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From: garyp@cognos.UUCP (Gary Puckering)
Newsgroups: comp.unix.wizards
Subject: Re: Date conversion question
Message-ID: <416@cognos.UUCP>
Date: Sun, 1-Mar-87 19:54:31 EST
Article-I.D.: cognos.416
Posted: Sun Mar  1 19:54:31 1987
Date-Received: Tue, 3-Mar-87 18:35:52 EST
References: <222@devon.UUCP> <2590003@hpisod2.HP.COM> <9945@teknowledge-vaxc.ARPA>
Reply-To: garyp@cognos.UUCP (Gary Puckering)
Organization: Cognos Incorporated, Ottawa, Canada
Lines: 54

In article <9945@teknowledge-vaxc.ARPA> mkhaw@teknowledge-vaxc.UUCP (Michael Khaw) writes:
>Is there a clever formula that will give you the day of the week (as a number
>between 1 and 7 or 0 and 6) given year, month, and date?

This question came up in September of last year.  Here is the response I
submitted at that time:

There is an formula known as Zeller's Congruence which can be used to
calculate the day of the week given any date.  I found this somewhere,
years ago when I was a teenager, memorized it and never forgot it.  I
know it works for any year after 1700, maybe even earlier.  I can't
remember where it came from (I did well to remember the algorithm!).
Since it uses only integer addition and division, and one comparison
operation, its fairly cheap to implement.

Here it is:

	Let k be the day of the month
	    m be the month (March=1, April=2, ... December=10, January
			    and February are months 11 and 12 of the
			    previous year)
	    C be the century
	    D be the year of the century (adjusted according to m)
	    Z be the day of the week (0=Sunday, 6=Saturday)

	Then:

	  Z = { (26m - 2)//10 + k + D + D//4 + C//4 - 2C } mod 7

	  where // represents integer division with truncation


	Example:  for February 28, 1986

		k = 28
		y = 1986
		m = 2 - 2 = 0
		if m<1 then m=m+12, y=y-1
		C = 19
		D = 85

	Therefore:

		Z = { (26*12)//10 + 28 + 85 + 85//4 + 19//4 - 2*19} mod 7

		  = {      31     + 28 + 85 +  21   +   4   -  38 } mod 7
		  = { 131 } mod 7

		  = 5 (Friday)

-- 
Gary Puckering        3755 Riverside Dr.
Cognos Incorporated   Ottawa, Ontario       decvax!utzoo!dciem!
(613) 738-1440        CANADA  K1G 3N3       nrcaer!cognos!garyp