Rational approximation with bounded denominator


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".

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

The exported frac function takes three 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.

For example:

> // var frac = require('frac'); // uncomment this line if in node
> frac(Math.PI,100); // [ 0, 22, 7 ]
> frac(Math.PI,100,true); // [ 3, 1, 7 ]
> frac(-Math.PI,100); // [ 0, -22, 7 ]
> frac(-Math.PI,100,true); // [ -4, 6, 7 ] // the approximation is (-4) + (6/7)

frac.cont implements the Aberth algorithm (input and output specifications match the original frac function)

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)"

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.