lazy NaN

[stla]

Hello,

For my new R package lazyNumbers I want to be able to deal with NaN values.

I'm able to create a lazy NaN by doing lazyNumber(0) / lazyNumber(0). Then I indeed get NaN when I call as_double on this lazy number.

But how to test whether a lazy number is NaN? I could test whether its double approximation is NaN but this is not a good solution, I don't want to call as_double everytime.

I already deal with missing values by using std::optional. So I cannot use std::optional for the NaN values.

[stla]

Hmm I've just have an idea: a lazy number is NaN if and only if its enclosing interval is ]-Inf, Inf[. Is it a reasonable way?

[stla]

a lazy number is NaN if and only if its enclosing interval is ]-Inf, Inf[. Is it a reasonable way?

Wrong. The enclosing interval of an infinite lazy number is ]-Inf, Inf[ as well.

This is unexpected to me: why the interval of the positive infinite lazy number is not inf = sup = Inf?

[stla]

Updated idea: a lazy number x is NaN if and only if the enclosing interval of x is ]-Inf, Inf[ and the enclosing interval of 1/x is ]-Inf, Inf[. Is it correct?

[MaelRL]

a lazy number is NaN if and only if its enclosing interval is ]-Inf, Inf[. Is it a reasonable way?

Wrong. The enclosing interval of an infinite lazy number is ]-Inf, Inf[ as well.

This is unexpected to me: why the interval of the positive infinite lazy number is not inf = sup = Inf?

In CGAL::Interval_nt, _inf is actually - inf, not inf. You should access the inf bound with inf(), and not look at _inf.

[stla]

Updated idea: a lazy number x is NaN if and only if the enclosing interval of x is ]-Inf, Inf[ and the enclosing interval of 1/x is ]-Inf, Inf[. Is it correct?

Wrong again :-( Sounds strange: if x is lazyNumber(Inf), then the enclosing interval of 1/x is ]-Inf, Inf[ (while the double approximation of x is as expected 0).

[MaelRL]

Each number type NT in CGAL has a specialization Is_valid<NT>, e.g.:

template< class ET >
class Is_valid< Lazy_exact_nt<ET> >
  : public CGAL::cpp98::unary_function< Lazy_exact_nt<ET>, bool > {
  public :
    bool operator()( const Lazy_exact_nt<ET>& x ) const {
      return is_valid(x.approx());
    }
};

which will check if the number is valid (which includes not being a NaN). Could you use this?

[stla]

Thanks. I've just tried CGAL::is_valid(x) and this returns true for x = lazyNumber(0) / lazyNumber(0).

[stla]

Still attempted with no luck. My conclusion is that there's no way without using the double approximation.