Re: floats and intervals, constants, 0.1, 1e400 and Inf

[Christian Keil <c.keil@xxxxxxxxxxxxx>]

> > If converting to a wider type, no rounding occurs.
>
> This depends upon whether one adopts the Kuki or Cody view of FP
> numbers:  Are the unwritten bits random, or all zero?  If one adopts the
> view that unwritten bits are all zero, then no rounding is needed.  If
> one adopts the view that unwritten bits are random then downward
> "rounding" of negative lower bounds and upward "rounding" of positive
> upper bounds are needed.  By "rounding" in this context I mean filling
> the new bits of the fraction with ones instead of zeroes.  For positive
> lower bounds or negative upper bounds, the correct thing to do is fill
> the new bits of the fraction with zeroes.

I don't think this is appropriate for bounds in intervals. We want these 
to be rigorous so for example a two bit upper bound of 1.0 is mandated 
to mean that every number contained in the interval is less than 1.0. 
1.0001 cannot be inside the interval, therefore a widening should always 
return an upper bound like 1.0000 instead of 1.0111.

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