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5.9 Date Forms

A date form represents a date and possibly an associated time. Simple date arithmetic is supported: Adding a number to a date produces a new date shifted by that many days; adding an HMS form to a date shifts it by that many hours. Subtracting two date forms computes the number of days between them (represented as a simple number). Many other operations, such as multiplying two date forms, are nonsensical and are not allowed by Calc.

Date forms are entered and displayed enclosed in ‘< >’ brackets. The default format is, e.g., ‘<Wed Jan 9, 1991>’ for dates, or ‘<3:32:20pm Wed Jan 9, 1991>’ for dates with times. Input is flexible; date forms can be entered in any of the usual notations for dates and times. See Date Formats.

Date forms are stored internally as numbers, specifically the number of days since midnight on the morning of January 1 of the year 1 AD. If the internal number is an integer, the form represents a date only; if the internal number is a fraction or float, the form represents a date and time. For example, ‘<6:00am Wed Jan 9, 1991>’ is represented by the number 726842.25. The standard precision of 12 decimal digits is enough to ensure that a (reasonable) date and time can be stored without roundoff error.

If the current precision is greater than 12, date forms will keep additional digits in the seconds position. For example, if the precision is 15, the seconds will keep three digits after the decimal point. Decreasing the precision below 12 may cause the time part of a date form to become inaccurate. This can also happen if astronomically high years are used, though this will not be an issue in everyday (or even everymillennium) use. Note that date forms without times are stored as exact integers, so roundoff is never an issue for them.

You can use the v p (calc-pack) and v u (calc-unpack) commands to get at the numerical representation of a date form. See Packing and Unpacking.

Date forms can go arbitrarily far into the future or past. Negative year numbers represent years BC. Calc uses a combination of the Gregorian and Julian calendars, following the history of Great Britain and the British colonies. This is the same calendar that is used by the cal program in most Unix implementations.

Some historical background: The Julian calendar was created by Julius Caesar in the year 46 BC as an attempt to fix the gradual drift caused by the lack of leap years in the calendar used until that time. The Julian calendar introduced an extra day in all years divisible by four. After some initial confusion, the calendar was adopted around the year we call 8 AD. Some centuries later it became apparent that the Julian year of 365.25 days was itself not quite right. In 1582 Pope Gregory XIII introduced the Gregorian calendar, which added the new rule that years divisible by 100, but not by 400, were not to be considered leap years despite being divisible by four. Many countries delayed adoption of the Gregorian calendar because of religious differences; in Britain it was put off until the year 1752, by which time the Julian calendar had fallen eleven days behind the true seasons. So the switch to the Gregorian calendar in early September 1752 introduced a discontinuity: The day after Sep 2, 1752 is Sep 14, 1752. Calc follows this convention. To take another example, Russia waited until 1918 before adopting the new calendar, and thus needed to remove thirteen days (between Feb 1, 1918 and Feb 14, 1918). This means that Calc's reckoning will be inconsistent with Russian history between 1752 and 1918, and similarly for various other countries.

Today's timekeepers introduce an occasional “leap second” as well, but Calc does not take these minor effects into account. (If it did, it would have to report a non-integer number of days between, say, ‘<12:00am Mon Jan 1, 1900>’ and ‘<12:00am Sat Jan 1, 2000>’.)

Calc uses the Julian calendar for all dates before the year 1752, including dates BC when the Julian calendar technically had not yet been invented. Thus the claim that day number -10000 is called “August 16, 28 BC” should be taken with a grain of salt.

Please note that there is no “year 0”; the day before ‘<Sat Jan 1, +1>’ is ‘<Fri Dec 31, -1>’. These are days 0 and -1 respectively in Calc's internal numbering scheme.

Another day counting system in common use is, confusingly, also called “Julian.” The Julian day number is the numbers of days since 12:00 noon (GMT) on Jan 1, 4713 BC, which in Calc's scheme (in GMT) is -1721423.5 (recall that Calc starts at midnight instead of noon). Thus to convert a Calc date code obtained by unpacking a date form into a Julian day number, simply add 1721423.5 after compensating for the time zone difference. The built-in t J command performs this conversion for you.

The Julian day number is based on the Julian cycle, which was invented in 1583 by Joseph Justus Scaliger. Scaliger named it the Julian cycle since it involves the Julian calendar, but some have suggested that Scaliger named it in honor of his father, Julius Caesar Scaliger. The Julian cycle is based on three other cycles: the indiction cycle, the Metonic cycle, and the solar cycle. The indiction cycle is a 15 year cycle originally used by the Romans for tax purposes but later used to date medieval documents. The Metonic cycle is a 19 year cycle; 19 years is close to being a common multiple of a solar year and a lunar month, and so every 19 years the phases of the moon will occur on the same days of the year. The solar cycle is a 28 year cycle; the Julian calendar repeats itself every 28 years. The smallest time period which contains multiples of all three cycles is the least common multiple of 15 years, 19 years and 28 years, which (since they're pairwise relatively prime) is 15*19*28 = 7980 years. This is the length of a Julian cycle. Working backwards, the previous year in which all three cycles began was 4713 BC, and so Scaliger chose that year as the beginning of a Julian cycle. Since at the time there were no historical records from before 4713 BC, using this year as a starting point had the advantage of avoiding negative year numbers. In 1849, the astronomer John Herschel (son of William Herschel) suggested using the number of days since the beginning of the Julian cycle as an astronomical dating system; this idea was taken up by other astronomers. (At the time, noon was the start of the astronomical day. Herschel originally suggested counting the days since Jan 1, 4713 BC at noon Alexandria time; this was later amended to noon GMT.) Julian day numbering is largely used in astronomy.

The Unix operating system measures time as an integer number of seconds since midnight, Jan 1, 1970. To convert a Calc date value into a Unix time stamp, first subtract 719164 (the code for ‘<Jan 1, 1970>’), then multiply by 86400 (the number of seconds in a day) and press R to round to the nearest integer. If you have a date form, you can simply subtract the day ‘<Jan 1, 1970>’ instead of unpacking and subtracting 719164. Likewise, divide by 86400 and add ‘<Jan 1, 1970>’ to convert from Unix time to a Calc date form. (Note that Unix normally maintains the time in the GMT time zone; you may need to subtract five hours to get New York time, or eight hours for California time. The same is usually true of Julian day counts.) The built-in t U command performs these conversions.