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\n \n About stdlib...\n \n

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

\n

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

\n

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

\n

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

\n
\n\n# continued-fraction\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \n\n> [Continued fraction][continued-fraction] approximation.\n\n
\n\n## Installation\n\n```bash\nnpm install @stdlib/math-base-tools-continued-fraction\n```\n\n
\n\n
\n\n## Usage\n\n```javascript\nvar continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' );\n```\n\n#### continuedFraction( generator\\[, options ] )\n\nEvaluates the continued fraction described by the supplied `generator` argument. `generator` can be either a function which returns an array with two elements, the `a` and `b` terms of the fraction, or an ES6 [Generator object][es6-generator]. By default, the function computes\n\n\n\n
\n \"Continued\n
\n
-->\n\n\n\nUsing an ES6 [Generator object][es6-generator]:\n\n\n\n```javascript\n// Continued fraction for (e-1)^(-1):\nvar gen = generator();\nvar out = continuedFraction( gen );\n// returns ~0.582\n\nfunction* generator() {\n var i = 0;\n while ( true ) {\n i += 1;\n yield [ i, i ];\n }\n}\n```\n\nAlternatively, one can use a closure to achieve the same goal:\n\n```javascript\n// Continued fraction for (e-1)^(-1):\nvar gen = generator();\nvar out = continuedFraction( gen );\n// returns ~0.582\n\nfunction generator() {\n var i = 0;\n return gen;\n\n function gen() {\n i += 1;\n return [ i, i ];\n }\n}\n```\n\nThe function accepts the following `options`:\n\n- **maxIter**: `integer` denoting the maximum number of times the supplied generator object will be called. Default: `1000000`.\n- **tolerance**: `number` primitive specifying the used tolerance to assess convergence. Default: `2.22e-16`.\n- **keep**: `boolean` primitive indicating whether to keep the `b0` term in the continued fraction. Default: `false`.\n\nTo evaluate\n\n\n\n\n\nset the `keep` option to `true`.\n\n```javascript\nvar out = continuedFraction( generator(), {\n 'keep': true\n});\n// returns ~1.718\n\nfunction generator() {\n var i = 0;\n return gen;\n\n function gen() {\n i += 1;\n return [ i, i ];\n }\n}\n```\n\nTo change the maximum number of iterations, set the `maxIter` option.\n\n```javascript\nvar out = continuedFraction( generator(), {\n 'maxIter': 10\n});\n// returns ~0.582\n\nfunction generator() {\n var i = 0;\n return gen;\n\n function gen() {\n i += 1;\n return [ i, i ];\n }\n}\n```\n\nThe default tolerance of `2.22e-16` to assess convergence can be changed via the `tolerance` option.\n\n```javascript\nvar out = continuedFraction( generator(), {\n 'tolerance': 1e-1\n});\n// returns ~0.579\n\nfunction generator() {\n var i = 0;\n return gen;\n\n function gen() {\n i += 1;\n return [ i, i ];\n }\n}\n```\n\n
\n\n\n\n
\n\n## Examples\n\n\n\n\n\n```javascript\nvar continuedFraction = require( '@stdlib/math-base-tools-continued-fraction' );\nvar out;\n\nfunction* generator() {\n while ( true ) {\n yield [ 1, 1 ];\n }\n}\n\nfunction closure() {\n var ones = [ 1, 1 ];\n return gen;\n\n function gen() {\n return ones;\n }\n}\n\nout = continuedFraction( generator(), {\n 'keep': true\n});\nconsole.log( 'Golden ratio (generator): %d,', out );\n\nout = continuedFraction( closure(), {\n 'keep': true\n});\nconsole.log( 'Golden ratio (closure): %d', out );\n```\n\n
\n\n\n\n\n\n
\n\n
\n\n\n\n\n\n\n
\n\n* * *\n\n## Notice\n\nThis package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.\n\nFor more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].\n\n#### Community\n\n[![Chat][chat-image]][chat-url]\n\n---\n\n## License\n\nSee [LICENSE][stdlib-license].\n\n\n## Copyright\n\nCopyright © 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n
\n\n\n\n\n\n
\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-tools-continued-fraction.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-base-tools-continued-fraction\n\n[test-image]: https://github.com/stdlib-js/math-base-tools-continued-fraction/actions/workflows/test.yml/badge.svg?branch=v0.2.3\n[test-url]: https://github.com/stdlib-js/math-base-tools-continued-fraction/actions/workflows/test.yml?query=branch:v0.2.3\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-tools-continued-fraction/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-base-tools-continued-fraction?branch=main\n\n\n\n[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg\n[chat-url]: https://stdlib.zulipchat.com\n\n[stdlib]: https://github.com/stdlib-js/stdlib\n\n[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors\n\n[umd]: https://github.com/umdjs/umd\n[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules\n\n[deno-url]: https://github.com/stdlib-js/math-base-tools-continued-fraction/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-base-tools-continued-fraction/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-base-tools-continued-fraction/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-base-tools-continued-fraction/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-base-tools-continued-fraction/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-base-tools-continued-fraction/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-base-tools-continued-fraction/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-tools-continued-fraction/main/LICENSE\n\n[continued-fraction]: https://en.wikipedia.org/wiki/Continued_fraction\n\n[es6-generator]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Statements/function*\n\n
\n\n\n","readmeFilename":"README.md"}