Re: Float conversion

[Shark8 <onewingedshark@gmail.com>]

On Aug 7, 2:56 am, Georg Bauhaus <rm-host.bauh...@maps.futureapps.de>
wrote:
> On 8/7/10 7:54 AM, Shark8 wrote:
>
> > Function Min( A, B, C : SOME_TYPE ) is
> > begin
> > If A<  B AND A<  C then
> >     return A;                -- We know A is the smallest valued var
> > here...
> > elsif B<  C then            -- and in the ELSE case we know that it is
> > not the smallest value.
> >                              -- If A is equal to C or B then returning
> > that value is equivalent to returning A's value.
> >     return B;
>
> Generalizing, when Min returns not the values but identities,
> will the equivalence of A and B work when stable sorting is needed?
>
> Another question, are there algorithms that rely on
> the representation of A, B, and C so that equivalence
> doesn't establish equality?
>
> Georg

Good questions.
In regard to the stability, I'm under the impression that is a
property of the algorithm rather than the comparative-operation.
{For example Shell sort is NOT a "stable" sot, but it uses the same
operator that merge sort uses; merge sort *is* stable.}

For the equivalence/equality question I think it's a matter of the
data-type rather than the algorithm that determines it. For example we
could define a Set Type with the operation "<" returning true if Left
is a proper/strict subset of Right (that is to say fully contained by
the superset and NOT equal to it). Now, given a set [Red, Blue, Green,
Purple, Yellow, Gray] both [Red,Green,Blue] & [Red, Yellow, Blue] are
subsets thereof and return true for "<". However, neither of the
subsets are equal or subsets of one another; so we cannot use "<"
alone to determine how to 'sort' this group of sets.