Re: Motion P1788/M0032:midpoint -- voting period begins YES
I vote YES for the motion M0032.
This motion:
1) repeats Level 1 definition of mid(X) from John's Level 1 draft
that was defined for nonempty bounded intervals and undefined otherwise;
>> At level 1: mid(X) = (inf(X) + sup(X))/2
I agree.
2) it formulates Level 2 definiton of mid(X) for nonempty bounded and unbounded intervals;
>> Coercion to level 2: For some implicit or explicit IFbar
>> based on a some floating-point system F we have that
>>
>> mid_F(X) = if ((inf(X) == -\infty)&& (sup(X) == +\infty)) then 0
>> else if (round2Nearest_F(mid(X)) == +\infty)
>> then nextDown_F(+\infty)
>> else if (round2Nearest_F(mid(X)) == -\infty)
>> then nextUp_F(-\infty)
>> else round2Nearest_F(mid(X))
>>
>> Note that midpoint has been generalized to include Entire via
>> the means of the arbitrary choice of zero as its midpoint.
>> This choice is part of this motion. Midpoint is still not
>> defined for Empty& any generalization to include Empty is
>> not part of this motion.
My opinion is that Level 2 definition should pick some arbitrary number for unbounded intervals
though I understand arguments of thos who consider that the result should be NaN.
The choices of 0, F_max, -F_max in the definition (2) seems the best for me.
So I agree with meaning of (2) too. The wording could of (2) be other:
"For any floating-point system T and for any interval type T"
This doesn't break the definition, it extends it.
3) also the motion contains some properties of Level 1 and Level 2 definition.
The properties for Level 1 are fine;
The current formulation of properties for Level 2 was broken by Vincent's example,
but I know how to reformulate them.
I consider that this motion is about semantics of mid(X), not about of exact wording in the standard.
The semantics is good for me.
The wording could me as small as a line in a table and a remark below the table.
So I would like that this motion was accepted as semantic Level 2 definition on nonempty intervals.
The Level 2 definition of mid(Empty) is a topic of future discussion.
The exact wording in Level 2 part of the standard also could be discussed later.
-Dima
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От: rbk5287@xxxxxxxxxxxxx
Кому: stds-1788@xxxxxxxxxxxxxxxxx
Отправленные: Понедельник, 2 Апрель 2012 г 0:12:15 GMT +04:00 Абу-Даби, Маскат
Тема: Motion P1788/M0032:midpoint -- voting period begins
P-1788:
The voting period herewith
begins. Voting will continue until after Tuesday, April 17, 2012.
Voting on this motion will proceed according to the rules for
position papers (quorum and simple majority).
Comment can continue during voting, but the motion
cannot be changed during voting.
Juergen: Please update the web page with this action.
Acting secretary: Please record the transaction in the minutes.
The motion appears in the private area of the IEEE P-1788 site:
http://grouper.ieee.org/groups/1788/private/Motions/AllMotions.html
As usual, please contact me if you need the password to the private
area.
Best regards,
Baker (acting as chair, P-1788)
P.S. Note that Motions 30, 31, and 32 are now all under vote.
Please carefully consider each, and vote.
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Ralph Baker Kearfott, rbk@xxxxxxxxxxxxx (337) 482-5346 (fax)
(337) 482-5270 (work) (337) 993-1827 (home)
URL: http://interval.louisiana.edu/kearfott.html
Department of Mathematics, University of Louisiana at Lafayette
(Room 217 Maxim D. Doucet Hall, 1403 Johnston Street)
Box 4-1010, Lafayette, LA 70504-1010, USA
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