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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 [](https://saucelabs.com/u/frac) [](https://travis-ci.org/SheetJS/frac) [](https://coveralls.io/r/SheetJS/frac?branch=master) [](https://npmjs.org/package/frac) [](https://david-dm.org/sheetjs/frac) [](https://ghit.me/repo/sheetjs/js-xlsx) [](https://github.com/SheetJS/frac)

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