Re: Bare decorations (was ...level 2 datums)
Nate, John, Vladik, Arnold, et al,
Having "swapped out" my attention to the list for a couple of days, I am
somewhat bewildered by this line. In particular, where is it leading?
Is it getting us any closer to standard wording upon which we can agree?
My understanding was that the original intent of the levels in P-754 was
as a device to aid in developing the standard and coming to a consensus,
not as a set of dictates from a higher power to be upheld at all costs
and to engender controversy. Furthermore, I also am a bit confused by what
exactly the levels are, if they they are taken to be as defined on page 10
of the draft standard. In particular, already at level 2, we are talking
of "machine intervals."
I'm hoping we can quickly get beyond the sticking points here and resolve what I
feel are true issues (e.g. do we specify mid / rad operations, exactly
how do the decorations behave and what decorations do we have).
Sincerely,
Baker
On 10/25/2010 4:31 AM, John Pryce wrote:
Nate
On 25 Oct 2010, at 06:09, Nate Hayes wrote:
It is possible to discuss Level 2 in the abstract, but there is NO way to
define a specific Level 2 floating-point or interval datatype without
describing it by some sort of formula, which usually amounts to a
representation.
I'm sorry, John, but this is not true.
It is done all the time. A good reference is Bertrand Meyer's book on
object-oriented design where he describes an abstract datatype (ADT) purely
in mathematical terms by:
-- its types (i.e., its mathematical sets)
-- its functions
-- its axioms
-- its preconditions (if any)
I have read books on OO design; indeed I consulted one of Grady Booch's while composing that last email. Maybe what's at issue is what my words "amounts to a representation" mean. So I ask you
How can one specify the set F of level 2 datums of IEEE 754's
"binary32" datatype in a representation-free way?
The specification must enable one to answer the question "how many such datums are there?", i.e. to find the cardinality of F explicitly -- a boring but valid level 2 question.
John
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