The floor of each shard, computed from its histogram and then measured

The floor of each shard, computed from its histogram and then measured

8 shards of 40,000 arrivals of stationary Zipf — the control, where a window is a smaller sample, partitioned round-robin: every key on every shard, each summarised by 32 counters. The pale bar is the naive estimate: the mass outside the shard's top 32 keys divided by 32. The mid bar is the fixed point, which divides the same mass by the number of slots that are actually churning. The dark bar is the smallest counter the structure settled at. The fixed point is within 0.6% of it on average; the naive estimate is low by about a factor of 1.8.

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

7 essays call predicted-floor. 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.