/* $selId: jewish.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 * 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 * 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 *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. * * VALID RANGE * * 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. * * CALENDAR OVERVIEW * * 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 29-30 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 Ha-Shanah) 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. * * GLOSSARY * * 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 Ha-Shanah The first day of the Jewish year (Tishri 1). * * Tishri The first month of the Jewish year. * * ALGORITHMS * * 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. * * TESTING * * 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 in this * package. * * REFERENCES * * 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] * **************************************************************************/ #if defined(PHP_WIN32) && _MSC_VER >= 1200 #pragma setlocale("english") #endif #include "sdncal.h" #define HALAKIM_PER_HOUR 1080 #define HALAKIM_PER_DAY 25920 #define HALAKIM_PER_LUNAR_CYCLE ((29 * HALAKIM_PER_DAY) + 13753) #define HALAKIM_PER_METONIC_CYCLE (HALAKIM_PER_LUNAR_CYCLE * (12 * 19 + 7)) #define JEWISH_SDN_OFFSET 347997 #define NEW_MOON_OF_CREATION 31524 #define SUNDAY 0 #define MONDAY 1 #define TUESDAY 2 #define WEDNESDAY 3 #define THURSDAY 4 #define FRIDAY 5 #define SATURDAY 6 #define NOON (18 * HALAKIM_PER_HOUR) #define AM3_11_20 ((9 * HALAKIM_PER_HOUR) + 204) #define AM9_32_43 ((15 * HALAKIM_PER_HOUR) + 589) static int monthsPerYear[19] = { 12, 12, 13, 12, 12, 13, 12, 13, 12, 12, 13, 12, 12, 13, 12, 12, 13, 12, 13 }; static int yearOffset[19] = { 0, 12, 24, 37, 49, 61, 74, 86, 99, 111, 123, 136, 148, 160, 173, 185, 197, 210, 222 }; char *JewishMonthName[14] = { "", "Tishri", "Heshvan", "Kislev", "Tevet", "Shevat", "AdarI", "AdarII", "Nisan", "Iyyar", "Sivan", "Tammuz", "Av", "Elul" }; char *JewishMonthHebName[14] = { "", "תשרי", "חשון", "כסלו", "טבת", "שבט", "אדר", "'אדר ב", "ניסן", "אייר", "סיון", "תמוז", "אב", "אלול" }; /************************************************************************ * Given the year within the 19 year metonic cycle and the time of a molad * (new moon) which starts that year, this routine will calculate what day * will be the actual start of the year (Tishri 1 or Rosh Ha-Shanah). This * first day of the year will be the day of the molad unless one of 4 rules * (called dehiyyot) delays it. These 4 rules can delay the start of the * year by as much as 2 days. */ static long int Tishri1( int metonicYear, long int moladDay, long int moladHalakim) { long int tishri1; int dow; int leapYear; int lastWasLeapYear; tishri1 = moladDay; dow = tishri1 % 7; leapYear = metonicYear == 2 || metonicYear == 5 || metonicYear == 7 || metonicYear == 10 || metonicYear == 13 || metonicYear == 16 || metonicYear == 18; lastWasLeapYear = metonicYear == 3 || metonicYear == 6 || metonicYear == 8 || metonicYear == 11 || metonicYear == 14 || metonicYear == 17 || metonicYear == 0; /* Apply rules 2, 3 and 4. */ if ((moladHalakim >= NOON) || ((!leapYear) && dow == TUESDAY && moladHalakim >= AM3_11_20) || (lastWasLeapYear && dow == MONDAY && moladHalakim >= AM9_32_43)) { tishri1++; dow++; if (dow == 7) { dow = 0; } } /* Apply rule 1 after the others because it can cause an additional * delay of one day. */ if (dow == WEDNESDAY || dow == FRIDAY || dow == SUNDAY) { tishri1++; } return (tishri1); } /************************************************************************ * Given a metonic cycle number, calculate the date and time of the molad * (new moon) that starts that cycle. Since the length of a metonic cycle * is a constant, this is a simple calculation, except that it requires an * intermediate value which is bigger that 32 bits. Because this * intermediate value only needs 36 to 37 bits and the other numbers are * constants, the process has been reduced to just a few steps. */ static void MoladOfMetonicCycle( int metonicCycle, long int *pMoladDay, long int *pMoladHalakim) { register unsigned long int r1, r2, d1, d2; /* Start with the time of the first molad after creation. */ r1 = NEW_MOON_OF_CREATION; /* Calculate metonicCycle * HALAKIM_PER_METONIC_CYCLE. The upper 32 * bits of the result will be in r2 and the lower 16 bits will be * in r1. */ r1 += metonicCycle * (HALAKIM_PER_METONIC_CYCLE & 0xFFFF); r2 = r1 >> 16; r2 += metonicCycle * ((HALAKIM_PER_METONIC_CYCLE >> 16) & 0xFFFF); /* Calculate r2r1 / HALAKIM_PER_DAY. The remainder will be in r1, the * upper 16 bits of the quotient will be in d2 and the lower 16 bits * will be in d1. */ d2 = r2 / HALAKIM_PER_DAY; r2 -= d2 * HALAKIM_PER_DAY; r1 = (r2 << 16) | (r1 & 0xFFFF); d1 = r1 / HALAKIM_PER_DAY; r1 -= d1 * HALAKIM_PER_DAY; *pMoladDay = (d2 << 16) | d1; *pMoladHalakim = r1; } /************************************************************************ * Given a day number, find the molad of Tishri (the new moon at the start * of a year) which is closest to that day number. It's not really the * *closest* molad that we want here. If the input day is in the first two * months, we want the molad at the start of the year. If the input day is * in the fourth to last months, we want the molad at the end of the year. * If the input day is in the third month, it doesn't matter which molad is * returned, because both will be required. This type of "rounding" allows * us to avoid calculating the length of the year in most cases. */ static void FindTishriMolad( long int inputDay, int *pMetonicCycle, int *pMetonicYear, long int *pMoladDay, long int *pMoladHalakim) { long int moladDay; long int moladHalakim; int metonicCycle; int metonicYear; /* Estimate the metonic cycle number. Note that this may be an under * estimate because there are 6939.6896 days in a metonic cycle not * 6940, but it will never be an over estimate. The loop below will * correct for any error in this estimate. */ metonicCycle = (inputDay + 310) / 6940; /* Calculate the time of the starting molad for this metonic cycle. */ MoladOfMetonicCycle(metonicCycle, &moladDay, &moladHalakim); /* If the above was an under estimate, increment the cycle number until * the correct one is found. For modern dates this loop is about 98.6% * likely to not execute, even once, because the above estimate is * really quite close. */ while (moladDay < inputDay - 6940 + 310) { metonicCycle++; moladHalakim += HALAKIM_PER_METONIC_CYCLE; moladDay += moladHalakim / HALAKIM_PER_DAY; moladHalakim = moladHalakim % HALAKIM_PER_DAY; } /* Find the molad of Tishri closest to this date. */ for (metonicYear = 0; metonicYear < 18; metonicYear++) { if (moladDay > inputDay - 74) { break; } moladHalakim += HALAKIM_PER_LUNAR_CYCLE * monthsPerYear[metonicYear]; moladDay += moladHalakim / HALAKIM_PER_DAY; moladHalakim = moladHalakim % HALAKIM_PER_DAY; } *pMetonicCycle = metonicCycle; *pMetonicYear = metonicYear; *pMoladDay = moladDay; *pMoladHalakim = moladHalakim; } /************************************************************************ * Given a year, find the number of the first day of that year and the date * and time of the starting molad. */ static void FindStartOfYear( int year, int *pMetonicCycle, int *pMetonicYear, long int *pMoladDay, long int *pMoladHalakim, int *pTishri1) { *pMetonicCycle = (year - 1) / 19; *pMetonicYear = (year - 1) % 19; MoladOfMetonicCycle(*pMetonicCycle, pMoladDay, pMoladHalakim); *pMoladHalakim += HALAKIM_PER_LUNAR_CYCLE * yearOffset[*pMetonicYear]; *pMoladDay += *pMoladHalakim / HALAKIM_PER_DAY; *pMoladHalakim = *pMoladHalakim % HALAKIM_PER_DAY; *pTishri1 = Tishri1(*pMetonicYear, *pMoladDay, *pMoladHalakim); } /************************************************************************ * Given a serial day number (SDN), find the corresponding year, month and * day in the Jewish calendar. The three output values will always be * modified. If the input SDN is before the first day of year 1, they 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. */ void SdnToJewish( long int sdn, int *pYear, int *pMonth, int *pDay) { long int inputDay; long int day; long int halakim; int metonicCycle; int metonicYear; int tishri1; int tishri1After; int yearLength; if (sdn <= JEWISH_SDN_OFFSET) { *pYear = 0; *pMonth = 0; *pDay = 0; return; } inputDay = sdn - JEWISH_SDN_OFFSET; FindTishriMolad(inputDay, &metonicCycle, &metonicYear, &day, &halakim); tishri1 = Tishri1(metonicYear, day, halakim); if (inputDay >= tishri1) { /* It found Tishri 1 at the start of the year. */ *pYear = metonicCycle * 19 + metonicYear + 1; if (inputDay < tishri1 + 59) { if (inputDay < tishri1 + 30) { *pMonth = 1; *pDay = inputDay - tishri1 + 1; } else { *pMonth = 2; *pDay = inputDay - tishri1 - 29; } return; } /* We need the length of the year to figure this out, so find * Tishri 1 of the next year. */ halakim += HALAKIM_PER_LUNAR_CYCLE * monthsPerYear[metonicYear]; day += halakim / HALAKIM_PER_DAY; halakim = halakim % HALAKIM_PER_DAY; tishri1After = Tishri1((metonicYear + 1) % 19, day, halakim); } else { /* It found Tishri 1 at the end of the year. */ *pYear = metonicCycle * 19 + metonicYear; if (inputDay >= tishri1 - 177) { /* It is one of the last 6 months of the year. */ if (inputDay > tishri1 - 30) { *pMonth = 13; *pDay = inputDay - tishri1 + 30; } else if (inputDay > tishri1 - 60) { *pMonth = 12; *pDay = inputDay - tishri1 + 60; } else if (inputDay > tishri1 - 89) { *pMonth = 11; *pDay = inputDay - tishri1 + 89; } else if (inputDay > tishri1 - 119) { *pMonth = 10; *pDay = inputDay - tishri1 + 119; } else if (inputDay > tishri1 - 148) { *pMonth = 9; *pDay = inputDay - tishri1 + 148; } else { *pMonth = 8; *pDay = inputDay - tishri1 + 178; } return; } else { if (monthsPerYear[(*pYear - 1) % 19] == 13) { *pMonth = 7; *pDay = inputDay - tishri1 + 207; if (*pDay > 0) return; (*pMonth)--; (*pDay) += 30; if (*pDay > 0) return; (*pMonth)--; (*pDay) += 30; } else { *pMonth = 6; *pDay = inputDay - tishri1 + 207; if (*pDay > 0) return; (*pMonth)--; (*pDay) += 30; } if (*pDay > 0) return; (*pMonth)--; (*pDay) += 29; if (*pDay > 0) return; /* We need the length of the year to figure this out, so find * Tishri 1 of this year. */ tishri1After = tishri1; FindTishriMolad(day - 365, &metonicCycle, &metonicYear, &day, &halakim); tishri1 = Tishri1(metonicYear, day, halakim); } } yearLength = tishri1After - tishri1; day = inputDay - tishri1 - 29; if (yearLength == 355 || yearLength == 385) { /* Heshvan has 30 days */ if (day <= 30) { *pMonth = 2; *pDay = day; return; } day -= 30; } else { /* Heshvan has 29 days */ if (day <= 29) { *pMonth = 2; *pDay = day; return; } day -= 29; } /* It has to be Kislev. */ *pMonth = 3; *pDay = day; } /************************************************************************ * Given a year, month and day in the Jewish calendar, find the * corresponding serial day number (SDN). Zero is returned when the input * date is detected as invalid. The return value will be > 0 for all valid * 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. */ long int JewishToSdn( int year, int month, int day) { long int sdn; int metonicCycle; int metonicYear; int tishri1; int tishri1After; long int moladDay; long int moladHalakim; int yearLength; int lengthOfAdarIAndII; if (year <= 0 || day <= 0 || day > 30) { return (0); } switch (month) { case 1: case 2: /* It is Tishri or Heshvan - don't need the year length. */ FindStartOfYear(year, &metonicCycle, &metonicYear, &moladDay, &moladHalakim, &tishri1); if (month == 1) { sdn = tishri1 + day - 1; } else { sdn = tishri1 + day + 29; } break; case 3: /* It is Kislev - must find the year length. */ /* Find the start of the year. */ FindStartOfYear(year, &metonicCycle, &metonicYear, &moladDay, &moladHalakim, &tishri1); /* Find the end of the year. */ moladHalakim += HALAKIM_PER_LUNAR_CYCLE * monthsPerYear[metonicYear]; moladDay += moladHalakim / HALAKIM_PER_DAY; moladHalakim = moladHalakim % HALAKIM_PER_DAY; tishri1After = Tishri1((metonicYear + 1) % 19, moladDay, moladHalakim); yearLength = tishri1After - tishri1; if (yearLength == 355 || yearLength == 385) { sdn = tishri1 + day + 59; } else { sdn = tishri1 + day + 58; } break; case 4: case 5: case 6: /* It is Tevet, Shevat or Adar I - don't need the year length. */ FindStartOfYear(year + 1, &metonicCycle, &metonicYear, &moladDay, &moladHalakim, &tishri1After); if (monthsPerYear[(year - 1) % 19] == 12) { lengthOfAdarIAndII = 29; } else { lengthOfAdarIAndII = 59; } if (month == 4) { sdn = tishri1After + day - lengthOfAdarIAndII - 237; } else if (month == 5) { sdn = tishri1After + day - lengthOfAdarIAndII - 208; } else { sdn = tishri1After + day - lengthOfAdarIAndII - 178; } break; default: /* It is Adar II or later - don't need the year length. */ FindStartOfYear(year + 1, &metonicCycle, &metonicYear, &moladDay, &moladHalakim, &tishri1After); switch (month) { case 7: sdn = tishri1After + day - 207; break; case 8: sdn = tishri1After + day - 178; break; case 9: sdn = tishri1After + day - 148; break; case 10: sdn = tishri1After + day - 119; break; case 11: sdn = tishri1After + day - 89; break; case 12: sdn = tishri1After + day - 60; break; case 13: sdn = tishri1After + day - 30; break; default: return (0); } } return (sdn + JEWISH_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 */