Type of a range.

size v returns the number of integers in v, i.e. v.hi - v.lo + 1.

member t k returns true if t contains k.

String representation of an range, intended only for human legibility.

to_list v returns the set of integers contained in v, in ascending order.

overlap u v returns amount of overlap between two ranges. A positive value indicates number of integers common to u and v. A negative value indicates the number of integers in between non-overlapping ranges. A zero value means the ranges are exactly adjacent to each other. The relation is symmetric.

gap u v returns the size of the gap between u and v. It is equivalent to the negative of overlap.

union u v returns the range(s) representing the union of u and v. If u and v overlap, their union can be represented as a single range. If not, their union is a disjoint combination of two ranges.

intersect u v returns the range representing the intersection of u and v. Return None if intersection is empty.

before u v is true if strict_before u v || equal u v.

after u v is equivalent to before v u.

strict_before u v is true if u.lo < v.lo && u.hi < v.hi.

strict_after u v is equivalent to strict_before v u.

compare_positional u v returns -1 if u is strictly before v, 0 if u is equal to v, +1 if u is strictly after v, and returns None otherwise.

subset u v is true if u is a subset of v.

superset u v is true if u is a superset of v.

strict_subset u v is true if u is a strict subset of v.

strict_superset u v is true if u is a strict superset of v.

compare_containment u v returns -1 if u is a strict subset of v, 0 if u is equal to v, +1 if u is a strict superset of v, and returns None otherwise.

Return true if any pair of given ranges overlap each other.

Return true if all pairs of given ranges are positionally comparable.

Return maximum gap between adjacent pairs of given ranges. Raise Failure if any pairs of given ranges not positionally comparable, or if given less than two ranges.

find_min_range v pred i finds the minimum sized range within v centered around i that satisfies pred. Successively larger ranges are created starting from [i, i] and the first one to satisfy pred is returned. None is returned if the given range v itself is reached and pred still fails. Raise Failure if i not within v.

The first range tried is [i, i], by default the second is [i, i+1], the third [i-1, i+1], the fourth [i-1, i+2], and so on. The optional init_direction must be either "fwd" or "rev". If "fwd", which is the default, the range size is initially increased in the forward direction. If "rev", the second range tried will be [i-1, i]. If the range boundary is reached on either side, the size continues to be increased by incrementing on the opposing side.

exp_assoc_list dat returns a list associating each integer i with the list of values associated with all ranges overlapping i in dat. The set of integers considered is the union of all in given dat.

TO DO: fill in this documentation. For now see Math.find_regions.

make_random t returns a random range that is a subset of t. May raise Failure if given range bounds exceed largest value handled by Random module.