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Annotation of 43BSDReno/usr.bin/cal/README, revision 1.1.1.1

1.1       root        1: Program Design
                      2: 
                      3: This program exactly duplicates the operation of the original unix "cal"
                      4: program.  It was designed with that intent, so no "improvements" were made
                      5: to either the command line syntax or to the error reporting.  The main
                      6: goal was to allow replacement of the existing binary with a freely
                      7: redistibutable version without breaking any existing applications that
                      8: might be built on top of the original.
                      9: 
                     10: The date routines were written from scratch, basically from first
                     11: principles.  The algorithm for calculating the day of week from any
                     12: gregorian date was "reverse engineered". This was necessary as most of
                     13: the documented algorithms have to do with date calculations for other
                     14: calendars (e.g. julian) and are only accurate when converted to gregorian
                     15: within a narrow range of dates.
                     16: 
                     17: I take 1 jan 1 to be a Saturday because that's what cal says and I couldn't
                     18: change that even if I was dumb enough to try. From this we can easily
                     19: calculate the day of week for any date. The algorithm for a zero based
                     20: day of week:
                     21: 
                     22:        calculate the number of days in all prior years (year-1)*365
                     23:        add the number of leap years (days?) since year 1 
                     24:                (not including this year as that is covered later)
                     25:        add the day number within the year
                     26:                this compensates for the non-inclusive leap year
                     27:                calculation
                     28:        if the day in question occurs before the gregorian reformation
                     29:                (3 sep 1752 for our purposes), then simply return 
                     30:                (value so far - 1 + SATURDAY's value of 6) modulo 7.
                     31:        if the day in question occurs during the reformation (3 sep 1752
                     32:                to 13 sep 1752 inclusive) return THURSDAY. This is my
                     33:                idea of what happened then. It does not matter much as
                     34:                this program never tries to find day of week for any day
                     35:                that is not the first of a month.
                     36:        otherwise, after the reformation, use the same formula as the
                     37:                days before with the additional step of subtracting the
                     38:                number of days (11) that were adjusted out of the calendar
                     39:                just before taking the modulo.
                     40: 
                     41: It must be noted that the number of leap years calculation is sensitive
                     42: to the date for which the leap year is being calculated. A year that occurs
                     43: before the reformation is determined to be a leap year if its modulo of
                     44: 4 equals zero. But after the reformation, a year is only a leap year if
                     45: its modulo of 4 equals zero and its modulo of 100 does not. Of course,
                     46: there is an exception for these century years. If the modulo of 400 equals
                     47: zero, then the year is a leap year anyway. This is, in fact, what the
                     48: gregorian reformation was all about (a bit of error in the old algorithm
                     49: that caused the calendar to be inaccurate.)
                     50: 
                     51: Once we have the day in year for the first of the month in question, the
                     52: rest is trivial. Running diff on any output of this program and the
                     53: equivalent output from the original cal reports no difference.  This was
                     54: confirmed by a script that ran them for all possible inputs (and took
                     55: approximately 36 hours to complete on a sun-3.)

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