| 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. |