You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
129 lines
4.0 KiB
129 lines
4.0 KiB
# 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)
|