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A calendrical calculation is a calculation concerning calendar dates. Calendrical calculations can be considered an area of applied mathematics. Some examples of calendrical calculations: Converting a Julian or Gregorian calendar date to its Julian day number and vice versa (see § Julian day number calculation within that article for details).
Give February the appropriate number of days for the calendar being converted into. When subtracting days to calculate the Gregorian equivalent of 29 February (Julian), 29 February is discounted. Thus if the calculated value is −4 the Gregorian equivalent of this date is 24 February. [29] [30]
Gregorian dates before that are proleptic, that is, using the Gregorian rules to reckon backward from October 15, 1582. Years are given in astronomical year numbering. Augustus corrected errors in the observance of leap years by omitting leap days until AD 8. Julian calendar dates before March AD 4 are proleptic, and do not necessarily match ...
A full calendar system has a different calendar date for every day. [20] [21] Thus the week cycle is by itself not a full calendar system; [22] neither is a system to name the days within a year without a system for identifying the years. The simplest calendar system just counts time periods from a reference date. [23]
Lilian dates can be used to calculate the number of days between any two dates occurring since the beginning of the Gregorian calendar. It is currently used by date conversion routines that are part of IBM Language Environment (LE) software [2] and in IBM AIX COBOL. [3] The Lilian date is only a date format: it is not tied to any particular ...
The basic approach of nearly all of the methods to calculate the day of the week begins by starting from an "anchor date": a known pair (such as 1 January 1800 as a Wednesday), determining the number of days between the known day and the day that you are trying to determine, and using arithmetic modulo 7 to find a new numerical day of the week.
The overall function, , normalizes the result to reside in the range of 0 to 6, which yields the index of the correct day of the week for the date being analyzed. The reason that the formula differs between calendars is that the Julian calendar does not have a separate rule for leap centuries and is offset from the Gregorian calendar by a fixed ...
The doomsday's anchor day calculation is effectively calculating the number of days between any given date in the base year and the same date in the current year, then taking the remainder modulo 7. When both dates come after the leap day (if any), the difference is just 365y + y / 4 (rounded down). But 365 equals 52 × 7 + 1, so after ...