How Can I Use plot2d code for presence of singularities?

Yes, "exterior" intervals can handle 1/y, but not x/y=x*(1/y).  The problem isn't inversion, but multiplication.

For example, a rational function should have interval pieces to handle each of its poles, so the amount of storage for the interval pieces is likely to grow as the number of poles.

At 10:43 AM 1/3/2013, Richard Fateman wrote:
One alternative is to have exterior intervals.  That is 1/[-1,1] becomes  [1, -1]  where the latter represents [-infinity,-1] U [1,infinity].
>(or if you join the reals at +- inf, it is all of them except [0,1].
>
>There is an IEEE working group constructing a standard for intervals, based on the IEEE 754 float standard.  754 has
>NaNs and signed 0 and infinity.
>
>There is a large literature   (see journal Reliable Computing...) on intervals and related techniques.
>
>RJF