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Pointed intervals to the rescue [Make CLAM great again] (Was: Can CLAM do bidrectional rounding?)

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Hi,

My recent thinking is such rounding could have
a place in CLAM (Constraint Logic Abstract Machine),
as part of some interval arithmetic. Particularly
pointed intervals, like 145.6 is basically the
interval [145.55 .. 145.65),

including the lower bound excluding the upper bound.
The value 145.6 is associated with the interval, and
not some midpoint, has to do that the rounded value is
the associated point. So all values in the interval round to

the associated rounded value. But I didn’t do a thorough
research yet. It would basically give a different rationalize
and associated interval computation from input, a more business
like rationalize that requires that the number

scanner tokenizer also records the number of fractional
digits in the input. So that for example 90 and 90.0 are
not the same when it comes to rationalize and associated
interval computation from some given input.

Most fixnum rounding have midpoint = rounded value:

145.6 ~~> [145.55 .. 145.65) ~~> (145.55 + 145.65) = 145.6
90    ~~> [89.5 ..90.5)      ~~> (89.5 + 90.5) = 90

But some rounding, like for example automatically
choosing a scale, i.e. going from bytes to kilo bytes,
mega bytes, giga bytes etc.., many directory listings
can do that when they show a file size,

I guess the associated intervals and
rounded values are more exotic.

Bye

Mild Shock schrieb:
> The conversion factor in the units database is:
> 
> ?- qeval(X*1 is mi/km).
> X = 1.609344.
> 
> I had first used 1.60934, but then used
> 1.609344. But I think this here is not a
> symmetric answer, and a symmetric answer
> using constraint logic programming
> 
> maybe impossible:
> 
> ?- qeval((145.6*km =:= 90*usc:mile+quantity Eps, SIEps is Eps in km)).
> Eps = 0.4716455897558234*kind_of(isq:length)[usc:mile],
> SIEps = 0.7590399999999958*kind_of(isq:length)[si:kilo(si:metre)].
> 
> Do you have intervals associated with
> units, so you can write “in km”?
> 
> I computes 145.6*km - 90*mile in terms of km, so it computes:
> 
> /* Windows 11 Calcultator */
> 145.6 - 90*1.609344 = 0.75904
> 
> /* SWI-Prolog Evaluator */
> ?- X is 145.6 - 90*1.609344.
> X = 0.7590399999999988
> 
> So to be correctly rounded to one digit after
> the period, the eps would need to be smaller. But for
> the other direction, whether the conversion
> from km to mile was correct, I guess a
> 
> 2nd query would be needed. But still I would
> be interested whether constraint logic programming
> can answer such questions in one query, like
> whether CLAM (the idea of Constraint Logic
> 
> Abstract Machines) has a rounding bidirectionality?
> Giving new momentum to the dream that
> CLAM is a silver bullet.
> 
> Mild Shock schrieb:
>> Do these units packages define rounding? Is this correct:
>>
>> https://www.shutterstock.com/de/image-photo/road-sign-longest-straight-australia-548866177 
>>
>>
>> I think one way its correct:
>>
>> 145.6 km ÷ 1.609344 km/mile = 90.47 miles
>>
>> The other way its incorrect:
>>
>> 90 miles × 1.609344 km/mile = 144.84 km
>>
>> Mild Shock schrieb:
>>> Hi,
>>>
>>> So how does academic purity compare to industrial
>>> success? Well this talk by Martin Odersky has some
>>> interesting slides comparing past and present:
>>>
>>> Evolving Scala by Martin Odersky | Scalar Conference 2025
>>> https://www.youtube.com/watch?v=DI0NOh9r1f8
>>>
>>> Where Scala ranked in 2014, versus where Scala
>>> ranks in 2025. Haskell gone, Clojure gone.
>>>
>>> LoL
>>>
>>> Bye
> 

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