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Re: Midpoint paper (2012-02-08 version)



Dmitry and other participants in this discussion

On 10 Feb 2012, at 19:06, Dmitry Nadezhin wrote:
> So the question that bothers me is:
> What properties do we expect from width(X)/midpoint(X)/radius(X) when
> X is of implicit interval type or X is of explicit interval type of wider number format ?

Remember that a general implicit type has essentially NO structure. It is an arbitrary finite set T of mathematical intervals that includes Entire and Empty. I don't think anyone would object if we restricted attention to symmetric types (X in T implies -X in T) so feel free to assume that. And, probably relevant to the present discussion, it has a hull operation as part of the definition.

But AT PRESENT it has no Level 2 number system associated, whether fixed point or floating point, or Aztec (was it?) quipus of knotted string.

When I suggested a while back that a floating point format F should be associated to T as part of its definition, I seem to recall this was pooh-poohed as unnecessary. But the current discussion shows, IMO, that it IS necessary, and might indicate some requirements for such an F. 

John Pryce