- 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.