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Vincent Lefevere wrote:
On 2012-04-05 10:26:15 -0500, Nate Hayes wrote:Vincent Lefevre wrote: >>In my opinion, P1788 should consider restricting Level 1 to bounded >>intervals and introduce "overflown" intervals at Level 2. After the >>recent >>discussion on midpoint, it seems the committee is already leaning in >>this >>direction anyways. It also means the formulas in Motion 13 which are >>very >>simple and efficient could still be used for implementations. > >I don't see the discussion on midpoint changing anything about such >intervals. I'm not sure what you mean by this comment. My observation is that Midpoint is not defined at Level 1 for unbounded intervals.I agree. But there will be no "overflown" intervals at Level 2. AFAIK, the Level 2 choice for the midpoint on unbounded intervals has been done for practical reasons, not because of some notion of "overflown" intervals (if this is what you meant).
Nope. That's not what I meant. What I meant is that at Level 1 there is no definition of midpoint for unbounded intervals. So why include unbounded intervals in the Level 1 model? Especially when a similar treatment at Level 2 of "overflown" intervals can provide the same practical benefits? IMO the Level 1 model is then cleaner and simpler. Another example: the algebraic structure of intervals is stronger at Level 1 when restricted to bounded intervals, since the cancellation property A + X = B + X ---> A = B is true only when A, B, and X are bounded. The current P1788 Level 1 model that includes unbounded intervals has no cancellation property. I know: some algebraic properties will always be lost at Level 2 and "overflown" intervals don't solve that problem; but again my point and opinion (for what it's worth) is that the Level 1 model I believe is simpler, cleaner and algebraically stronger without unbounded intervals. Nate