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      1  1.1  cgd The cal(1) date routines were written from scratch, basically from first
      2  1.1  cgd principles.  The algorithm for calculating the day of week from any
      3  1.1  cgd Gregorian date was "reverse engineered".  This was necessary as most of
      4  1.1  cgd the documented algorithms have to do with date calculations for other
      5  1.1  cgd calendars (e.g. julian) and are only accurate when converted to gregorian
      6  1.1  cgd within a narrow range of dates.
      7  1.1  cgd 
      8  1.1  cgd 1 Jan 1 is a Saturday because that's what cal says and I couldn't change
      9  1.1  cgd that even if I was dumb enough to try.  From this we can easily calculate
     10  1.1  cgd the day of week for any date.  The algorithm for a zero based day of week:
     11  1.1  cgd 
     12  1.1  cgd 	calculate the number of days in all prior years (year-1)*365
     13  1.1  cgd 	add the number of leap years (days?) since year 1 
     14  1.1  cgd 		(not including this year as that is covered later)
     15  1.1  cgd 	add the day number within the year
     16  1.1  cgd 		this compensates for the non-inclusive leap year
     17  1.1  cgd 		calculation
     18  1.1  cgd 	if the day in question occurs before the gregorian reformation
     19  1.1  cgd 		(3 sep 1752 for our purposes), then simply return 
     20  1.1  cgd 		(value so far - 1 + SATURDAY's value of 6) modulo 7.
     21  1.1  cgd 	if the day in question occurs during the reformation (3 sep 1752
     22  1.1  cgd 		to 13 sep 1752 inclusive) return THURSDAY. This is my
     23  1.1  cgd 		idea of what happened then. It does not matter much as
     24  1.1  cgd 		this program never tries to find day of week for any day
     25  1.1  cgd 		that is not the first of a month.
     26  1.1  cgd 	otherwise, after the reformation, use the same formula as the
     27  1.1  cgd 		days before with the additional step of subtracting the
     28  1.1  cgd 		number of days (11) that were adjusted out of the calendar
     29  1.1  cgd 		just before taking the modulo.
     30  1.1  cgd 
     31  1.1  cgd It must be noted that the number of leap years calculation is sensitive
     32  1.1  cgd to the date for which the leap year is being calculated.  A year that occurs
     33  1.1  cgd before the reformation is determined to be a leap year if its modulo of
     34  1.1  cgd 4 equals zero.  But after the reformation, a year is only a leap year if
     35  1.1  cgd its modulo of 4 equals zero and its modulo of 100 does not.  Of course,
     36  1.1  cgd there is an exception for these century years.  If the modulo of 400 equals
     37  1.1  cgd zero, then the year is a leap year anyway.  This is, in fact, what the
     38  1.1  cgd gregorian reformation was all about (a bit of error in the old algorithm
     39  1.1  cgd that caused the calendar to be inaccurate.)
     40  1.1  cgd 
     41  1.1  cgd Once we have the day in year for the first of the month in question, the
     42  1.1  cgd rest is trivial.
     43