Microsoft Kuwaiti Algorithm for Islamic Calendar

classic Classic list List threaded Threaded
6 messages Options
Reply | Threaded
Open this post in threaded view
|

Microsoft Kuwaiti Algorithm for Islamic Calendar

Palmen, KEV (Karl)
Dear Calendar People

The wikipedia page
http://en.wikipedia.org/wiki/Kuwaiti_algorithm
says the Microsoft use a 'Kuwaiti' algorithm for the Islamic calendar and claims that this algorithm is just a variation of the Tabular Islamic calendar.

Is this true?
If so, what variation?

I have a vague memory that this may have been discussed on this list before.

Karl

07(15(14 till noon
Reply | Threaded
Open this post in threaded view
|

Re: Microsoft Kuwaiti Algorithm for Islamic Calendar

Caius
Palmen, KEV (Karl) wrote:

> The wikipedia page
> http://en.wikipedia.org/wiki/Kuwaiti_algorithm
> says the Microsoft use a 'Kuwaiti' algorithm for the Islamic calendar and claims that this algorithm is just a variation of the Tabular Islamic calendar.
>
> Is this true?
> If so, what variation?

I made that change to the article. When I first encountered it it was
rather biassed on Microsoft's PR, supporting their claim that they had
developed an algorithm using statistical analysis (blah blah..)

If you follow the first external link on the article, you'll see it's
what Van Gent calls Ia whereas the most common tabular islamic calendar
is IIc. Also see the errata to Calendrical Calculations:

http://emr.cs.iit.edu/home/reingold/calendar-book/second-edition/errata.pdf

Basically, the epoch is placed 1 day earlier and the rounding of the
accumulated 11/30 values is upwards at .5 which means the 6th leap year
of the cycle falls one year earlier.

When I first read this, I checked Windows' builtin islamic calendar with
my own implementation and sure enough they matched for 1000+ years.

Marc.
Reply | Threaded
Open this post in threaded view
|

Re: Microsoft Kuwaiti Algorithm for Islamic Calendar

Palmen, KEV (Karl)
In reply to this post by Palmen, KEV (Karl)
Dear Marc and Calendar People

Thank you Marc for the information.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Marc Schoolderman
Sent: 15 December 2005 09:47
To: [hidden email]
Subject: Re: Microsoft Kuwaiti Algorithm for Islamic Calendar


Palmen, KEV (Karl) wrote:

> The wikipedia page
> http://en.wikipedia.org/wiki/Kuwaiti_algorithm
> says the Microsoft use a 'Kuwaiti' algorithm for the Islamic calendar and claims that this algorithm is just a variation of the Tabular Islamic calendar.
>
> Is this true?
> If so, what variation?

I made that change to the article. When I first encountered it it was
rather biassed on Microsoft's PR, supporting their claim that they had
developed an algorithm using statistical analysis (blah blah..)

If you follow the first external link on the article, you'll see it's
what Van Gent calls Ia whereas the most common tabular islamic calendar
is IIc. Also see the errata to Calendrical Calculations:

http://emr.cs.iit.edu/home/reingold/calendar-book/second-edition/errata.pdf

Basically, the epoch is placed 1 day earlier and the rounding of the
accumulated 11/30 values is upwards at .5 which means the 6th leap year
of the cycle falls one year earlier.

When I first read this, I checked Windows' builtin islamic calendar with
my own implementation and sure enough they matched for 1000+ years.

KARL SAYS:
I'm aware of Van Gent's types I, II, III and IV, but the a and c suffixes are new to me. Reading the linked article reveals that they indicate the epoch.

c 15 July 622 (Civil)
a 16 July 622 (Astronomical)

So the Kuwaiti algorithm has leap years 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29 and epoch 16 July 622 (Julian Calendar). So the epoch is one day LATER.


I've recently noticed on
http://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.html
that arithmetic Islamic calendar (assumed to be IIc) is presently TWO days ahead of the observational Islamic calendar.

This year 1426 is the only year of the 30-year cycle that Ia is TWO days behind IIc and so the Kuwaiti date would actually agree with the observational date today.

It is the 16th (not 6th) year of the cycle that begins a day later in I than in II (two days in Ia than in IIc).

Karl

07(15(15
Reply | Threaded
Open this post in threaded view
|

Re: Microsoft Kuwaiti Algorithm for Islamic Calendar

Palmen, KEV (Karl)
In reply to this post by Palmen, KEV (Karl)
Dear Calendar People

Oops! I misread it Robert's web page. It is 15 July 622 that is the astronomical 'a' epoch and 16 July that is the civil 'c' epoch.

So Ia is one day ahead of IIc every year of the 30-year cycle except this year (the 16th) when it is in sync.

Robert's calculator reckons the day of the month of today to be
Ic   13
Ia   14 (Kuwaiti algorithm)
IIc  14 (usual)
IIa  15
IIIc 14
IIIa 15
IVc  14
IVa  15
All without exception are ahead of the observational calendar as calculated at
http://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.html
which is day 12 of the month.

Karl

07(15(15

-----Original Message-----
From: Palmen, KEV (Karl)
Sent: 15 December 2005 12:47
To: 'East Carolina University Calendar discussion List'
Subject: RE: Microsoft Kuwaiti Algorithm for Islamic Calendar


Dear Marc and Calendar People

Thank you Marc for the information.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Marc Schoolderman
Sent: 15 December 2005 09:47
To: [hidden email]
Subject: Re: Microsoft Kuwaiti Algorithm for Islamic Calendar


Palmen, KEV (Karl) wrote:

> The wikipedia page
> http://en.wikipedia.org/wiki/Kuwaiti_algorithm
> says the Microsoft use a 'Kuwaiti' algorithm for the Islamic calendar and claims that this algorithm is just a variation of the Tabular Islamic calendar.
>
> Is this true?
> If so, what variation?

I made that change to the article. When I first encountered it it was
rather biassed on Microsoft's PR, supporting their claim that they had
developed an algorithm using statistical analysis (blah blah..)

If you follow the first external link on the article, you'll see it's
what Van Gent calls Ia whereas the most common tabular islamic calendar
is IIc. Also see the errata to Calendrical Calculations:

http://emr.cs.iit.edu/home/reingold/calendar-book/second-edition/errata.pdf

Basically, the epoch is placed 1 day earlier and the rounding of the
accumulated 11/30 values is upwards at .5 which means the 6th leap year
of the cycle falls one year earlier.

When I first read this, I checked Windows' builtin islamic calendar with
my own implementation and sure enough they matched for 1000+ years.

KARL SAYS:
I'm aware of Van Gent's types I, II, III and IV, but the a and c suffixes are new to me. Reading the linked article reveals that they indicate the epoch.

c 15 July 622 (Civil)
a 16 July 622 (Astronomical)

So the Kuwaiti algorithm has leap years 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29 and epoch 16 July 622 (Julian Calendar). So the epoch is one day LATER.


I've recently noticed on
http://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.html
that arithmetic Islamic calendar (assumed to be IIc) is presently TWO days ahead of the observational Islamic calendar.

This year 1426 is the only year of the 30-year cycle that Ia is TWO days behind IIc and so the Kuwaiti date would actually agree with the observational date today.

It is the 16th (not 6th) year of the cycle that begins a day later in I than in II (two days in Ia than in IIc).

Karl

07(15(15
Reply | Threaded
Open this post in threaded view
|

Re: Microsoft Kuwaiti Algorithm for Islamic Calendar

Caius
In reply to this post by Palmen, KEV (Karl)
By the way, regarding your other message, I too get 1 January 2005 for
the Dee-Cecil calendar (using Mozilla 1.7.11).

Note that I noticed the calendar also uses a simple Julian formula for
the French republican calendar. Haven't checked the other calendars yet.

Palmen, KEV (Karl) wrote:

> I'm aware of Van Gent's types I, II, III and IV, but the a and c suffixes are new to me. Reading the linked article reveals that they indicate the epoch.
>
> c 15 July 622 (Civil)
> a 16 July 622 (Astronomical)
>
> So the Kuwaiti algorithm has leap years 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29 and
 > epoch 16 July 622 (Julian Calendar). So the epoch is one day LATER.

It's exactly the reverse:

"Of each calendar scheme two variants are possible depending on whether
the epoch of the Islamic calendar (1 Muharram, 1 AH) is assumed to be 15
July, 622 CE (known as the “Thursday” or “astronomical” epoch) or 16
July, 622 CE (“Friday” or “civil” epoch)."

As an aside, most sources tend to forget that it's Islamic custom to
start the day at sunset, I'm wondering if this difference in epoch could
be attributed to that as well?

> This year 1426 is the only year of the 30-year cycle that Ia is TWO days behind IIc and so the Kuwaiti date would actually agree with the observational date today.

No, the year 1426 is actually a year where both algorithms agree with
eachother. You can verify this at Van Gent's page.

This will lasts until 30 January 2006, which the 'common' tabular
Islamic calendar will consider the 30th day of al-Hijja 1426, whereas
the Kuwaiti algorithm will consider it 1 Muharram 1427.

> It is the 16th (not 6th) year of the cycle that begins a day later in I than in II (two days in Ia than in IIc).

I was talking about the 6th *leap* year.

Basically, a calendar is a leap year if

tabular | (11*y+14) mod 30 < 11    (II)
kuwaiti | (11*y+15) mod 30 < 11    (I)

Hence my remark about rounding.

As a service to the reader, the other two from Van Gent's list

indian? | (11*y+11) mod 30 < 11    (III)
?       | (11*y+9)  mod 30 < 11    (IV)

I think I understand the Indian leap year scheme. It's equivalent to:

    11*(y+1) mod 30 < 11

And judging from the Hindu epochs, Indians had a penchant for starting
to count at zero instead of one, which might explains this.

Marc.
Reply | Threaded
Open this post in threaded view
|

Re: Microsoft Kuwaiti Algorithm for Islamic Calendar

Palmen, KEV (Karl)
In reply to this post by Palmen, KEV (Karl)
Dear Marc and Calendar People

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:[hidden email]]On Behalf Of Marc Schoolderman
Sent: 15 December 2005 14:04
To: [hidden email]
Subject: Re: Microsoft Kuwaiti Algorithm for Islamic Calendar


Basically, a calendar is a leap year if

tabular | (11*y+14) mod 30 < 11    (II)
kuwaiti | (11*y+15) mod 30 < 11    (I)

Hence my remark about rounding.

As a service to the reader, the other two from Van Gent's list

indian? | (11*y+11) mod 30 < 11    (III)
?       | (11*y+9)  mod 30 < 11    (IV)

I think I understand the Indian leap year scheme. It's equivalent to:

    11*(y+1) mod 30 < 11

And judging from the Hindu epochs, Indians had a penchant for starting
to count at zero instead of one, which might explains this.

KARL SAYS:
I can work out relative meridians of these by taking one unit the K in

(11*y+K) mod 30 < 11

to be 12 degrees further East. This places the Indian calendar West of the tabular   calendar, opposite to what I'd expect. I think Marc's explanation of the Indian choice of K=11 is a plausible explanation of this.

                                       Meridian West of (I)'s
Kuwaiti | (11*y+15) mod 30 < 11    (I)        0
tabular | (11*y+14) mod 30 < 11    (II)      12
Indian? | (11*y+11) mod 30 < 11    (III)     48
?       | (11*y+9)  mod 30 < 11    (IV)      72

I shall mention again that all four have the property that it has a leap year 10 years after another leap year IN THE SAME 30-YEAR CYCLE.

Kuwaiti | (11*y+15) mod 30 < 11    (I)   [ 5,15]
tabular | (11*y+14) mod 30 < 11    (II)  [16,26]
Indian? | (11*y+11) mod 30 < 11    (III) [19,29]
?       | (11*y+9)  mod 30 < 11    (IV)  [11,21]

Note that K=13 [27,7] and K=10 [30,10] have no leap year 10 years after another leap year in the same 30-year cycle (but in the previous 30-year cycle).

Karl

07(15(15