The run stack over 128 pushes, four-entry rule

The run stack over 128 pushes, four-entry rule

One column per run pushed, each block a pending run with its height proportional to its length. The stack peaked at 7 entries over 128 runs and 4,096 elements, and 127 merges were performed. The policy exists to keep this shallow and the merges balanced: a stack that simply grew would merge one huge run against one tiny one at the end, which is the cost the whole mechanism is avoiding.

Drawn at 700 × 400, wide on the page. Everything above is what merge-stack returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

2 essays call merge-stack. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about — which is what optcheck and figfill exist to catch.