# 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 SheetJS Libraries to
replicate fraction formats.
## Installation
### JS
With [`npm`](https://www.npmjs.org/package/frac):
```bash
$ npm install frac
```
In the browser:
```html
```
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)