frac/README.md

# 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".

## Installation

### JS

With [npm](https://www.npmjs.org/package/frac):

    $ npm install frac

In the browser:

    <script src="frac.js"></script>

The script will manipulate `module.exports` if available (e.g. in a CommonJS
`require` context).  This is not always desirable.  To prevent the behavior,
define `DO_NOT_EXPORT_FRAC`

### Python

From [PyPI](https://pypi.python.org/pypi/frac):

    $ 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 ]
>>> frac.med(1.3, 9, True)   # [  1,  2, 7 ]
>>> frac.med(-1.3, 9)        # [  0, -9, 7 ]
>>> frac.med(-1.3, 9, True)  # [ -2,  5, 7 ]

>>> frac.cont(1.3, 9)        # [  0,  4, 3 ]
>>> frac.cont(1.3, 9, True)  # [  1,  1, 3 ]
>>> frac.cont(-1.3, 9)       # [  0, -4, 3 ]
>>> frac.cont(-1.3, 9, True) # [ -2,  2, 3 ]
```

## Testing

`make test` will run the node-based tests.

Tests generated from Excel have 4 columns.  To produce a similar test:

- Column A contains the raw values
- Column B format "Up to one digit (1/4)"
- Column C format "Up to two digits (21/25)"
- Column D format "Up to three digits (312/943)"

## 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.

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