------------------
  
  /**
   * Convert from ecliptic to equatorial coordinates.
   *
   * @param ecliptic  A point in the sky in ecliptic coordinates.
   * @return          The corresponding point in equatorial coordinates.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::Equatorial& CalendarAstronomer::eclipticToEquatorial(CalendarAstronomer::Equatorial& result, const CalendarAstronomer::Ecliptic& ecliptic)
  {
      return eclipticToEquatorial(result, ecliptic.longitude, ecliptic.latitude);
  }
  
  /**
   * Convert from ecliptic to equatorial coordinates.
   *
   * @param eclipLong     The ecliptic longitude
   * @param eclipLat      The ecliptic latitude
   *
   * @return              The corresponding point in equatorial coordinates.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::Equatorial& CalendarAstronomer::eclipticToEquatorial(CalendarAstronomer::Equatorial& result, double eclipLong, double eclipLat)
  {
      // See page 42 of "Practial Astronomy with your Calculator",
      // by Peter Duffet-Smith, for details on the algorithm.
  
      double obliq = eclipticObliquity();
      double sinE = ::sin(obliq);
      double cosE = cos(obliq);
  
      double sinL = ::sin(eclipLong);
      double cosL = cos(eclipLong);
  
      double sinB = ::sin(eclipLat);
      double cosB = cos(eclipLat);
      double tanB = tan(eclipLat);
  
      result.set(atan2(sinL*cosE - tanB*sinE, cosL),
          asin(sinB*cosE + cosB*sinE*sinL) );
      return result;
  }
  
  /**
   * Convert from ecliptic longitude to equatorial coordinates.
   *
   * @param eclipLong     The ecliptic longitude
   *
   * @return              The corresponding point in equatorial coordinates.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::Equatorial& CalendarAstronomer::eclipticToEquatorial(CalendarAstronomer::Equatorial& result, double eclipLong)
  {
      return eclipticToEquatorial(result, eclipLong, 0);  // TODO: optimize
  }
  
  /**
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::Horizon& CalendarAstronomer::eclipticToHorizon(CalendarAstronomer::Horizon& result, double eclipLong)
  {
      Equatorial equatorial;
      eclipticToEquatorial(equatorial, eclipLong);
  
      double H = getLocalSidereal()*CalendarAstronomer::PI/12 - equatorial.ascension;     // Hour-angle
  
      double sinH = ::sin(H);
      double cosH = cos(H);
      double sinD = ::sin(equatorial.declination);
      double cosD = cos(equatorial.declination);
      double sinL = ::sin(fLatitude);
      double cosL = cos(fLatitude);
  
      double altitude = asin(sinD*sinL + cosD*cosL*cosH);
      double azimuth  = atan2(-cosD*cosL*sinH, sinD - sinL * ::sin(altitude));
  
      result.set(azimuth, altitude);
      return result;
  }
  
  
  //-------------------------------------------------------------------------
  // The Sun
  //-------------------------------------------------------------------------
  
  //
  // Parameters of the Sun's orbit as of the epoch Jan 0.0 1990
  // Angles are in radians (after multiplying by CalendarAstronomer::PI/180)
  //
  #define JD_EPOCH  2447891.5 // Julian day of epoch
  
  #define SUN_ETA_G    (279.403303 * CalendarAstronomer::PI/180) // Ecliptic longitude at epoch
  #define SUN_OMEGA_G  (282.768422 * CalendarAstronomer::PI/180) // Ecliptic longitude of perigee
  #define SUN_E         0.016713          // Eccentricity of orbit
  //double sunR0        1.495585e8        // Semi-major axis in KM
  //double sunTheta0    (0.533128 * CalendarAstronomer::PI/180) // Angular diameter at R0
  
  // The following three methods, which compute the sun parameters
  // given above for an arbitrary epoch (whatever time the object is
  // set to), make only a small difference as compared to using the
  // above constants.  E.g., Sunset times might differ by ~12
  // seconds.  Furthermore, the eta-g computation is befuddled by
  // Duffet-Smith's incorrect coefficients (p.86).  I've corrected
  // the first-order coefficient but the others may be off too - no
  // way of knowing without consulting another source.
  
  //  /**
  //   * Return the sun's ecliptic longitude at perigee for the current time.
  //   * See Duffett-Smith, p. 86.
  //   * @return radians
  //   */
  //  private double getSunOmegaG() {
  //      double T = getJulianCentury();
  //      return (281.2208444 + (1.719175 + 0.000452778*T)*T) * DEG_RAD;
  //  }
  
  //  /**
  //   * Return the sun's ecliptic longitude for the current time.
  //   * See Duffett-Smith, p. 86.
  //   * @return radians
  //   */
  //  private double getSunEtaG() {
  //      double T = getJulianCentury();
  //      //return (279.6966778 + (36000.76892 + 0.0003025*T)*T) * DEG_RAD;
  //      //
  //      // The above line is from Duffett-Smith, and yields manifestly wrong
  //      // results.  The below constant is derived empirically to match the
  //      // constant he gives for the 1990 EPOCH.
  //      //
  //      return (279.6966778 + (-0.3262541582718024 + 0.0003025*T)*T) * DEG_RAD;
  //  }
  
  //  /**
  //   * Return the sun's eccentricity of orbit for the current time.
  //   * See Duffett-Smith, p. 86.
  //   * @return double
  //   */
  //  private double getSunE() {
  //      double T = getJulianCentury();
  //      return 0.01675104 - (0.0000418 + 0.000000126*T)*T;
  //  }
  
  /**
   * Find the "true anomaly" (longitude) of an object from
   * its mean anomaly and the eccentricity of its orbit.  This uses
   * an iterative solution to Kepler's equation.
   *
   * @param meanAnomaly   The object's longitude calculated as if it were in
   *                      a regular, circular orbit, measured in radians
   *                      from the point of perigee.
   *
   * @param eccentricity  The eccentricity of the orbit
   *
   * @return The true anomaly (longitude) measured in radians
   */
  static double trueAnomaly(double meanAnomaly, double eccentricity)
  {
      // First, solve Kepler's equation iteratively
      // Duffett-Smith, p.90
      double delta;
      double E = meanAnomaly;
      do {
          delta = E - eccentricity * ::sin(E) - meanAnomaly;
          E = E - delta / (1 - eccentricity * ::cos(E));
      }
      while (uprv_fabs(delta) > 1e-5); // epsilon = 1e-5 rad
  
      return 2.0 * ::atan( ::tan(E/2) * ::sqrt( (1+eccentricity)
                                               /(1-eccentricity) ) );
  }
  
  /**
   * The longitude of the sun at the time specified by this object.
   * The longitude is measured in radians along the ecliptic
   * from the "first point of Aries," the point at which the ecliptic
   * crosses the earth's equatorial plane at the vernal equinox.
   * <p>
   * Currently, this method uses an approximation of the two-body Kepler's
   * equation for the earth and the sun.  It does not take into account the
   * perturbations caused by the other planets, the moon, etc.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getSunLongitude()
  {
      // See page 86 of "Practial Astronomy with your Calculator",
      // by Peter Duffet-Smith, for details on the algorithm.
  
      if (isINVALID(sunLongitude)) {
          getSunLongitude(getJulianDay(), sunLongitude, meanAnomalySun);
      }
      return sunLongitude;
  }
  
  /**
   * TODO Make this public when the entire class is package-private.
   */
  /*public*/ void CalendarAstronomer::getSunLongitude(double jDay, double &longitude, double &meanAnomaly)
  {
      // See page 86 of "Practial Astronomy with your Calculator",
      // by Peter Duffet-Smith, for details on the algorithm.
  
      double day = jDay - JD_EPOCH;       // Days since epoch
  
      // Find the angular distance the sun in a fictitious
      // circular orbit has travelled since the epoch.
      double epochAngle = norm2PI(CalendarAstronomer_PI2/TROPICAL_YEAR*day);
  
      // The epoch wasn't at the sun's perigee; find the angular distance
      // since perigee, which is called the "mean anomaly"
      meanAnomaly = norm2PI(epochAngle + SUN_ETA_G - SUN_OMEGA_G);
  
      // Now find the "true anomaly", e.g. the real solar longitude
      // by solving Kepler's equation for an elliptical orbit
      // NOTE: The 3rd ed. of the book lists omega_g and eta_g in different
      // equations; omega_g is to be correct.
      longitude =  norm2PI(trueAnomaly(meanAnomaly, SUN_E) + SUN_OMEGA_G);
  }
  
  /**
   * The position of the sun at this object's current date and time,
   * in equatorial coordinates.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  CalendarAstronomer::Equatorial& CalendarAstronomer::getSunPosition(CalendarAstronomer::Equatorial& result) {
      return eclipticToEquatorial(result, getSunLongitude(), 0);
  }
  
  
  /**
   * Constant representing the vernal equinox.
   * For use with {@link #getSunTime getSunTime}.
   * Note: In this case, "vernal" refers to the northern hemisphere's seasons.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  /*double CalendarAstronomer::VERNAL_EQUINOX() {
    return 0;
  }*/
  
  /**
   * Constant representing the summer solstice.
   * For use with {@link #getSunTime getSunTime}.
   * Note: In this case, "summer" refers to the northern hemisphere's seasons.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::SUMMER_SOLSTICE() {
      return  (CalendarAstronomer::PI/2);
  }
  
  /**
   * Constant representing the autumnal equinox.
   * For use with {@link #getSunTime getSunTime}.
   * Note: In this case, "autumn" refers to the northern hemisphere's seasons.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  /*double CalendarAstronomer::AUTUMN_EQUINOX() {
    return  (CalendarAstronomer::PI);
  }*/
  
  /**
   * Constant representing the winter solstice.
   * For use with {@link #getSunTime getSunTime}.
   * Note: In this case, "winter" refers to the northern hemisphere's seasons.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::WINTER_SOLSTICE() {
      return  ((CalendarAstronomer::PI*3)/2);
  }
  
  CalendarAstronomer::AngleFunc::~AngleFunc() {}
  
  /**
   * Find the next time at which the sun's ecliptic longitude will have
   * the desired value.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  class SunTimeAngleFunc : public CalendarAstronomer::AngleFunc {
  public:
      virtual ~SunTimeAngleFunc();
      virtual double eval(CalendarAstronomer& a) { return a.getSunLongitude(); }
  };
  
  SunTimeAngleFunc::~SunTimeAngleFunc() {}
  
  UDate CalendarAstronomer::getSunTime(double desired, UBool next)
  {
      SunTimeAngleFunc func;
      return timeOfAngle( func,
                          desired,
                          TROPICAL_YEAR,
                          MINUTE_MS,
                          next);
  }
  
  CalendarAstronomer::CoordFunc::~CoordFunc() {}
  
  class RiseSetCoordFunc : public CalendarAstronomer::CoordFunc {
  public:
      virtual ~RiseSetCoordFunc();
      virtual void eval(CalendarAstronomer::Equatorial& result, CalendarAstronomer&a) {  a.getSunPosition(result); }
  };
  
  RiseSetCoordFunc::~RiseSetCoordFunc() {}
  
  UDate CalendarAstronomer::getSunRiseSet(UBool rise)
  {
      UDate t0 = fTime;
  
      // Make a rough guess: 6am or 6pm local time on the current day
      double noon = ClockMath::floorDivide(fTime + fGmtOffset, (double)DAY_MS)*DAY_MS - fGmtOffset + (12*HOUR_MS);
  
      U_DEBUG_ASTRO_MSG(("Noon=%.2lf, %sL, gmtoff %.2lf\n", noon, debug_astro_date(noon+fGmtOffset), fGmtOffset));
      setTime(noon +  ((rise ? -6 : 6) * HOUR_MS));
      U_DEBUG_ASTRO_MSG(("added %.2lf ms as a guess,\n", ((rise ? -6. : 6.) * HOUR_MS)));
  
      RiseSetCoordFunc func;
      double t = riseOrSet(func,
                           rise,
                           .533 * DEG_RAD,        // Angular Diameter
                           34. /60.0 * DEG_RAD,    // Refraction correction
                           MINUTE_MS / 12.);       // Desired accuracy
  
      setTime(t0);
      return t;
  }
  
  // Commented out - currently unused. ICU 2.6, Alan
  //    //-------------------------------------------------------------------------
  //    // Alternate Sun Rise/Set
  //    // See Duffett-Smith p.93
  //    //-------------------------------------------------------------------------
  //
  //    // This yields worse results (as compared to USNO data) than getSunRiseSet().
  //    /**
  //     * TODO Make this when the entire class is package-private.
  //     */
  //    /*public*/ long getSunRiseSet2(boolean rise) {
  //        // 1. Calculate coordinates of the sun's center for midnight
  //        double jd = uprv_floor(getJulianDay() - 0.5) + 0.5;
  //        double[] sl = getSunLongitude(jd);//        double lambda1 = sl[0];
  //        Equatorial pos1 = eclipticToEquatorial(lambda1, 0);
  //
  //        // 2. Add ... to lambda to get position 24 hours later
  //        double lambda2 = lambda1 + 0.985647*DEG_RAD;
  //        Equatorial pos2 = eclipticToEquatorial(lambda2, 0);
  //
  //        // 3. Calculate LSTs of rising and setting for these two positions
  //        double tanL = ::tan(fLatitude);
  //        double H = ::acos(-tanL * ::tan(pos1.declination));
  //        double lst1r = (CalendarAstronomer_PI2 + pos1.ascension - H) * 24 / CalendarAstronomer_PI2;
  //        double lst1s = (pos1.ascension + H) * 24 / CalendarAstronomer_PI2;
  //               H = ::acos(-tanL * ::tan(pos2.declination));
  //        double lst2r = (CalendarAstronomer_PI2-H + pos2.ascension ) * 24 / CalendarAstronomer_PI2;
  //        double lst2s = (H + pos2.ascension ) * 24 / CalendarAstronomer_PI2;
  //        if (lst1r > 24) lst1r -= 24;
  //        if (lst1s > 24) lst1s -= 24;
  //        if (lst2r > 24) lst2r -= 24;
  //        if (lst2s > 24) lst2s -= 24;
  //
  //        // 4. Convert LSTs to GSTs.  If GST1 > GST2, add 24 to GST2.
  //        double gst1r = lstToGst(lst1r);
  //        double gst1s = lstToGst(lst1s);
  //        double gst2r = lstToGst(lst2r);
  //        double gst2s = lstToGst(lst2s);
  //        if (gst1r > gst2r) gst2r += 24;
  //        if (gst1s > gst2s) gst2s += 24;
  //
  //        // 5. Calculate GST at 0h UT of this date
  //        double t00 = utToGst(0);
  //
  //        // 6. Calculate GST at 0h on the observer's longitude
  //        double offset = ::round(fLongitude*12/PI); // p.95 step 6; he _rounds_ to nearest 15 deg.
  //        double t00p = t00 - offset*1.002737909;
  //        if (t00p < 0) t00p += 24; // do NOT normalize
  //
  //        // 7. Adjust
  //        if (gst1r < t00p) {
  //            gst1r += 24;
  //            gst2r += 24;
  //        }
  //        if (gst1s < t00p) {
  //            gst1s += 24;
  //            gst2s += 24;
  //        }
  //
  //        // 8.
  //        double gstr = (24.07*gst1r-t00*(gst2r-gst1r))/(24.07+gst1r-gst2r);
  //        double gsts = (24.07*gst1s-t00*(gst2s-gst1s))/(24.07+gst1s-gst2s);
  //
  //        // 9. Correct for parallax, refraction, and sun's diameter
  //        double dec = (pos1.declination + pos2.declination) / 2;
  //        double psi = ::acos(sin(fLatitude) / cos(dec));
  //        double x = 0.830725 * DEG_RAD; // parallax+refraction+diameter
  //        double y = ::asin(sin(x) / ::sin(psi)) * RAD_DEG;
  //        double delta_t = 240 * y / cos(dec) / 3600; // hours
  //
  //        // 10. Add correction to GSTs, subtract from GSTr
  //        gstr -= delta_t;
  //        gsts += delta_t;
  //
  //        // 11. Convert GST to UT and then to local civil time
  //        double ut = gstToUt(rise ? gstr : gsts);
  //        //System.out.println((rise?"rise=":"set=") + ut + ", delta_t=" + delta_t);
  //        long midnight = DAY_MS * (time / DAY_MS); // Find UT midnight on this day
  //        return midnight + (long) (ut * 3600000);
  //    }
  
  // Commented out - currently unused. ICU 2.6, Alan
  //    /**
  //     * Convert local sidereal time to Greenwich sidereal time.
  //     * Section 15.  Duffett-Smith p.21
  //     * @param lst in hours (0..24)
  //     * @return GST in hours (0..24)
  //     */
  //    double lstToGst(double lst) {
  //        double delta = fLongitude * 24 / CalendarAstronomer_PI2;
  //        return normalize(lst - delta, 24);
  //    }
  
  // Commented out - currently unused. ICU 2.6, Alan
  //    /**
  //     * Convert UT to GST on this date.
  //     * Section 12.  Duffett-Smith p.17
  //     * @param ut in hours
  //     * @return GST in hours
  //     */
  //    double utToGst(double ut) {
  //        return normalize(getT0() + ut*1.002737909, 24);
  //    }
  
  // Commented out - currently unused. ICU 2.6, Alan
  //    /**
  //     * Convert GST to UT on this date.
  //     * Section 13.  Duffett-Smith p.18
  //     * @param gst in hours
  //     * @return UT in hours
  //     */
  //    double gstToUt(double gst) {
  //        return normalize(gst - getT0(), 24) * 0.9972695663;
  //    }
  
  // Commented out - currently unused. ICU 2.6, Alan
  //    double getT0() {
  //        // Common computation for UT <=> GST
  //
  //        // Find JD for 0h UT
  //        double jd = uprv_floor(getJulianDay() - 0.5) + 0.5;
  //
  //        double s = jd - 2451545.0;
  //        double t = s / 36525.0;
  //        double t0 = 6.697374558 + (2400.051336 + 0.000025862*t)*t;
  //        return t0;
  //    }
  
  // Commented out - currently unused. ICU 2.6, Alan
  //    //-------------------------------------------------------------------------
  //    // Alternate Sun Rise/Set
  //    // See sci.astro FAQ
  //    // http://www.faqs.org/faqs/astronomy/faq/part3/section-5.html
  //    //-------------------------------------------------------------------------
  //
  //    // Note: This method appears to produce inferior accuracy as
  //    // compared to getSunRiseSet().
  //
  //    /**
  //     * TODO Make this when the entire class is package-private.
  //     */
  //    /*public*/ long getSunRiseSet3(boolean rise) {
  //
  //        // Compute day number for 0.0 Jan 2000 epoch
  //        double d = (double)(time - EPOCH_2000_MS) / DAY_MS;
  //
  //        // Now compute the Local Sidereal Time, LST:
  //        //
  //        double LST  =  98.9818  +  0.985647352 * d  +  /*UT*15  +  long*/
  //            fLongitude*RAD_DEG;
  //        //
  //        // (east long. positive).  Note that LST is here expressed in degrees,
  //        // where 15 degrees corresponds to one hour.  Since LST really is an angle,
  //        // it's convenient to use one unit---degrees---throughout.
  //
  //        //    COMPUTING THE SUN'S POSITION
  //        //    ----------------------------
  //        //
  //        // To be able to compute the Sun's rise/set times, you need to be able to
  //        // compute the Sun's position at any time.  First compute the "day
  //        // number" d as outlined above, for the desired moment.  Next compute:
  //        //
  //        double oblecl = 23.4393 - 3.563E-7 * d;
  //        //
  //        double w  =  282.9404  +  4.70935E-5   * d;
  //        double M  =  356.0470  +  0.9856002585 * d;
  //        double e  =  0.016709  -  1.151E-9     * d;
  //        //
  //        // This is the obliquity of the ecliptic, plus some of the elements of
  //        // the Sun's apparent orbit (i.e., really the Earth's orbit): w =
  //        // argument of perihelion, M = mean anomaly, e = eccentricity.
  //        // Semi-major axis is here assumed to be exactly 1.0 (while not strictly
  //        // true, this is still an accurate approximation).  Next compute E, the
  //        // eccentric anomaly:
  //        //
  //        double E = M + e*(180/PI) * ::sin(M*DEG_RAD) * ( 1.0 + e*cos(M*DEG_RAD) );
  //        //
  //        // where E and M are in degrees.  This is it---no further iterations are
  //        // needed because we know e has a sufficiently small value.  Next compute
  //        // the true anomaly, v, and the distance, r:
  //        //
  //        /*      r * cos(v)  =  */ double A  =  cos(E*DEG_RAD) - e;
  //        /*      r * ::sin(v)  =  */ double B  =  ::sqrt(1 - e*e) * ::sin(E*DEG_RAD);
  //        //
  //        // and
  //        //
  //        //      r  =  sqrt( A*A + B*B )
  //        double v  =  ::atan2( B, A )*RAD_DEG;
  //        //
  //        // The Sun's true longitude, slon, can now be computed:
  //        //
  //        double slon  =  v + w;
  //        //
  //        // Since the Sun is always at the ecliptic (or at least very very close to
  //        // it), we can use simplified formulae to convert slon (the Sun's ecliptic
  //        // longitude) to sRA and sDec (the Sun's RA and Dec):
  //        //
  //        //                   ::sin(slon) * cos(oblecl)
  //        //     tan(sRA)  =  -------------------------
  //        //            cos(slon)
  //        //
  //        //     ::sin(sDec) =  ::sin(oblecl) * ::sin(slon)
  //        //
  //        // As was the case when computing az, the Azimuth, if possible use an
  //        // atan2() function to compute sRA.
  //
  //        double sRA = ::atan2(sin(slon*DEG_RAD) * cos(oblecl*DEG_RAD), cos(slon*DEG_RAD))*RAD_DEG;
  //
  //        double sin_sDec = ::sin(oblecl*DEG_RAD) * ::sin(slon*DEG_RAD);
  //        double sDec = ::asin(sin_sDec)*RAD_DEG;
  //
  //        //    COMPUTING RISE AND SET TIMES
  //        //    ----------------------------
  //        //
  //        // To compute when an object rises or sets, you must compute when it
  //        // passes the meridian and the HA of rise/set.  Then the rise time is
  //        // the meridian time minus HA for rise/set, and the set time is the
  //        // meridian time plus the HA for rise/set.
  //        //
  //        // To find the meridian time, compute the Local Sidereal Time at 0h local
  //        // time (or 0h UT if you prefer to work in UT) as outlined above---name
  //        // that quantity LST0.  The Meridian Time, MT, will now be:
  //        //
  //        //     MT  =  RA - LST0
  //        double MT = normalize(sRA - LST, 360);
  //        //
  //        // where "RA" is the object's Right Ascension (in degrees!).  If negative,
  //        // add 360 deg to MT.  If the object is the Sun, leave the time as it is,
  //        // but if it's stellar, multiply MT by 365.2422/366.2422, to convert from
  //        // sidereal to solar time.  Now, compute HA for rise/set, name that
  //        // quantity HA0:
  //        //
  //        //                 ::sin(h0)  -  ::sin(lat) * ::sin(Dec)
  //        // cos(HA0)  =  ---------------------------------
  //        //                      cos(lat) * cos(Dec)
  //        //
  //        // where h0 is the altitude selected to represent rise/set.  For a purely
  //        // mathematical horizon, set h0 = 0 and simplify to:
  //        //
  //        //    cos(HA0)  =  - tan(lat) * tan(Dec)
  //        //
  //        // If you want to account for refraction on the atmosphere, set h0 = -35/60
  //        // degrees (-35 arc minutes), and if you want to compute the rise/set times
  //        // for the Sun's upper limb, set h0 = -50/60 (-50 arc minutes).
  //        //
  //        double h0 = -50/60 * DEG_RAD;
  //
  //        double HA0 = ::acos(
  //          (sin(h0) - ::sin(fLatitude) * sin_sDec) /
  //          (cos(fLatitude) * cos(sDec*DEG_RAD)))*RAD_DEG;
  //
  //        // When HA0 has been computed, leave it as it is for the Sun but multiply
  //        // by 365.2422/366.2422 for stellar objects, to convert from sidereal to
  //        // solar time.  Finally compute:
  //        //
  //        //    Rise time  =  MT - HA0
  //        //    Set  time  =  MT + HA0
  //        //
  //        // convert the times from degrees to hours by dividing by 15.
  //        //
  //        // If you'd like to check that your calculations are accurate or just
  //        // need a quick result, check the USNO's Sun or Moon Rise/Set Table,
  //        // <URL:http://aa.usno.navy.mil/AA/data/docs/RS_OneYear.html>.
  //
  //        double result = MT + (rise ? -HA0 : HA0); // in degrees
  //
  //        // Find UT midnight on this day
  //        long midnight = DAY_MS * (time / DAY_MS);
  //
  //        return midnight + (long) (result * 3600000 / 15);
  //    }
  
  //-------------------------------------------------------------------------
  // The Moon
  //-------------------------------------------------------------------------
  
  #define moonL0  (318.351648 * CalendarAstronomer::PI/180 )   // Mean long. at epoch
  #define moonP0 ( 36.340410 * CalendarAstronomer::PI/180 )   // Mean long. of perigee
  #define moonN0 ( 318.510107 * CalendarAstronomer::PI/180 )   // Mean long. of node
  #define moonI  (   5.145366 * CalendarAstronomer::PI/180 )   // Inclination of orbit
  #define moonE  (   0.054900 )            // Eccentricity of orbit
  
  // These aren't used right now
  #define moonA  (   3.84401e5 )           // semi-major axis (km)
  #define moonT0 (   0.5181 * CalendarAstronomer::PI/180 )     // Angular size at distance A
  #define moonPi (   0.9507 * CalendarAstronomer::PI/180 )     // Parallax at distance A
  
  /**
   * The position of the moon at the time set on this
   * object, in equatorial coordinates.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  const CalendarAstronomer::Equatorial& CalendarAstronomer::getMoonPosition()
  {
      //
      // See page 142 of "Practial Astronomy with your Calculator",
      // by Peter Duffet-Smith, for details on the algorithm.
      //
      if (moonPositionSet == FALSE) {
          // Calculate the solar longitude.  Has the side effect of
          // filling in "meanAnomalySun" as well.
          getSunLongitude();
  
          //
          // Find the # of days since the epoch of our orbital parameters.
          // TODO: Convert the time of day portion into ephemeris time
          //
          double day = getJulianDay() - JD_EPOCH;       // Days since epoch
  
          // Calculate the mean longitude and anomaly of the moon, based on
          // a circular orbit.  Similar to the corresponding solar calculation.
          double meanLongitude = norm2PI(13.1763966*PI/180*day + moonL0);
          meanAnomalyMoon = norm2PI(meanLongitude - 0.1114041*PI/180 * day - moonP0);
  
          //
          // Calculate the following corrections:
          //  Evection:   the sun's gravity affects the moon's eccentricity
          //  Annual Eqn: variation in the effect due to earth-sun distance
          //  A3:         correction factor (for ???)
          //
          double evection = 1.2739*PI/180 * ::sin(2 * (meanLongitude - sunLongitude)
              - meanAnomalyMoon);
          double annual   = 0.1858*PI/180 * ::sin(meanAnomalySun);
          double a3       = 0.3700*PI/180 * ::sin(meanAnomalySun);
  
          meanAnomalyMoon += evection - annual - a3;
  
          //
          // More correction factors:
          //  center  equation of the center correction
          //  a4      yet another error correction (???)
          //
          // TODO: Skip the equation of the center correction and solve Kepler's eqn?
          //
          double center = 6.2886*PI/180 * ::sin(meanAnomalyMoon);
          double a4 =     0.2140*PI/180 * ::sin(2 * meanAnomalyMoon);
  
          // Now find the moon's corrected longitude
          moonLongitude = meanLongitude + evection + center - annual + a4;
  
          //
          // And finally, find the variation, caused by the fact that the sun's
          // gravitational pull on the moon varies depending on which side of
          // the earth the moon is on
          //
          double variation = 0.6583*CalendarAstronomer::PI/180 * ::sin(2*(moonLongitude - sunLongitude));
  
          moonLongitude += variation;
  
          //
          // What we've calculated so far is the moon's longitude in the plane
          // of its own orbit.  Now map to the ecliptic to get the latitude
          // and longitude.  First we need to find the longitude of the ascending
          // node, the position on the ecliptic where it is crossed by the moon's
          // orbit as it crosses from the southern to the northern hemisphere.
          //
          double nodeLongitude = norm2PI(moonN0 - 0.0529539*PI/180 * day);
  
          nodeLongitude -= 0.16*PI/180 * ::sin(meanAnomalySun);
  
          double y = ::sin(moonLongitude - nodeLongitude);
          double x = cos(moonLongitude - nodeLongitude);
  
          moonEclipLong = ::atan2(y*cos(moonI), x) + nodeLongitude;
          double moonEclipLat = ::asin(y * ::sin(moonI));
  
          eclipticToEquatorial(moonPosition, moonEclipLong, moonEclipLat);
          moonPositionSet = TRUE;
      }
      return moonPosition;
  }
  
  /**
   * The "age" of the moon at the time specified in this object.
   * This is really the angle between the
   * current ecliptic longitudes of the sun and the moon,
   * measured in radians.
   *
   * @see #getMoonPhase
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getMoonAge() {
      // See page 147 of "Practial Astronomy with your Calculator",
      // by Peter Duffet-Smith, for details on the algorithm.
      //
      // Force the moon's position to be calculated.  We're going to use
      // some the intermediate results cached during that calculation.
      //
      getMoonPosition();
  
      return norm2PI(moonEclipLong - sunLongitude);
  }
  
  /**
   * Calculate the phase of the moon at the time set in this object.
   * The returned phase is a <code>double</code> in the range
   * <code>0 <= phase < 1</code>, interpreted as follows:
   * <ul>
   * <li>0.00: New moon
   * <li>0.25: First quarter
   * <li>0.50: Full moon
   * <li>0.75: Last quarter
   * </ul>
   *
   * @see #getMoonAge
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  double CalendarAstronomer::getMoonPhase() {
      // See page 147 of "Practial Astronomy with your Calculator",
      // by Peter Duffet-Smith, for details on the algorithm.
      return 0.5 * (1 - cos(getMoonAge()));
  }
  
  /**
   * Constant representing a new moon.
   * For use with {@link #getMoonTime getMoonTime}
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  const CalendarAstronomer::MoonAge CalendarAstronomer::NEW_MOON() {
      return  CalendarAstronomer::MoonAge(0);
  }
  
  /**
   * Constant representing the moon's first quarter.
   * For use with {@link #getMoonTime getMoonTime}
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  /*const CalendarAstronomer::MoonAge CalendarAstronomer::FIRST_QUARTER() {
    return   CalendarAstronomer::MoonAge(CalendarAstronomer::PI/2);
  }*/
  
  /**
   * Constant representing a full moon.
   * For use with {@link #getMoonTime getMoonTime}
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  const CalendarAstronomer::MoonAge CalendarAstronomer::FULL_MOON() {
      return   CalendarAstronomer::MoonAge(CalendarAstronomer::PI);
  }
  /**
   * Constant representing the moon's last quarter.
   * For use with {@link #getMoonTime getMoonTime}
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  
  class MoonTimeAngleFunc : public CalendarAstronomer::AngleFunc {
  public:
      virtual ~MoonTimeAngleFunc();
      virtual double eval(CalendarAstronomer&a) { return a.getMoonAge(); }
  };
  
  MoonTimeAngleFunc::~MoonTimeAngleFunc() {}
  
  /*const CalendarAstronomer::MoonAge CalendarAstronomer::LAST_QUARTER() {
    return  CalendarAstronomer::MoonAge((CalendarAstronomer::PI*3)/2);
  }*/
  
  /**
   * Find the next or previous time at which the Moon's ecliptic
   * longitude will have the desired value.
   * <p>
   * @param desired   The desired longitude.
   * @param next      <tt>true</tt> if the next occurrance of the phase
   *                  is desired, <tt>false</tt> for the previous occurrance.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  UDate CalendarAstronomer::getMoonTime(double desired, UBool next)
  {
      MoonTimeAngleFunc func;
      return timeOfAngle( func,
                          desired,
                          SYNODIC_MONTH,
                          MINUTE_MS,
                          next);
  }
  
  /**
   * Find the next or previous time at which the moon will be in the
   * desired phase.
   * <p>
   * @param desired   The desired phase of the moon.
   * @param next      <tt>true</tt> if the next occurrance of the phase
   *                  is desired, <tt>false</tt> for the previous occurrance.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  UDate CalendarAstronomer::getMoonTime(const CalendarAstronomer::MoonAge& desired, UBool next) {
      return getMoonTime(desired.value, next);
  }
  
  class MoonRiseSetCoordFunc : public CalendarAstronomer::CoordFunc {
  public:
      virtual ~MoonRiseSetCoordFunc();
      virtual void eval(CalendarAstronomer::Equatorial& result, CalendarAstronomer&a) { result = a.getMoonPosition(); }
  };
  
  MoonRiseSetCoordFunc::~MoonRiseSetCoordFunc() {}
  
  /**
   * Returns the time (GMT) of sunrise or sunset on the local date to which
   * this calendar is currently set.
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  UDate CalendarAstronomer::getMoonRiseSet(UBool rise)
  {
      MoonRiseSetCoordFunc func;
      return riseOrSet(func,
                       rise,
                       .533 * DEG_RAD,        // Angular Diameter
                       34 /60.0 * DEG_RAD,    // Refraction correction
                       MINUTE_MS);            // Desired accuracy
  }
  
  //-------------------------------------------------------------------------
  // Interpolation methods for finding the time at which a given event occurs
  //-------------------------------------------------------------------------
  
  UDate CalendarAstronomer::timeOfAngle(AngleFunc& func, double desired,
                                        double periodDays, double epsilon, UBool next)
  {
      // Find the value of the function at the current time
      double lastAngle = func.eval(*this);
  
      // Find out how far we are from the desired angle
      double deltaAngle = norm2PI(desired - lastAngle) ;
  
      // Using the average period, estimate the next (or previous) time at
      // which the desired angle occurs.
      double deltaT =  (deltaAngle + (next ? 0.0 : - CalendarAstronomer_PI2 )) * (periodDays*DAY_MS) / CalendarAstronomer_PI2;
  
      double lastDeltaT = deltaT; // Liu
      UDate startTime = fTime; // Liu
  
      setTime(fTime + uprv_ceil(deltaT));
  
      // Now iterate until we get the error below epsilon.  Throughout
      // this loop we use normPI to get values in the range -Pi to Pi,
      // since we're using them as correction factors rather than absolute angles.
      do {
          // Evaluate the function at the time we've estimated
          double angle = func.eval(*this);
  
          // Find the # of milliseconds per radian at this point on the curve
          double factor = uprv_fabs(deltaT / normPI(angle-lastAngle));
  
          // Correct the time estimate based on how far off the angle is
          deltaT = normPI(desired - angle) * factor;
  
          // HACK:
          //
          // If abs(deltaT) begins to diverge we need to quit this loop.
          // This only appears to happen when attempting to locate, for
          // example, a new moon on the day of the new moon.  E.g.:
          //
          // This result is correct:
          // newMoon(7508(Mon Jul 23 00:00:00 CST 1990,false))=
          //   Sun Jul 22 10:57:41 CST 1990
          //
          // But attempting to make the same call a day earlier causes deltaT
          // to diverge:
          // CalendarAstronomer.timeOfAngle() diverging: 1.348508727575625E9 ->
          //   1.3649828540224032E9
          // newMoon(7507(Sun Jul 22 00:00:00 CST 1990,false))=
          //   Sun Jul 08 13:56:15 CST 1990
          //
          // As a temporary solution, we catch this specific condition and
          // adjust our start time by one eighth period days (either forward
          // or backward) and try again.
          // Liu 11/9/00
          if (uprv_fabs(deltaT) > uprv_fabs(lastDeltaT)) {
              double delta = uprv_ceil (periodDays * DAY_MS / 8.0);
              setTime(startTime + (next ? delta : -delta));
              return timeOfAngle(func, desired, periodDays, epsilon, next);
          }
  
          lastDeltaT = deltaT;
          lastAngle = angle;
  
          setTime(fTime + uprv_ceil(deltaT));
      }
      while (uprv_fabs(deltaT) > epsilon);
  
      return fTime;
  }
  
  UDate CalendarAstronomer::riseOrSet(CoordFunc& func, UBool rise,
                                      double diameter, double refraction,
                                      double epsilon)
  {
      Equatorial pos;
      double      tanL   = ::tan(fLatitude);
      double     deltaT = 0;
      int32_t         count = 0;
  
      //
      // Calculate the object's position at the current time, then use that
      // position to calculate the time of rising or setting.  The position
      // will be different at that time, so iterate until the error is allowable.
      //
      U_DEBUG_ASTRO_MSG(("setup rise=%s, dia=%.3lf, ref=%.3lf, eps=%.3lf\n",
          rise?"T":"F", diameter, refraction, epsilon));
      do {
          // See "Practical Astronomy With Your Calculator, section 33.
          func.eval(pos, *this);
          double angle = ::acos(-tanL * ::tan(pos.declination));
          double lst = ((rise ? CalendarAstronomer_PI2-angle : angle) + pos.ascension ) * 24 / CalendarAstronomer_PI2;
  
          // Convert from LST to Universal Time.
          UDate newTime = lstToUT( lst );
  
          deltaT = newTime - fTime;
          setTime(newTime);
          U_DEBUG_ASTRO_MSG(("%d] dT=%.3lf, angle=%.3lf, lst=%.3lf,   A=%.3lf/D=%.3lf\n",
              count, deltaT, angle, lst, pos.ascension, pos.declination));
      }
      while (++ count < 5 && uprv_fabs(deltaT) > epsilon);
  
      // Calculate the correction due to refraction and the object's angular diameter
      double cosD  = ::cos(pos.declination);
      double psi   = ::acos(sin(fLatitude) / cosD);
      double x     = diameter / 2 + refraction;
      double y     = ::asin(sin(x) / ::sin(psi));
      long  delta  = (long)((240 * y * RAD_DEG / cosD)*SECOND_MS);
  
      return fTime + (rise ? -delta : delta);
  }
  											   /**
   * Return the obliquity of the ecliptic (the angle between the ecliptic
   * and the earth's equator) at the current time.  This varies due to
   * the precession of the earth's axis.
   *
   * @return  the obliquity of the ecliptic relative to the equator,
   *          measured in radians.
   */
  double CalendarAstronomer::eclipticObliquity() {
      if (isINVALID(eclipObliquity)) {
          const double epoch = 2451545.0;     // 2000 AD, January 1.5
  
          double T = (getJulianDay() - epoch) / 36525;
  
          eclipObliquity = 23.439292
              - 46.815/3600 * T
              - 0.0006/3600 * T*T
              + 0.00181/3600 * T*T*T;
  
          eclipObliquity *= DEG_RAD;
      }
      return eclipObliquity;
  }
  
  
  //-------------------------------------------------------------------------
  // Private data
  //-------------------------------------------------------------------------
  void CalendarAstronomer::clearCache() {
      const double INVALID = uprv_getNaN();
  
      julianDay       = INVALID;
      julianCentury   = INVALID;
      sunLongitude    = INVALID;
      meanAnomalySun  = INVALID;
      moonLongitude   = INVALID;
      moonEclipLong   = INVALID;
      meanAnomalyMoon = INVALID;
      eclipObliquity  = INVALID;
      siderealTime    = INVALID;
      siderealT0      = INVALID;
      moonPositionSet = FALSE;
  }
  
  //private static void out(String s) {
  //    System.out.println(s);
  //}
  
  //private static String deg(double rad) {
  //    return Double.toString(rad * RAD_DEG);
  //}
  
  //private static String hours(long ms) {
  //    return Double.toString((double)ms / HOUR_MS) + " hours";
  //}
  
  /**
   * @internal
   * @deprecated ICU 2.4. This class may be removed or modified.
   */
  /*UDate CalendarAstronomer::local(UDate localMillis) {
    // TODO - srl ?
    TimeZone *tz = TimeZone::createDefault();
    int32_t rawOffset;
    int32_t dstOffset;
    UErrorCode status = U_ZERO_ERROR;
    tz->getOffset(localMillis, TRUE, rawOffset, dstOffset, status);
    delete tz;
    return localMillis - rawOffset;
  }*/
  
  // Debugging functions
  UnicodeString CalendarAstronomer::Ecliptic::toString() const
  {
  #ifdef U_DEBUG_ASTRO
      char tmp[800];
      sprintf(tmp, "[%.5f,%.5f]", longitude*RAD_DEG, latitude*RAD_DEG);
      return UnicodeString(tmp, "");
  #else
      return UnicodeString();
  #endif
  }
  
  UnicodeString CalendarAstronomer::Equatorial::toString() const
  {
  #ifdef U_DEBUG_ASTRO
      char tmp[400];
      sprintf(tmp, "%f,%f",
          (ascension*RAD_DEG), (declination*RAD_DEG));
      return UnicodeString(tmp, "");
  #else
      return UnicodeString();
  #endif
  }
  
  UnicodeString CalendarAstronomer::Horizon::toString() const
  {
  #ifdef U_DEBUG_ASTRO
      char tmp[800];
      sprintf(tmp, "[%.5f,%.5f]", altitude*RAD_DEG, azimuth*RAD_DEG);
      return UnicodeString(tmp, "");
  #else
      return UnicodeString();
  #endif
  }
  
  
  //  static private String radToHms(double angle) {
  //    int hrs = (int) (angle*RAD_HOUR);
  //    int min = (int)((angle*RAD_HOUR - hrs) * 60);
  //    int sec = (int)((angle*RAD_HOUR - hrs - min/60.0) * 3600);
  
  //    return Integer.toString(hrs) + "h" + min + "m" + sec + "s";
  //  }
  
  //  static private String radToDms(double angle) {
  //    int deg = (int) (angle*RAD_DEG);
  //    int min = (int)((angle*RAD_DEG - deg) * 60);
  //    int sec = (int)((angle*RAD_DEG - deg - min/60.0) * 3600);
  
  //    return Integer.toString(deg) + "\u00b0" + min + "'" + sec + "\"";
  //  }
  
  // =============== Calendar Cache ================
  
  void CalendarCache::createCache(CalendarCache** cache, UErrorCode& status) {
      ucln_i18n_registerCleanup(UCLN_I18N_ASTRO_CALENDAR, calendar_astro_cleanup);
      if(cache == NULL) {
          status = U_MEMORY_ALLOCATION_ERROR;
      } else {
          *cache = new CalendarCache(32, status);
          if(U_FAILURE(status)) {
              delete *cache;
              *cache = NULL;
          }
      }
  }
  
  int32_t CalendarCache::get(CalendarCache** cache, int32_t key, UErrorCode &status) {
      int32_t res;
  
      if(U_FAILURE(status)) {
          return 0;
      }
      umtx_lock(&ccLock);
  
      if(*cache == NULL) {
          createCache(cache, status);
          if(U_FAILURE(status)) {
              umtx_unlock(&ccLock);
              return 0;
          }
      }
  
      res = uhash_igeti((*cache)->fTable, key);
      U_DEBUG_ASTRO_MSG(("%p: GET: [%d] == %d\n", (*cache)->fTable, key, res));
  
      umtx_unlock(&ccLock);
      return res;
  }
  
  void CalendarCache::put(CalendarCache** cache, int32_t key, int32_t value, UErrorCode &status) {
      if(U_FAILURE(status)) {
          return;
      }
      umtx_lock(&ccLock);
  
      if(*cache == NULL) {
          createCache(cache, status);
          if(U_FAILURE(status)) {
              umtx_unlock(&ccLock);
              return;
          }
      }
  
      uhash_iputi((*cache)->fTable, key, value, &status);
      U_DEBUG_ASTRO_MSG(("%p: PUT: [%d] := %d\n", (*cache)->fTable, key, value));
  
      umtx_unlock(&ccLock);
  }
  
  CalendarCache::CalendarCache(int32_t size, UErrorCode &status) {
      fTable = uhash_openSize(uhash_hashLong, uhash_compareLong, NULL, size, &status);
      U_DEBUG_ASTRO_MSG(("%p: Opening.\n", fTable));
  }
  
  CalendarCache::~CalendarCache() {
      if(fTable != NULL) {
          U_DEBUG_ASTRO_MSG(("%p: Closing.\n", fTable));
          uhash_close(fTable);
      }
  }
  
  U_NAMESPACE_END
  
  #endif //  !UCONFIG_NO_FORMATTING
  