Re: Method to Calculate the Day of the Week for All Dates 1905-2099
Milton Lachman
- via transmogrification of Hans Lachman's Method of Congruence -
Strictly adhering to Lachman's Maxim (Complexity is a diseconomy of scale)
a reworking of Hans' Method has been coded as a stand-alone function when
your only recourse is to call a 68k ASM program via AMS on TI calculators:
i.e. no values looked up in tables, files or libraries when executing, no
kernel, no system calls, no exception processing, minimal registers to be
used, nor the need to save any. It is for valid Gregorian dates from 1582,
as of the Ides of October, to 4004 A.D.
Although using as unsophisticated a processor as a 68k on programmable TI
calculators, this reworking of Hans' Method is more efficient than others.
It succeeds where other methods do not when computing the day of the week
even on the lowliest 68k device: having no need of extra instructions for
data stored in tables as in Babwani's Method nor for redundant operations
as in Zeller's or Tondering's--nor even a C compiler running on a bloated
development system as in Mike Keith's--yet executing in less than 2 dozen
operations, and needing just 2 registers.
The function below returns the corresponding ISO-compatible weekday number
when called with 2 inputs loaded from the following 2 locations:
; WDN, an address for storing result d0
; DATE, basic ISO-format date-stamp cymd as 2 pairs of base-100 bytes
;
movem.l DATE,d1,d2
;
; STEP 1
andi.l #$f00,d1
divu #100,d1
add.w #$7a,d1
andi.l #$7f,d1 ; Month Index
;
; STEP 2
add.b d2,d1
swap d2
add.b d2,d1
swap d2
subi.l #$300,d2
lsl #6,d2
rol #3,d2
addq.b #8,d1
sub.b d2,d1
movi.l #27,d0
lsr d0,d2
add.b d1,d2 ; QRdiv4 + y + MI + d + under+under
;
divu #7,d2
swap d2 ; D2.W BECOMES THE WEEKDAY NUMBER
;
; RETURN THE WEEKDAY NUMBER TO LOCATION WDN
move.b d2,WDN
rts
;
; Days of the week correspond to weekday numbers as:
; Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6
Inputs are to be passed in the proper format:
No component of a Date may be passed as a pair of base 10 nibbles.
--
REFERENCES
http://oz.ccnet.us/dayofweek/
http://www.guernsey.net/~sgibbs/roman.html
http://www.merlyn.demon.co.uk/zel-like.htm#Keith
http://www.tondering.dk/claus/cal/node3.html#SECTION00360000000000000000
babwani-congruence.blogspot.com/search/label/Frequently%20Asked%20Questions
Milton Lachman
day is singularly in want of April Fools' Easter eggs]
TEXAS 2-STEP 2.2 TO CALCULATE THE DAY OF THE WEEK AS OF 1582 TO 2Y2K2
- via transfiguration of Hans Lachman's Method of Congruence -
Strictly adhering to Lachman's Maxim (Complexity is a diseconomy of scale)
a reworking of Hans' Method has been coded as a stand-alone function when
your only recourse is to call a 68k ASM program via AMS on TI calculators:
i.e. no values looked up in tables, files or libraries when executing, no
kernel, no system calls, no exception processing, minimal registers to be
used, nor the need to save any. It is for valid Gregorian dates from 1582,
as of the Ides of October, to 4004 A.D.
Although using as unsophisticated a processor as a 68k on programmable TI
calculators, this reworking of Hans' Method is more efficient than others.
It succeeds where other methods do not when computing the day of the week
even on the lowliest 68k device: having no need of extra instructions for
data stored in tables as in Babwani's Method nor for redundant operations
as in Zeller's or Tondering's--nor even a C compiler running on a bloated
development system as in Mike Keith's--yet executing in less than 2 dozen
operations, and needing just 2 registers.
The function below returns the corresponding ISO-compatible weekday number
when called with 2 inputs loaded from the following 2 locations:
; WDN, an address for storing result d2
; DATE, basic ISO-format date-stamp CYmd as 2 pairs of base-10^2 bytes
;
movem.l DATE,d1,d2
;
; APPLY STEP 1 OF HANS LACHMAN'S METHOD OF CONGRUENCE
andi.l #$f00,d1
divu #100,d1
add.w #94,d1
andi.l #$ff,d1
divu #100,d1 ; Month Index
;
; STEP 2
add.l d2,d1
swap d1
add.b d2,d1
subi.l #$300,d2
lsl #6,d2
rol #3,d2
addq.b #8,d1
sub.b d2,d1
lsr #7,d2
lsr #7,d2
lsr #7,d2
lsr #6,d2
add.w d1,d2 ; QRdiv4 + Y + MI + d + under+under
Milton Lachman
bogus versions for April Fools' & Good Freyaday (each one using
a different approach) and implements the approach as posted for
four-function calculators. The eminently more suitable code for
the digital approach of the 2.0 kind is left for avid coders to
figure out for themselves.]
TEXAS 2-STEP 2.2 TO CALCULATE THE DAY OF THE WEEK AS OF 1582 TO 2Y2K2
- via an elaboration of Hans Lachman's Method of Congruence -
Strictly adhering to Lachman's Maxim (Complexity is a diseconomy of scale)
a reworking of Hans' Method has been coded as a stand-alone function when
your only recourse is to call a 68k ASM program via AMS on TI calculators:
i.e. no values looked up in tables, files or libraries when executing, no
kernel, no system calls, no exception processing, minimal registers to be
used, nor the need to save any. It is for valid Gregorian dates from 1582,
as of the Ides of October, to 4004 A.D.
Although using as unsophisticated a processor as a 68k on programmable TI
calculators, this reworking of Hans' Method is more efficient than others.
It succeeds where other methods do not when computing the day of the week
even on the lowliest 68k device: having no need of extra instructions for
data stored in tables as in Babwani's Method nor for redundant operations
as in Zeller's or Tondering's--nor even a C compiler running on a bloated
development system as in Mike Keith's--yet executing in less than 2 dozen
operations, and needing just 2 registers.
The function below returns the corresponding ISO-compatible weekday number
when called with 2 inputs loaded from the following 2 locations:
; WDN, an address for storing result d2
; DATE, basic ISO-format date-stamp CYmd as 2 pairs of base-10^2 bytes
;
movem.l DATE,d1,d2
;
; APPLY STEP 1 (HANS LACHMAN'S METHOD OF CONGRUENCE)
andi.l #$f00,d1
divu #100,d1
add.w #94,d1
andi.l #$ff,d1
divu #100,d1 ; Month Index
;
; STEP 2
add.l d2,d1
swap d1
add.b d2,d1
subi.l #$300,d2
lsl #6,d2
rol #3,d2
addq.b #8,d1
sub.b d2,d1
lsr #7,d2
lsr #7,d2
lsr #7,d2
lsr #6,d2
add.b d1,d2 ; QRdiv4 + Y + MI + d + under+under
lac...@ebony.ppc.ubc.ca
Or, for the less avid, they can ferret it out for themselves at:
gopher://gopherite.org/1/users/lachman/TemporalRetrology/68k/
Happy Groundhog Day!
lachman wrote:
[ . . . The eminently more suitable code for the digital approach of
TEXAS 2-STEP 2.2 TO CALCULATE THE DAY OF THE WEEK AS OF 1582 TO 2Y2K2
- via an elaboration of Hans Lachman's Method of Congruence -
Charles Richmond
news:jgehql$hr1$1...@odin.sdf-eu.org...
> Or, for the less avid, they can ferret it out for themselves at:
>
> gopher://gopherite.org/1/users/lachman/TemporalRetrology/68k/
>
> Happy Groundhog Day!
>
> lachman wrote:
> [ . . . The eminently more suitable code for the digital approach of
> the 2.0 kind is left for avid coders to figure out for themselves.]
>
you can use Zeller's Congruence:
http://en.wikipedia.org/wiki/Zeller%27s_congruence
Here is a function in C that I wrote to do this. Changing it to 68k
assembly should be straightforward:
int weekday(day,month,year) /* find the day of week from */
int day, month, year; /* day, month, and year */
{ /* Sunday..Saturday is
0..6 */
int index, yrndx, mondx;
if(month <= 2) { /* Jan or Feb month adjust */
month += 12;
year--;
}
yrndx = year + (year/4) - (year/100) + (year/400);
mondx = (2 * month) + (3 * (month + 1)) / 5;
index = day + mondx + yrndx + CONST;
return(index % 7);
}
--
+<><><><><><><><><><><><><><><><><><><>+
| Charles Richmond nume...@aquaporin4.com |
+<><><><><><><><><><><><><><><><><><><>+
Dr J R Stockton
02:50:52, Charles Richmond <net...@aquaporin4.com> posted:
one should be able to number the days of the week with any chosen day
being zero. Make Monday so, add 1, and you have the ISO numbering.
Some implementations written & "tested" before AD 2000 fail where mod-
of-negative is taken for some dates early in a century; but yours looks
OK. Zeller understood the possibility.
Zeller's relevant papers & Card, imaged and translated, can be found via
<http://www.merlyn.demon.co.uk/undex.htm#dat> subsection 2.9.
For 1901 to 2099, the 100 & 400 terms can be omitted, if CONST is
correspondingly adjusted.
Zeller also did Easter code, OK in the papers but wrong in the Card.
--
(c) John Stockton, nr London, UK. ?@merlyn.demon.co.uk Turnpike v6.05.
Website <http://www.merlyn.demon.co.uk/> - w. FAQish topics, links, acronyms
PAS EXE etc. : <http://www.merlyn.demon.co.uk/programs/> - see in 00index.htm
Dates - miscdate.htm estrdate.htm js-dates.htm pas-time.htm critdate.htm etc.
Charles Richmond
news:JakN$7dH8v...@invalid.uk.co.demon.merlyn.invalid...
>
> [snip...] [snip...] [snip...]
> OK at first sight, except that CONST appears undefined. By varying it
> one should be able to number the days of the week with any chosen day
> being zero. Make Monday so, add 1, and you have the ISO numbering.
>
1 to have the day names fall as the comment promises.
> Some implementations written & "tested" before AD 2000 fail where mod-
> of-negative is taken for some dates early in a century; but yours looks
> OK. Zeller understood the possibility.
>
> Zeller's relevant papers & Card, imaged and translated, can be found via
> <http://www.merlyn.demon.co.uk/undex.htm#dat> subsection 2.9.
>
is linked to the Wikipedia site for Zeller himself.
> For 1901 to 2099, the 100 & 400 terms can be omitted, if CONST is
> correspondingly adjusted.
>
> Zeller also did Easter code, OK in the papers but wrong in the Card.
>
Easter, which often do *not* fall on the same Sunday. In one of the
problems at the end of a chapter in _Fundamental Algorithms_, Knuth
discusses the algorithm for calculating Easter.
Dr J R Stockton
21:48:28, Milton Lachman <lac...@ebony.ppc.ubc.ca> posted:
> The function below returns the corresponding ISO-compatible weekday number
> when called with 2 inputs loaded from the following 2 locations:
> ; Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6
Day 7. Subtract 1 (by altering a constant?) before divu #7,d2 and
add 1 after; or append something implementing Result or= 7 or else
if result = 0 then result = 7.
Since the Gregorian Calendar is by definition perpetual and immutable,
there is no need to apply an upper limit to the range until the
algorithm has a numeric overflow.
Since the Gregorian Calendar may be used proleptically, it would be nice
if the lower limit were the date 0000-01-01, which, as you may remember,
was a Saturday.
If your code works, or can be adjusted to work, for years 0000 to 0399
inclusive, then your code can be made perpetual by starting with
year = year mod 400.
Charles Richmond
> 21:48:28, Milton Lachman <lac...@ebony.ppc.ubc.ca> posted:
>
>
>> The function below returns the corresponding ISO-compatible weekday
>> number
>> when called with 2 inputs loaded from the following 2 locations:
>
>
>> ; Days of the week correspond to weekday numbers as:
>> ; Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6
>
> That is only ISO 8601 compatible if Sundays are ignored; Sunday is ISO
> Day 7. Subtract 1 (by altering a constant?) before divu #7,d2 and
> add 1 after; or append something implementing Result or= 7 or else
> if result = 0 then result = 7.
>
zero, because arrays in C are zero-based. So the array of pointers to the
names of the days of the week... will have subscripts from 0 to 6.
> Since the Gregorian Calendar is by definition perpetual and immutable,
> there is no need to apply an upper limit to the range until the
> algorithm has a numeric overflow.
>
> Since the Gregorian Calendar may be used proleptically, it would be nice
> if the lower limit were the date 0000-01-01, which, as you may remember,
> was a Saturday.
>
that 0001-01-01 was a Monday. :-)
> If your code works, or can be adjusted to work, for years 0000 to 0399
> inclusive, then your code can be made perpetual by starting with
> year = year mod 400.
>
period between 401 through 800 inclusive contains an exact number of weeks.
(That would be 20,871 weeks to be exact.) And each one of the 400 year
periods beginning in 1, 401, 801, 1201, 1601, 2001, etc... all begin on a
Monday. Although the function given may *not* be perpetual, it works for
most years that one would reasonably expect to be checked.
Dr J R Stockton
13:50:48, Charles Richmond <net...@aquaporin4.com> posted:
>There is also good info in Wikipedia for calculating Easter and
>Orthodox Easter, which often do *not* fall on the same Sunday. In one
>of the problems at the end of a chapter in _Fundamental Algorithms_,
>Knuth discusses the algorithm for calculating Easter.
Zeller did day-of-week and Easter Sunday for both the Julian and
Gregorian Calendars. Transferring Julian (Orthodox) Easter to the
Gregorian Calendar is simple; just allow for the changes to the secular
calendar made by the Papal Bull Inter Gravissimas.
Knuth is, no doubt, right - or mostly so; I see that in critdate.htm I
have
9006-04-20 Sun</tt> - First Easter date for which Knuth's code
has a problem with Epact :
<a href="http://www.sunvaley.com/TEMP/Formulas.pdf">J D McC</a>
But I do not know how traceable his algorithm is to true authority.
My own algorithm is traceably (as shown) derived from UK (and therefore
US) authority - the Prayer Book effectively reproduces the relevant
parts of the Calendar Act of 1751, as passed. It agrees with Knuth and
others for the full 5,700,000 year period, It also agrees with one -
possibly the slowest in captivity - in which I implemented in a literal
fashion the algorithm that Clavius wrote for Pope Gregory.
The older Prayer Book defines Julian Easter.
However, the UK algorithm is truly defined only to the year 8599 (but
there is no doubt about the extrapolation); and, although I have found
that part in Clavius, Clavius wrote about alternatives and I have not
managed to identify there a definitive statement of what should be used
past AD 4999.
If anyone here reads Latin ...
I also have code from Al Petrofsky which is correct, compact, and fast,
but has unexplained numbers in it.
Dr J R Stockton
07:50:58, Charles Richmond <net...@aquaporin4.com> posted:
>"Dr J R Stockton" <repl...@merlyn.demon.co.uk> wrote in message
>news:THIb4oHo...@invalid.uk.co.demon.merlyn.invalid...
>> In sci.math message <ipkkfb$9u3$1...@speranza.aioe.org>, Sun, 1 May 2011
>> 21:48:28, Milton Lachman <lac...@ebony.ppc.ubc.ca> posted:
>>
>>
>>> The function below returns the corresponding ISO-compatible weekday
>>>number
>>> when called with 2 inputs loaded from the following 2 locations:
>>
>>
>>> ; Days of the week correspond to weekday numbers as:
>>> ; Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6
>>
>> That is only ISO 8601 compatible if Sundays are ignored; Sunday is ISO
>> Day 7. Subtract 1 (by altering a constant?) before divu #7,d2 and
>> add 1 after; or append something implementing Result or= 7 or else
>> if result = 0 then result = 7.
>>
>
>I was *not* worried about ISO 8601 compatibility. I wanted Sunday to
>be zero, because arrays in C are zero-based. So the array of pointers
>to the names of the days of the week... will have subscripts from 0 to
>6.
>> Since the Gregorian Calendar is by definition perpetual and immutable,
>> there is no need to apply an upper limit to the range until the
>> algorithm has a numeric overflow.
>>
>> Since the Gregorian Calendar may be used proleptically, it would be nice
>> if the lower limit were the date 0000-01-01, which, as you may remember,
>> was a Saturday.
>>
>
>I was *not* immediately aware that 0000-01-01 was a Saturday, but I
>know that 0001-01-01 was a Monday. :-)
>> If your code works, or can be adjusted to work, for years 0000 to 0399
>> inclusive, then your code can be made perpetual by starting with
>> year = year mod 400.
>>
>
>I am aware that the patterns of years repeat every 400 years, and that
>the period between 401 through 800 inclusive contains an exact number
>of weeks. (That would be 20,871 weeks to be exact.) And each one of
>the 400 year periods beginning in 1, 401, 801, 1201, 1601, 2001, etc...
>all begin on a Monday. Although the function given may *not* be
>perpetual, it works for most years that one would reasonably expect to
>be checked.
I still had it, but RFC 3339 of 2002 corresponds. It had C code,
derived from Zeller, for day-of-week. No doubt it had been tested, and
passed, with a selection of nearby dates, and perhaps to some extent for
other years. But, evidently, it had not been fully tested, since it
failed (mod of negative not giving desired result, for quite a few days
after 2000-02-29 and for fewer days in each following year until about
2019 (or similar; that's from memory).
Zeller knew about that :
<http://www.merlyn.demon.co.uk/zel-82px.htm>, page 313, section II,
Aufg. 1, Regel a, end, reads k/4 - 2e (od. + 5e)
and similarly in other papers.
With a computer, one might as well test comprehensively; this machine,
using Zeller's Easter code, does around four million years per second.
Microsoft VBScript DatePart is documented as giving ISO 8601 week
numbers. I dare say they tested it, to some extent. But it is wrong
for one day in three of each 28 consecutive "Julian-type" years, plus
one further day for each 400 years - details in my vb-date2.htm. As far
as I can tell, that code is still in current products, even though
there's been correct bug-fix code on their Web site for years
(appallingly bodged code; I've sent them much better code; no effect).
Charles Richmond
> 07:50:58, Charles Richmond <net...@aquaporin4.com> posted:
>
>>"Dr J R Stockton" <repl...@merlyn.demon.co.uk> wrote in message
>>news:THIb4oHo...@invalid.uk.co.demon.merlyn.invalid...
>>> In sci.math message <ipkkfb$9u3$1...@speranza.aioe.org>, Sun, 1 May 2011
>>> 21:48:28, Milton Lachman <lac...@ebony.ppc.ubc.ca> posted:
>>>
>>>
>>>> The function below returns the corresponding ISO-compatible weekday
>>>>number
>>>> when called with 2 inputs loaded from the following 2 locations:
>>>
>>>
>>>> ; Days of the week correspond to weekday numbers as:
>>>> ; Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6
>>>
>>> That is only ISO 8601 compatible if Sundays are ignored; Sunday is ISO
>>> Day 7. Subtract 1 (by altering a constant?) before divu #7,d2 and
>>> add 1 after; or append something implementing Result or= 7 or else
>>> if result = 0 then result = 7.
>>>
>>
>>I was *not* worried about ISO 8601 compatibility. I wanted Sunday to
>>be zero, because arrays in C are zero-based. So the array of pointers
>>to the names of the days of the week... will have subscripts from 0 to
>>6.
>
> But, as quoted, you asserted ISO compatibility.
>
function was ISO 8601 compatible. I was only marginally aware of ISO 8601
until you mentioned it. I just wanted something that *worked*. I have used
similar functions when writing PHP code to determine what day was the third
Thursday of the month... for reminders to be auto-posted for a club meeting.
Also I have used the weekday function to help calculated which weekend would
be the "spring forward" and "fall back" for daylight saving time.
>
>>> Since the Gregorian Calendar is by definition perpetual and immutable,
>>> there is no need to apply an upper limit to the range until the
>>> algorithm has a numeric overflow.
>>>
>>> Since the Gregorian Calendar may be used proleptically, it would be nice
>>> if the lower limit were the date 0000-01-01, which, as you may remember,
>>> was a Saturday.
>>>
>>
>>I was *not* immediately aware that 0000-01-01 was a Saturday, but I
>>know that 0001-01-01 was a Monday. :-)
>
> Y2K-day, 2000 years later, was a Saturday.
>
lac...@ebony.ppc.ubc.ca
>>> 21:48:28, Milton Lachman <lac...@ebony.ppc.ubc.ca> posted:
>>>> The function below returns the corresponding ISO-compatible weekday
>>>>number
>>>> ; Sun=0 Mon=1 Tue=2 Wed=3 Thu=4 Fri=5 Sat=6
>>>
>>> That is only ISO 8601 compatible if Sundays are ignored; Sunday is ISO
>>> Day 7.
In keeping with other Easter/Beltane eggs hid in parody
posts to this thread, it might have said "ISO compliant,"
but that wouldn't have been hiding anything very well,
would it?
Dr J R Stockton
23:04:52, lac...@ebony.ppc.ubc.ca posted:
does not.
However, in languages where arrays start ay zero, it can be useful to
provide the DoW TLAs as an array with elements
Sun Mon Tue Wed Thu Fri Sat Sun
so that both 0 & 7 find Sun.
Also, in JavaScript the DoW of a Date Object D can be obtained using
D.getDay() || 7
but note that a NaN date gives an ISO Sunday.