/* $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
*
* Julius Caesar 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"
#include <limits.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) {
goto fail;
}
/* Check for overflow */
if (sdn > (LONG_MAX - JULIAN_SDN_OFFSET * 4 + 1) / 4 || sdn < LONG_MIN / 4) {
goto fail;
}
temp = sdn * 4 + (JULIAN_SDN_OFFSET * 4 - 1);
/* Calculate the year and day of year (1 <= dayOfYear <= 366). */
{
long yearl = temp / DAYS_PER_4_YEARS;
if (yearl > INT_MAX || yearl < INT_MIN) {
goto fail;
}
year = (int) yearl;
}
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;
return;
fail:
*pYear = 0;
*pMonth = 0;
*pDay = 0;
}
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
*/