02-14-2009
I wrote those functions and I cannot explain them. I surfed the web and found date calculation routines in a variety of languages. I converted to ksh and benchmarked them. I took the fastest routines and used them. I gave datecalc a finite range, 1860 to 3999. 1860 is when the US bought Alaska and mandated that Alaska migrate from the julian to the gregorian calendar. Whether or not the year 4000 will be a leap year is controversial.
I manually verified that Jan 1, 1860 works right. Then I used a verification script to generate the dates between 1860 and 3999 by incrementing the day, month, and year. Each date was fed to datecalc for conversion to modified julian day. The script verified that the mjd incremented by 1 each day. The mjd was fed to datecalc for conversion back to year, month, and day and this final output was compared to the original date. So I know for sure that the routines work between the limits I set.
I don't understand the algorithms. But I know that they work. Calendar algorithms are not worth studying. Why not study an interesting algorithm instead? For example: how to accurately calculate x^y in extended floating point using only extended floating point for all intermediate calculations? I've been trying to figure that one out all week. It's much harder than it looks.
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LEARN ABOUT FREEBSD
ndaysg
CALENDAR(3) BSD Library Functions Manual CALENDAR(3)
NAME
easterg, easterog, easteroj, gdate, jdate, ndaysg, ndaysj, week, weekday -- Calendar arithmetic for the Christian era
LIBRARY
Calendar Arithmetic Library (libcalendar, -lcalendar)
SYNOPSIS
#include <calendar.h>
struct date *
easterg(int year, struct date *dt);
struct date *
easterog(int year, struct date *dt);
struct date *
easteroj(int year, struct date *dt);
struct date *
gdate(int nd, struct date *dt);
struct date *
jdate(int nd, struct date *dt);
int
ndaysg(struct date *dt);
int
ndaysj(struct date *dt);
int
week(int nd, int *year);
int
weekday(int nd);
DESCRIPTION
These functions provide calendar arithmetic for a large range of years, starting at March 1st, year zero (i.e., 1 B.C.) and ending way beyond
year 100000.
Programs should be linked with -lcalendar.
The functions easterg(), easterog() and easteroj() store the date of Easter Sunday into the structure pointed at by dt and return a pointer
to this structure. The function easterg() assumes Gregorian Calendar (adopted by most western churches after 1582) and the functions
easterog() and easteroj() compute the date of Easter Sunday according to the orthodox rules (Western churches before 1582, Greek and Russian
Orthodox Church until today). The result returned by easterog() is the date in Gregorian Calendar, whereas easteroj() returns the date in
Julian Calendar.
The functions gdate(), jdate(), ndaysg() and ndaysj() provide conversions between the common "year, month, day" notation of a date and the
"number of days" representation, which is better suited for calculations. The days are numbered from March 1st year 1 B.C., starting with
zero, so the number of a day gives the number of days since March 1st, year 1 B.C. The conversions work for nonnegative day numbers only.
The gdate() and jdate() functions store the date corresponding to the day number nd into the structure pointed at by dt and return a pointer
to this structure.
The ndaysg() and ndaysj() functions return the day number of the date pointed at by dt.
The gdate() and ndaysg() functions assume Gregorian Calendar after October 4, 1582 and Julian Calendar before, whereas jdate() and ndaysj()
assume Julian Calendar throughout.
The two calendars differ by the definition of the leap year. The Julian Calendar says every year that is a multiple of four is a leap year.
The Gregorian Calendar excludes years that are multiples of 100 and not multiples of 400. This means the years 1700, 1800, 1900, 2100 are
not leap years and the year 2000 is a leap year. The new rules were inaugurated on October 4, 1582 by deleting ten days following this date.
Most catholic countries adopted the new calendar by the end of the 16th century, whereas others stayed with the Julian Calendar until the
20th century. The United Kingdom and their colonies switched on September 2, 1752. They already had to delete 11 days.
The function week() returns the number of the week which contains the day numbered nd. The argument *year is set with the year that contains
(the greater part of) the week. The weeks are numbered per year starting with week 1, which is the first week in a year that includes more
than three days of the year. Weeks start on Monday. This function is defined for Gregorian Calendar only.
The function weekday() returns the weekday (Mo = 0 .. Su = 6) of the day numbered nd.
The structure date is defined in <calendar.h>. It contains these fields:
int y; /* year (0000 - ????) */
int m; /* month (1 - 12) */
int d; /* day of month (1 - 31) */
The year zero is written as "1 B.C." by historians and "0" by astronomers and in this library.
SEE ALSO
ncal(1), strftime(3)
STANDARDS
The week number conforms to ISO 8601: 1988.
HISTORY
The calendar library first appeared in FreeBSD 3.0.
AUTHORS
This manual page and the library was written by Wolfgang Helbig <helbig@FreeBSD.org>.
BUGS
The library was coded with great care so there are no bugs left.
BSD
November 29, 1997 BSD