Every essay — page 13
What a bound is Counting The floors What the machine does Structures Two parameters The other axis When the algorithm flips a coin What the libraries do When it does not fit One pass, and no room The data that is not a number When the algorithm is a table The index that replaces the text What is taught wrongly Ladders Objects Search
What is taught wrongly
The comparisons that are made without units, the averages quoted without their distributions, and the bounds treated as predictions of speed.
The deepest text is punctuation
Eight source files reach depth 78 in a parse, on a collection with no version history in it at all. The positions between depth 20 and depth 72 are the same 48 characters at every level, and every one of them is a dash in a comment separator.
Three savings in three currencies
The same six occurrences, found four ways. The table computes 60,000 cells and reads 60,000 characters. The counting filter computes 6,251 cells and reads 13,022 characters. The seed filter computes 3,325 and reads 550. The index walk computes none, reads none, and performs 18,645 ranks.
What the approximation gives up
Compared at every one of the 3,736 decisions a search could ask about, the published shift rules and the exact ones agree at all of them on a set of 128 patterns. At two patterns they differ at five of 84, by up to four positions — and the run reads 6.3% more characters.
The operations a candidate count leaves out
The grid examines 33 candidates where the scan examines 4,355 — a factor of 132. Counted in the operations each of them performs, the same query is 2,471 against 4,355, and the factor is 1.8.
The cap that binds on one text and not another
A periodic text looks like the one made of chains and pays 1.11 times the phrases for a cap of four. A text that repeats itself pays 2.96. The guess is backwards, and the reason is that depth measures nesting rather than repetition.
A sixth of what, exactly
The saving from a counting-only reverse half is 30.5% at one sampled position in four and 14.0% at one in a hundred and twenty-eight. A number quoted without its sampling rate is a number about a setting somebody chose.
The pruning that loses an occurrence
Two versions of the same lower-bound pruning, each one character away from correct. Both return only real occurrences, both return fewer of them, and no check that asks whether the answers are right can tell either from the truth.
The ratio that was an implementation
This collection published a factor of forty-two between two shift rules' preprocessing. Sixty-nine per cent of the denominator was a table the published rule never reads, and the numerator was a definition rather than a construction. The corrected ratio is 1.6.
The occurrences a join invents
Eight documents run together hold forty-nine eight-character windows that span a join, twenty-three of which occur in no document at all. Every index built over the concatenation reports them, and five essays of this collection paid that cost silently.
A schedule nobody writes down
A search scheme is valid when its searches between them cover every way the errors can fall — ten cases at two errors, enumerable in a line. A scheme missing one of them finds seven occurrences of eight, all real, at the right error counts, and reports nothing wrong.
The level where compression stops paying
Choosing the best coding for every level of the grid separately, rather than one for all twelve, saves 26 bits out of 47,668 — five hundredths of one per cent. The apparatus for choosing costs more than that to describe.
What a quadratic construction was setting
A depth cap of one costs 90% of an 8,192-character text in phrases, and 86% of a 65,536-character one. The ladder's conclusions hold at thirty-two times the size — and the number the ladder could not reach, the deepest chain a real collection produces, turns out to be fourteen.
The dial that has no setting
The generator has one parameter. The real version history's run count asks it for 2.3% and its phrase count asks for 3.2% — and the reason is not that the dial is badly calibrated. Real edits average 7.3 characters a block and generated ones average 1.04.
A boundary that costs nothing
A separator occurs nowhere else in the collection, so it must break a phrase that would have spanned it. Cutting a repetitive text into a hundred and twenty-eight documents raises its run count by two per cent, and cutting prose raises it by ten.
One copy per document is one occurrence per document
The output-sensitive listing apparatus wins when a pattern occurs far more often than it occurs in documents. A collection of versions was supposed to be that case, and it is the one collection where the two numbers are equal by construction.
A saving quoted without its collection
A check asking whether a compressed document array is smaller than the plain one passes on the rounding whenever the document count is not a power of two. It would report a saving of nothing as sixteen per cent, on a collection that has no redundancy at all.
One set, three orders
The symbols an interval holds do not depend on the tree's shape. The order they come out in does, and a search that accumulates a running count as it reads them computes a plausible number that is wrong on eighty per cent of queries.
A walk that does not prune
Remove the emptiness test and the descent visits every node of the tree, returns exactly the same symbols with exactly the same intervals, and costs sixty per cent more. No test of the answer can see it.
Where the sparse representation loses
At every row marked, Elias–Fano costs twice the plain vector. The crossing is at one row in four, which is a sampling rate a real index uses — so the choice between the two is a choice, not an improvement.
A price with no structure under it
A class in this collection has charged Elias–Fano's price for several strands and stores an array of positions searched by binary search. The accounting is right about space to a bit per thousand and wrong about one operation by a factor of eight.
Two factors that do not multiply
Eleven times and seventy-eight times against the same baseline, so an index with both should be eight hundred and sixty. It is seventy-eight, and the shortfall is eleven — the first factor, exactly, because the second operation already contains it.
A constant factor, not a term
The substitution was expected to remove a quantity proportional to the answer. Both traversals hold a quantity proportional to the answer, and what it removes is a factor of 1.6 that shrinks as the collection grows.
A cache below the reachable set
A lazy machine with a cache of two hundred and fifty-six states costs fifty-one operations a character and a plain non-deterministic simulation costs fifty-three. At five hundred and twelve it costs eleven. The line is flat across two orders of magnitude and then falls off a cliff.
The folklore is about a matcher
Four million steps against three hundred and twenty-nine, on a twenty-character expression matched against twenty characters. One of the two machines doubles with every character of the input and the other does not, and only one of them is what a regular expression is.