Design parameter — where it appears
Named by 11 essays across 5 fields — each of them below, with the objects they name alongside it.
The bound a block can and cannot have
Knuth's condition turns an interval table's cubic fill into a quadratic one by bounding each cell's best split between its two neighbours'. A blocked fill cannot use it a cell at a time, and the two cells that bound a block lie outside the block — one to its left, one below it. The schedule has finished both for ten per cent of the blocks, the bound then removes eleven per cent of the splits, and it removes half a per cent of the cache misses, because the splits it skips are the ones already in the cache.
What a planner pays to find out what to pay
Insurance against a row estimate is set from the error's median and spread, and a running system knows neither — it has to fit them from executed queries. Fitted from one query the divisor costs 1.263 times the better plan against 1.215 for a planner that never insures at all, so learning is worse than not learning until about sixteen queries have run. The tail, though, is bought immediately: one observation already holds the worst case to 24.7 against 36.6.
A decay measured from where it started
An exponentially decayed counter is one number because its weights fade by elapsed time alone. Forward decay keeps a polynomial weight in one number too, by measuring each arrival from a fixed landmark. Its memory is then a share of the time since that landmark: at β = 2 an arrival counts half at 29% of that time. Anchored at the start of a stream, it takes 5.3 seconds to register a fourfold rise twenty seconds in and 83 seconds when the rise comes at five minutes.
The sibling a full leaf asks first
The rule databases use to fix ascending inserts fills their leaves completely and collapses to 53.4% when one key in a hundred arrives late. A leaf that offers a key to a sibling before it splits, and splits two full leaves into three when neither will take one, holds 84.2% on the same stream — and is better with a trickle of late keys than without one, because a perfectly ascending stream has no sibling with room.
The bits given to the wrong keys
A fingerprint table that gives later arrivals longer fingerprints holds 3.6% where a table that reserves nothing holds 21.1%, and it never runs out of reserve because it has none. It also dies at exactly the same size as the table that reserved nothing — 32 times its forecast, on the same key — because every generation shares one quotient, and the generation with the shortest fingerprint is the one that arrived first.
The read a filter has no key for
A Bloom filter on every run of a log-structured store turns a lookup for a missing key from a read of every level into a fraction of one — 0.72 transfers across eight levels at five bits a key, and 0.00027 at twenty. A range query over the same store reads nine transfers at five bits and nine at twenty, because a filter answers whether one named key is in a run and a range has no key to name.
Positions confined to one line
A Bloom filter lookup reads 5.55 cache lines because its six positions are scattered across the whole filter. Confining them to a 512-bit block makes it exactly one, and costs 7% more false positives at eight bits a key. At sixteen bits a key the same block costs 91%, and the two-value trick that is free across a whole filter costs another 135% inside one — because a block is a small filter, and small filters are where the penalty lives.
A key passed along the row
A full B+-tree leaf that offers a key to its immediate neighbours before splitting leaves an ascending stream 67.2% full. Let it look one sibling further and the same stream fills its leaves completely, 2,048 leaves where there were 3,048, for about the same key moves. On random keys each doubling of the reach adds a few points of fill and more writes than it saves, and at the whole parent a key travels sixteen leaves on average. On a stream that is mostly in order the same reach costs almost nothing.
A lookup that stops caring how wide an entry is
Buckets of eight entries aligned to a cache line read 1.20 lines a lookup when an entry is eight bytes and 19.25 when it is 128, because the bound was arithmetic about alignment and the arithmetic stops holding. Keeping one byte of each key's hash in a separate array and the entries in a parallel one reads 2.21 lines at every width from four bytes to sixty-four — and for a key the table does not hold, 2.05 against 31.98.
Two blocks and the chances they add
Send each key to the emptier of two 512-bit blocks and the busiest block of a filter at sixteen bits a key holds 38 keys instead of 55. The false-positive rate does not move: 0.100% against 0.095%. At eight bits a key it doubles. A lookup cannot tell which block a key went to, so it has to ask both, and asking twice is two chances to be wrong. The repair that tames a hash table's worst bucket buys a filter nothing that a block twice as wide does not.
Eight cells at once
The anti-diagonal fill order exists because its cells do not depend on one another, and every table filled here has been walked one cell at a time anyway. Computed eight at a time, a step touches 5.71 cache lines on the layout that stores the table by diagonals and 10.87 on the one that stores it by rows — and per cell the first keeps falling to 0.42 while the second stops at 1.27. The prediction that a diagonal step would touch three or four lines was wrong, and line-aligning each diagonal only takes it to 4.94.
Named alongside it
The objects these essays reach for when they reach for this one.
Space time tradeLocalityBloom filterFalse-positive rateCacheHonest limitMemory layoutAlignmentAmortisationApproximate membershipB-treeBalls in bins