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jdn.c

/* jdn.c -- Julian Day Number computation
**
** public domain Julian Day Number functions
**
** Based on formulae originally posted by
**    Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
**       in the UseNet newsgroup sci.astro.
**    Reposted 14 May 1991 in FidoNet C Echo conference by
**       Paul Schlyter (Stockholm)
** Minor corrections, added JDN to julian, and recast into C by
**    Raymond Gardner  Englewood, Colorado
**
** Synopsis:
**      long ymd_to_jdn(int year, int month, int day, int julian_flag)
**      void jdn_to_ymd(long jdn, int *year, int *month, int *day,
**                                                      int julian_flag)
**      year is negative if BC
**      if julian_flag is >  0, use Julian calendar
**      if julian_flag is == 0, use Gregorian calendar
**      if julian_flag is <  0, routines decide based on date
**
** These routines convert Gregorian and Julian calendar dates to and 
** from Julian Day Numbers.  Julian Day Numbers (JDN) are used by 
** astronomers as a date/time measure independent of calendars and 
** convenient for computing the elapsed time between dates.  The JDN 
** for any date/time is the number of days (including fractional 
** days) elapsed since noon, 1 Jan 4713 BC.  Julian Day Numbers were 
** originated by Joseph Scaliger in 1582 and named after his father 
** Julius, not after Julius Caesar.  They are not related to the 
** Julian calendar. 
** 
** For dates from 1 Jan 4713 BC thru 12 Dec Feb 32766 AD, ymd_to_jdn() 
** will give the JDN for noon on that date.  jdn_to_ymd() will compute 
** the year, month, and day from the JDN.  Years BC are given (and 
** returned) as negative numbers.  Note that there is no year 0 BC; 
** the day before 1 Jan 1 AD is 31 Dec 1 BC.  Note also that 1 BC, 
** 5 BC, etc. are leap years.
** 
** Pope Gregory XIII decreed that the Julian calendar would end on 
** 4 Oct 1582 AD and that the next day would be 15 Oct 1582 in the 
** Gregorian Calendar.  The only other change is that centesimal 
** years (years ending in 00) would no longer be leap years 
** unless divisible by 400.  Britain and its possessions and 
** colonies continued to use the Julian calendar up until 2 Sep 
** 1752, when the next day became 14 Sep 1752 in the Gregorian 
** Calendar.  These routines can be compiled to use either 
** convention.  By default, the British convention will be used.  
** Simply #define PAPAL to use Pope Gregory's convention. 
** 
** Each routine takes, as its last argument, a flag to indicate 
** whether to use the Julian or Gregorian calendar convention.  If 
** this flag is negative, the routines decide based on the date 
** itself, using the changeover date described in the preceding 
** paragraph.  If the flag is zero, Gregorian conventions will be used, 
** and if the flag is positive, Julian conventions will be used. 
*/


#ifdef PAPAL                    /* Pope Gregory XIII's decree */
#define LASTJULDATE 15821004L   /* last day to use Julian calendar */
#define LASTJULJDN  2299160L    /* jdn of same */
#else                           /* British-American usage */
#define LASTJULDATE 17520902L   /* last day to use Julian calendar */
#define LASTJULJDN  2361221L    /* jdn of same */
#endif


long ymd_to_jdn(int y, int m, int d, int julian)
{
        long jdn;

        if (julian < 0)         /* set Julian flag if auto set */
                julian = (((y * 100L) + m) * 100 + d  <=  LASTJULDATE);

        if (y < 0)              /* adjust BC year */
                y++;

        if (julian)
                jdn = 367L * y - 7 * (y + 5001L + (m - 9) / 7) / 4
                + 275 * m / 9 + d + 1729777L;
        else
                jdn = (long)(d - 32076)
                + 1461L * (y + 4800L + (m - 14) / 12) / 4
                + 367 * (m - 2 - (m - 14) / 12 * 12) / 12
                - 3 * ((y + 4900L + (m - 14) / 12) / 100) / 4
                + 1;            /* correction by rdg */

        return jdn;
}


void jdn_to_ymd(long jdn, int *yy, int *mm, int *dd, int julian)
{
        long x, z, m, d, y;
        long daysPer400Years = 146097L;
        long fudgedDaysPer4000Years = 1460970L + 31;

        if (julian < 0)                 /* set Julian flag if auto set */
                julian = (jdn <= LASTJULJDN);

        x = jdn + 68569L;
        if ( julian )
        {
                x += 38;
                daysPer400Years = 146100L;
                fudgedDaysPer4000Years = 1461000L + 1;
        }
        z = 4 * x / daysPer400Years;
        x = x - (daysPer400Years * z + 3) / 4;
        y = 4000 * (x + 1) / fudgedDaysPer4000Years;
        x = x - 1461 * y / 4 + 31;
        m = 80 * x / 2447;
        d = x - 2447 * m / 80;
        x = m / 11;
        m = m + 2 - 12 * x;
        y = 100 * (z - 49) + y + x;

        *yy = (int)y;
        *mm = (int)m;
        *dd = (int)d;

        if (*yy <= 0)                   /* adjust BC years */
                (*yy)--;
}

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