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Re: Motion 31 draft text V04.4, extra notes

Vincent Lefevre wrote:

>>Well, how am I to not work with unbounded intervals at Level 1 if the
>>standard requires they may be there?
>
>Since your system works only with bounded intervals, you must have
>some hypotheses that guaranty that unbounded intervals will never
>occur (e.g. if you consider 1 / X, you need to know that X doesn't
>contain 0). So, you can just ignore unbounded intervals globally.
It appears you are changing the subject again, for the same reasons
mentioned above.

Anyhow, at Level 2 there is no practical difference between Inf/OVR in
the
interval arithmetics:
Decorations and compressed intervals can make the distinction that you
mention in both cases. For example, the full decorated result of 1 /
[0,1]
may be
   ([1,+OVR],somewhereDefined)
and with compressed intervals the result may be either the bare interval
   [1,+OVR]
or the bare decoration
   somewhereDefined.
So nothing is lost over the current P1788 model, i.e., what you're
talking
about isn't any argument in favor of unbounded intervals or against
family
of intervals (in fact, its not really relevant at all).


Since there is no practical difference, between Inf and OVR, I don't
see why you are complaining about unbounded intervals.

I may ask the same question of you about OVR.

But instead, let me point out you have agreed (several times) unbounded
intervals are unnecessary.

If they are unnecessary, I am interested to see how removing them from the
Level 1 model affects the rest of the standard. Midpoint is currently not
defined at Level 1 for unbounded intervals; and John Pryce has already
admitted comparison operations on unbounded intervals violates the
"principle of least astonishment". I suspect other edge-cases may be
revealed as P1788 moves forward, too. OVR is an alternative to study and
consider. That is the only commitment I've made to this idea so far.

You may see this as "complaining". But one could view your unwillingness to
consider alternatives as something less than scientific, as well.



>>I can't ignore anything the standard mandates unless I don't follow the
>>standard.
>
>The standard mandates that unbounded intervals are supported by the
>implementation, not that they will occur in the user application.
It mandates they are in the Level 1 math equations, which are then no
longer
cancellative.


Level 1 will never occur in the implementation of the standard. On your
side, you can use whatever you like for math equations.

This applies to you, as well.




>>Development of Kaucher arithmetic *requires* cancellation property!!!
>
>The standard is not about the Kaucher arithmetic anyway.
That's news to me. The name of P1788 is "Standard for Interval
Arithmetic"... and Kaucher arithmetic is "interval arithmetic".


It is a *particular* interval arithmetic, actually an extension of
conventional interval arithmetic. P1788 doesn't contain anything
about an implementation of Kaucher arithmetic (at least currently).

Our rendering software is starting to be used by production studios. Users
already ask when will the modal interval ASIC be available, and they
understand why a conventional interval ASIC will not run the application as
fast. I think if there is no Kaucher arithmetic in P1788 that industry will
not be interested in the standard.



>>>BTW, cancellation is invalid at Level 2.
>>I already pointed that out just the other day.
>
>+ the fact that you do not want to work at Level 1, this makes it
>useless.
I have never said I don't want to work at Level 1. I've said I want to
work
in a Level 1 model that is cancellative. Please stop putting words in my
mouth.


I recall what you've said:

| So why include unbounded intervals in the Level 1 model? Especially
| when a similar treatment at Level 2 of "overflown" intervals can
| provide the same practical benefits?

Basically this means: do not use Level 1, use Level 2.

No. It means what I've said above.
Nate