Two floors, 8 distinct values among 256

Two floors, 8 distinct values among 256

Every sort's comparison count on an input drawn from 8 distinct values, on a logarithmic axis, with both floors marked. The right-hand line is log₂(n!) = 1,684 bits, which is the floor every table quotes. The left-hand line is the log of the multinomial — 739 bits — which is the number of outcomes a sort must actually separate, and it is 2.28 times lower. Merge sort sits exactly on the right-hand line and is 2.28 times above the left-hand one.

Drawn at 700 × 418, wide on the page. Everything above is what entropy-floor 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 entropy-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.