/* $selId: julian.c,v 2.0 1995/10/24 01:13:06 lees Exp $ * Copyright 1993-1995, Scott E. Lee, all rights reserved. * Permission granted to use, copy, modify, distribute and sell so long as * the above copyright and this permission statement are retained in all * copies. THERE IS NO WARRANTY - USE AT YOUR OWN RISK. */ /************************************************************************** * * These are the externally visible components of this file: * * void * SdnToJulian( * long int sdn, * int *pYear, * int *pMonth, * int *pDay); * * Convert a SDN to a Julian calendar date. If the input SDN is less than * 1, the three output values will all be set to zero, otherwise *pYear * will be >= -4713 and != 0; *pMonth will be in the range 1 to 12 * inclusive; *pDay will be in the range 1 to 31 inclusive. * * long int * JulianToSdn( * int inputYear, * int inputMonth, * int inputDay); * * Convert a Julian calendar date to a SDN. Zero is returned when the * input date is detected as invalid or out of the supported range. The * return value will be > 0 for all valid, supported dates, but there are * some invalid dates that will return a positive value. To verify that a * date is valid, convert it to SDN and then back and compare with the * original. * * VALID RANGE * * 4713 B.C. to at least 10000 A.D. * * Although this software can handle dates all the way back to 4713 * B.C., such use may not be meaningful. The calendar was created in * 46 B.C., but the details did not stabilize until at least 8 A.D., * and perhaps as late at the 4th century. Also, the beginning of a * year varied from one culture to another - not all accepted January * as the first month. * * CALENDAR OVERVIEW * * Julias Ceasar created the calendar in 46 B.C. as a modified form of * the old Roman republican calendar which was based on lunar cycles. * The new Julian calendar set fixed lengths for the months, abandoning * the lunar cycle. It also specified that there would be exactly 12 * months per year and 365.25 days per year with every 4th year being a * leap year. * * Note that the current accepted value for the tropical year is * 365.242199 days, not 365.25. This lead to an 11 day shift in the * calendar with respect to the seasons by the 16th century when the * Gregorian calendar was created to replace the Julian calendar. * * The difference between the Julian and today's Gregorian calendar is * that the Gregorian does not make centennial years leap years unless * they are a multiple of 400, which leads to a year of 365.2425 days. * In other words, in the Gregorian calendar, 1700, 1800 and 1900 are * not leap years, but 2000 is. All centennial years are leap years in * the Julian calendar. * * The details are unknown, but the lengths of the months were adjusted * until they finally stablized in 8 A.D. with their current lengths: * * January 31 * February 28/29 * March 31 * April 30 * May 31 * June 30 * Quintilis/July 31 * Sextilis/August 31 * September 30 * October 31 * November 30 * December 31 * * In the early days of the calendar, the days of the month were not * numbered as we do today. The numbers ran backwards (decreasing) and * were counted from the Ides (15th of the month - which in the old * Roman republican lunar calendar would have been the full moon) or * from the Nonae (9th day before the Ides) or from the beginning of * the next month. * * In the early years, the beginning of the year varied, sometimes * based on the ascension of rulers. It was not always the first of * January. * * Also, today's epoch, 1 A.D. or the birth of Jesus Christ, did not * come into use until several centuries later when Christianity became * a dominant religion. * * ALGORITHMS * * The calculations are based on two different cycles: a 4 year cycle * of leap years and a 5 month cycle of month lengths. * * The 5 month cycle is used to account for the varying lengths of * months. You will notice that the lengths alternate between 30 and * 31 days, except for three anomalies: both July and August have 31 * days, both December and January have 31, and February is less than * 30. Starting with March, the lengths are in a cycle of 5 months * (31, 30, 31, 30, 31): * * Mar 31 days \ * Apr 30 days | * May 31 days > First cycle * Jun 30 days | * Jul 31 days / * * Aug 31 days \ * Sep 30 days | * Oct 31 days > Second cycle * Nov 30 days | * Dec 31 days / * * Jan 31 days \ * Feb 28/9 days | * > Third cycle (incomplete) * * For this reason the calculations (internally) assume that the year * starts with March 1. * * TESTING * * This algorithm has been tested from the year 4713 B.C. to 10000 A.D. * The source code of the verification program is included in this * package. * * REFERENCES * * Conversions Between Calendar Date and Julian Day Number by Robert J. * Tantzen, Communications of the Association for Computing Machinery * August 1963. (Also published in Collected Algorithms from CACM, * algorithm number 199). [Note: the published algorithm is for the * Gregorian calendar, but was adjusted to use the Julian calendar's * simpler leap year rule.] * **************************************************************************/ #include "sdncal.h" #define JULIAN_SDN_OFFSET 32083 #define DAYS_PER_5_MONTHS 153 #define DAYS_PER_4_YEARS 1461 void SdnToJulian( long int sdn, int *pYear, int *pMonth, int *pDay) { int year; int month; int day; long int temp; int dayOfYear; if (sdn <= 0) { *pYear = 0; *pMonth = 0; *pDay = 0; return; } temp = (sdn + JULIAN_SDN_OFFSET) * 4 - 1; /* Calculate the year and day of year (1 <= dayOfYear <= 366). */ year = temp / DAYS_PER_4_YEARS; dayOfYear = (temp % DAYS_PER_4_YEARS) / 4 + 1; /* Calculate the month and day of month. */ temp = dayOfYear * 5 - 3; month = temp / DAYS_PER_5_MONTHS; day = (temp % DAYS_PER_5_MONTHS) / 5 + 1; /* Convert to the normal beginning of the year. */ if (month < 10) { month += 3; } else { year += 1; month -= 9; } /* Adjust to the B.C./A.D. type numbering. */ year -= 4800; if (year <= 0) year--; *pYear = year; *pMonth = month; *pDay = day; } long int JulianToSdn( int inputYear, int inputMonth, int inputDay) { int year; int month; /* check for invalid dates */ if (inputYear == 0 || inputYear < -4713 || inputMonth <= 0 || inputMonth > 12 || inputDay <= 0 || inputDay > 31) { return (0); } /* check for dates before SDN 1 (Jan 2, 4713 B.C.) */ if (inputYear == -4713) { if (inputMonth == 1 && inputDay == 1) { return (0); } } /* Make year always a positive number. */ if (inputYear < 0) { year = inputYear + 4801; } else { year = inputYear + 4800; } /* Adjust the start of the year. */ if (inputMonth > 2) { month = inputMonth - 3; } else { month = inputMonth + 9; year--; } return ((year * DAYS_PER_4_YEARS) / 4 + (month * DAYS_PER_5_MONTHS + 2) / 5 + inputDay - JULIAN_SDN_OFFSET); } /* * Local variables: * tab-width: 4 * c-basic-offset: 4 * End: * vim600: sw=4 ts=4 fdm=marker * vim<600: sw=4 ts=4 */