Keep track of the union and (set) subtraction of integer ranges, accounting for the number of times a number was added. For example adding the set {1,2,3,4} (represented by Range(1,4)) and the set {3,4,5,6} (Range(3,4)) will result in a single range, Range(1,6). But internally, it is known that 3 and 4 appeared twice so that removing {2,3,4} (Range(2,3)) will result in a set {1,3,4,5,6}, i.e. the ranges Range(1,1) and Range(3,4).
This class is mostly meant as a utility for tvm::interal::VariableCountingVector. The idea is that tvm::VariableVector is not keeping track of how many time a part of a variable has been added or removed, and has limitations when it comes to adding or removing subvariable. This class can be used on the ranges of subvariables within their supervariable to keep track of the parts present after all the add and remove.
Internally, the ranges are represented by their limits, following the idea in https://stackoverflow.com/a/32869470/11611648, e.g. Range(1,4) = {1,2,3,4} is represented by {(1,+), (5,-)} where the lower limit (opening, denoted by +) is included and the upper limit (closing, denoted by -) is excluded. A list of such limits is kept as a representation of the current state. The number of appearances of an integer is encoded by the number of + and - appearing to reach that number from the start of this list. For example, if the list is {(1,+), (3,+), (5,-), (6,+), (7,-), (7,-), (9,+), (10,-)}, all number up to 0 don't appear, 1 and appear once, 3 and 4 appear twice, 5 appears once, 6 appears twice, 7 and 8 don't appear, 9 appears once and all numbers from 10 don't appear. The resulting range representation is { Range(1,7), Range(9,1) }. Compared to the above link, we add also the notion of cut (denoted by | ), that is useful to keep track of the fact that two ranges were stitched together. For example adding {1,2} (Range(1,2)) and {3,4} (Range(3,2)) results in {1,2,3,4} (Range(1,4)), but is represented internally by {(1,+), (3,|), (5,-)}. The following rules are enforced for the internal representation: (1) limits appears in lexicographic order with + < | < - (2) (i,|) can only appear once for a given i (3) the sequence (i,+), (i,-) is replaced by (i,|) (4) the sequence (i,+), (i,|), (i,-) is replaced by (i,|) (5) the representation starts with (i,+) and finish with (j,-) i<j (6) cuts can't appear at depth 0
1.9.1