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PP-1788: The voting period herewith begins. Voting will continue until after Saturday, November 10, 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 I have also attached the motion, for your convenience. As usual, please contact me if you need the password to the private area. Best regards, Baker (acting as chair, P-1788) ================================================================== ================================================================== This motion about midpoint and radius is based on the discussions during our 2012 annual meeting at SCAN'2012, specifically on the idea proposed by Siegfried Rump: ******************************************************* Definition of the _midpoint_ of an interval [a,b]: * we compute the mathematical midpoint (a + b) / 2 in the extended real line (whenever it is possible), and then take a finite computer representable floating point number which is the closest to this mathematical midpoint; if there are two closest numbers, we use rounding to even, i.e., select the one whose binary expansion ends in 0 * the only interval for which the mathematical midpoint is not defined is the interval (-oo, +oo); for this interval, natural symmetry prompts us to define the midpoint as 0; Examples: * for an interval [a, +oo) with finite a, the midpoint is the number closest to +oo, i.e., MAXREAL * for an interval (-oo, a) with finite a, the midpoint is the number closest to -oo, i.e., -MAXREAL * for an interval [1, 1 + u], where 1 + u is the number closest to 1, the mathematical midpoint is 1 + (u / 2), so the closest numbers are 1 and 1 + u; rounding to even results in 1 being the desired midpoint Please note that a midpoint is, in general, different from a bisection point used to bisect an interval in different interval algorithms ************************************************************ For any interval [a, b], once its midpoint m is defined, we can define its _radius_ r as the smallest computer representable floating point number (finite or infinite) for which the interval [m - r, m + r] contains the original interval [a, b]. Examples: * for the interval [1, 1 + u], the radius is u * for the intervals [a, + oo) and (-oo, a), the radius is oo; this example shows the need for using an infinite number. ================================================================== ================================================================== -- --------------------------------------------------------------- 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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