29-mar-2007 NvE New memberfunction Almanac() introduced in AliTimestamp to provide a

[u/mrichter/AliRoot.git] / RALICE / AliTimestamp.cxx

/**************************************************************************
 * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
 *                                                                        *
 * Author: The ALICE Off-line Project.                                    *
 * Contributors are mentioned in the code where appropriate.              *
 *                                                                        *
 * Permission to use, copy, modify and distribute this software and its   *
 * documentation strictly for non-commercial purposes is hereby granted   *
 * without fee, provided that the above copyright notice appears in all   *
 * copies and that both the copyright notice and this permission notice   *
 * appear in the supporting documentation. The authors make no claims     *
 * about the suitability of this software for any purpose. It is          *
 * provided "as is" without express or implied warranty.                  *
 **************************************************************************/

// $Id$

///////////////////////////////////////////////////////////////////////////
// Class AliTimestamp
// Handling of timestamps for (astro)particle physics reserach.
//
// This class is derived from TTimeStamp and provides additional
// facilities (e.g. Julian date) which are commonly used in the
// field of (astro)particle physics.
//
// The Julian Date (JD) indicates the number of days since noon (UT) on
// 01 jan -4712 (i.e. noon 01 jan 4713 BC), being day 0 of the Julian calendar.
//
// The Modified Julian Date (MJD) indicates the number of days since midnight
// (UT) on 17-nov-1858, which corresponds to 2400000.5 days after day 0 of the
// Julian calendar.
//
// The Truncated Julian Date (TJD) corresponds to 2440000.5 days after day 0
// of the Julian calendar and consequently TJD=MJD-40000.
// This TJD date indication was used by the Vela and Batse missions in
// view of Gamma Ray Burst investigations.
//
// The Julian Epoch (JE) indicates the fractional elapsed Julian year count
// since the start of the Gregorian year count.
// A Julian year is defined to be 365.25 days and starts at 01-jan 12:00:00 UT.
// As such, the integer part of JE corresponds to the usual Gregorian year count,
// apart from 01-jan before 12:00:00 UT.
// So, 01-jan-1965 12:00:00 UT corresponds to JE=1965.0
//
// The Besselian Epoch (BE) indicates the fractional elapsed Besselian year count
// since the start of the Gregorian year count.
// A Besselian (or tropical) year is defined to be 365.242198781 days.
// The date 31-dec-1949 22:09:46.862 UT corresponds to BE=1950.0
//
// The Besselian and Julian epochs are used in astronomical catalogs
// to denote values of time varying observables like e.g. right ascension.
//
// Because of the fact that the Julian date indicators are all w.r.t. UT
// they provide an absolute timescale irrespective of timezone or daylight
// saving time (DST).
//
// In view of astronomical observations and positioning it is convenient
// to have also a UT equivalent related to stellar meridian transitions.
// This is achieved by the Greenwich Sidereal Time (GST).
// The GST is defined as the right ascension of the objects passing
// the Greenwich meridian at 00:00:00 UT.
// Due to the rotation of the Earth around the Sun, a sidereal day
// lasts 86164.09 seconds (23h 56m 04.09s) compared to the mean solar
// day of 86400 seconds (24h).
// Furthermore, precession of the earth's spin axis results in the fact
// that the zero point of right ascension (vernal equinox) gradually 
// moves along the celestial equator.
// In addition, tidal friction and ocean and atmospheric effects will
// induce seasonal variations in the earth's spin rate and polar motion
// of the earth's spin axis.
// Taking the above effects into account leads to what is called
// the Greenwich Mean Sidereal Time (GMST).
// In case also the nutation of the earth's spin axis is taken into
// account we speak of the Greenwich Apparent Sidereal Time (GAST).
//
// This AliTimestamp facility allows for picosecond precision, in view
// of time of flight analyses for particle physics experiments.
// For normal date/time indication the standard nanosecond precision
// will in general be sufficient.
// Note that when the fractional JD, MJD and TJD counts are used instead
// of the integer (days,sec,ns) specification, the nanosecond precision
// may be lost due to computer accuracy w.r.t. floating point operations.
//
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to JD=2440587.5 or the start of MJD=40587 or TJD=587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input (M/T)JD and time.
// Obviously this TTimeStamp implementation would prevent usage of values
// smaller than JD=2440587.5 or MJD=40587 or TJD=587.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (M/T)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later (M/T)JD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.
// This implies that for these earlier/later (M/T)JD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.
// As such the standard TTimeStamp parameters do not appear on the print output
// when invoking the Date() memberfunction for these earlier/later (M/T)JD values.  
//
// Examples :
// ==========
//
// Note : All TTimeStamp functionality is available as well.
//
// AliTimestamp t;
//
// t.Date();
// 
// // Retrieve Julian Date
// Int_t jd,jsec,jns;
// t.GetJD(jd,jsec,jns);
//
// // Retrieve fractional Truncated Julian Date
// Double_t tjd=t.GetTJD();
//
// // Retrieve fractional Julian Epoch
// Double_t je=t.GetJE();
//
// // Set to a specific Modified Julian Date
// Int_t mjd=50537;
// Int_t mjsec=1528;
// Int_t mjns=185643;
// t.SetMJD(mjd,mjsec,mjns);
//
// t.Date();
//
// // Time intervals for e.g. trigger or TOF analysis
// AliEvent evt;
// AliTrack* tx=evt.GetTrack(5);
// AliTimestamp* timex=tx->GetTimestamp();
// Double_t dt=evt.GetDifference(timex,"ps");
// AliTimestamp trig((AliTimestamp)evt);
// trig.Add(0,0,2,173);
// AliSignal* sx=evt.GetHit(23);
// AliTimestamp* timex=sx->GetTimestamp();
// Double_t dt=trig.GetDifference(timex,"ps");
// Int_t d,s,ns,ps;
// trig.GetDifference(timex,d,s,ns,ps);
//
// // Some practical conversion facilities
// // Note : They don't influence the actual date/time settings
// //        and as such can also be invoked as AliTimestamp::Convert(...) etc...
// Int_t y=1921;
// Int_t m=7;
// Int_t d=21;
// Int_t hh=15;
// Int_t mm=23;
// Int_t ss=47;
// Int_t ns=811743;
// Double_t jdate=t.GetJD(y,m,d,hh,mm,ss,ns);
//
// Int_t days,secs,nsecs;
// Double_t date=421.1949327;
// t.Convert(date,days,secs,nsecs);
//
// days=875;
// secs=23;
// nsecs=9118483;
// date=t.Convert(days,secs,nsecs);
//
// Double_t mjdate=40563.823744;
// Double_t epoch=t.GetJE(mjdate,"mjd");
//
//--- Author: Nick van Eijndhoven 28-jan-2005 Utrecht University.
//- Modified: NvE $Date$ Utrecht University.
///////////////////////////////////////////////////////////////////////////

#include "AliTimestamp.h"
#include "Riostream.h"

ClassImp(AliTimestamp) // Class implementation to enable ROOT I/O
 
AliTimestamp::AliTimestamp() : TTimeStamp()
{
// Default constructor
// Creation of an AliTimestamp object and initialisation of parameters.
// All attributes are initialised to the current date/time as specified
// in the docs of TTimeStamp.

 FillJulian();
 fJps=0;
}
///////////////////////////////////////////////////////////////////////////
AliTimestamp::AliTimestamp(TTimeStamp& t) : TTimeStamp(t)
{
// Creation of an AliTimestamp object and initialisation of parameters.
// All attributes are initialised to the values of the input TTimeStamp.

 FillJulian();
 fJps=0;
}
///////////////////////////////////////////////////////////////////////////
AliTimestamp::~AliTimestamp()
{
// Destructor to delete dynamically allocated memory.
}
///////////////////////////////////////////////////////////////////////////
AliTimestamp::AliTimestamp(const AliTimestamp& t) : TTimeStamp(t)
{
// Copy constructor

 fMJD=t.fMJD;
 fJsec=t.fJsec;
 fJns=t.fJns;
 fJps=t.fJps;
 fCalcs=t.fCalcs;
 fCalcns=t.fCalcns;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::Date(Int_t mode,Double_t offset)
{
// Print date/time info.
//
// mode = 1 ==> Only the UT yy-mm-dd hh:mm:ss.sss and GMST info is printed
//        2 ==> Only the Julian parameter info is printed
//        3 ==> Both the UT, GMST and Julian parameter info is printed
//       -1 ==> Only the UT yy-mm-dd hh:mm:ss.sss and GAST info is printed
//       -3 ==> Both the UT, GAST and Julian parameter info is printed
//
// offset : Local time offset from UT (and also GMST) in fractional hours.
//
// When an offset value is specified, the corresponding local times
// LT and LMST (or LAST) are printed as well.
//
// The default values are mode=3 and offset=0.
//
// Note : In case the (M/T)JD falls outside the TTimeStamp range,
//        the yy-mm-dd info will be omitted.

 Int_t mjd,mjsec,mjns,mjps;
 GetMJD(mjd,mjsec,mjns);
 mjps=GetPs();

 TString month[12]={"Jan","Feb","Mar","Apr","May","Jun","Jul","Aug","Sep","Oct","Nov","Dec"};
 TString day[7]={"Mon","Tue","Wed","Thu","Fri","Sat","Sun"};
 UInt_t y,m,d,wd;
 Int_t hh,mm,ss,ns,ps;
 Double_t gast;
 
 if (abs(mode)==1 || abs(mode)==3)
 {
  if (mjd>=40587 && (mjd<65442 || (mjd==65442 && mjsec<8047)))
  {
   GetDate(kTRUE,0,&y,&m,&d);
   wd=GetDayOfWeek(kTRUE,0);
   cout << " " << day[wd-1].Data() << ", " << setfill('0') << setw(2) << d << " "
        << setfill(' ') << month[m-1].Data() << " " << y << " ";
  }
  else
  {
   cout << " Time ";
  }
  GetUT(hh,mm,ss,ns,ps);
  cout << setfill('0') << setw(2) << hh << ":"
       << setw(2) << mm << ":" << setw(2) << ss << "."
       << setw(9) << ns << setw(3) << ps << " (UT)  ";
  if (mode>0)
  {
   GetGMST(hh,mm,ss,ns,ps);
  }
  else
  {
   gast=GetGAST();
   Convert(gast,hh,mm,ss,ns,ps);
  }
  cout << setfill('0') << setw(2) << hh << ":"
       << setw(2) << mm << ":" << setw(2) << ss << "."
       << setw(9) << ns << setw(3) << ps;
  if (mode>0)
  {
   cout << " (GMST)" << endl;
  }
  else
  {
   cout << " (GAST)" << endl;
  }

  // Local time information
  if (offset)
  {
   // Determine the new date by including the offset
   AliTimestamp t2(*this);
   t2.Add(offset);
   Int_t mjd2,mjsec2,mjns2;
   t2.GetMJD(mjd2,mjsec2,mjns2);
   if (mjd2>=40587 && (mjd2<65442 || (mjd2==65442 && mjsec2<8047)))
   {
    t2.GetDate(kTRUE,0,&y,&m,&d);
    wd=t2.GetDayOfWeek(kTRUE,0);
    cout << " " << day[wd-1].Data() << ", " << setfill('0') << setw(2) << d << " "
         << setfill(' ') << month[m-1].Data() << " " << y << " ";
   }
   else
   {
    cout << " Time ";
   }
   // Determine the local time by including the offset w.r.t. the original timestamp
   Double_t hlt=GetLT(offset);
   Double_t hlst=0;
   if (mode>0)
   {
    hlst=GetLMST(offset);
   }
   else
   {
    hlst=GetLAST(offset);
   }
   PrintTime(hlt,12); cout << " (LT)  "; PrintTime(hlst,12);
   if (mode>0)
   {
    cout << " (LMST)" << endl;
   }
   else
   {
    cout << " (LAST)" << endl;
   }
  }
 }
 if (abs(mode)==2 || abs(mode)==3)
 {
  Int_t jd,jsec,jns;
  GetJD(jd,jsec,jns);
  Int_t tjd,tjsec,tjns;
  GetTJD(tjd,tjsec,tjns);
  cout << " Julian Epoch : " << setprecision(25) << GetJE()
       << " Besselian Epoch : " << setprecision(25) << GetBE() << endl;
  cout << " JD : " << jd << " sec : " << jsec << " ns : " << jns << " ps : " << fJps
       << " Fractional : " << setprecision(25) << GetJD() << endl;
  cout << " MJD : " << mjd << "  sec : " << mjsec << " ns : " << mjns << " ps : " << fJps
       << " Fractional : " << setprecision(25) << GetMJD() << endl;
  cout << " TJD : " << tjd << "  sec : " << tjsec << " ns : " << tjns << " ps : " << fJps
       << " Fractional : " << setprecision(25) << GetTJD() << endl;
 }
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetJD(Int_t y,Int_t m,Int_t d,Int_t hh,Int_t mm,Int_t ss,Int_t ns) const
{
// Provide the (fractional) Julian Date (JD) corresponding to the UT date
// and time in the Gregorian calendar as specified by the input arguments.
//
// The input arguments represent the following :
// y  : year in UT (e.g. 1952, 2003 etc...)
// m  : month in UT (1=jan  2=feb etc...)
// d  : day in UT (1-31)
// hh : elapsed hours in UT (0-23) 
// mm : elapsed minutes in UT (0-59)
// ss : elapsed seconds in UT (0-59)
// ns : remaining fractional elapsed second of UT in nanosecond
//
// This algorithm is valid for all AD dates in the Gregorian calendar
// following the recipe of R.W. Sinnott Sky & Telescope 82, (aug. 1991) 183.
// See also http://scienceworld.wolfram.com/astronomy/JulianDate.html
//
// In case of invalid input, a value of -1 is returned.
//
// Note :
// ------
// This memberfunction only provides the JD corresponding to the
// UT input arguments. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp. 

 if (y<0 || m<1 || m>12 || d<1 || d>31) return -1;
 if (hh<0 || hh>23 || mm<0 || mm>59 || ss<0 || ss>59 || ns<0 || ns>1e9) return -1;

 // The UT daytime in fractional hours
 Double_t ut=double(hh)+double(mm)/60.+(double(ss)+double(ns)*1.e-9)/3600.;

 Double_t JD=0;
 
 JD=367*y-int(7*(y+int((m+9)/12))/4)
    -int(3*(int((y+(m-9)/7)/100)+1)/4)
    +int(275*m/9)+d+1721028.5+ut/24.;

 return JD;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetMJD(Int_t y,Int_t m,Int_t d,Int_t hh,Int_t mm,Int_t ss,Int_t ns) const
{
// Provide the (fractional) Modified Julian Date corresponding to the UT
// date and time in the Gregorian calendar as specified by the input arguments.
//
// The input arguments represent the following :
// y  : year in UT (e.g. 1952, 2003 etc...)
// m  : month in UT (1=jan  2=feb etc...)
// d  : day in UT (1-31)
// hh : elapsed hours in UT (0-23) 
// mm : elapsed minutes in UT (0-59)
// ss : elapsed seconds in UT (0-59)
// ns : remaining fractional elapsed second of UT in nanosecond
//
// This algorithm is valid for all AD dates in the Gregorian calendar
// following the recipe of R.W. Sinnott Sky & Telescope 82, (aug. 1991) 183.
// See also http://scienceworld.wolfram.com/astronomy/JulianDate.html
//
// In case of invalid input, a value of -1 is returned.
//
// Note :
// ------
// This memberfunction only provides the MJD corresponding to the
// UT input arguments. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.

 Double_t JD=GetJD(y,m,d,hh,mm,ss,ns);

 if (JD<0) return JD;

 Double_t MJD=JD-2400000.5;

 return MJD; 
} 
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetTJD(Int_t y,Int_t m,Int_t d,Int_t hh,Int_t mm,Int_t ss,Int_t ns) const
{
// Provide the (fractional) Truncated Julian Date corresponding to the UT
// date and time in the Gregorian calendar as specified by the input arguments.
//
// The input arguments represent the following :
// y  : year in UT (e.g. 1952, 2003 etc...)
// m  : month in UT (1=jan  2=feb etc...)
// d  : day in UT (1-31)
// hh : elapsed hours in UT (0-23) 
// mm : elapsed minutes in UT (0-59)
// ss : elapsed seconds in UT (0-59)
// ns : remaining fractional elapsed second of UT in nanosecond
//
// This algorithm is valid for all AD dates in the Gregorian calendar
// following the recipe of R.W. Sinnott Sky & Telescope 82, (aug. 1991) 183.
// See also http://scienceworld.wolfram.com/astronomy/JulianDate.html
//
// In case of invalid input, a value of -1 is returned.
//
// Note :
// ------
// This memberfunction only provides the TJD corresponding to the
// UT input arguments. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.

 Double_t JD=GetJD(y,m,d,hh,mm,ss,ns);

 if (JD<0) return JD;

 Double_t TJD=JD-2440000.5;

 return TJD; 
} 
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetJE(Double_t date,TString mode) const
{
// Provide the Julian Epoch (JE) corresponding to the specified date.
// The argument "mode" indicates the type of the argument "date".
//
// Available modes are :
// mode = "jd"  ==> date represents the Julian Date
//      = "mjd" ==> date represents the Modified Julian Date
//      = "tjd" ==> date represents the Truncated Julian Date
//
// The default is mode="jd".
//
// In case of invalid input, a value of -99999 is returned.
//
// Note :
// ------
// This memberfunction only provides the JE corresponding to the
// input arguments. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.

 if ((mode != "jd") && (mode != "mjd") && (mode != "tjd")) return -99999;

 Double_t jd=date;
 if (mode=="mjd") jd=date+2400000.5;
 if (mode=="tjd") jd=date+2440000.5;

 Double_t je=2000.+(jd-2451545.)/365.25;

 return je;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetBE(Double_t date,TString mode) const
{
// Provide the Besselian Epoch (JE) corresponding to the specified date.
// The argument "mode" indicates the type of the argument "date".
//
// Available modes are :
// mode = "jd"  ==> date represents the Julian Date
//      = "mjd" ==> date represents the Modified Julian Date
//      = "tjd" ==> date represents the Truncated Julian Date
//
// The default is mode="jd".
//
// In case of invalid input, a value of -99999 is returned.
//
// Note :
// ------
// This memberfunction only provides the BE corresponding to the
// input arguments. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.

 if ((mode != "jd") && (mode != "mjd") && (mode != "tjd")) return -99999;

 Double_t jd=date;
 if (mode=="mjd") jd=date+2400000.5;
 if (mode=="tjd") jd=date+2440000.5;

 Double_t be=1900.+(jd-2415020.31352)/365.242198781;

 return be;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::Convert(Double_t date,Int_t& days,Int_t& secs,Int_t& ns) const
{
// Convert date as fractional day count into integer days, secs and ns.
//
// Note : Due to computer accuracy the ns value may become inaccurate.
//
// The arguments represent the following :
// date : The input date as fractional day count
// days : Number of elapsed days
// secs : Remaining number of elapsed seconds
// ns   : Remaining fractional elapsed second in nanoseconds
//
// Note :
// ------
// This memberfunction only converts the input date into the corresponding
// integer parameters. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.
 
 days=int(date);
 date=date-double(days);
 Int_t daysecs=24*3600;
 date=date*double(daysecs);
 secs=int(date);
 date=date-double(secs);
 ns=int(date*1.e9);
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::Convert(Int_t days,Int_t secs,Int_t ns) const
{
// Convert date in integer days, secs and ns into fractional day count. 
//
// Note : Due to computer accuracy the ns precision may be lost.
//
// The input arguments represent the following :
// days : Number of elapsed days
// secs : Remaining number of elapsed seconds
// ns   : Remaining fractional elapsed second in nanoseconds
//
// Note :
// ------
// This memberfunction only converts the input integer parameters into the
// corresponding fractional day count. It does NOT set the corresponding
// Julian parameters for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.

 Double_t frac=double(secs)+double(ns)*1.e-9;
 Int_t daysecs=24*3600;
 frac=frac/double(daysecs);
 Double_t date=double(days)+frac;
 return date;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::Convert(Double_t h,Int_t& hh,Int_t& mm,Int_t& ss,Int_t& ns,Int_t& ps) const
{
// Convert fractional hour count h into hh:mm:ss:ns:ps.
// The sign of the input value will be neglected, so h<0 will result in
// the same output values as h>0.
//
// Note : Due to computer accuracy the ps value may become inaccurate.
//
// Note :
// ------
// This memberfunction only converts the input "h" into the corresponding
// integer parameters. It does NOT set the corresponding Julian parameters
// for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.
 
 // Neglect sign of h
 h=fabs(h);

 hh=int(h);
 h=h-double(hh);
 h=h*60.;
 mm=int(h);
 h=h-double(mm);
 h=h*60.;
 ss=int(h);
 h=h-double(ss);
 h=h*1.e9;
 ns=int(h);
 h=h-double(ns);
 h=h*1000.;
 ps=int(h);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::Convert(Double_t h,Int_t& hh,Int_t& mm,Double_t& ss) const
{
// Convert fractional hour count h into hh:mm:ss.s.
// The sign of the input value will be neglected, so h<0 will result in
// the same output values as h>0.
//
// Notes :
// -------
// 1) This memberfunction only converts the input "h" into the corresponding
//    hh:mm:ss.s values. It does NOT set the corresponding Julian parameters
//    for the current AliTimestamp instance.
//    As such the TTimeStamp limitations do NOT apply to this memberfunction.
//    To set the Julian parameters for the current AliTimestamp instance,
//    please use the corresponding SET() memberfunctions of either AliTimestamp
//    or TTimeStamp.
// 2) This facility can also be used to convert degrees in arcminutes etc...
 
 // Neglect sign of h
 h=fabs(h);
 
 hh=int(h);
 h=h-double(hh);
 h=h*60.;
 mm=int(h);
 h=h-double(mm);
 ss=h*60.;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::Convert(Int_t hh,Int_t mm,Int_t ss,Int_t ns,Int_t ps) const
{
// Convert hh:mm:ss:ns:ps into fractional hour count. 
// The sign of the input values will be neglected, so the output value
// will always correspond to a positive hh:mm:ss:ns:ps specification.
//
// Note : Due to computer accuracy the ps precision may be lost.
//
// Note :
// ------
// This memberfunction only converts the input integer parameters into the
// corresponding fractional hour count. It does NOT set the corresponding
// Julian parameters for the current AliTimestamp instance.
// As such the TTimeStamp limitations do NOT apply to this memberfunction.
// To set the Julian parameters for the current AliTimestamp instance,
// please use the corresponding SET() memberfunctions of either AliTimestamp
// or TTimeStamp.

 // Neglect the sign of the input values
 hh=abs(hh);
 mm=abs(mm);
 ss=abs(ss);
 ns=abs(ns);
 ps=abs(ps);

 Double_t h=hh;
 h+=double(mm)/60.+(double(ss)+double(ns)*1.e-9+double(ps)*1.e-12)/3600.;

 return h;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::Convert(Int_t hh,Int_t mm,Double_t ss) const
{
// Convert hh:mm:ss.s into fractional hour count. 
// The sign of the input values will be neglected, so the output value
// will always correspond to a positive hh:mm:ss.s specification.
//
// Notes :
// -------
// 1) This memberfunction only converts the input hh:mm:ss.s data into the
//    corresponding fractional hour count. It does NOT set the corresponding
//    Julian parameters for the current AliTimestamp instance.
//    As such the TTimeStamp limitations do NOT apply to this memberfunction.
//    To set the Julian parameters for the current AliTimestamp instance,
//    please use the corresponding SET() memberfunctions of either AliTimestamp
//    or TTimeStamp.
// 2) This facility can also be used to convert ddd:mm:ss.s into fractional degrees.

 // Neglect the sign of the input values
 hh=abs(hh);
 mm=abs(mm);
 ss=fabs(ss);

 Double_t h=hh;
 h+=double(mm)/60.+ss/3600.;

 return h;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::PrintTime(Double_t h,Int_t ndig) const
{
// Print a fractional hour count in hh:mm:ss.ssss format.
// The range of the printed hour value is : -24 < hh < 24.
// The argument "ndig" specifies the number of digits for the fractional
// seconds (e.g. ndig=6 corresponds to microsecond precision).
// No rounding will be performed, so a second count of 3.473 with ndig=1
// will appear as 03.4 on the output.
// Due to computer accuracy, precision on the picosecond level may get lost.
//
// The default is ndig=1.
//
// Note : The time info is printed without additional spaces or "endline".
//        This allows the print to be included in various composite output formats.

 Int_t hh,mm,ss;
 ULong64_t sfrac;
 Double_t s;

 while (h<-24)
 {
  h+=24.;
 }
 while (h>24)
 {
  h-=24.;
 }
   
 Convert(h,hh,mm,s);
 ss=Int_t(s);
 s-=Double_t(ss);
 s*=pow(10.,ndig);
 sfrac=ULong64_t(s);

 if (h<0) cout << "-";
 cout << setfill('0')
      << setw(2) << hh << ":" << setw(2) << mm << ":"
      << setw(2) << ss << "." << setw(ndig) << sfrac;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::FillJulian()
{
// Calculation and setting of the Julian date/time parameters corresponding
// to the current TTimeStamp date/time parameters.

 UInt_t y,m,d,hh,mm,ss;

 GetDate(kTRUE,0,&y,&m,&d);
 GetTime(kTRUE,0,&hh,&mm,&ss);
 Int_t ns=GetNanoSec();

 Double_t mjd=GetMJD(y,m,d,hh,mm,ss,ns);

 fMJD=int(mjd);
 fJsec=GetSec()%(24*3600); // Daytime in elapsed seconds
 fJns=ns;                  // Remaining fractional elapsed second in nanoseconds

 // Store the TTimeStamp seconds and nanoseconds values
 // for which this Julian calculation was performed.
 fCalcs=GetSec();
 fCalcns=GetNanoSec();
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::GetMJD(Int_t& mjd,Int_t& sec,Int_t& ns)
{
// Provide the Modified Julian Date (MJD) and time corresponding to the
// currently stored AliTimestamp date/time parameters.
//
// The returned arguments represent the following :
// mjd : The modified Julian date.
// sec : The number of seconds elapsed within the MJD.
// ns  : The remaining fractional number of seconds (in ns) elapsed within the MJD.

 if (fCalcs != GetSec() || fCalcns != GetNanoSec()) FillJulian();

 mjd=fMJD;
 sec=fJsec;
 ns=fJns;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetMJD()
{
// Provide the (fractional) Modified Julian Date (MJD) corresponding to the
// currently stored AliTimestamp date/time parameters.
//
// Due to computer accuracy the ns precision may be lost.
// It is advised to use the (mjd,sec,ns) getter instead.

 Int_t mjd=0;
 Int_t sec=0;
 Int_t ns=0;
 GetMJD(mjd,sec,ns);

 Double_t date=Convert(mjd,sec,ns);

 return date;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::GetTJD(Int_t& tjd,Int_t& sec, Int_t& ns)
{
// Provide the Truncated Julian Date (TJD) and time corresponding to the
// currently stored AliTimestamp date/time parameters.
//
// The returned arguments represent the following :
// tjd : The modified Julian date.
// sec : The number of seconds elapsed within the MJD.
// ns  : The remaining fractional number of seconds (in ns) elapsed within the MJD.

 Int_t mjd=0;
 GetMJD(mjd,sec,ns);

 tjd=mjd-40000;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetTJD()
{
// Provide the (fractional) Truncated Julian Date (TJD) corresponding to the
// currently stored AliTimestamp date/time parameters.
//
// Due to computer accuracy the ns precision may be lost.
// It is advised to use the (mjd,sec,ns) getter instead.

 Int_t tjd=0;
 Int_t sec=0;
 Int_t ns=0;
 GetTJD(tjd,sec,ns);

 Double_t date=Convert(tjd,sec,ns);

 return date;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::GetJD(Int_t& jd,Int_t& sec, Int_t& ns)
{
// Provide the Julian Date (JD) and time corresponding to the currently
// stored AliTimestamp date/time parameters.
//
// The returned arguments represent the following :
// jd  : The Julian date.
// sec : The number of seconds elapsed within the JD.
// ns  : The remaining fractional number of seconds (in ns) elapsed within the JD.

 Int_t mjd=0;
 GetMJD(mjd,sec,ns);

 jd=mjd+2400000;
 sec+=12*3600;
 if (sec >= 24*3600)
 {
  sec-=24*3600;
  jd+=1;
 }
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetJD()
{
// Provide the (fractional) Julian Date (JD) corresponding to the currently
// stored AliTimestamp date/time parameters.
//
// Due to computer accuracy the ns precision may be lost.
// It is advised to use the (jd,sec,ns) getter instead.

 Int_t jd=0;
 Int_t sec=0;
 Int_t ns=0;
 GetJD(jd,sec,ns);

 Double_t date=Convert(jd,sec,ns);

 return date;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetJE()
{
// Provide the Julian Epoch (JE) corresponding to the currently stored
// AliTimestamp date/time parameters.

 Double_t jd=GetJD();
 Double_t je=GetJE(jd);
 return je;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetBE()
{
// Provide the Besselian Epoch (BE) corresponding to the currently stored
// AliTimestamp date/time parameters.

 Double_t jd=GetJD();
 Double_t be=GetBE(jd);
 return be;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetMJD(Int_t mjd,Int_t sec,Int_t ns,Int_t ps)
{
// Set the Modified Julian Date (MJD) and time and update the TTimeStamp
// parameters accordingly (if possible).
//
// Note :
// ------
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to the start of MJD=40587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input MJD and time.
// Obviously this TTimeStamp implementation would prevent usage of MJD values
// smaller than 40587.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (M)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later MJD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.  
// This implies that for these earlier/later MJD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.  
//
// The input arguments represent the following :
// mjd : The modified Julian date.
// sec : The number of seconds elapsed within the MJD.
// ns  : The remaining fractional number of seconds (in ns) elapsed within the MJD.
// ps  : The remaining fractional number of nanoseconds (in ps) elapsed within the MJD.
//
// Note : ps=0 is the default value.

 if (sec<0 || sec>=24*3600 || ns<0 || ns>=1e9 || ps<0 || ps>=1000)
 {
  cout << " *AliTimestamp::SetMJD* Invalid input."
       << " sec : " << sec << " ns : " << ns << endl; 
  return;
 }

 fMJD=mjd;
 fJsec=sec;
 fJns=ns;
 fJps=ps;

 Int_t epoch=40587; // MJD of the start of the epoch
 Int_t limit=65442; // MJD of the latest possible TTimeStamp date/time
 
 Int_t date,time;
 if (mjd<epoch || mjd>limit || (mjd==limit && sec>=8047))
 {
  Set(0,kFALSE,0,kFALSE);
  date=GetDate();
  time=GetTime();
  Set(date,time,0,kTRUE,0);
 }
 else
 {
  // The elapsed time since start of EPOCH
  Int_t days=mjd-epoch;
  UInt_t secs=days*24*3600;
  secs+=sec;
  Set(secs,kFALSE,0,kFALSE);
  date=GetDate();
  time=GetTime();
  Set(date,time,ns,kTRUE,0);
 }

 // Denote that the Julian and TTimeStamp parameters are synchronised,
 // even in the case the MJD falls outside the TTimeStamp validity range.
 // The latter still allows retrieval of Julian parameters for these
 // earlier times.
 fCalcs=GetSec();
 fCalcns=GetNanoSec();
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetMJD(Double_t mjd)
{
// Set the Modified Julian Date (MJD) and time and update the TTimeStamp
// parameters accordingly (if possible).
//
// Note :
// ------
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to the start of MJD=40587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input MJD and time.
// Obviously this TTimeStamp implementation would prevent usage of MJD values
// smaller than 40587.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (M)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later MJD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.  
// This implies that for these earlier/later MJD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.  
//
// Due to computer accuracy the ns precision may be lost.
// It is advised to use the (mjd,sec,ns) setting instead.
//
// The input argument represents the following :
// mjd : The modified Julian date as fractional day count.

 Int_t days=0;
 Int_t secs=0;
 Int_t ns=0;
 Convert(mjd,days,secs,ns);
 SetMJD(days,secs,ns);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetJD(Int_t jd,Int_t sec,Int_t ns,Int_t ps)
{
// Set the Julian Date (JD) and time and update the TTimeStamp
// parameters accordingly (if possible).
//
// Note :
// ------
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to JD=2440587.5 or the start of MJD=40587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input MJD and time.
// Obviously this TTimeStamp implementation would prevent usage of values
// smaller than JD=2440587.5.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (M)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later JD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.  
// This implies that for these earlier/later (M)JD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.  
//
// The input arguments represent the following :
// jd  : The Julian date.
// sec : The number of seconds elapsed within the JD.
// ns  : The remaining fractional number of seconds (in ns) elapsed within the JD.
// ps  : The remaining fractional number of nanoseconds (in ps) elapsed within the JD.
//
// Note : ps=0 is the default value.

 Int_t mjd=jd-2400000;
 sec-=12*3600;
 if (sec<0)
 {
  sec+=24*3600;
  mjd-=1;
 }

 SetMJD(mjd,sec,ns,ps);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetJD(Double_t jd)
{
// Set the Julian Date (JD) and time and update the TTimeStamp
// parameters accordingly (if possible).
//
// Note :
// ------
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to JD=2440587.5 or the start of MJD=40587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input MJD and time.
// Obviously this TTimeStamp implementation would prevent usage of values
// smaller than JD=2440587.5.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (M)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later JD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.  
// This implies that for these earlier/later (M)JD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.  
//
// Due to computer accuracy the ns precision may be lost.
// It is advised to use the (jd,sec,ns) setting instead.
//
// The input argument represents the following :
// jd : The Julian date as fractional day count.

 Int_t days=0;
 Int_t secs=0;
 Int_t ns=0;
 Convert(jd,days,secs,ns);

 SetJD(days,secs,ns);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetTJD(Int_t tjd,Int_t sec,Int_t ns,Int_t ps)
{
// Set the Truncated Julian Date (TJD) and time and update the TTimeStamp
// parameters accordingly (if possible).
//
// Note :
// ------
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to JD=2440587.5 or the start of TJD=587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input MJD and time.
// Obviously this TTimeStamp implementation would prevent usage of values
// smaller than TJD=587.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (T)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later JD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.  
// This implies that for these earlier/later (T)JD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.  
//
// The input arguments represent the following :
// tjd : The Truncated Julian date.
// sec : The number of seconds elapsed within the JD.
// ns  : The remaining fractional number of seconds (in ns) elapsed within the JD.
// ps  : The remaining fractional number of nanoseconds (in ps) elapsed within the JD.
//
// Note : ps=0 is the default value.

 Int_t mjd=tjd+40000;

 SetMJD(mjd,sec,ns,ps);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetTJD(Double_t tjd)
{
// Set the Truncated Julian Date (TJD) and time and update the TTimeStamp
// parameters accordingly (if possible).
//
// Note :
// ------
// The TTimeStamp EPOCH starts at 01-jan-1970 00:00:00 UTC
// which corresponds to JD=2440587.5 or the start of TJD=587.
// Using the corresponding MJD of this EPOCH allows construction of
// the yy-mm-dd hh:mm:ss:ns TTimeStamp from a given input MJD and time.
// Obviously this TTimeStamp implementation would prevent usage of values
// smaller than TJD=587.
// Furthermore, due to a limitation on the "seconds since the EPOCH start" count
// in TTimeStamp, the latest accessible date/time is 19-jan-2038 02:14:08 UTC.
// However, this AliTimestamp facility provides support for the full range
// of (T)JD values, but the setting of the corresponding TTimeStamp parameters
// is restricted to the values allowed by the TTimeStamp implementation.
// For these earlier/later JD values, the standard TTimeStamp parameters will
// be set corresponding to the start of the TTimeStamp EPOCH.  
// This implies that for these earlier/later (T)JD values the TTimeStamp parameters
// do not match the Julian parameters of AliTimestamp.  
//
// Due to computer accuracy the ns precision may be lost.
// It is advised to use the (jd,sec,ns) setting instead.
//
// The input argument represents the following :
// tjd : The Truncated Julian date as fractional day count.

 Int_t days=0;
 Int_t secs=0;
 Int_t ns=0;
 Convert(tjd,days,secs,ns);

 SetTJD(days,secs,ns);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetNs(Int_t ns)
{
// Set the remaining fractional number of seconds in nanosecond precision.
// Notes :
// -------
// 1) The allowed range for the argument "ns" is [0,99999999].
//    Outside that range no action is performed.
// 2) The ns fraction can also be entered directly via SetMJD() etc...
// 3) For additional accuracy see SetPs().

 if (ns>=0 && ns<=99999999) fJns=ns; 
}
///////////////////////////////////////////////////////////////////////////
Int_t AliTimestamp::GetNs() const
{
// Provide the remaining fractional number of seconds in nanosecond precision.
// This function allows trigger/timing analysis for (astro)particle physics
// experiments.
// Note : For additional accuracy see also GetPs().

 return fJns; 
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetPs(Int_t ps)
{
// Set the remaining fractional number of nanoseconds in picoseconds.
// Notes :
// -------
// 1) The allowed range for the argument "ps" is [0,999].
//    Outside that range no action is performed.
// 2) The ps fraction can also be entered directly via SetMJD() etc...

 if (ps>=0 && ps<=999) fJps=ps; 
}
///////////////////////////////////////////////////////////////////////////
Int_t AliTimestamp::GetPs() const
{
// Provide remaining fractional number of nanoseconds in picoseconds.
// This function allows time of flight analysis for particle physics
// experiments.

 return fJps; 
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::Add(Int_t d,Int_t s,Int_t ns,Int_t ps)
{
// Add (or subtract) a certain time difference to the current timestamp.
// Subtraction can be achieved by entering negative values as input arguments.
//
// The time difference is entered via the following input arguments :
//
// d  : elapsed number of days
// s  : (remaining) elapsed number of seconds
// ns : (remaining) elapsed number of nanoseconds
// ps : (remaining) elapsed number of picoseconds
//
// The specified d, s, ns and ps values will be used in an additive
// way to determine the time difference.
// So, specification of d=1, s=100, ns=0, ps=0 will result in the
// same time difference addition as d=0, s=24*3600+100, ns=0, ps=0.
// However, by making use of the latter the user should take care
// of possible integer overflow problems in the input arguments,
// which obviously will provide incorrect results. 
//
// Note : ps=0 is the default value.

 Int_t days=0;
 Int_t secs=0;
 Int_t nsec=0;
 // Use Get functions to ensure updated Julian parameters. 
 GetMJD(days,secs,nsec);
 Int_t psec=GetPs();

 psec+=ps%1000;
 nsec+=ps/1000;
 while (psec<0)
 {
  nsec-=1;
  psec+=1000;
 }
 while (psec>999)
 {
  nsec+=1;
  psec-=1000;
 }

 nsec+=ns%1000000000;
 secs+=ns/1000000000;
 while (nsec<0)
 {
  secs-=1;
  nsec+=1000000000;
 }
 while (nsec>999999999)
 {
  secs+=1;
  nsec-=1000000000;
 }

 secs+=s%(24*3600);
 days+=s/(24*3600);
 while (secs<0)
 {
  days-=1;
  secs+=24*3600;
 }
 while (secs>=24*3600)
 {
  days+=1;
  secs-=24*3600;
 }

 days+=d;

 SetMJD(days,secs,nsec,psec);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::Add(Double_t hours)
{
// Add (or subtract) a certain time difference to the current timestamp.
// The time difference is specified as a (fractional) number of hours.
// Subtraction can be achieved by entering a negative value as input argument.

 Int_t d,s,ns,ps;
 Double_t h=fabs(hours);
 d=int(h/24.);
 h-=double(d)*24.;
 h*=3600.;
 s=int(h);
 h-=double(s);
 h*=1.e9;
 ns=int(h);
 h-=double(ns);
 ps=int(h*1000.);
 if (hours>0) Add(d,s,ns,ps);
 if (hours<0) Add(-d,-s,-ns,-ps);
}
///////////////////////////////////////////////////////////////////////////
Int_t AliTimestamp::GetDifference(AliTimestamp* t,Int_t& d,Int_t& s,Int_t& ns,Int_t& ps)
{
// Provide the time difference w.r.t the AliTimestamp specified on the input.
// This memberfunction supports both very small (i.e. time of flight analysis
// for particle physics experiments) and very long (i.e. investigation of
// astrophysical phenomena) timescales.
//
// The time difference is returned via the following output arguments :
// d  : elapsed number of days
// s  : remaining elapsed number of seconds
// ns : remaining elapsed number of nanoseconds
// ps : remaining elapsed number of picoseconds
//
// Note :
// ------
// The calculated time difference is the absolute value of the time interval.
// This implies that the values of d, s, ns and ps are always positive or zero.
//
// The integer return argument indicates whether the AliTimestamp specified
// on the input argument occurred earlier (-1), simultaneously (0) or later (1).

 if (!t) return 0;

 // Ensure updated Julian parameters for this AliTimestamp instance 
 if (fCalcs != GetSec() || fCalcns != GetNanoSec()) FillJulian();

 // Use Get functions to ensure updated Julian parameters. 
 t->GetMJD(d,s,ns);
 ps=t->GetPs();

 d-=fMJD;
 s-=fJsec;
 ns-=fJns;
 ps-=fJps;

 if (!d && !s && !ns && !ps) return 0;

 Int_t sign=0;

 if (d>0) sign=1;
 if (d<0) sign=-1;

 if (!sign && s>0) sign=1;
 if (!sign && s<0) sign=-1;

 if (!sign && ns>0) sign=1; 
 if (!sign && ns<0) sign=-1;

 if (!sign && ps>0) sign=1; 
 if (!sign && ps<0) sign=-1;

 // In case the input stamp was earlier, take the reverse difference
 // to simplify the algebra.
 if (sign<0)
 {
  d=-d;
  s=-s;
  ns=-ns;
  ps=-ps;
 }

 // Here we always have a positive time difference
 // and can now unambiguously correct for other negative values.
 if (ps<0)
 {
  ns-=1;
  ps+=1000;
 }

 if (ns<0)
 {
  s-=1;
  ns+=1000000000;
 }

 if (s<0)
 {
  d-=1;
  s+=24*3600;
 }

 return sign;
}
///////////////////////////////////////////////////////////////////////////
Int_t AliTimestamp::GetDifference(AliTimestamp& t,Int_t& d,Int_t& s,Int_t& ns,Int_t& ps)
{
// Provide the time difference w.r.t the AliTimestamp specified on the input.
// This memberfunction supports both very small (i.e. time of flight analysis
// for particle physics experiments) and very long (i.e. investigation of
// astrophysical phenomena) timescales.
//
// The time difference is returned via the following output arguments :
// d  : elapsed number of days
// s  : remaining elapsed number of seconds
// ns : remaining elapsed number of nanoseconds
// ps : remaining elapsed number of picoseconds
//
// Note :
// ------
// The calculated time difference is the absolute value of the time interval.
// This implies that the values of d, s, ns and ps are always positive or zero.
//
// The integer return argument indicates whether the AliTimestamp specified
// on the input argument occurred earlier (-1), simultaneously (0) or later (1).

 return GetDifference(&t,d,s,ns,ps);
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetDifference(AliTimestamp* t,TString u,Int_t mode)
{
// Provide the time difference w.r.t the AliTimestamp specified on the input
// argument in the units as specified by the TString argument.
// A positive return value means that the AliTimestamp specified on the input
// argument occurred later, whereas a negative return value indicates an
// earlier occurence. 
//  
// The units may be specified as :
// u = "d"  ==> Time difference returned as (fractional) day count
//     "s"  ==> Time difference returned as (fractional) second count
//     "ns" ==> Time difference returned as (fractional) nanosecond count
//     "ps" ==> Time difference returned as picosecond count
//
// It may be clear that for a time difference of several days, the picosecond
// and even the nanosecond accuracy may be lost.
// To cope with this, the "mode" argument has been introduced to allow 
// timestamp comparison on only the specified units.
//
// The following operation modes are supported :
// mode = 1 : Full time difference is returned in specified units
//        2 : Time difference is returned in specified units by
//            neglecting the elapsed time for the larger units than the
//            ones specified.
//        3 : Time difference is returned in specified units by only
//            comparing the timestamps on the level of the specified units.
//
// Example :
// ---------
// AliTimestamp t1; // Corresponding to days=3, secs=501, ns=31, ps=7 
// AliTimestamp t2; // Corresponding to days=5, secs=535, ns=12, ps=15
//
// The statement : Double_t val=t1.GetDifference(t2,....)
// would return the following values :
// val=(2*24*3600)+34-(19*1e-9)+(8*1e-12) for u="s" and mode=1
// val=34-(19*1e-9)+(8*1e-12)             for u="s" and mode=2
// val=34                                 for u="s" and mode=3
// val=-19                                for u="ns" and mode=3
//
// The default is mode=1.

 if (!t || mode<1 || mode>3) return 0;

 Double_t dt=0;

 // Ensure updated Julian parameters for this AliTimestamp instance 
 if (fCalcs != GetSec() || fCalcns != GetNanoSec()) FillJulian();

 Int_t dd=0;
 Int_t ds=0;
 Int_t dns=0;
 Int_t dps=0;

 // Use Get functions to ensure updated Julian parameters. 
 t->GetMJD(dd,ds,dns);
 dps=t->GetPs();

 dd-=fMJD;
 ds-=fJsec;
 dns-=fJns;
 dps-=fJps;

 // Time difference for the specified units only
 if (mode==3)
 {
  if (u=="d") dt=dd;
  if (u=="s") dt=ds;
  if (u=="ns") dt=dns;
  if (u=="ps") dt=dps;
  return dt;
 }

 // Suppress elapsed time for the larger units than specified
 if (mode==2)
 {
  if (u=="s") dd=0;
  if (u=="ns")
  {
   dd=0;
   ds=0;
  }
  if (u=="ps")
  {
   dd=0;
   ds=0;
   dns=0;
  }
 }

 // Compute the time difference as requested 
 if (u=="s" || u=="d")
 {
  // The time difference in (fractional) seconds
  dt=double(dd*24*3600+ds)+(double(dns)*1e-9)+(double(dps)*1e-12);
  if (u=="d") dt=dt/double(24*3600);
 }
 if (u=="ns") dt=(double(dd*24*3600+ds)*1e9)+double(dns)+(double(dps)*1e-3);
 if (u=="ps") dt=(double(dd*24*3600+ds)*1e12)+(double(dns)*1e3)+double(dps);

 return dt;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetDifference(AliTimestamp& t,TString u,Int_t mode)
{
// Provide the time difference w.r.t the AliTimestamp specified on the input
// argument in the units as specified by the TString argument.
// A positive return value means that the AliTimestamp specified on the input
// argument occurred later, whereas a negative return value indicates an
// earlier occurence. 
//  
// The units may be specified as :
// u = "d"  ==> Time difference returned as (fractional) day count
//     "s"  ==> Time difference returned as (fractional) second count
//     "ns" ==> Time difference returned as (fractional) nanosecond count
//     "ps" ==> Time difference returned as picosecond count
//
// It may be clear that for a time difference of several days, the picosecond
// and even the nanosecond accuracy may be lost.
// To cope with this, the "mode" argument has been introduced to allow 
// timestamp comparison on only the specified units.
//
// The following operation modes are supported :
// mode = 1 : Full time difference is returned in specified units
//        2 : Time difference is returned in specified units by
//            neglecting the elapsed time for the larger units than the
//            ones specified.
//        3 : Time difference is returned in specified units by only
//            comparing the timestamps on the level of the specified units.
//
// Example :
// ---------
// AliTimestamp t1; // Corresponding to days=3, secs=501, ns=31, ps=7 
// AliTimestamp t2; // Corresponding to days=5, secs=535, ns=12, ps=15
//
// The statement : Double_t val=t1.GetDifference(t2,....)
// would return the following values :
// val=(2*24*3600)+34-(19*1e-9)+(8*1e-12) for u="s" and mode=1
// val=34-(19*1e-9)+(8*1e-12)             for u="s" and mode=2
// val=34                                 for u="s" and mode=3
// val=-19                                for u="ns" and mode=3
//
// The default is mode=1.

 return GetDifference(&t,u,mode);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetUT(Int_t y,Int_t m,Int_t d,Int_t hh,Int_t mm,Int_t ss,Int_t ns,Int_t ps)
{
// Set the AliTimestamp parameters corresponding to the UT date and time
// in the Gregorian calendar as specified by the input arguments.
// This facility is exact upto picosecond precision and as such is
// for scientific observations preferable above the corresponding
// Set function(s) of TTimestamp.
// The latter has a random spread in the sub-second part, which
// might be of use in generating distinguishable timestamps while
// still keeping second precision.
//
// The input arguments represent the following :
// y  : year in UT (e.g. 1952, 2003 etc...)
// m  : month in UT (1=jan  2=feb etc...)
// d  : day in UT (1-31)
// hh : elapsed hours in UT (0-23) 
// mm : elapsed minutes in UT (0-59)
// ss : elapsed seconds in UT (0-59)
// ns : remaining fractional elapsed second of UT in nanosecond
// ps : remaining fractional elapsed nanosecond of UT in picosecond
//
// Note : ns=0 and ps=0 are the default values.
//
// This facility first determines the elapsed days, seconds etc...
// since the beginning of the specified UT year on basis of the
// input arguments. Subsequently it invokes the SetUT memberfunction
// for the elapsed timespan.
// As such this facility is valid for all AD dates in the Gregorian
// calendar with picosecond precision.

 Int_t day=GetDayOfYear(d,m,y);
 Int_t secs=hh*3600+mm*60+ss;
 SetUT(y,day-1,secs,ns,ps);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetUT(Int_t y,Int_t d,Int_t s,Int_t ns,Int_t ps)
{
// Set the AliTimestamp parameters corresponding to the specified elapsed
// timespan since the beginning of the new UT year.
// This facility is exact upto picosecond precision and as such is
// for scientific observations preferable above the corresponding
// Set function(s) of TTimestamp.
// The latter has a random spread in the sub-second part, which
// might be of use in generating distinguishable timestamps while
// still keeping second precision.
//
// The UT year and elapsed time span is entered via the following input arguments :
//
// y  : year in UT (e.g. 1952, 2003 etc...)
// d  : elapsed number of days 
// s  : (remaining) elapsed number of seconds
// ns : (remaining) elapsed number of nanoseconds
// ps : (remaining) elapsed number of picoseconds
//
// The specified d, s, ns and ps values will be used in an additive
// way to determine the elapsed timespan.
// So, specification of d=1, s=100, ns=0, ps=0 will result in the
// same elapsed time span as d=0, s=24*3600+100, ns=0, ps=0.
// However, by making use of the latter the user should take care
// of possible integer overflow problems in the input arguments,
// which obviously will provide incorrect results. 
//
// Note : ns=0 and ps=0 are the default values.
//
// This facility first sets the (M)JD corresponding to the start (01-jan 00:00:00)
// of the specified UT year following the recipe of R.W. Sinnott
// Sky & Telescope 82, (aug. 1991) 183.
// Subsequently the day and (sub)second parts are added to the AliTimestamp.
// As such this facility is valid for all AD dates in the Gregorian calendar.

 Double_t jd=GetJD(y,1,1,0,0,0,0);
 SetJD(jd);

 Int_t mjd,sec,nsec;
 GetMJD(mjd,sec,nsec);
 SetMJD(mjd,0,0,0);
 Add(d,s,ns,ps);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::GetUT(Int_t& hh,Int_t& mm,Int_t& ss,Int_t& ns,Int_t& ps)
{
// Provide the corrresponding UT as hh:mm:ss:ns:ps.
// This facility is based on the MJD, so the TTimeStamp limitations
// do not apply here.

 Int_t mjd,sec,nsec,psec;

 GetMJD(mjd,sec,nsec);
 psec=GetPs();

 hh=sec/3600;
 sec=sec%3600;
 mm=sec/60;
 ss=sec%60;
 ns=nsec;
 ps=psec;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetUT()
{
// Provide the corrresponding UT in fractional hours.
// This facility is based on the MJD, so the TTimeStamp limitations
// do not apply here.

 Int_t hh,mm,ss,ns,ps;

 GetUT(hh,mm,ss,ns,ps);

 Double_t ut=Convert(hh,mm,ss,ns,ps);

 return ut;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::GetGMST(Int_t& hh,Int_t& mm,Int_t& ss,Int_t& ns,Int_t& ps)
{
// Provide the corrresponding Greenwich Mean Sideral Time (GMST).
// The algorithm used is the one described at p. 83 of the book
// Astronomy Methods by Hale Bradt.
// This facility is based on the MJD, so the TTimeStamp limitations
// do not apply here.

 Int_t mjd,sec,nsec,psec;

 // The current UT based timestamp data
 GetMJD(mjd,sec,nsec);
 psec=fJps;

 // The basis for the daily corrections in units of Julian centuries w.r.t. J2000.
 // Note : Epoch J2000 starts at 01-jan-2000 12:00:00 UT.
 Double_t tau=(GetJD()-2451545.)/36525.;

 // Syncronise sidereal time with current timestamp
 AliTimestamp sid;
 sid.SetMJD(mjd,sec,nsec,psec);

 // Add offset for GMST start value defined as 06:41:50.54841 at 01-jan 00:00:00 UT
 sec=6*3600+41*60+50;
 nsec=548410000;
 psec=0;
 sid.Add(0,sec,nsec,psec);

 // Daily correction for precession and polar motion 
 Double_t addsec=8640184.812866*tau+0.093104*pow(tau,2)-6.2e-6*pow(tau,3);
 sec=int(addsec);
 addsec-=double(sec);
 nsec=int(addsec*1.e9);
 addsec-=double(nsec)*1.e-9;
 psec=int(addsec*1.e12);
 sid.Add(0,sec,nsec,psec);

 sid.GetMJD(mjd,sec,nsec);
 psec=sid.GetPs();

 hh=sec/3600;
 sec=sec%3600;
 mm=sec/60;
 ss=sec%60;
 ns=nsec;
 ps=psec;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetGMST()
{
// Provide the corrresponding Greenwich Mean Sideral Time (GMST)
// in fractional hours.
// This facility is based on the MJD, so the TTimeStamp limitations
// do not apply here.

 Int_t hh,mm,ss,ns,ps;

 GetGMST(hh,mm,ss,ns,ps);

 Double_t gst=Convert(hh,mm,ss,ns,ps);

 return gst;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetGAST()
{
// Provide the corrresponding Greenwich Apparent Sideral Time (GAST)
// in fractional hours.
// In case a hh:mm:ss.sss format is needed, please invoke the Convert()
// memberfunction for conversion of the provided fractional hour value.
//
// The GAST is the GMST corrected for the shift of the vernal equinox
// due to nutation. The right ascension component of the nutation correction
// of the vernal equinox is called the "equation of the equinoxes".
// So we have :
//
//      GAST = GMST + (equation of the equinoxes)
//
// The equation of the equinoxes is determined via the Almanac() memberfunction.
// 
// Since GMST is based on the MJD, the TTimeStamp limitations do not apply here.

 Double_t da=Almanac();

 // Convert to fractional hours
 da/=3600.;

 Double_t gast=GetGMST()+da;

 while (gast<0)
 {
  gast+=24.;
 }
 while (gast>24.)
 {
  gast-=24.;
 }

 return gast;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetLT(Double_t offset)
{
// Provide the corresponding local time in fractional hours.
// The "offset" denotes the time difference in (fractional) hours w.r.t. UT.
// A mean solar day lasts 24h (i.e. 86400s).
//
// In case a hh:mm:ss format is needed, please use the Convert() facility. 

 // Current UT time in fractional hours
 Double_t h=GetUT();
 
 h+=offset;

 while (h<0)
 {
  h+=24.;
 }
 while (h>24)
 {
  h-=24.;
 }

 return h;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetLMST(Double_t offset)
{
// Provide the corresponding Local Mean Sidereal Time (LMST) in fractional hours.
// The "offset" denotes the time difference in (fractional) hours w.r.t. GMST.
// A sidereal day corresponds to 23h 56m 04.09s (i.e. 86164.09s) mean solar time.
// The definition of GMST is such that a sidereal clock corresponds with
// 24 sidereal hours per revolution of the Earth.
// As such, local time offsets w.r.t. UT and GMST can be treated similarly. 
//
// In case a hh:mm:ss format is needed, please use the Convert() facility. 

 // Current GMST time in fractional hours
 Double_t h=GetGMST();

 h+=offset;

 while (h<0)
 {
  h+=24.;
 }
 while (h>24)
 {
  h-=24.;
 }

 return h;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetLAST(Double_t offset)
{
// Provide the corresponding Local Apparent Sidereal Time (LAST) in fractional hours.
// The "offset" denotes the time difference in (fractional) hours w.r.t. GAST.
// A sidereal day corresponds to 23h 56m 04.09s (i.e. 86164.09s) mean solar time.
// The definition of GMST and GAST is such that a sidereal clock corresponds with
// 24 sidereal hours per revolution of the Earth.
// As such, local time offsets w.r.t. UT, GMST and GAST can be treated similarly. 
//
// In case a hh:mm:ss.sss format is needed, please use the Convert() facility. 

 // Current GAST time in fractional hours
 Double_t h=GetGAST();

 h+=offset;

 while (h<0)
 {
  h+=24.;
 }
 while (h>24)
 {
  h-=24.;
 }

 return h;
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetLT(Double_t dt,Int_t y,Int_t m,Int_t d,Int_t hh,Int_t mm,Int_t ss,Int_t ns,Int_t ps)
{
// Set the AliTimestamp parameters corresponding to the LT date and time
// in the Gregorian calendar as specified by the input arguments.
// This facility is exact upto picosecond precision and as such is
// for scientific observations preferable above the corresponding
// Set function(s) of TTimestamp.
// The latter has a random spread in the sub-second part, which
// might be of use in generating distinguishable timestamps while
// still keeping second precision.
//
// The input arguments represent the following :
//
// dt : the local time offset in fractional hours w.r.t. UT.
// y  : year in LT (e.g. 1952, 2003 etc...)
// m  : month in LT (1=jan  2=feb etc...)
// d  : day in LT (1-31)
// hh : elapsed hours in LT (0-23) 
// mm : elapsed minutes in LT (0-59)
// ss : elapsed seconds in LT (0-59)
// ns : remaining fractional elapsed second of LT in nanosecond
// ps : remaining fractional elapsed nanosecond of LT in picosecond
//
// Note : ns=0 and ps=0 are the default values.
//
// This facility first sets the UT as specified by the input arguments
// and then corrects the UT by subtracting the local time offset w.r.t. UT.
// As such this facility is valid for all AD dates in the Gregorian
// calendar with picosecond precision.

 SetUT(y,m,d,hh,mm,ss,ns,ps);
 Add(-dt);
}
///////////////////////////////////////////////////////////////////////////
void AliTimestamp::SetLT(Double_t dt,Int_t y,Int_t d,Int_t s,Int_t ns,Int_t ps)
{
// Set the AliTimestamp parameters corresponding to the specified elapsed
// timespan since the beginning of the new LT year.
// This facility is exact upto picosecond precision and as such is
// for scientific observations preferable above the corresponding
// Set function(s) of TTimestamp.
// The latter has a random spread in the sub-second part, which
// might be of use in generating distinguishable timestamps while
// still keeping second precision.
//
// The LT year and elapsed time span is entered via the following input arguments :
//
// dt : the local time offset in fractional hours w.r.t. UT.
// y  : year in LT (e.g. 1952, 2003 etc...)
// d  : elapsed number of days 
// s  : (remaining) elapsed number of seconds
// ns : (remaining) elapsed number of nanoseconds
// ps : (remaining) elapsed number of picoseconds
//
// The specified d, s, ns and ps values will be used in an additive
// way to determine the elapsed timespan.
// So, specification of d=1, s=100, ns=0, ps=0 will result in the
// same elapsed time span as d=0, s=24*3600+100, ns=0, ps=0.
// However, by making use of the latter the user should take care
// of possible integer overflow problems in the input arguments,
// which obviously will provide incorrect results. 
//
// Note : ns=0 and ps=0 are the default values.
//
// This facility first sets the UT as specified by the input arguments
// and then corrects the UT by subtracting the local time offset w.r.t. UT.
// As such this facility is valid for all AD dates in the Gregorian calendar.

 SetUT(y,d,s,ns,ps);
 Add(-dt);
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetJD(Double_t e,TString mode) const
{
// Provide the fractional Julian Date from epoch e.
// The sort of epoch may be specified via the "mode" parameter.
//
// mode = "J" ==> Julian epoch
//        "B" ==> Besselian epoch
//
// The default value is mode="J".

 Double_t jd=0;

 if (mode=="J" || mode=="j") jd=(e-2000.0)*365.25+2451545.0;

 if (mode=="B" || mode=="b") jd=(e-1900.0)*365.242198781+2415020.31352;

 return jd;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetMJD(Double_t e,TString mode) const
{
// Provide the fractional Modified Julian Date from epoch e.
// The sort of epoch may be specified via the "mode" parameter.
//
// mode = "J" ==> Julian epoch
//        "B" ==> Besselian epoch
//
// The default value is mode="J".

 Double_t mjd=GetJD(e,mode)-2400000.5;

 return mjd;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::GetTJD(Double_t e,TString mode) const
{
// Provide the fractional Truncated Julian Date from epoch e.
// The sort of epoch may be specified via the "mode" parameter.
//
// mode = "J" ==> Julian epoch
//        "B" ==> Besselian epoch
//
// The default value is mode="J".

 Double_t tjd=GetJD(e,mode)-2440000.5;

 return tjd;
}
///////////////////////////////////////////////////////////////////////////
Double_t AliTimestamp::Almanac(Double_t* dpsi,Double_t* deps,Double_t* eps)
{
// Determination of some astronomical observables which may be needed
// for further calculations like e.g. precession of coordinates.
//
// The standard returned value is the "equation of the equinoxes" 
// (i.e. the nutational shift of the RA of the vernal equinox) in seconds.
// The memberfunction arguments provide the possibility of retrieving
// optional returned values. The corresponding observables are :
//
// dpsi : Nutational shift in ecliptic longitude in arcseconds
// deps : Nutational shift in ecliptic obliquity in arcseconds
// eps  : Mean obliquity of the ecliptic in arcseconds
//
// All shifts are determined for the current timestamp with
// J2000.0 (i.e. 01-jan-2000 12:00:00 UT) as the reference epoch.
//
// Invokation example :
// --------------------
// AliTimestamp t;
// Double_t da,dpsi,deps,eps;
// da=t.Almanac(&dpsi,&deps,&eps); 
//
// The nutation model used is the new one as documented in :
//   "The IAU Resolutions on Astronomical Reference Systems,
//    Time Scales and Earth Rotation Models".
// This document is freely available as Circular 179 (2005) of the
// United States Naval Observatory (USNO).
// (See : http://aa.usno.navy.mil/publications/docs).
//
// The change in ecliptic longitude (dpsi) and ecliptic obliquity (deps)
// are evaluated using the IAU 2000A nutation series expansion
// as provided in the USNO Circular 179.
// The new expression for the equation of the equinoxes is based on a series
// expansion and is the most accurate one known to date.
// The components are documented on p.17 of the USNO Circular 179.
//
// In the current implementation only the first 28 terms of the nutation series
// are used. This provides an accuracy of about 0.01 arcsec corresponding to 0.001 sec.
// In case a better accuracy is required, the series can be extended.
// The total series expansion consists of 1365 terms.
// 
// Since all calculations are based on the JD, the TTimeStamp limitations
// do not apply here.

 Double_t pi=acos(-1.);

 Double_t t;       // Time difference in fractional Julian centuries w.r.t. the start of J2000.
 Double_t epsilon; // Mean obliquity of the ecliptic
 Double_t l;       // Mean anomaly of the Moon
 Double_t lp;      // Mean anomaly of the Sun
 Double_t f;       // Mean argument of latitude of the moon
 Double_t d;       // Mean elongation of the Moon from the Sun
 Double_t om;      // Mean longitude of the Moon's mean ascending mode

 t=(GetJD()-2451545.0)/36525.;

 // Values of epsilon and the fundamental luni-solar arguments in arcseconds
 epsilon=84381.406-46.836769*t-0.0001831*pow(t,2)+0.00200340*pow(t,3)
         -0.000000576*pow(t,4)-0.0000000434*pow(t,5);
 l=485868.249036+1717915923.2178*t+31.8792*pow(t,2)+0.051635*pow(t,3)-0.00024470*pow(t,4);
 lp=1287104.79305+129596581.0481*t-0.5532*pow(t,2)+0.000136*pow(t,3)-0.00001149*pow(t,4);
 f=335779.526232+1739527262.8478*t-12.7512*pow(t,2)-0.001037*pow(t,3)+0.00000417*pow(t,4);
 d=1072260.70369+1602961601.2090*t-6.3706*pow(t,2)+0.006593*pow(t,3)-0.00003169*pow(t,4);
 om=450160.398036-6962890.5431*t+7.4722*pow(t,2)+0.007702*pow(t,3)-0.00005939*pow(t,4);

 if (eps) *eps=epsilon;

 // Convert to radians
 epsilon=epsilon*pi/(180.*3600.);
 f=f*pi/(180.*3600.);
 d=d*pi/(180.*3600.);
 l=l*pi/(180.*3600.);
 lp=lp*pi/(180.*3600.);
 om=om*pi/(180.*3600.);

 //The IAU 2000A nutation series expansion.
 Double_t phi[28]={om,2.*(f-d+om),2.*(f+om),2.*om,lp,lp+2.*(f-d+om),l,
                   2.*f+om,l+2.*(f+om),2.*(f-d+om)-lp,2.*(f-d)+om,2.*(f+om)-l,2.*d-l,l+om,
                   om-l,2.*(f+d+om)-l,l+2.*f+om,2.*(f-l)+om,2.*d,2.*(f+d+om),2.*(f-d+om-lp),
                   2.*(d-l),2.*(l+d+om),l+2.*(f-d+om),2.*f+om-l,2.*l,2.*f,lp+om};
 Double_t s[28]={-17.2064161,-1.3170907,-0.2276413, 0.2074554, 0.1475877,-0.0516821, 0.0711159,
                  -0.0387298,-0.0301461, 0.0215829, 0.0128227, 0.0123457, 0.0156994, 0.0063110,
                  -0.0057976,-0.0059641,-0.0051613, 0.0045893, 0.0063384,-0.0038571, 0.0032481,
                  -0.0047722,-0.0031046, 0.0028593, 0.0020441, 0.0029243, 0.0025887,-0.0014053};
 Double_t sd[28]={-0.0174666,-0.0001675,-0.0000234, 0.0000207,-0.0003633, 0.0001226, 0.0000073,
                  -0.0000367,-0.0000036,-0.0000494, 0.0000137, 0.0000011, 0.0000010, 0.0000063,
                  -0.0000063,-0.0000011,-0.0000042, 0.0000050, 0.0000011,-0.0000001, 0.0000000,
                   0.0000000,-0.0000001, 0.0000000, 0.0000021, 0.0000000, 0.0000000,-0.0000025};
 Double_t cp[28]={ 0.0033386,-0.0013696, 0.0002796,-0.0000698, 0.0011817,-0.0000524,-0.0000872,
                   0.0000380, 0.0000816, 0.0000111, 0.0000181, 0.0000019,-0.0000168, 0.0000027,
                  -0.0000189, 0.0000149, 0.0000129, 0.0000031,-0.0000150, 0.0000158, 0.0000000,
                  -0.0000018, 0.0000131,-0.0000001, 0.0000010,-0.0000074,-0.0000066, 0.0000079};
 Double_t c[28]= { 9.2052331, 0.5730336, 0.0978459,-0.0897492, 0.0073871, 0.0224386,-0.0006750,
                   0.0200728, 0.0129025,-0.0095929,-0.0068982,-0.0053311,-0.0001235,-0.0033228,
                   0.0031429, 0.0025543, 0.0026366,-0.0024236,-0.0001220, 0.0016452,-0.0013870,
                   0.0000477, 0.0013238,-0.0012338,-0.0010758,-0.0000609,-0.0000550, 0.0008551};
 Double_t cd[28]={ 0.0009086,-0.0003015,-0.0000485, 0.0000470,-0.0000184,-0.0000677, 0.0000000,
                   0.0000018,-0.0000063, 0.0000299,-0.0000009, 0.0000032, 0.0000000, 0.0000000,
                   0.0000000,-0.0000011, 0.0000000,-0.0000010, 0.0000000,-0.0000011, 0.0000000,
                   0.0000000,-0.0000011, 0.0000010, 0.0000000, 0.0000000, 0.0000000,-0.0000002};
 Double_t sp[28]={ 0.0015377,-0.0004587, 0.0001374,-0.0000291,-0.0001924,-0.0000174, 0.0000358,
                   0.0000318, 0.0000367, 0.0000132, 0.0000039,-0.0000004, 0.0000082,-0.0000009,
                  -0.0000075, 0.0000066, 0.0000078, 0.0000020, 0.0000029, 0.0000068, 0.0000000,
                  -0.0000025, 0.0000059,-0.0000003,-0.0000003, 0.0000013, 0.0000011,-0.0000045};
 
 Double_t dp=0,de=0,da=0;
 for (Int_t i=0; i<28; i++)
 {
  dp+=(s[i]+sd[i]*t)*sin(phi[i])+cp[i]*cos(phi[i]);
  de+=(c[i]+cd[i]*t)*cos(phi[i])+sp[i]*sin(phi[i]);
 }

 da=dp*cos(epsilon)+0.00264096*sin(om)+0.00006352*sin(2.*om)
     +0.00001175*sin(2.*f-2.*d+3.*om)+0.00001121*sin(2.*f-2.*d+om)
     -0.00000455*sin(2.*f-2.*d+2.*om)+0.00000202*sin(2.*f+3.*om)+0.00000198*sin(2.*f+om)
     -0.00000172*sin(3.*om)-0.00000087*t*sin(om);

 if (dpsi) *dpsi=dp;
 if (deps) *deps=de;

 // Convert to seconds
 da/=15.;

 return da;
}
///////////////////////////////////////////////////////////////////////////