# NAME

Date::Day - Perl extension for converting a date to its respective day.

# SYNOPSIS

```
use Date::Day;
## The following will print the weekday corresponding
## to the date March 11, 1998.
$result = &day(03,11,1998);
print "$result";
```

# DESCRIPTION

After noticing the complexity of some modules for determining the day of a specific date, I decided to write this module. It is by far the shortest module of its kind performing the above task. This module exports a subroutine called day() which takes as arguments numerical month, day, and year. See Synopsis for example. As far as range of usage, the day() function will return a proper day for all dates starting from year 0 through infinity. There are no restrictions. If you pass bad data to the function, a day will still be returned, it just won't have any meaning. So March 45, 2001 will return a day, just one with no meaning. So make sure you pass real dates.

After initial release of this module, I decided to elaborate on the mathematical foundations for the algorithm used. Most other day of week modules use the dooms day algorithm. Date::Day uses a single line formula.

Not getting into too much detail, we take the fact that March 1, 0000 fell on a Wednesday. Knowing this, we can determine the day of week March 1 will fall on in any given year y > 0. That is:

` 3 + y + [y/4] - [y/100] + [y/400] mod 7 `

[y/4] represents the integer part of (year) divided by (4). Weekdays correspond to the following numbers:

Sun Mon Tue Wed Thu Fri Sat 0 1 2 3 4 5 6

So for example, look at March 1, 1994:

` 3 + 1994 + [1994/4] - [1994/100] + [1994/400] mod 7 = 2 mod 7`

And so March 1, 1994 is a Tuesday. So now we can find the day of week for March 1 in any given year. How do we find the day corresponding to a date other than March 1? Since March 1, 0000 has number 3 (Wednesday), than April 1, 0000 has number 3 + 31 mod 7 = 6 mod 7 since March has 31 days. We can do the same thing for May, June and so on. Thus giving the following table:

(Day of week for first day in given month in year 0000)

Mar 1 Apr 1 May 1 Jun 1 Jul 1 Aug 1 Sep 1 Oct 1 Nov 1 Dec 1 Jan 1 Feb 1 3 6 1 4 6 2 5 0 3 5 1 4

And we treat March as month 1, April as month 2, and so on. We denote these numbers by 1 + j(m), where j(m), for m=1,2,...,12 (with m=1 as March, m=2 as April, and so on), is defined by:

j(m):2,5,0,3,5,1,4,6,2,4,0,3.

So we refine our table:

Month 1 2 3 4 5 6 7 8 9 10 11 12 Value 0 3 2 5 0 3 5 1 4 6 2 4

The above table is very important in our final formula. So for example, the month June is numerical 6, and 6 goes to value 3. 3 is then used in our final formula.

With all the above data, it follows that month m, day 1, year y, has day of week number:

` 1 + j(m) + y + [y/4] - [y/100] + [y/400] mod 7`

And to get a formula that handles any given day, we use the formula:

` d + j(m) + y + [y/4] - [y/100] + [y/400] mod 7 (***)`

So for example, we want to find the day of week corresponding to April 8, 2002. If March is month 1, then April is month 2, hence m=2. So j(2)=5. Thus we have:

```
8 + 5 + 2002 + [2002/4] - [2002/100] + [2002/400] mod 7
which is, 1 mod 7. So 4/8/2002 is a Monday.
```

So when you look at the code portion of Day.pm you see only two important lines of code. One line is for the associative array that implements j(m). The other line is for implementing formula (***). Thats it.

# AUTHOR

John Von Essen, john@essenz.com

# SEE ALSO

perl(1).