[std-interval] More on interval computations as proofs

[Ron Avitzur]

>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.

>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?