If your area is "sparse", that is, the number of regions is far smaller than the number of points in your space, I think using arithmetic instead of a bitmask will be much faster.
The two regions can be ordered by the numerical order of their lower bound, and if the two are equal, by their upper bound. Two regions then overlap iff
the lower bound of the upper region is smaller than the upper bound of the lower region.
Alternatively, if you have many one-dimensional regions, or regions with holes in them, and a large space, like Unicode has, Inversion Lists (also greping big numbers) might be a good approach to do fast set operations.
