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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.