loops

Orders directed edges into rings and chains. This kernel links each edge to the edge that follows it (next) and marks the edges a chain starts with (head); the jump and loops_cut and loops_place kernels do the rest.

For the boundary of a mesh (core.boundary runs the sequence), the directed edges are its open edges run the way their one face runs them (tail is a when the core.edges table's reversed is 0, else b). The whole sequence over m edges and npts points:

1. loops (STAGE clear, claim, link): next, head.
2. jump (MODE min), ceil(log2 m) rounds, starting from parent = next and value = the edge index: every edge holds the smallest index within reach, and parent holds the edge 2^k steps ahead.
3. loops_cut (STAGE head, cut): a ring (a cycle) starts at its smallest edge; a chain starts at its head. The edge before each start becomes the end of its list.
4. jump (MODE rank) over the cut lists, starting with value 1 on every non-end edge: each edge's end and its distance to it.
5. loops_place (STAGE claim, place): each edge's ring (the first edge of its list) and its position along the ring.

A compaction of the first edges numbers the rings, and a prefix sum of ring lengths (rank of the first edge plus 1) gives the ring starts; an edge's place in the ordered listing is its ring's start plus its position.

Over a live count (COUNT=device, see the abi README) the stages claim and link run over a capacity of edges whose live count is domain_count, and the n and npts params are not read. Stage clear runs over the capacity of points and writes the cleared value into every slot, which is the value a slot past the live points holds. In stage link a slot past the live edges links to itself and is no head. It binds 7 storage buffers (6 in the plain variant).