/* $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]
*
**************************************************************************/
#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 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"
};
/************************************************************************
* 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 <= SDN_OFFSET) {
*pYear = 0;
*pMonth = 0;
*pDay = 0;
return;
}
inputDay = sdn - 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 + SDN_OFFSET);
}
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