rational approximation with bounded denominator
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README.md

frac

Rational approximation to a floating point number with bounded denominator.

Uses the 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:

$ 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:

$ 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:

> // 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:

>>> 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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