[std-interval] More on interval computations as proofs

[Sylvain Pion]

Ron Avitzur a écrit :
>> The discussion showed that Standard functions MUST set a flag when
>> the argument interval is not completely contained in the domain of
>> the function. Otherwise (i.e without the flag) verification of the
>> result with fixed points or other assertions that need continuity is
>> not possible
> 
> For my graphics application of intervals, as well, it is also
> sometimes necessary to track both continuity of functions and
> the domain over which they are well-defined.

Could you please provide more details on your needs for detecting
discontinuities?  I don't see many functions considered here which
are not continuous on there definition domain, so maybe we only
need special treatment instead of a general scheme.

>> I hope you are proposing these operations in addition to the
>> corresponding operations without the flag....
>> without two different functions, the user has no way to say either
>> "I don't care about domain errors" or "I am quite sure there is no
>> domain error here".  The result is substantial overhead in fairly
>> primitive functions.
> 
> Seconded. Requiring all usage of the library to pay for the overhead
> seems unreasonable.
> 
> Which functions would need variants which flag out of domain arguments?
> 
>  divide logb acos acosh  asin  sqrt atanh
>  log log10 log2 log1p lgamma tgamma
> 
> Are there others? Is that too large a cost to impose on implementors?

I don't think it would be costly.

-- 
Sylvain