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 /************************************************************************

  * 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 UMutex ccLock = U_MUTEX_INITIALIZER;

 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