Re: Bare decorations (was ...level 2 datums) - level 2 versus level 3
Ian, Vincent
On 25 Oct 2010, at 22:49, Ian McIntosh wrote:
> JP> How can one specify the set F of level 2 datums of IEEE 754's
> JP> "binary32" datatype in a representation-free way?
> JP> The specification must enable one to answer the question "how many such datums are there?",
> JP> i.e. to find the cardinality of F explicitly -- a boring but valid level 2 question.
>
> Ignoring operations, rounding, exceptions etc., which are not part of the set of datums:
>
> * Level 3: There is a sign bit, stored as the uppermost bit, with 0 meaning positive and 1 meaning negative.
>
> Level 2: There is a sign, which is either positive or negative.
> ...
What Ian calls level 3 here, I would rather call level 4.
As for his level 2 description, this IS a matter of usage of (human) language. To me, a "representation" of a set S means a (specified) map rep() from a (specified, and typically more concrete than S) set R *onto* S. That is, by ranging over R and applying rep() I guarantee to get every element of S, possibly several times.
So when he uses formulae, e.g.
> there is a base 2 exponents 2^-62 to 2^+62 ...
to me, that's representation -- part of the description of either rep() or R.
Is this an eccentric use of language?
John