Re: Zeller's Algorithm

[t_wolf@angelfire.com (Thomas Wolf)]

Paul A Storm <paul.a.storm@lmco.com> wrote in message news:<3D470EEE.811F758D@lmco.com>...
> Rick Maffei wrote:
> 
> > 
> > While reviewing the latest Risks Digest, I came across the following
> > item titled "Possible day-of-week error" concerning the Zeller
> > algorithm:
> > 
> > http://catless.ncl.ac.uk/Risks/22.18.html#subj10.1
> > 
> > Just thought it may be of interest in this thread.
> > 
> > Rick Maffei
> 
> Thanks.

That message in the Risks Digest relates to the possibility of
the left operand of the final "mod" operation in Zeller's formula
becoming negative in some cases. This may be a problem in languages
such as C, where e.g. -30 % 7 = -2. In Ada 95, using "mod", this is
not a problem, for A mod B is defined to return a modulus in the
range 0 .. B-1 for positive B, regardless of the sign of A.

If you want to avoid a negative left operand altogether, use the
formula

  Z := (Integer (Day) + (13 * M - 1) / 5 + Y + Y / 4 +
        Century / 4 + 5 * Century) mod 7;

instead of Zeller's

  Z := (Integer (Day) + (13 * M - 1) / 5 + Y + Y / 4 +
        Century / 4 - 2 * Century) mod 7;
 
Adding 7 * Century doesn't change the final result (because it's
a multiple of 7), but ensures that the left operand is always
positive.

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Thomas Wolf                            e-mail: t_wolf@angelfire.com