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Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"},"license":"Apache-2.0","homepage":"https://stdlib.io","keywords":["stdlib","stdmath","mathematics","math","statistics","stats","prng","rng","pseudorandom","random","rand","randn","normal","gaussian","bell","generator","improved","ziggurat","doornik","seed","seedable"],"repository":{"type":"git","url":"git://github.com/stdlib-js/random-base-improved-ziggurat.git"},"description":"Normally distributed pseudorandom numbers using the improved Ziggurat method.","contributors":[{"name":"The Stdlib Authors","url":"https://github.com/stdlib-js/stdlib/graphs/contributors"}],"maintainers":[{"name":"stdlib-bot","email":"kgryte+stdlibbot@gmail.com"},{"name":"kgryte","email":"kgryte@gmail.com"},{"name":"planeshifter","email":"pgb@andrew.cmu.edu"},{"name":"rreusser","email":"rsreusser@gmail.com"}],"readme":"<!--\n\n@license Apache-2.0\n\nCopyright (c) 2018 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-->\n\n\n<details>\n  <summary>\n    About stdlib...\n  </summary>\n  <p>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.</p>\n  <p>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.</p>\n  <p>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.</p>\n  <p>To join us in bringing numerical computing to the web, get started by checking us out on <a href=\"https://github.com/stdlib-js/stdlib\">GitHub</a>, and please consider <a href=\"https://opencollective.com/stdlib\">financially supporting stdlib</a>. We greatly appreciate your continued support!</p>\n</details>\n\n# Improved Ziggurat Method\n\n[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->\n\n> Standard normally distributed pseudorandom numbers using the [Improved Ziggurat][ziggurat-algorithm] method.\n\n<section class=\"installation\">\n\n## Installation\n\n```bash\nnpm install @stdlib/random-base-improved-ziggurat\n```\n\n</section>\n\n<section class=\"usage\">\n\n## Usage\n\n```javascript\nvar randn = require( '@stdlib/random-base-improved-ziggurat' );\n```\n\n#### randn()\n\nReturns a standard normally distributed pseudorandom number.\n\n```javascript\nvar r = randn();\n// returns <number>\n```\n\n#### randn.factory( \\[options] )\n\nReturns a pseudorandom number generator (PRNG) for generating standard normally distributed pseudorandom numbers.\n\n```javascript\nvar rand = randn.factory();\n```\n\nThe function accepts the following `options`:\n\n-   **prng**: pseudorandom number generator for generating uniformly distributed pseudorandom numbers on the interval `[0,1)`. If provided, the function **ignores** both the `state` and `seed` options. In order to seed the returned pseudorandom number generator, one must seed the provided `prng` (assuming the provided `prng` is seedable).\n-   **seed**: pseudorandom number generator seed.\n-   **state**: a [`Uint32Array`][@stdlib/array/uint32] containing pseudorandom number generator state. If provided, the function ignores the `seed` option.\n-   **copy**: `boolean` indicating whether to copy a provided pseudorandom number generator state. Setting this option to `false` allows sharing state between two or more pseudorandom number generators. Setting this option to `true` ensures that a returned generator has exclusive control over its internal state. Default: `true`.\n\nTo use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the `prng` option.\n\n```javascript\nvar minstd = require( '@stdlib/random-base-minstd' );\n\nvar rand = randn.factory({\n    'prng': minstd.normalized\n});\n\nvar r = rand();\n// returns <number>\n```\n\nTo seed a pseudorandom number generator, set the `seed` option.\n\n```javascript\nvar rand1 = randn.factory({\n    'seed': 12345\n});\n\nvar r1 = rand1();\n// returns <number>\n\nvar rand2 = randn.factory({\n    'seed': 12345\n});\n\nvar r2 = rand2();\n// returns <number>\n\nvar bool = ( r1 === r2 );\n// returns true\n```\n\nTo return a generator having a specific initial state, set the generator `state` option.\n\n```javascript\nvar rand;\nvar bool;\nvar r;\nvar i;\n\n// Generate pseudorandom numbers, thus progressing the generator state:\nfor ( i = 0; i < 1000; i++ ) {\n    r = randn();\n}\n\n// Create a new PRNG initialized to the current state of `randn`:\nrand = randn.factory({\n    'state': randn.state\n});\n\n// Test that the generated pseudorandom numbers are the same:\nbool = ( rand() === randn() );\n// returns true\n```\n\n#### randn.NAME\n\nThe generator name.\n\n```javascript\nvar str = randn.NAME;\n// returns 'improved-ziggurat'\n```\n\n#### randn.PRNG\n\nThe underlying pseudorandom number generator for uniformly distributed numbers on the interval `[0,1)`.\n\n```javascript\nvar prng = randn.PRNG;\n// returns <Function>\n```\n\n#### randn.seed\n\nThe value used to seed `randn()`.\n\n```javascript\nvar rand;\nvar r;\nvar i;\n\n// Generate pseudorandom values...\nfor ( i = 0; i < 100; i++ ) {\n    r = randn();\n}\n\n// Generate the same pseudorandom values...\nrand = randn.factory({\n    'seed': randn.seed\n});\nfor ( i = 0; i < 100; i++ ) {\n    r = rand();\n}\n```\n\nIf provided a PRNG for uniformly distributed numbers, this value is `null`.\n\n<!-- eslint-disable stdlib/no-builtin-math -->\n\n```javascript\nvar rand = randn.factory({\n    'prng': Math.random\n});\n\nvar seed = rand.seed;\n// returns null\n```\n\n#### randn.seedLength\n\nLength of generator seed.\n\n```javascript\nvar len = randn.seedLength;\n// returns <number>\n```\n\nIf provided a PRNG for uniformly distributed numbers, this value is `null`.\n\n<!-- eslint-disable stdlib/no-builtin-math -->\n\n```javascript\nvar rand = randn.factory({\n    'prng': Math.random\n});\n\nvar len = rand.seedLength;\n// returns null\n```\n\n#### randn.state\n\nWritable property for getting and setting the generator state.\n\n```javascript\nvar r = randn();\n// returns <number>\n\nr = randn();\n// returns <number>\n\n// ...\n\n// Get a copy of the current state:\nvar state = randn.state;\n// returns <Uint32Array>\n\nr = randn();\n// returns <number>\n\nr = randn();\n// returns <number>\n\n// Reset the state:\nrandn.state = state;\n\n// Replay the last two pseudorandom numbers:\nr = randn();\n// returns <number>\n\nr = randn();\n// returns <number>\n\n// ...\n```\n\nIf provided a PRNG for uniformly distributed numbers, this value is `null`.\n\n<!-- eslint-disable stdlib/no-builtin-math -->\n\n```javascript\nvar rand = randn.factory({\n    'prng': Math.random\n});\n\nvar state = rand.state;\n// returns null\n```\n\n#### randn.stateLength\n\nLength of generator state.\n\n```javascript\nvar len = randn.stateLength;\n// returns <number>\n```\n\nIf provided a PRNG for uniformly distributed numbers, this value is `null`.\n\n<!-- eslint-disable stdlib/no-builtin-math -->\n\n```javascript\nvar rand = randn.factory({\n    'prng': Math.random\n});\n\nvar len = rand.stateLength;\n// returns null\n```\n\n#### randn.byteLength\n\nSize (in bytes) of generator state.\n\n```javascript\nvar sz = randn.byteLength;\n// returns <number>\n```\n\nIf provided a PRNG for uniformly distributed numbers, this value is `null`.\n\n<!-- eslint-disable stdlib/no-builtin-math -->\n\n```javascript\nvar rand = randn.factory({\n    'prng': Math.random\n});\n\nvar sz = rand.byteLength;\n// returns null\n```\n\n#### randn.toJSON()\n\nSerializes the pseudorandom number generator as a JSON object.\n\n```javascript\nvar o = randn.toJSON();\n// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }\n```\n\nIf provided a PRNG for uniformly distributed numbers, this method returns `null`.\n\n<!-- eslint-disable stdlib/no-builtin-math -->\n\n```javascript\nvar rand = randn.factory({\n    'prng': Math.random\n});\n\nvar o = rand.toJSON();\n// returns null\n```\n\n</section>\n\n<!-- /.usage -->\n\n<section class=\"notes\">\n\n## Notes\n\n-   If PRNG state is \"shared\" (meaning a state array was provided during PRNG creation and **not** copied) and one sets the generator state to a state array having a different length, the PRNG does **not** update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for **each** relevant PRNG must be **explicitly** set.\n-   If PRNG state is \"shared\" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).\n\n</section>\n\n<!-- /.notes -->\n\n<section class=\"examples\">\n\n## Examples\n\n<!-- eslint no-undef: \"error\" -->\n\n```javascript\nvar randn = require( '@stdlib/random-base-improved-ziggurat' );\n\nvar seed;\nvar rand;\nvar i;\n\n// Generate pseudorandom numbers...\nfor ( i = 0; i < 100; i++ ) {\n    console.log( randn() );\n}\n\n// Create a new pseudorandom number generator...\nseed = 1234;\nrand = randn.factory({\n    'seed': seed\n});\nfor ( i = 0; i < 100; i++ ) {\n    console.log( rand() );\n}\n\n// Create another pseudorandom number generator using a previous seed...\nrand = randn.factory({\n    'seed': randn.seed\n});\nfor ( i = 0; i < 100; i++ ) {\n    console.log( rand() );\n}\n```\n\n</section>\n\n<!-- /.examples -->\n\n* * *\n\n<section class=\"references\">\n\n## References\n\n-   Doornik, Jurgen A. 2005. \"An Improved Ziggurat Method to Generate Normal Random Samples.\" [&lt;https://www.doornik.com/research/ziggurat.pdf>][@doornik:2005].\n-   Marsaglia, George, and Wai Wan Tsang. 2000. \"The Ziggurat Method for Generating Random Variables.\" _Journal of Statistical Software_ 5 (1): 1–7. doi:[10.18637/jss.v005.i08][@marsaglia:2000b].\n-   Marsaglia, George. 1964. \"Generating a Variable from the Tail of the Normal Distribution.\" _Technometrics_ 6 (1): 101–2. doi:[10.1080/00401706.1964.10490150][@marsaglia:1964b].\n\n</section>\n\n<!-- /.references -->\n\n<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->\n\n<section class=\"related\">\n\n* * *\n\n## See Also\n\n-   <span class=\"package-name\">[`@stdlib/random-iter/improved-ziggurat`][@stdlib/random/iter/improved-ziggurat]</span><span class=\"delimiter\">: </span><span class=\"description\">create an iterator for generating pseudorandom numbers drawn from a standard normal distribution using the Improved Ziggurat algorithm.</span>\n-   <span class=\"package-name\">[`@stdlib/random-streams/improved-ziggurat`][@stdlib/random/streams/improved-ziggurat]</span><span class=\"delimiter\">: </span><span class=\"description\">create a readable stream for generating pseudorandom numbers drawn from a standard normal distribution using the Improved Ziggurat algorithm.</span>\n\n</section>\n\n<!-- /.related -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n\n<section class=\"main-repo\" >\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 &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].\n\n</section>\n\n<!-- /.stdlib -->\n\n<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->\n\n<section class=\"links\">\n\n[npm-image]: http://img.shields.io/npm/v/@stdlib/random-base-improved-ziggurat.svg\n[npm-url]: https://npmjs.org/package/@stdlib/random-base-improved-ziggurat\n\n[test-image]: https://github.com/stdlib-js/random-base-improved-ziggurat/actions/workflows/test.yml/badge.svg?branch=v0.2.2\n[test-url]: https://github.com/stdlib-js/random-base-improved-ziggurat/actions/workflows/test.yml?query=branch:v0.2.2\n\n[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/random-base-improved-ziggurat/main.svg\n[coverage-url]: https://codecov.io/github/stdlib-js/random-base-improved-ziggurat?branch=main\n\n<!--\n\n[dependencies-image]: https://img.shields.io/david/stdlib-js/random-base-improved-ziggurat.svg\n[dependencies-url]: https://david-dm.org/stdlib-js/random-base-improved-ziggurat/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/random-base-improved-ziggurat/tree/deno\n[deno-readme]: https://github.com/stdlib-js/random-base-improved-ziggurat/blob/deno/README.md\n[umd-url]: https://github.com/stdlib-js/random-base-improved-ziggurat/tree/umd\n[umd-readme]: https://github.com/stdlib-js/random-base-improved-ziggurat/blob/umd/README.md\n[esm-url]: https://github.com/stdlib-js/random-base-improved-ziggurat/tree/esm\n[esm-readme]: https://github.com/stdlib-js/random-base-improved-ziggurat/blob/esm/README.md\n[branches-url]: https://github.com/stdlib-js/random-base-improved-ziggurat/blob/main/branches.md\n\n[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/random-base-improved-ziggurat/main/LICENSE\n\n[ziggurat-algorithm]: https://en.wikipedia.org/wiki/Ziggurat_algorithm\n\n[@doornik:2005]: https://www.doornik.com/research/ziggurat.pdf\n\n[@marsaglia:2000b]: http://dx.doi.org/10.18637/jss.v005.i08\n\n[@marsaglia:1964b]: https://doi.org/10.1080/00401706.1964.10490150\n\n[@stdlib/array/uint32]: https://www.npmjs.com/package/@stdlib/array-uint32\n\n<!-- <related-links> -->\n\n[@stdlib/random/iter/improved-ziggurat]: https://www.npmjs.com/package/@stdlib/random-iter-improved-ziggurat\n\n[@stdlib/random/streams/improved-ziggurat]: https://www.npmjs.com/package/@stdlib/random-streams-improved-ziggurat\n\n<!-- </related-links> -->\n\n</section>\n\n<!-- /.links -->\n","readmeFilename":"README.md"}