Re: A question Re: Level 1 <---> level 2 mappings; arithmetic versus applications
Nate,
On 6/30/2010 19:56, Nate Hayes wrote:
Dan Zuras writes:
Nate,
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Baker Kearfott wrote:
Nate,
On 6/30/2010 16:42, Nate Hayes wrote:
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It will often return an interval that is slightly wider
than would be returned in an inf-sup form but only by
an ULP on one side or the other. This will piss off
the inf-sup guys who want narrowest interval ...
>> but it is the price of
freedom from concern about the nature of the format.
My point is this: WHY do we even need to make these restrictions and
compromises, when everything we already hope to achieve is already
specified
by simply saying something along the lines:
"The Level 2 result of an operation is the tightest possible superset of
the
true result within the set of floating-point intervals represented by the
Level 2 type."
This may potentially result in some widening when converting from
mid-rad to
inf-sup. But it doesn't require any restrictions on mid-rad Level 2
objects,
and Dan's solution causes widening in this case anyways.
That was my thought, in exploring allowing separate representations
of intervals over a floating point type to be considered as a separate
interval types. (The problem is that the conceptual end points
of an interval of the mid-rad type are not necessarily representable
in the floating point type.)
However, I can now see what I think is Dan's view on the subject:
it might be better to have just one such interval type, because
multiple interval types built on the same floating point type
(presumably most often an IEEE double) would weaken the standard
in the sense that we would still have a proliferation of arithmetics,
making reproducibility and portability more difficult. I'm not sure
two interval types can be avoided, however, if we have strict
accuracy requirements and require both mid-rad and inf-sup. We may
need to make a decision or whether we want two types or to relax
the accuracy requirement. If we relax the accuracy requirement and
require both mid-rad and inf-sup, it may be difficult (or impossible?)
to define the standard to ensure cross-implementation uniqueness
(i.e. reproducibility) of results of operations, even at level 2.
Does anyone have corrections to anything I just expounded above?
Does anyone have suggestions of how to proceed efficiently with motions to
resolve this?
Baker
Nate
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