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From: christer@zeus.cs.umu.se (Christer Ericson)
Newsgroups: comp.lang.pascal
Subject: Re: Day-of-week algorithm, please!
Message-ID: <838@umecs.cs.umu.se>
Date: 14 Apr 89 11:16:13 GMT
References: <19065@adm.BRL.MIL> <2684@ilium.cs.swarthmore.edu>
Sender: news@umecs.cs.umu.se
Reply-To: christer@zeus.cs.umu.se (Christer Ericson)
Organization: Dep. of Inform.Proc.,University of Umea,Sweden
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In article <2684@ilium.cs.swarthmore.edu> jackiw@ilium.UUCP (Nick Jackiw) writes:
>I know this ain't too helpful, but...
>
>There's a simple (five term) non-iterative formula called Ziegler's
>Congruence (or possible Zegler's Congruence --- or was it Confluence? :-))
>that returns 0..6 for the day of the week of any day since the last
>MAJOR calendar adjustment (1818?).
>


The formula which you are refering to is called Zeller's Congruence. Actually,
the first program our students of CS has to write [in a functional language
called ML] is an implementation of this formula. Anyway, here it is:

      weekday=([2.6*m-0.2] + d + y + [y/4] + [c/4] - 2*c) mod 7

Where c,y,m,d denotes century, year (last two digits only), month, and day
respectively. [x] is the integer part of x.  The number in weekday is
interpreted as 0=Sunday, 1=Monday, 2=Tuesday, ...

In pascal it could look like this:

FUNCTION Zeller(y,m,d:INTEGER):INTEGER;
VAR c : INTEGER;
BEGIN
  c:=y DIV 100;
  y:=y MOD 100;
  Zeller:=((26*m-2) DIV 10 + d + y + y DIV 4 + c DIV 4 - 2*c) MOD 7;
END;

Oh, there is a small 'trap' in this formula and that is that the parenthesis
before the modula can be negative, and many computer modulas don't handle
negative numbers the correct way, so add [say] 777 to the left side before
doing the modula.


>     _  _|\____    Nick Jackiw | Visual Geometry Project | Math Department
>   / /_/   O>  \   ------------+-------------------------+ Swarthmore College
>   |       O>   |  215-328-8225| jackiw@cs.swarthmore.edu| Swarthmore PA 19081
>    \_Guernica_/   ------------+-------------------------+                 USA



/Christer


+-------------------------------+-------------------------------------------+
| Christer Ericson              |  Inst. for Information Processing,        |
| Internet: christer@cs.umu.se  |  University of Umea, S-90187 UMEA, Sweden |
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