EVERYTHING FROM THE OTHER REPO

2026-07-29 03:36:26 +03:00
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+The cal(1) date routines were written from scratch, basically from first
+principles.  The algorithm for calculating the day of week from any
+Gregorian date was "reverse engineered".  This was necessary as most of
+the documented algorithms have to do with date calculations for other
+calendars (e.g. julian) and are only accurate when converted to gregorian
+within a narrow range of dates.
+
+1 Jan 1 is a Saturday because that's what cal says and I couldn't change
+that even if I was dumb enough to try.  From this we can easily calculate
+the day of week for any date.  The algorithm for a zero based day of week:
+
+	calculate the number of days in all prior years (year-1)*365
+	add the number of leap years (days?) since year 1
+		(not including this year as that is covered later)
+	add the day number within the year
+		this compensates for the non-inclusive leap year
+		calculation
+	if the day in question occurs before the gregorian reformation
+		(3 sep 1752 for our purposes), then simply return
+		(value so far - 1 + SATURDAY's value of 6) modulo 7.
+	if the day in question occurs during the reformation (3 sep 1752
+		to 13 sep 1752 inclusive) return THURSDAY. This is my
+		idea of what happened then. It does not matter much as
+		this program never tries to find day of week for any day
+		that is not the first of a month.
+	otherwise, after the reformation, use the same formula as the
+		days before with the additional step of subtracting the
+		number of days (11) that were adjusted out of the calendar
+		just before taking the modulo.
+
+It must be noted that the number of leap years calculation is sensitive
+to the date for which the leap year is being calculated.  A year that occurs
+before the reformation is determined to be a leap year if its modulo of
+4 equals zero.  But after the reformation, a year is only a leap year if
+its modulo of 4 equals zero and its modulo of 100 does not.  Of course,
+there is an exception for these century years.  If the modulo of 400 equals
+zero, then the year is a leap year anyway.  This is, in fact, what the
+gregorian reformation was all about (a bit of error in the old algorithm
+that caused the calendar to be inaccurate.)
+
+Once we have the day in year for the first of the month in question, the
+rest is trivial.