MetaCardians,
Last week I submitted a version of the Julian/Gregorian/Zeller Algorithm date
convertor (say that three time!)
Supposedly, it would return the "Day-of-the-Week" for any date....
Well, after an initial blush of success, I dug into the "reality" of the Zeller
Algorithm and the assumptions we
make.
First, I’d made an error in the adjusted algorithm (initial blush)
Second, returning any day of the week is the easy part, but is it the "correct" day?
Without going into the long chant of the inaccuracies of both the Julian and Gregorian
calendars (if we used the
highly accurate Toltec calendar, we would not be in this mess, Ollie!), I looked at
the way HyperCard uses the
"dateItems" function. HC doesn’t convert to the Julian then back to the Gregorian to
determine the day of the week.
If the date is valid,(not May 35, 1999, for example), HC probably computes the day of
the week according to the
following*:
The day of the week 'W' (0 = Sunday) is given by
W = ((13*M - 1) / 5 + D + Y + Y/4 + C/4 - (2*C) mod 7 + 7) mod 7;
where
C is the century (year DIV 100)
Y is the last two digits of the year (year MOD 100)
D is the day of the month
M is a special month number, where Jan and Feb are taken as
month 11 and 12 of the previous year (subtract 1 from the year)
and each division is truncating division, and cannot be combined.
(* from Alan P Barrett)
The section "mod 7 + 7) mod 7" is to insure a positive result.
Ok, you ask, is it correct now? Well, a definite YES and NO! It’s not easy to find out
what dates in history fall on
what day of the week. We do know that President Lincoln was shot on Friday, April 15,
1865. (Note: We can’t convert
to seconds with any degree of accuracy either. MC converts April, 14, 1865 to
1,003,413,469 seconds. HyperCard sez
it’s -1,221,609,600 seconds.)
HC agrees that 4/15/1865 was a Friday. And the newly revised Julian/Gregorian/Zeller
Algorithm (see below) also
concurs! (Small huzzah). Everything works fine until we jump back past December 31,
1801. Then the dateItems
function in MC smokes a little. Actually, a lot.. The month and day are sort of
randomly created. And dates beyond
2034 are total bogus.
The seconds and dateitems function are crucial to historian, scientists, engineers and
writers. MetaCard needs to
address this issue. Perhaps we could agree on a starting point (like 1/01/0001). That
would be about
63,480,164,515.776001 (plus or minus) second ago.... Heck, that’s less than 2^33
seconds.
--- (Author Message)
It’s time break out of the 2-bit mentality of the 60’s DOS world. Today’s PCs and Mac
can handle reeeaaallly big
numbers without belching. How ‘about it, Scott?
--- (end Author Message)
The newly revised Julian/Gregorian/Zeller Algorithm. Watch for line wrap!!
---
function setTheDate pDate,theForm
-- theForm is either “long” or “short”
put Date2Julian(pDate) into jDate
put Julian2Date(jDate,theForm) into jDate
return jDate
end setTheDate
function Date2Julian pDate
--ask pDate
if "/" is in pDate then
--## short date format
set the itemDelimiter to "/"
put number of items in pDate into itemNum
if itemNum = 3 then
put last word of last item of pDate into tYear
else
answer warning "Error: Date [" & pDate &"] format is incorrect."
exit to metaCard
end if
else
put last word of last item of pDate into tYear
end if
set the ItemDelimiter to ","
convert pDate to dateItems
put item 2 of pDate into tMonth
put item 3 of pDate into tDay
if tMonth < 3 then
add 12 to tMonth
subtract 1 from tYear
end if
put trunc(tYear/100) into aa
put (2-aa+trunc(aa/4)) into bb
put trunc(365.25*tYear) into cc
put trunc(30.6001*(tMonth+1)) into dd
return (bb+cc+dd+tDay+1720995)
end Date2Julian
function Julian2Date pJulianDate,theForm
local tYear, tDay, tMonth, aa, bb, cc, dd, ee, gg
local monthList, daysOfTheWeek, XX
## -- Your language may vary!
put "January,February,March,April,May,June,July," into monthList
put "August,September,October,November,December" after monthList
put "Sunday,Monday,Tuesday,Wednesday,Thursday,Friday,Saturday" into daysOfTheWeek
put trunc((pJulianDate-1867216.25)/36524.25) into aa
put pJulianDate+1+aa-trunc(aa/4) into bb
Put bb+1524 into cc
put trunc((cc-122.1)/365.25) into dd
put trunc(365.25*dd) into ee
put trunc((cc-ee)/30.6001) into gg
--### break into date items
put cc-ee-trunc(30.6001*gg) into tDay
if gg<13.5 then put gg-1 into tMonth else put gg-13 into tMonth
if tMonth>2.5 then put dd-4716 into tYear else put dd-4715 into tYear
put tYear into cYear
-- ## calc the day of the week
-- ## from Zeller's Algorithm
put cYear div 100 into centuryYear
put cYear mod 100 into digitYr
put trunc(2.6 * tMonth - 5.39) into mm1
put trunc(centuryYear/4) into mm2
put trunc(digitYr/4) into mm3
put abs((mm1 + mm2 + mm3 + tDay + digitYr - (2 * centuryYear))) mod 7 into dayNumber
add 1 to dayNumber -- Sunday = 0!
put item dayNumber of daysOfTheWeek into weekDay
put item tMonth of monthList into thisMonth
if theForm = "long" then
return weekDay &", " & thisMonth && tDay & ", " & tYear
else
return tMonth &"/"& tDay &"/"& tYear
end if
end Julian2Date
----
--
Ray G. Miller
-----------
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