negative integer division

[Mark Jackson]

sjmachin at lexicon.net (John Machin) writes:
> mjackson at alumni.caltech.edu (Mark Jackson) wrote in message news:<cu91bf$9nk$1 at news.wrc.xerox.com>...
> > 
> > A:  42
> > 
> > Q:  What multiple of 7 did I add to the critical expression in the Zeller
> >     algorithm so it would remain nonnegative for the next few centuries?
> 
> What are you calling "the Zeller algorithm", and what is the "critical
> expression"?

A C function in calendar.c, encountered in the source code for xvtdl:

int zeller (month, day, year)
int month, day, year;
{
  int century;
  month -= 2;       /* Years start on March 1 so adjust standard date */
  if (month < 1) {
     month += 12;
     year--;
  }
  century = year / 100;
  year = (int)year % (int)100;
  return ((int)((2.6 * month - 0.1) + day + year + year / 4  + century / 4 - century * 2) % 7);
}

The expression upon which "% 7" acts is negative when "year" is small.
This caused errors beginning in March 2000; which could be deferred by
adding a suitably-large multiple of 7 to the expression.  The choice
was obvious. :-)

> I've no doubt you came across a stuffed-up date-to-days calculation
> routine and fixed it, but it's a bit unfair to lumber Zeller with the
> blame. If it was a days-to-date routine, then Zeller is not even
> standing next to the real target.

Fair enough, although I'm not responsible for having named the function
(which appears to date from 1991).  The original author is identified
in the code (available at
http://www.alumni.caltech.edu/~mjackson/xvtdl.html) and is findable via
the Web; you might take the matter up with him.

-- 
Mark Jackson - http://www.alumni.caltech.edu/~mjackson
	People who write obscurely are either unskilled in writing
	or up to mischief.		- Sir Peter Medawar