/* 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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