xref: /netbsd-src/usr.bin/cal/README (revision 61f282557f0bc41c0b762c629a2f4c14be8b7591)
1*61f28255ScgdThe cal(1) date routines were written from scratch, basically from first
2*61f28255Scgdprinciples.  The algorithm for calculating the day of week from any
3*61f28255ScgdGregorian date was "reverse engineered".  This was necessary as most of
4*61f28255Scgdthe documented algorithms have to do with date calculations for other
5*61f28255Scgdcalendars (e.g. julian) and are only accurate when converted to gregorian
6*61f28255Scgdwithin a narrow range of dates.
7*61f28255Scgd
8*61f28255Scgd1 Jan 1 is a Saturday because that's what cal says and I couldn't change
9*61f28255Scgdthat even if I was dumb enough to try.  From this we can easily calculate
10*61f28255Scgdthe day of week for any date.  The algorithm for a zero based day of week:
11*61f28255Scgd
12*61f28255Scgd	calculate the number of days in all prior years (year-1)*365
13*61f28255Scgd	add the number of leap years (days?) since year 1
14*61f28255Scgd		(not including this year as that is covered later)
15*61f28255Scgd	add the day number within the year
16*61f28255Scgd		this compensates for the non-inclusive leap year
17*61f28255Scgd		calculation
18*61f28255Scgd	if the day in question occurs before the gregorian reformation
19*61f28255Scgd		(3 sep 1752 for our purposes), then simply return
20*61f28255Scgd		(value so far - 1 + SATURDAY's value of 6) modulo 7.
21*61f28255Scgd	if the day in question occurs during the reformation (3 sep 1752
22*61f28255Scgd		to 13 sep 1752 inclusive) return THURSDAY. This is my
23*61f28255Scgd		idea of what happened then. It does not matter much as
24*61f28255Scgd		this program never tries to find day of week for any day
25*61f28255Scgd		that is not the first of a month.
26*61f28255Scgd	otherwise, after the reformation, use the same formula as the
27*61f28255Scgd		days before with the additional step of subtracting the
28*61f28255Scgd		number of days (11) that were adjusted out of the calendar
29*61f28255Scgd		just before taking the modulo.
30*61f28255Scgd
31*61f28255ScgdIt must be noted that the number of leap years calculation is sensitive
32*61f28255Scgdto the date for which the leap year is being calculated.  A year that occurs
33*61f28255Scgdbefore the reformation is determined to be a leap year if its modulo of
34*61f28255Scgd4 equals zero.  But after the reformation, a year is only a leap year if
35*61f28255Scgdits modulo of 4 equals zero and its modulo of 100 does not.  Of course,
36*61f28255Scgdthere is an exception for these century years.  If the modulo of 400 equals
37*61f28255Scgdzero, then the year is a leap year anyway.  This is, in fact, what the
38*61f28255Scgdgregorian reformation was all about (a bit of error in the old algorithm
39*61f28255Scgdthat caused the calendar to be inaccurate.)
40*61f28255Scgd
41*61f28255ScgdOnce we have the day in year for the first of the month in question, the
42*61f28255Scgdrest is trivial.
43