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node_modules/frac/README.md

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+# frac
+
+Rational approximation to a floating point number with bounded denominator.
+
+Uses the [Mediant Method](https://en.wikipedia.org/wiki/Mediant_method).
+
+This module also provides an implementation of the continued fraction method as
+described by Aberth in "A method for exact computation with rational numbers".
+The algorithm is used in <a href="http://sheetjs.com">SheetJS Libraries</a> to
+replicate fraction formats.
+
+## Installation
+
+### JS
+
+With [`npm`](https://www.npmjs.org/package/frac):
+
+```bash
+$ npm install frac
+```
+
+In the browser:
+
+```html
+<script src="frac.js"></script>
+```
+
+The script will manipulate `module.exports` if available .  This is not always
+desirable.  To prevent the behavior, define `DO_NOT_EXPORT_FRAC`
+
+### Python
+
+From [`PyPI`](https://pypi.python.org/pypi/frac):
+
+```bash
+$ pip install frac
+```
+
+## Usage
+
+In all cases, the relevant function takes 3 arguments:
+
+ - `x` the number we wish to approximate
+ - `D` the maximum denominator
+ - `mixed` if true, return a mixed fraction; if false, improper
+
+The return value is an array of the form `[quot, num, den]` where `quot==0`
+for improper fractions.  `quot <= x` for mixed fractions, which may lead to some
+unexpected results when rendering negative numbers.
+
+### JS
+
+The exported `frac` function implements the Mediant method.
+
+`frac.cont` implements the Aberth algorithm
+
+For example:
+
+```js
+> // var frac = require('frac'); // uncomment this line if in node
+> frac(1.3, 9);              // [  0,  9, 7 ] //  1.3 ~       9/7
+> frac(1.3, 9, true);        // [  1,  2, 7 ] //  1.3 ~  1 +  2/7
+> frac(-1.3, 9);             // [  0, -9, 7 ] // -1.3 ~      -9/7
+> frac(-1.3, 9, true);       // [ -2,  5, 7 ] // -1.3 ~ -2 +  5/7
+
+> frac.cont(1.3, 9);         // [  0,  4, 3 ] //  1.3 ~       4/3
+> frac.cont(1.3, 9, true);   // [  1,  1, 3 ] //  1.3 ~  1 +  1/3
+> frac.cont(-1.3, 9);        // [  0, -4, 3 ] // -1.3 ~      -4/3
+> frac.cont(-1.3, 9, true);  // [ -2,  2, 3 ] // -1.3 ~ -2 +  2/3
+```
+
+
+### Python
+
+`frac.med` implements Mediant method.
+
+`frac.cont` implements Aberth algorithm.
+
+For example:
+
+```py
+>>> import frac
+>>> frac.med(1.3, 9)         ## [  0,  9, 7 ] ##  1.3 ~       9/7
+>>> frac.med(1.3, 9, True)   ## [  1,  2, 7 ] ##  1.3 ~  1 +  2/7
+>>> frac.med(-1.3, 9)        ## [  0, -9, 7 ] ## -1.3 ~      -9/7
+>>> frac.med(-1.3, 9, True)  ## [ -2,  5, 7 ] ## -1.3 ~ -2 +  5/7
+
+>>> frac.cont(1.3, 9)        ## [  0,  4, 3 ] ##  1.3 ~       4/3
+>>> frac.cont(1.3, 9, True)  ## [  1,  1, 3 ] ##  1.3 ~  1 +  1/3
+>>> frac.cont(-1.3, 9)       ## [  0, -4, 3 ] ## -1.3 ~      -4/3
+>>> frac.cont(-1.3, 9, True) ## [ -2,  2, 3 ] ## -1.3 ~ -2 +  2/3
+```
+
+## Testing
+
+The test TSV baselines in the `test_files` directory have four columns:
+
+- Column A contains the raw values
+- Column B format "Up to one digit (1/4)" (`denominator = 9`)
+- Column C format "Up to two digits (21/25)" (`denominator = 99`)
+- Column D format "Up to three digits (312/943)" (`denominator = 999`)
+
+`make test` will run the node-based tests.
+
+`make pytest` will run the python tests against the system Python version.
+
+`make pypytest` will run the python tests against `pypy` if installed
+
+## License
+
+Please consult the attached LICENSE file for details.  All rights not explicitly
+granted by the Apache 2.0 License are reserved by the Original Author.
+
+## Badges
+
+[![Build Status](https://saucelabs.com/browser-matrix/frac.svg)](https://saucelabs.com/u/frac)
+
+[![Build Status](https://travis-ci.org/SheetJS/frac.svg?branch=master)](https://travis-ci.org/SheetJS/frac)
+
+[![Coverage Status](http://img.shields.io/coveralls/SheetJS/frac/master.svg)](https://coveralls.io/r/SheetJS/frac?branch=master)
+
+[![NPM Downloads](https://img.shields.io/npm/dt/frac.svg)](https://npmjs.org/package/frac)
+
+[![Dependencies Status](https://david-dm.org/sheetjs/frac/status.svg)](https://david-dm.org/sheetjs/frac)
+
+[![ghit.me](https://ghit.me/badge.svg?repo=sheetjs/js-xlsx)](https://ghit.me/repo/sheetjs/js-xlsx)
+
+[![Analytics](https://ga-beacon.appspot.com/UA-36810333-1/SheetJS/frac?pixel)](https://github.com/SheetJS/frac)