Calendrical Calculations

Calendrical calculations are ubiquitous. Banks need to calculate interest on a daily basis. Operating systems need to switch to and from daylight savings time. Dates of secular and religious holidays need to be computed for consideration in planning events. Paychecks need to be issued on weekly, biweekly, or monthly schedules. Bills and statements must be generated periodically. Most of these calculations are not difEcult because the rules of our civil calendar (the Gregorian calendar) are straightforward. Complications begin when we need to know the day of the week on which a given date falls or when various religious holidays based on other calendars occur. These complications lead to difficult programming tasks-not difficult in an algorithmic sense, but difficult because it can be extremely tedious to delve, for example, into the complexities of the Hebrew calendar and its relation to the civil calendar. The purpose of this paper is to present, in a completely algorithmic form, a description of five basic calendars and how they relate to one another: the present civil calendar (Gregorian), the recent IS0 commercial calendar, the old civil calendar (Julian), the Islamic (Moslem) calendar, and the Hebrew (Jewish) calendar. Information that is sufficiently detailed to allow computer implementation is difficult to find for the Islamic and Hebrew calendars since the published material is often inaccessible, ecclesiastically oriented, incomplete, inaccurate, based on extensive tables, overburdened with extraneous material, focused on shortcuts for hand calculation to