43 lines
2.2 KiB
Text
43 lines
2.2 KiB
Text
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The cal(1) date routines were written from scratch, basically from first
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principles. The algorithm for calculating the day of week from any
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Gregorian date was "reverse engineered". This was necessary as most of
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the documented algorithms have to do with date calculations for other
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calendars (e.g. julian) and are only accurate when converted to gregorian
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within a narrow range of dates.
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1 Jan 1 is a Saturday because that's what cal says and I couldn't change
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that even if I was dumb enough to try. From this we can easily calculate
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the day of week for any date. The algorithm for a zero based day of week:
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calculate the number of days in all prior years (year-1)*365
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add the number of leap years (days?) since year 1
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(not including this year as that is covered later)
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add the day number within the year
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this compensates for the non-inclusive leap year
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calculation
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if the day in question occurs before the gregorian reformation
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(3 sep 1752 for our purposes), then simply return
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(value so far - 1 + SATURDAY's value of 6) modulo 7.
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if the day in question occurs during the reformation (3 sep 1752
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to 13 sep 1752 inclusive) return THURSDAY. This is my
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idea of what happened then. It does not matter much as
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this program never tries to find day of week for any day
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that is not the first of a month.
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otherwise, after the reformation, use the same formula as the
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days before with the additional step of subtracting the
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number of days (11) that were adjusted out of the calendar
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just before taking the modulo.
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It must be noted that the number of leap years calculation is sensitive
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to the date for which the leap year is being calculated. A year that occurs
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before the reformation is determined to be a leap year if its modulo of
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4 equals zero. But after the reformation, a year is only a leap year if
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its modulo of 4 equals zero and its modulo of 100 does not. Of course,
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there is an exception for these century years. If the modulo of 400 equals
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zero, then the year is a leap year anyway. This is, in fact, what the
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gregorian reformation was all about (a bit of error in the old algorithm
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that caused the calendar to be inaccurate.)
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Once we have the day in year for the first of the month in question, the
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rest is trivial.
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