Glossary

Terms that appear across the guide and the reference, in plain language. Where a term has a precise technical meaning as well, the plain one comes first.

Numbers and precision

binary64 — The only number type JavaScript has for arithmetic (number). 64 bits, about 15–17 decimal digits of precision, and a range up to roughly 1.8e308. Everything below is a consequence of that being finite.

ulp — “Unit in the last place”: the gap between one representable number and the next one along. Saying a result is “three ulps off” means it is three representable steps away from the true answer — a far more useful measure than a fixed decimal count, because the gap grows with the magnitude.

overflow — What happens when a result is too large to represent. In binary64 it becomes Infinity, and every digit is lost at once.

underflow — The same at the small end: a result too close to zero becomes exactly 0. This is how a tail probability quietly disappears.

catastrophic cancellation — Subtracting two nearly equal numbers. The leading digits agree and cancel out, leaving only the rounding noise that was below them. This is why 1 - erf(x) fails and erfc(x) exists.

tolerance — How close is close enough. Every iterative routine takes one; what it is measured against differs per routine and is documented on each.

convergence — An iterative routine closing in on its answer. A routine converged if it met its tolerance, and did not if it ran out of iterations first. See convergence and iteration limits.

Statistics

distribution — A description of how likely each possible outcome is.

CDF (cumulative distribution function) — “What fraction of outcomes are no bigger than this?” Always between 0 and 1, and always increasing.

survival function — The complement of the CDF: “what fraction are bigger than this?” Usually the one you want when the answer is small.

quantile — The CDF run backwards: “which value sits at the 90th percentile?”. Also called the inverse CDF or the percent-point function.

p-value — The probability of seeing a result at least as extreme as the one observed, if nothing interesting were going on. Computed from a survival function, which is why the small-answer accuracy of those functions matters.

regularized — Normalized so the result lands in [0, 1]. The word is spelled out in these function names because libraries disagree about whether the bare name means the ratio or the unnormalised integral, and the difference is silent.

shape parameter — A number that changes the form of a distribution rather than shifting or stretching it. Conventionally a and b in these pages.

Numerical methods

closed form — An answer you can write down as a finite expression. Most of what is on these pages exists because the thing being computed has none.

bracket — Two points with a root guaranteed between them, because the function has opposite signs at each. See root finding.

quadrature — The traditional name for numerical integration: computing an area under a curve by evaluating the curve at points rather than by integrating symbolically.

discretisation error — The error you get from approximating a smooth thing with a finite number of pieces. Shrinks as you add pieces, unlike rounding error, which grows.

continued fraction — An expression of the form b₀ + a₁/(b₁ + a₂/(b₂ + ⋯)). Often converges much faster than the equivalent infinite sum. See continued fractions.

This project

portable (P) — Runs on any JavaScript runtime: Node, browsers, Deno, Bun and edge. Imports no host built-ins.

host-bound (H) — Depends on a specific runtime, in practice Node. A portable package never depends on a host-bound one.

illustration — A figure showing what something typically produces.

evidence — A figure demonstrating a specific measurable claim the prose makes. Labelled as such, and backed by a test that asserts the same claim.