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diff --git a/Documentation/cal.txt b/Documentation/cal.txt new file mode 100644 index 0000000..8305165 --- /dev/null +++ b/Documentation/cal.txt @@ -0,0 +1,42 @@ +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. |