The ulp — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
What a float can hold
The representable numbers are not a fine fuzz spread evenly over the line. They are evenly spaced inside each power-of-two interval and twice as far apart in the next one up, and almost everything else in this subject is a consequence of that one fact.
A coin flip that fixes the average
Add 0.1 to 256 a thousand times at eight significand bits and the answer is 256. Not approximately — the total never moves, not once, and no error bound says so. Round up one time in twenty instead of never, and it arrives at 348 against a true 356.
The generator that rounded its own product
A one-pass variance leaned the same way on forty-one seeds, and the low bits of a congruential generator were the suspect. Replacing the lowest five bits made the lean larger, not smaller. The generator was not congruential at all: written in double precision, its product of two 31-bit numbers was rounded before the modulus, its states collapsed onto a handful of low bytes, and those are the bits a running sum near a billion throws away. The exact recurrence does not lean, and random bits are not neutral either: fewer of them than the sum discards all round one way.
Named alongside it
The objects these essays reach for when they reach for this one.
Error accumulationUnit roundoffSignificandSummationCatastrophic cancellationFloating pointHalf-precisionMachine epsilonRoundingRounding modesSeeded generatorStagnation