Date: Sun, 1 Apr 2012 15:11:20 -0500 (CDT)
From: Ralph Baker Kearfott<rbk5287@xxxxxxxxxxxxx>
To: stds-1788<stds-1788@xxxxxxxxxxxxxxxxx>
Subject: 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.
--
---------------------------------------------------------------
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
---------------------------------------------------------------
Baker,
I asked that the text of the
motion be updated a few days ago.
And I vote YES on that motion.
Yours,
Dan
To: Ralph Baker Kearfott<rbk@xxxxxxxxxxxxx>,
"Corliss, George"<george.corliss@xxxxxxxxxxxxx>,
wolff@xxxxxxxxxxxxxxxxxxxxxxxxxxx
Cc: Dan Zuras Intervals<intervals08@xxxxxxxxxxxxxx>
From: Dan Zuras Intervals<intervals08@xxxxxxxxxxxxxx>
Subject: The text for motion 32 was amended...
Date: Wed, 28 Mar 2012 07:28:05 -0700
Baker, George, Juergen,
I accepted a friendly amendment to motion 32 some time
back. It was to the effect that the domain of the
function at level 1 was the bounded non-empty sets.
Please see to it that this is reflected in the posted
text. You may use the text below.
Thanks,
Dan
-----------------
The midpoint function for bounded, non-Empty intervals
------------------------------------------------------
At level 1: mid(X) = (inf(X) + sup(X))/2
Properties: For intervals X& Y& when using midpoint to
split an X into X1& X2 we have
X \subset (X1 \union X2)
[inf(X),mid(X)] \subset X1
[mid(X),sup(X)] \subset X2
mid(X) \element-of (X1 \intersect X2)
X \subset Y ==> if (inf(X)==inf(Y)) then mid(X)<= mid(Y)
X \subset Y ==> if (sup(X)==sup(Y)) then mid(X)>= mid(Y)
always. These are required. The first 4 properties are
required for containment to hold. The last 2 for weak
ordering.
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.
The coercion mid_F(X) always returns a finite result even
when mid(X) is infinite in F.
If, for any X& Y that live at level 2, we define intervals
X1& X2 to be the smallest representable intervals for which
[inf_F(X),mid_F(X)] \subset X1& [mid_F(X),sup_F(X)] \subset
X2 we have
X \subset (X1 \union X2)
[inf_F(X),mid_F(X)] \subset X1 (trivially)
[mid_F(X),sup_F(X)] \subset X2 (trivially)
mid_F(X) \element-of (X1 \intersect X2)
X \subset Y ==> if (inf_F(X)==inf_F(Y)) then mid_F(X)<= mid_F(Y)
X \subset Y ==> if (sup_F(X)==sup_F(Y)) then mid_F(X)>= mid_F(Y)
The first 4 assure containment. The last 2, weak ordering.