1*df930be7SderaadtThe cal(1) date routines were written from scratch, basically from first 2*df930be7Sderaadtprinciples. The algorithm for calculating the day of week from any 3*df930be7SderaadtGregorian date was "reverse engineered". This was necessary as most of 4*df930be7Sderaadtthe documented algorithms have to do with date calculations for other 5*df930be7Sderaadtcalendars (e.g. julian) and are only accurate when converted to gregorian 6*df930be7Sderaadtwithin a narrow range of dates. 7*df930be7Sderaadt 8*df930be7Sderaadt1 Jan 1 is a Saturday because that's what cal says and I couldn't change 9*df930be7Sderaadtthat even if I was dumb enough to try. From this we can easily calculate 10*df930be7Sderaadtthe day of week for any date. The algorithm for a zero based day of week: 11*df930be7Sderaadt 12*df930be7Sderaadt calculate the number of days in all prior years (year-1)*365 13*df930be7Sderaadt add the number of leap years (days?) since year 1 14*df930be7Sderaadt (not including this year as that is covered later) 15*df930be7Sderaadt add the day number within the year 16*df930be7Sderaadt this compensates for the non-inclusive leap year 17*df930be7Sderaadt calculation 18*df930be7Sderaadt if the day in question occurs before the gregorian reformation 19*df930be7Sderaadt (3 sep 1752 for our purposes), then simply return 20*df930be7Sderaadt (value so far - 1 + SATURDAY's value of 6) modulo 7. 21*df930be7Sderaadt if the day in question occurs during the reformation (3 sep 1752 22*df930be7Sderaadt to 13 sep 1752 inclusive) return THURSDAY. This is my 23*df930be7Sderaadt idea of what happened then. It does not matter much as 24*df930be7Sderaadt this program never tries to find day of week for any day 25*df930be7Sderaadt that is not the first of a month. 26*df930be7Sderaadt otherwise, after the reformation, use the same formula as the 27*df930be7Sderaadt days before with the additional step of subtracting the 28*df930be7Sderaadt number of days (11) that were adjusted out of the calendar 29*df930be7Sderaadt just before taking the modulo. 30*df930be7Sderaadt 31*df930be7SderaadtIt must be noted that the number of leap years calculation is sensitive 32*df930be7Sderaadtto the date for which the leap year is being calculated. A year that occurs 33*df930be7Sderaadtbefore the reformation is determined to be a leap year if its modulo of 34*df930be7Sderaadt4 equals zero. But after the reformation, a year is only a leap year if 35*df930be7Sderaadtits modulo of 4 equals zero and its modulo of 100 does not. Of course, 36*df930be7Sderaadtthere is an exception for these century years. If the modulo of 400 equals 37*df930be7Sderaadtzero, then the year is a leap year anyway. This is, in fact, what the 38*df930be7Sderaadtgregorian reformation was all about (a bit of error in the old algorithm 39*df930be7Sderaadtthat caused the calendar to be inaccurate.) 40*df930be7Sderaadt 41*df930be7SderaadtOnce we have the day in year for the first of the month in question, the 42*df930be7Sderaadtrest is trivial. 43