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‎.gitignore

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_
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.DS_Store
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node_modules

‎LICENSE

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MIT License
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Copyright (c) 2025 Robert Eisele
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.

‎README.md

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# ContinuedFraction.js
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[![NPM Package](https://img.shields.io/npm/v/continuedfraction.js.svg?style=flat)](https://npmjs.org/package/continuedfraction.js "View this project on npm")
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[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT)
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A lightweight JavaScript library sitting on the shoulders of [Fraction.js](https://github.com/rawify/Fraction.js) for generating and evaluating **standard** and **generalized** continued fractions. It is built with generator-based sequences and convergent recurrences for fast execution.
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## Features
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- Generate the simple continued‑fraction expansion of √N
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- Convert any real number or rational to its continued‑fraction
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- Infinite generators for classic constants: φ (golden ratio), e, π, 4/π
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- Evaluate (simple or generalized) continued fractions to a `Fraction`
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## Example
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```js
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const frac = ContinuedFraction.eval(
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ContinuedFraction.fromFraction(3021, 203),
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10 // Max Steps
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);
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console.log(frac.toString()); // → "3021/203"
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```
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## Installation
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You can install `ContinuedFraction.js` via npm:
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```bash
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npm install continuedfraction.js
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```
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Or with yarn:
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```bash
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yarn add continuedfraction.js
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```
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Alternatively, download or clone the repository:
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```bash
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git clone https://github.com/rawify/ContinuedFraction.js
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```
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## Usage
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Include the `continuedfraction.min.js` file in your project:
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```html
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<script src="path/to/continuedfraction.min.js"></script>
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<script>
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var x = ContinuedFraction.sqrt(2);
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</script>
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```
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Or in a Node.js project:
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```javascript
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const ContinuedFraction = require('continuedfraction.js');
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```
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or
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```javascript
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import ContinuedFraction from 'continuedfraction.js';
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```
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## ContinuedFraction API
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Import the static utility class and use its generators and evaluator:
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```javascript
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// 1) Continued‑fraction terms of √23
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const sqrtGen = ContinuedFraction.sqrt(23);
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console.log(sqrtGen.next().value); // 4
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console.log(sqrtGen.next().value); // 1, 3, 1, 8, …
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// 2) Continued‑fraction of a decimal
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let cnt = 0;
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for (let piCf of ContinuedFraction.fromNumber(Math.PI)) {
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console.log(piCf);
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if (cnt++ >= 10) break;
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}
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// 3) Golden ratio φ terms
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const phiGen = ContinuedFraction.PHI();
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console.log(phiGen.next().value); // 1, and forever 1…
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// 4) Evaluate the first 10 terms of e’s CF to a Fraction
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const approxE = ContinuedFraction.eval(ContinuedFraction.E, 10);
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console.log(approxE.toString()); // e ≈ “193/71”
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// 5) Generalized CF for π, 4/π
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const genPi = ContinuedFraction.PI();
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console.log(genPi.next().value); // { a: 3, b: 0 }
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console.log(genPi.next().value); // { a: 6, b: 1 }
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// 6) Continued‑fraction from two integers
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const halfCf = ContinuedFraction.fromFraction(1, 2);
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console.log([...halfCf]); // [0, 2]
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```
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### Methods
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| Method | Signature | Description |
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| ------------------------ | ----------------------------------------------------------------- | ----------------------------------------------------------------------- |
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| `sqrt(N: number)` | `Generator<number>` | Simple CF terms of √N |
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| `fromNumber(n)` | `Generator<number>` | CF terms of any real via Fraction.js |
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| `fromFraction(a, b)` | `Generator<number>` | CF terms of the rational a/b |
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| `PHI()` | `Generator<number>` | Infinite 1’s for the golden ratio |
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| `FOUR_OVER_PI()` | `Generator<CFTerm>` | Generalized CF terms for 4/π |
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| `PI()` | `Generator<CFTerm>` | Generalized CF terms for π |
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| `E()` | `Generator<number>` | CF expansion of e |
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| `eval(generator, steps)` | `(Generator|() => Generator, steps?: number) ⇒ Fraction` | Evaluate (generalized) continued fraction to a `Fraction` approximation |
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## Coding Style
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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.
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## Building the library
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After cloning the Git repository run:
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```
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npm install
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npm run build
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```
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## Copyright and Licensing
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Copyright (c) 2025, [Robert Eisele](https://raw.org/)
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Licensed under the MIT license.

‎continuedfraction.d.ts

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import type Fraction from 'fraction.js';
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/**
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* A term of a generalized continued fraction.
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*/
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export interface CFTerm {
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/** The aₙ coefficient */
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a: number;
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/** The bₙ coefficient */
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b: number;
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}
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/**
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* Utility class for generating continued-fraction expansions of various constants.
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* All methods are static.
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*/
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export default class ContinuedFraction {
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/**
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* Infinite generator for the continued‐fraction terms of √N.
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* @param N Integer whose square‐root CF expansion is desired (N ≥ 0)
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* @yields Next continued‐fraction term of √N
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*/
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static sqrt(N: number): Generator<number, void, unknown>;
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/**
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* Generator for continued‐fraction terms of any real number via Fraction.js.
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* @param n The real number to convert (as number, string, or bigint)
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* @yields Next continued‐fraction term of n
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*/
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static fromNumber(n: number | string | bigint): Generator<number, void, unknown>;
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/**
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* Generator for continued‐fraction terms of a rational a/b via Fraction.js.
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* @param a Numerator (number, string, bigint, or Fraction)
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* @param b Denominator (number, string, or bigint)
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* @yields Next continued‐fraction term of a/b
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*/
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static fromFraction(
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a: number | string | bigint | Fraction,
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b: number | string | bigint
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): Generator<number, void, unknown>;
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/**
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* Infinite generator of the golden ratio φ = [1; 1, 1, 1, …].
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* @yields Always 1
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*/
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static PHI(): Generator<number, void, unknown>;
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/**
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* Infinite generator for the generalized continued‐fraction terms of 4/π.
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* @yields Term pairs { a, b } for the continued‐fraction
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*/
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static FOUR_OVER_PI(): Generator<CFTerm, void, unknown>;
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/**
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* Infinite generator for the generalized continued‐fraction terms of π.
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* @yields Term pairs { a, b } for the continued‐fraction
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*/
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static PI(): Generator<CFTerm, void, unknown>;
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/**
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* Infinite generator of e = [2; 1, 2, 1, 1, 4, 1, …].
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* @yields Next continued‐fraction term of e
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*/
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static E(): Generator<number, void, unknown>;
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/**
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* Evaluate a (simple or generalized) continued fraction generator.
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* @param generator A CF term generator or a function returning one
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* @param steps Number of terms to include (default 10)
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* @returns Rational approximation as a Fraction
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*/
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static eval(
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generator:
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| Generator<number | CFTerm, any, any>
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| (() => Generator<number | CFTerm, any, any>),
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steps?: number
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): Fraction;
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}

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