ContinuedFraction.js

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.

Features

• 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

Example

const frac = ContinuedFraction.eval(
  ContinuedFraction.fromFraction(3021, 203),
  10 // Max Steps
);
console.log(frac.toString()); // → "3021/203"

Installation

You can install ContinuedFraction.js via npm:

npm install continuedfraction.js

Or with yarn:

yarn add continuedfraction.js

Alternatively, download or clone the repository:

git clone https://github.com/rawify/ContinuedFraction.js

Usage

Include 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';

ContinuedFraction API

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]

Methods

| 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 |

Coding Style

As every library I publish, ContinuedFraction is also built to be as small as possible after compressing it with Google Closure Compiler in advanced mode. Thus the coding style orientates a little on maxing-out the compression rate. Please make sure you keep this style if you plan to extend the library.

Building the library

After cloning the Git repository run:

npm install
npm run build

Copyright and Licensing

Copyright (c) 2025, Robert Eisele Licensed under the MIT license.