{"id":15578433,"url":"https://github.com/stdlib-js/math-iter-utils-continued-fraction","last_synced_at":"2025-04-24T02:27:37.169Z","repository":{"id":42454753,"uuid":"462667542","full_name":"stdlib-js/math-iter-utils-continued-fraction","owner":"stdlib-js","description":"Evaluate the terms of a continued fraction.","archived":false,"fork":false,"pushed_at":"2025-02-03T01:57:20.000Z","size":1071,"stargazers_count":2,"open_issues_count":0,"forks_count":0,"subscribers_count":3,"default_branch":"main","last_synced_at":"2025-04-12T08:06:58.557Z","etag":null,"topics":["approximation","continued","fraction","iterable","iterate","iterator","javascript","math","mathematics","node","node-js","nodejs","stdlib"],"latest_commit_sha":null,"homepage":"https://github.com/stdlib-js/stdlib","language":"JavaScript","has_issues":false,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"apache-2.0","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/stdlib-js.png","metadata":{"files":{"readme":"README.md","changelog":"CHANGELOG.md","contributing":"CONTRIBUTING.md","funding":null,"license":"LICENSE","code_of_conduct":"CODE_OF_CONDUCT.md","threat_model":null,"audit":null,"citation":"CITATION.cff","codeowners":null,"security":"SECURITY.md","support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null},"funding":{"github":["stdlib-js"],"open_collective":"stdlib","tidelift":"npm/@stdlib/stdlib"}},"created_at":"2022-02-23T09:31:52.000Z","updated_at":"2025-02-03T01:12:31.000Z","dependencies_parsed_at":"2024-01-01T04:42:05.562Z","dependency_job_id":"9dc173ba-ff02-4a1e-8523-c65b8dcbfdd1","html_url":"https://github.com/stdlib-js/math-iter-utils-continued-fraction","commit_stats":{"total_commits":46,"total_committers":1,"mean_commits":46.0,"dds":0.0,"last_synced_commit":"6a3e21694093f6a0ce8c3724a6a5f03dd1a3954e"},"previous_names":[],"tags_count":17,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-iter-utils-continued-fraction","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-iter-utils-continued-fraction/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-iter-utils-continued-fraction/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/stdlib-js%2Fmath-iter-utils-continued-fraction/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/stdlib-js","download_url":"https://codeload.github.com/stdlib-js/math-iter-utils-continued-fraction/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":250547327,"owners_count":21448469,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["approximation","continued","fraction","iterable","iterate","iterator","javascript","math","mathematics","node","node-js","nodejs","stdlib"],"created_at":"2024-10-02T19:10:27.386Z","updated_at":"2025-04-24T02:27:37.144Z","avatar_url":"https://github.com/stdlib-js.png","language":"JavaScript","funding_links":["https://github.com/sponsors/stdlib-js","https://opencollective.com/stdlib","https://tidelift.com/funding/github/npm/@stdlib/stdlib"],"categories":[],"sub_categories":[],"readme":"\u003c!--\n\n@license Apache-2.0\n\nCopyright (c) 2022 The Stdlib Authors.\n\nLicensed under the Apache License, Version 2.0 (the \"License\");\nyou may not use this file except in compliance with the License.\nYou may obtain a copy of the License at\n\n   http://www.apache.org/licenses/LICENSE-2.0\n\nUnless required by applicable law or agreed to in writing, software\ndistributed under the License is distributed on an \"AS IS\" BASIS,\nWITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\nSee the License for the specific language governing permissions and\nlimitations under the License.\n\n--\u003e\n\n\n\u003cdetails\u003e\n  \u003csummary\u003e\n    About stdlib...\n  \u003c/summary\u003e\n  \u003cp\u003eWe 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.\u003c/p\u003e\n  \u003cp\u003eThe 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.\u003c/p\u003e\n  \u003cp\u003eWhen 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.\u003c/p\u003e\n  \u003cp\u003eTo join us in bringing numerical computing to the web, get started by checking us out on \u003ca href=\"https://github.com/stdlib-js/stdlib\"\u003eGitHub\u003c/a\u003e, and please consider \u003ca href=\"https://opencollective.com/stdlib\"\u003efinancially supporting stdlib\u003c/a\u003e. We greatly appreciate your continued support!\u003c/p\u003e\n\u003c/details\u003e\n\n# iterContinuedFraction\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] \u003c!-- [![dependencies][dependencies-image]][dependencies-url] --\u003e\n\n\u003e Evaluate the terms of a continued fraction.\n\n\u003csection class=\"intro\"\u003e\n\nA **generalized continued fraction** has the form\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:continued_fraction\" align=\"center\" raw=\"x = b_0 + \\frac{a_1}{b_1+\\frac{a_2}{b_2+\\frac{a_3}{b_3+\\frac{a_4}{b_4+\\ldots}}}}\" alt=\"Continued fraction\"\u003e --\u003e\n\n```math\nx = b_0 + \\frac{a_1}{b_1+\\frac{a_2}{b_2+\\frac{a_3}{b_3+\\frac{a_4}{b_4+\\ldots}}}}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"x = b_0 + \\frac{a_1}{b_1+\\frac{a_2}{b_2+\\frac{a_3}{b_3+\\frac{a_4}{b_4+\\ldots}}}}\" data-equation=\"eq:continued_fraction\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d3cef42cbeb8499623814933ed4d906a345cec32/lib/node_modules/@stdlib/math/iter/utils/continued-fraction/docs/img/equation_continued_fraction.svg\" alt=\"Continued fraction\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nIf `a_i = 1` for all `i`, the above expression reduces to a **simple continued fraction**.\n\n\u003c!-- \u003cequation class=\"equation\" label=\"eq:simple_continued_fraction\" align=\"center\" raw=\"x = b_0 + \\frac{1}{b_1+\\frac{1}{b_2+\\frac{1}{b_3+\\frac{1}{b_4+\\ldots}}}}\" alt=\"Simple continued fraction\"\u003e --\u003e\n\n```math\nx = b_0 + \\frac{1}{b_1+\\frac{1}{b_2+\\frac{1}{b_3+\\frac{1}{b_4+\\ldots}}}}\n```\n\n\u003c!-- \u003cdiv class=\"equation\" align=\"center\" data-raw-text=\"x = b_0 + \\frac{1}{b_1+\\frac{1}{b_2+\\frac{1}{b_3+\\frac{1}{b_4+\\ldots}}}}\" data-equation=\"eq:simple_continued_fraction\"\u003e\n    \u003cimg src=\"https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@d3cef42cbeb8499623814933ed4d906a345cec32/lib/node_modules/@stdlib/math/iter/utils/continued-fraction/docs/img/equation_simple_continued_fraction.svg\" alt=\"Simple continued fraction\"\u003e\n    \u003cbr\u003e\n\u003c/div\u003e --\u003e\n\n\u003c!-- \u003c/equation\u003e --\u003e\n\nwhere the values `b_i` are called the **coefficients** or **terms** of the continued fraction.\n\n\u003c/section\u003e\n\n\u003c!-- /.intro --\u003e\n\n\u003c!-- Package usage documentation. --\u003e\n\n\u003csection class=\"installation\"\u003e\n\n## Installation\n\n```bash\nnpm install @stdlib/math-iter-utils-continued-fraction\n```\n\nAlternatively,\n\n-   To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]).\n-   If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions).\n-   For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]).\n\nThe [branches.md][branches-url] file summarizes the available branches and displays a diagram illustrating their relationships.\n\nTo view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.\n\n\u003c/section\u003e\n\n\u003csection class=\"usage\"\u003e\n\n## Usage\n\n```javascript\nvar iterContinuedFraction = require( '@stdlib/math-iter-utils-continued-fraction' );\n```\n\n#### iterContinuedFraction( iterator\\[, options] )\n\nEvaluates the terms of a continued fraction.\n\n```javascript\nvar array2iterator = require( '@stdlib/array-to-iterator' );\n\nvar arr = array2iterator( [ 3, 4, 12, 4 ] );\n\nvar v = iterContinuedFraction( arr );\n// returns ~3.245\n```\n\nThe function supports the following `options`:\n\n-   **iter**: maximum number of iterations. Default: `1e308`.\n-   **tol**: tolerance at which to terminate further evaluation of the continued fraction. Default: [floating-point epsilon][@stdlib/constants/float64/eps].\n\nTo explicitly cap the maximum number of iterations, set the `iter` option.\n\n```javascript\nvar array2iterator = require( '@stdlib/array-to-iterator' );\n\nvar arr = array2iterator( [ 3, 4, 12, 4 ] );\n\nvar opts = {\n    'iter': 2\n};\nvar v = iterContinuedFraction( arr, opts );\n// returns 3.25\n```\n\nThe function terminates continued fraction evaluation once the difference between continued fraction approximations is sufficiently small. The default tolerance is [floating-point epsilon][@stdlib/constants/float64/eps] (`~2.22e-16`). Once an update to a continued fraction approximation is less than or equal to this tolerance, the function terminates evaluation. To adjust the tolerance (e.g., to return a rough approximation), set the `tol` option.\n\n```javascript\nvar iterContinuedFractionSeq = require( '@stdlib/math-iter-sequences-continued-fraction' );\n\nvar opts = {\n    'tol': 1.0e-7\n};\nvar it = iterContinuedFractionSeq( 3.141592653589793, opts );\n// returns \u003cObject\u003e\n\nvar v = iterContinuedFraction( it );\n// returns ~3.14159292\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.usage --\u003e\n\n\u003c!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"notes\"\u003e\n\n## Notes\n\n-   If an iterated value is non-numeric (including `NaN`), the function returns `NaN`. If non-numeric iterated values are possible, you are advised to provide an [`iterator`][mdn-iterator-protocol] which type checks and handles non-numeric values accordingly.\n\n\u003c/section\u003e\n\n\u003c!-- /.notes --\u003e\n\n\u003c!-- Package usage examples. --\u003e\n\n\u003csection class=\"examples\"\u003e\n\n## Examples\n\n\u003c!-- eslint no-undef: \"error\" --\u003e\n\n```javascript\nvar iterContinuedFractionSeq = require( '@stdlib/math-iter-sequences-continued-fraction' );\nvar PI = require( '@stdlib/constants-float64-pi' );\nvar iterContinuedFraction = require( '@stdlib/math-iter-utils-continued-fraction' );\n\n// Create an iterator for returning the list of continued fraction terms:\nvar it = iterContinuedFractionSeq( PI );\n\n// Reconstitute the original value:\nvar v = iterContinuedFraction( it );\n// returns \u003cnumber\u003e\n\nconsole.log( 'Value: %d.', v );\n```\n\n\u003c/section\u003e\n\n\u003c!-- /.examples --\u003e\n\n\u003c!-- Section to include cited references. If references are included, add a horizontal rule *before* the section. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"references\"\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.references --\u003e\n\n\u003c!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --\u003e\n\n\u003csection class=\"related\"\u003e\n\n* * *\n\n## See Also\n\n-   \u003cspan class=\"package-name\"\u003e[`@stdlib/math-iter/sequences/continued-fraction`][@stdlib/math/iter/sequences/continued-fraction]\u003c/span\u003e\u003cspan class=\"delimiter\"\u003e: \u003c/span\u003e\u003cspan class=\"description\"\u003ecreate an iterator which generates a list of all continued fraction terms which can be obtained given the precision of a provided number.\u003c/span\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.related --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\n\u003csection class=\"main-repo\" \u003e\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 \u0026copy; 2016-2025. The Stdlib [Authors][stdlib-authors].\n\n\u003c/section\u003e\n\n\u003c!-- /.stdlib --\u003e\n\n\u003c!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --\u003e\n\n\u003csection class=\"links\"\u003e\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/math-iter-utils-continued-fraction.svg\n[npm-url]: https://npmjs.org/package/@stdlib/math-iter-utils-continued-fraction\n\n[test-image]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/actions/workflows/test.yml/badge.svg?branch=main\n[test-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/actions/workflows/test.yml?query=branch:main\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-iter-utils-continued-fraction/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/math-iter-utils-continued-fraction?branch=main\n\n\u003c!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/math-iter-utils-continued-fraction.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/math-iter-utils-continued-fraction/main\n\n--\u003e\n\n[chat-image]: https://img.shields.io/gitter/room/stdlib-js/stdlib.svg\n[chat-url]: https://app.gitter.im/#/room/#stdlib-js_stdlib:gitter.im\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-iter-utils-continued-fraction/tree/deno\n[deno-readme]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/tree/umd\n[umd-readme]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/tree/esm\n[esm-readme]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/math-iter-utils-continued-fraction/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-iter-utils-continued-fraction/main/LICENSE\n\n[mdn-iterator-protocol]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Iteration_protocols#The_iterator_protocol\n\n[@stdlib/constants/float64/eps]: https://github.com/stdlib-js/constants-float64-eps\n\n\u003c!-- \u003crelated-links\u003e --\u003e\n\n[@stdlib/math/iter/sequences/continued-fraction]: https://github.com/stdlib-js/math-iter-sequences-continued-fraction\n\n\u003c!-- \u003c/related-links\u003e --\u003e\n\n\u003c/section\u003e\n\n\u003c!-- /.links --\u003e\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fmath-iter-utils-continued-fraction","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fstdlib-js%2Fmath-iter-utils-continued-fraction","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fstdlib-js%2Fmath-iter-utils-continued-fraction/lists"}