Past uses of NaN?
Vincent Lefevre wrote:
[in: Re: Bare decorations (was ...level 2 datums)]
On 2010-11-02 02:16:24 -0700, Dan Zuras Intervals wrote:
Vincent,
While I do not agree with this approach to bare
intervals & bare decorations, I think Nate is
generally going in the right direction to treat
bare decorations as a flavor of NaI that is
generally NaI preserving.
You are also correct in that there will be some
minor exceptions. Some hypot cases are one.
Some selection functions are another. We may
have max([al,au],<bare_decoration>) want to be
the interval or we may want it to be [al,+inf].
Just as we may want max(interval,empty) to be
the interval. I'm not sure yet. There may be
some subtlties I'm missing.
With intervals, we would have both Empty/Entire and NaI, while IEEE 754
just has NaN. So I think it would make more sense and would be safer if
we had no exceptions concerning the NaI propagation. Now, I don't know
the implications on practical applications.
I don't think that we'll need any, given the decoration concept.
If there were an analogy we could make, I'd say that Empty and Entire
would be close to qNaN and NaI would be close to sNaN. Indeed a qNaN
can occur:
* [Empty] when one writes something that doesn't make sense,
e.g. sqrt(-1.0), i.e. something that could be seen as having
no solutions;
* [Entire] due to a succession of rounding errors on a mathematical
expression that makes sense (one gets a NaN and doesn't know
anything about the real value).
(Note: this is not exhaustive, Empty and Entire can have their own
meaning...)
To check that we forget nothing of relevance, it would be useful if
someone could collect the main different uses (or suggested uses)
that NaNs have in past applications. At present, I am aware of
three different systematic uses, the first two corresponding to
the above two cases:
-- signalling ''invalid''; e.g., sqrt(-1)=NaN;
-- signalling ''arbitrary''; e.g., 0/0=NaN; inf-inf=NaN;
-- signalling ''missing value''; e.g., max(1,NaN,4,2)=4.
Their interval analogues can be adequately handled using decorations.
So my questions are:
What other uses had been discussed in the 754-discussions?
What sorts of payloads were considered (potentially) useful?
Arnold Neumaier