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by jcranmer
2537 days ago
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The calculations are actually really easy. Note that the length of a (regular) year is 1 mod 7, which means weekdays slip by 1 day each year, except for leap years. Over the 400-year Gregorian calendar cycle, there are 97 leap years, for a total of 497 days of slip... so adding 400 years to the current calendar year will always yield the same calendar. More specifically, there are 14 possible calendars. The leap year cycle is 4 days (excluding the 100 year skips), and the weekday cycle is 7 days, so the leap year×weekday cycle is 28 years. So the starting weekdays are on a 28-year cycle, but you have to slip your resulting calculation by the number of centuries from the beginning of the 400-year cycle (i.e., integer division of year by 100). You'll reuse a leap year calendar in 28 years (40 years, if it crosses a round-hundred year), and you'll reuse a non-leap year calendar in 6 or 11 years (12 or 6 years, if it cross a round-hundred year). The easiest way to code it is to just precompute the year % 400 table and report the results. |
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If you are interested, Chrono [1] internally uses the exact table. Constants there refer to dominical letters [2].
[1] https://github.com/chronotope/chrono/blob/a4488007272569f752...
[2] https://en.wikipedia.org/wiki/Dominical_letter