2,048 keys in 256 buckets — multiply–shift, a chosen at random

2,048 keys in 256 buckets — multiply–shift, a chosen at random

Each bar is one bucket's load, with keys with nothing special about them. The average load is 8.0 and the worst bucket here holds 16. The multiplier was drawn at random from the family, so an adversary who does not know it cannot compute a colliding set. The collision rate over all pairs is 3.84e-3, against 3.91e-3 for a perfectly uniform map.

Drawn at 690 × 360, wide on the page. Everything above is what hash-loads returns with no arguments; the caption is the generator's own, computed from the numbers in the drawing rather than written beside it.

11 essays call hash-loads. 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.