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#include <librock/sdncalh.h> void librock_SdnToJewish( long int sdn, int *pYear, int *pMonth, int *pDay); /* Convert a SDN to a Jewish calendar date. If the input SDN is before the * first day of year 1, the three output values will all be set to zero, * otherwise *pYear will be > 0; *pMonth will be in the range 1 to 13 * inclusive; *pDay will be in the range 1 to 30 inclusive. Note that Adar * II is assigned the month number 7 and Elul is always 13. */ long int librock_JewishToSdn( int year, int month, int day); /* * Convert a Jewish 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. */ char *librock_JewishMonthName[14]; /* * Convert a Jewish month number (1 to 13) to the name of the Jewish month * (null terminated). An index of zero will return a zero length string. */
* This package defines a set of routines that convert calendar dates to * and from a serial day number (SDN). The SDN is a serial numbering of * days where SDN 1 is November 25, 4714 BC in the Gregorian calendar and * SDN 2447893 is January 1, 1990. This system of day numbering is * sometimes referred to as Julian days, but to avoid confusion with the * Julian calendar, it is referred to as serial day numbers here. The term * Julian days is also used to mean the number of days since the beginning * of the current year. * * The SDN can be used as an intermediate step in converting from one * calendar system to another (such as Gregorian to Jewish). It can also * be used for date computations such as easily comparing two dates, * determining the day of the week, finding the date of yesterday or * calculating the number of days between two dates. * * SDN values less than one are not supported. If a conversion routine * returns an SDN of zero, this means that the date given is either invalid * or is outside the supported range for that calendar. * * At least some validity checks are performed on input dates. For * example, a negative month number will result in the return of zero for * the SDN. A returned SDN greater than one does not necessarily mean that * the input date was valid. To determine if the date is valid, convert it * to SDN, and if the SDN is greater than zero, convert it back to a date * and compare to the original. For example: int y1, m1, d1; int y2, m2, d2; long int sdn; ... sdn = GregorianToSdn(y1, m1, d1); if (sdn > 0) { SdnToGregorian(sdn, &y2, &m2, &d2); if (y1 == y2 && m1 == m2 && d1 == d2) { ... date is valid ... } }
* * Although this software can handle dates all the way back to the year * 1 (3761 B.C.), such use may not be meaningful. * * The Jewish calendar has been in use for several thousand years, but * in the early days there was no formula to determine the start of a * month. A new month was started when the new moon was first * observed. * * It is not clear when the current rule based calendar replaced the * observation based calendar. According to the book "Jewish Calendar * Mystery Dispelled" by George Zinberg, the patriarch Hillel II * published these rules in 358 A.D. But, according to The * Encyclopedia Judaica, Hillel II may have only published the 19 year * rule for determining the occurrence of leap years. * * I have yet to find a specific date when the current set of rules * were known to be in use.
* * The Jewish calendar is based on lunar as well as solar cycles. A * month always starts on or near a new moon and has either 29 or 30 * days (a lunar cycle is about 29 1/2 days). Twelve of these * alternating 2930 day months gives a year of 354 days, which is * about 11 1/4 days short of a solar year. * * Since a month is defined to be a lunar cycle (new moon to new moon), * this 11 1/4 day difference cannot be overcome by adding days to a * month as with the Gregorian calendar, so an entire month is * periodically added to the year, making some years 13 months long. * * For astronomical as well as ceremonial reasons, the start of a new * year may be delayed until a day or two after the new moon causing * years to vary in length. Leap years can be from 383 to 385 days and * common years can be from 353 to 355 days. These are the months of * the year and their possible lengths: * * COMMON YEAR LEAP YEAR * 1 Tishri 30 30 30 30 30 30 * 2 Heshvan 29 29 30 29 29 30 (variable) * 3 Kislev 29 30 30 29 30 30 (variable) * 4 Tevet 29 29 29 29 29 29 * 5 Shevat 30 30 30 30 30 30 * 6 Adar I 29 29 29 30 30 30 (variable) * 7 Adar II    29 29 29 (optional) * 8 Nisan 30 30 30 30 30 30 * 9 Iyyar 29 29 29 29 29 29 * 10 Sivan 30 30 30 30 30 30 * 11 Tammuz 29 29 29 29 29 29 * 12 Av 30 30 30 30 30 30 * 13 Elul 29 29 29 29 29 29 *       * 353 354 355 383 384 385 * * Note that the month names and other words that appear in this file * have multiple possible spellings in the Roman character set. I have * chosen to use the spellings found in the Encyclopedia Judaica. * * Adar II, the month added for leap years, is sometimes referred to as * the 13th month, but I have chosen to assign it the number 7 to keep * the months in chronological order. This may not be consistent with * other numbering schemes. * * Leap years occur in a fixed pattern of 19 years called the metonic * cycle. The 3rd, 6th, 8th, 11th, 14th, 17th and 19th years of this * cycle are leap years. The first metonic cycle starts with Jewish * year 1, or 3761/60 B.C. This is believed to be the year of * creation. * * To construct the calendar for a year, you must first find the length * of the year by determining the first day of the year (Tishri 1, or * Rosh HaShanah) and the first day of the following year. This * selects one of the six possible month length configurations listed * above. * * Finding the first day of the year is the most difficult part. * Finding the date and time of the new moon (or molad) is the first * step. For this purpose, the lunar cycle is assumed to be 29 days 12 * hours and 793 halakim. A halakim is 1/1080th of an hour or 3 1/3 * seconds. (This assumed value is only about 1/2 second less than the * value used by modern astronomers  not bad for a number that was * determined so long ago.) The first molad of year 1 occurred on * Sunday at 11:20:11 P.M. This would actually be Monday, because the * Jewish day is considered to begin at sunset. * * Since sunset varies, the day is assumed to begin at 6:00 P.M. for * calendar calculation purposes. So, the first molad was 5 hours 793 * halakim after the start of Tishri 1, 0001 (which was Monday * September 7, 4761 B.C. by the Gregorian calendar). All subsequent * molads can be calculated from this starting point by adding the * length of a lunar cycle. * * Once the molad that starts a year is determined the actual start of * the year (Tishri 1) can be determined. Tishri 1 will be the day of * the molad unless it is delayed by one of the following four rules * (called dehiyyot). Each rule can delay the start of the year by one * day, and since rule #1 can combine with one of the other rules, it * can be delayed as much as two days. * * 1. Tishri 1 must never be Sunday, Wednesday or Friday. (This * is largely to prevent certain holidays from occurring on the * day before or after the Sabbath.) * * 2. If the molad occurs on or after noon, Tishri 1 must be * delayed. * * 3. If it is a common (not leap) year and the molad occurs on * Tuesday at or after 3:11:20 A.M., Tishri 1 must be delayed. * * 4. If it is the year following a leap year and the molad occurs * on Monday at or after 9:32:43 and 1/3 sec, Tishri 1 must be * delayed.
* * dehiyyot The set of 4 rules that determine when the new year * starts relative to the molad. * * halakim 1/1080th of an hour or 3 1/3 seconds. * * lunar cycle The period of time between mean conjunctions of the * sun and moon (new moon to new moon). This is * assumed to be 29 days 12 hours and 793 halakim for * calendar purposes. * * metonic cycle A 19 year cycle which determines which years are * leap years and which are common years. The 3rd, * 6th, 8th, 11th, 14th, 17th and 19th years of this * cycle are leap years. * * molad The date and time of the mean conjunction of the * sun and moon (new moon). This is the approximate * beginning of a month. * * Rosh HaShanah The first day of the Jewish year (Tishri 1). * * Tishri The first month of the Jewish year.
* * SERIAL DAY NUMBER TO JEWISH DATE * * The simplest approach would be to use the rules stated above to find * the molad of Tishri before and after the given day number. Then use * the molads to find Tishri 1 of the current and following years. * From this the length of the year can be determined and thus the * length of each month. But this method is used as a last resort. * * The first 59 days of the year are the same regardless of the length * of the year. As a result, only the day number of the start of the * year is required. * * Similarly, the last 6 months do not change from year to year. And * since it can be determined whether the year is a leap year by simple * division, the lengths of Adar I and II can be easily calculated. In * fact, all dates after the 3rd month are consistent from year to year * (once it is known whether it is a leap year). * * This means that if the given day number falls in the 3rd month or on * the 30th day of the 2nd month the length of the year must be found, * but in no other case. * * So, the approach used is to take the given day number and round it * to the closest molad of Tishri (first new moon of the year). The * rounding is not really to the *closest* molad, but is such that if * the day number is before the middle of the 3rd month the molad at * the start of the year is found, otherwise the molad at the end of * the year is found. * * Only if the day number is actually found to be in the ambiguous * period of 29 to 31 days is the other molad calculated. * * JEWISH DATE TO SERIAL DAY NUMBER * * The year number is used to find which 19 year metonic cycle contains * the date and which year within the cycle (this is a division and * modulus). This also determines whether it is a leap year. * * If the month is 1 or 2, the calculation is simple addition to the * first of the year. * * If the month is 8 (Nisan) or greater, the calculation is simple * subtraction from beginning of the following year. * * If the month is 4 to 7, it is considered whether it is a leap year * and then simple subtraction from the beginning of the following year * is used. * * Only if it is the 3rd month is both the start and end of the year * required. *
* * This algorithm has been tested in two ways. First, 510 dates from a * table in "Jewish Calendar Mystery Dispelled" were calculated and * compared to the table. Second, the calculation algorithm described * in "Jewish Calendar Mystery Dispelled" was coded and used to verify * all dates from the year 1 (3761 B.C.) to the year 13760 (10000 * A.D.). * * The source code of the verification program is included the sdncal * package. *
* * The Encyclopedia Judaica, the entry for "Calendar" * * The Jewish Encyclopedia * * Jewish Calendar Mystery Dispelled by George Zinberg, Vantage Press, * 1963 * * The Comprehensive Hebrew Calendar by Arthur Spier, Behrman House * * The Book of Calendars [note that this work contains many typos]
Copyright 19931995, Scott E. Lee, all rights reserved. Licensed under BSDish license, NO WARRANTY. Copies must retain this block. License text in <librock/license/sdncal.txt> librock_LIDESC_HC=553e181388455f0eef17ccd9e2a51c1f3ae8daf0
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