Overview

This library provides an alternative to the std Range types which supports finite interval normalization. When used with a bounded, finite data type, the interval will support set operations (unions, intersections, etc), and iteration over potentially disjoint sets of intervals can be represented efficiently as a tree of interval bounds.

Representations for infinite intervals

This library was previously designed to support infinite and finite data types, utilizing trait specialization to make normalization of infinite intervals a no-op. To allow building on stable, this feature has been disabled, so Interval<T> and Selection<T> are only usable if T: Finite. As such, there are many methods defined for selections and intervals which are essentially useless, as all intervals will be normalized into a closed representation after construction.

What is interval normalization?

Interval normalization ensures that equivalent intervals have the same representation. For instance, if we have an Interval<i32> covering (0, 15], the left bound is exclusive, and due to the finiteness of i32, the interval will be equivalent to [1, 15]. In this way, intervals over finite types can always be 'normalized' as closed finite intervals. Additionally, unions of nearby intervals may overlap if denormalized. [0, 4] union [5, 6] selects the same points as [0, 6], even though the intervals do not share bounds. Thus we also have to normalize intervals with respect to set operations.

How is interval normalization achieved?

Interval<T> is implemented as a normalizing wrapper around RawInterval<T>. Any type which implements Normalize will be automatically normalized after any operation performed on Interval<T>. Dynamic unions of intervals are implemented through Selection<T>, which is a normalizing wrapper around TineTree<T>, which ensures that interval operations are performed on the broadest 'denormalized' set of intervals possible before normalization occurs.