🚀 go-pugleaf

From: seismo!gatech!hpcnof!hpfcla!hpfclj!hpfcdg!rgt
Date: Mon, 12 Jan 87 15:21:04 est

> 2. If the year begins on Saturday and ends on Monday, it will have 54
>    weeks.  Obviously they cannot be numbered 00 to 52!

Sorry folks, but this is not a bug.  This was transcribed from the X3J11
documentation   titled   "Internationalizing   ANSI   C"  and   numbered
"X3J11/86-125R".  Section  3.2  describes   the  strftime   funtion  and
describes  the %U and %W  directives.  Both are  described as being week
numbers  beginning with either Sunday or Monday and both list a range of
00 to 52.  (The %W directive  was changed to a %V  directive  because it
conflicts with an existing X/OPEN directive for the nl_cxtime  function,
which is almost identical in operation to strftime.)

I believe that the intended week number computation is as described in a
paper  titled  "An  Overview  of  Internationalization"   by  Greger  K.
Leijonjufvud  of Sperry  Corporation  and Gary L.  Lindgren  of AT&T (no
date or number).  In section 3.4.2.4 titled "The Week" it states [with my
corrections and clarifications (rgt)]:

	The 7-day week is now predominant.  Each day has its name and is
	also  numbered.  the  number  depends on which day is counted as
	the  starting day of the week:  either  Sunday or Monday.  Weeks
	are also  numbered.  Which  week tath is  counted  as the  first
	depends on the  weekday of January  1st (i.e., if there are 4 or
	more  January  days in the week of Jan 1st, then that is week 1,
	[number 00 (rgt)]  otherwise  it is week [51 or (rgt)] 52 of the
	preceding year.  The calculation  also depends on whether Sunday
	is the first or the last day of the week.)

The  maximum  number of weeks in a year would  occur in a leap year with
January 1st on the  Wednesday  of the  Sunday-first  week.  Looking at a
perpetual  calendar,  1964 or 1992 are  useful  examples.  I derive  the
following table:

	1963 week ?? = Dec 22 to Dec 28
	1964 week 00 = Dec 29 to Jan 04
	...
	1964 week 52 = Dec 27 to Jan 02
	1965 week 00 = Jan 03 to Jan 09

Conversely,  the  minimum  number of weeks in a year would be occur in a
non-leap  year when  January 1st was on a Thursday  of the  Sunday-first
week.

	1986 week ?? = Dec 28 to Jan 03
	1987 week 00 = Jan 04 to Jan 10
	...
	1987 week 51 = Dec 27 to Jan 02
	1988 week 00 = Jan 03 to Jan 09

Conclusion:  A week-aligned  year may will have at least 52 weeks and at
most  53  weeks.  The  first  day  (00) of the  first  week  (00) of the
week-aligned  year may be as early as Dec 29 and as late as Jan 04.

All of the  arguements  can also be applied to a Monday  first week with
only minor changes.

Volume-Number: Volume 9, Number 33