A lightweight JavaScript library sitting on the shoulders of Fraction.js for generating and evaluating standard and generalized continued fractions. It is built with generator-based sequences and convergent recurrences for fast execution.
- Generate the simple continued‑fraction expansion of √N
- Convert any real number or rational to its continued‑fraction
- Infinite generators for classic constants: φ (golden ratio), e, π, 4/π
- Evaluate (simple or generalized) continued fractions to a
Fraction
const frac = ContinuedFraction.eval(
ContinuedFraction.fromFraction(3021, 203),
10 // Max Steps
);
console.log(frac.toString()); // → "3021/203"You can install ContinuedFraction.js via npm:
npm install continuedfraction.jsOr with yarn:
yarn add continuedfraction.jsAlternatively, download or clone the repository:
git clone https://github.com/rawify/ContinuedFraction.jsInclude the continuedfraction.min.js file in your project:
<script src="path/to/continuedfraction.min.js"></script>
<script>
var x = ContinuedFraction.sqrt(2);
</script>Or in a Node.js project:
const ContinuedFraction = require('continuedfraction.js');or
import ContinuedFraction from 'continuedfraction.js';Import the static utility class and use its generators and evaluator:
// 1) Continued‑fraction terms of √23
const sqrtGen = ContinuedFraction.sqrt(23);
console.log(sqrtGen.next().value); // 4
console.log(sqrtGen.next().value); // 1, 3, 1, 8, …// 2) Continued‑fraction of a decimal
let cnt = 0;
for (let piCf of ContinuedFraction.fromNumber(Math.PI)) {
console.log(piCf);
if (cnt++ >= 10) break;
}// 3) Golden ratio φ terms
const phiGen = ContinuedFraction.PHI();
console.log(phiGen.next().value); // 1, and forever 1…// 4) Evaluate the first 10 terms of e’s CF to a Fraction
const approxE = ContinuedFraction.eval(ContinuedFraction.E, 10);
console.log(approxE.toString()); // e ≈ “193/71”// 5) Generalized CF for π, 4/π
const genPi = ContinuedFraction.PI();
console.log(genPi.next().value); // { a: 3, b: 0 }
console.log(genPi.next().value); // { a: 6, b: 1 }// 6) Continued‑fraction from two integers
const halfCf = ContinuedFraction.fromFraction(1, 2);
console.log([...halfCf]); // [0, 2]| Method | Signature | Description |
|---|---|---|
sqrt(N: number) |
Generator<number> |
Simple CF terms of √N |
fromNumber(n) |
Generator<number> |
CF terms of any real via Fraction.js |
fromFraction(a, b) |
Generator<number> |
CF terms of the rational a/b |
PHI() |
Generator<number> |
Infinite 1’s for the golden ratio |
FOUR_OVER_PI() |
Generator<CFTerm> |
Generalized CF terms for 4/π |
PI() |
Generator<CFTerm> |
Generalized CF terms for π |
E() |
Generator<number> |
CF expansion of e |
eval(generator, steps) |
Generator (() => Generator, steps?: number) ⇒ Fraction |
Evaluate (generalized) continued fraction to a Fraction approximation |
Like all my libraries, ContinuedFraction.js is written to minimize size after compression with Google Closure Compiler in advanced mode. The code style is optimized to maximize compressibility. If you extend the library, please preserve this style.
After cloning the Git repository run:
npm install
npm run build
Copyright (c) 2025, Robert Eisele Licensed under the MIT license.