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represents the progression of the day of the week based on the year. Assuming that each year is 365 days long, the same date on each succeeding year will be offset by a value of =. Since there are 366 days in each leap year, this needs to be accounted for by adding another day to the day of the week offset value.
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 ...
The algorithm for the day-of-week of 1 Jan can be proven using modulo arithmetic. The main point is that because 365 % 7 = 1, each year adds 1 day to the progression. The rest is adjustment for leap year. The century-based versions have 36525 % 7 = 6. The table of month offsets show a divergence in February due to the leap year.
The 23rd is ante diem vii kalendas Martias, the next day in a leap year is a.d. bis sextum kal. Mart., the next day is the regular a.d.vi kal. Mart., and so to the end of the month. For example, in 2024 (=GF), all days preceding the leap day corresponded to a common-year G calendar, and all days afterward corresponded to a common-year F calendar.
This convention accounts for days in the period based on the portion in a leap year and the portion in a non-leap year. The days in the numerators are calculated on a Julian day difference basis. In this convention the first day of the period is included and the last day is excluded. The CouponFactor uses the same formula, replacing Date2 by Date3.
Subtract the weekday number from the ordinal day of the year. Add 10. Divide by 7, discard the remainder. If the week number thus obtained equals 0, it means that the given date belongs to the preceding (week-based) year. If a week number of 53 is obtained, one must check that the date is not actually in week 1 of the following year. Formula
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A calendar date is a reference to a particular day represented within a calendar system. The calendar date allows the specific day to be identified. The number of days between two dates may be calculated. For example, "25 January 2025" is ten days after "15 January 2025". The date of a particular event depends on the observed time zone.