Rational approximation with bounded denominator

npm install frac
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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", which appears to be used by spreadsheet programs for displaying fractions

JS Installation and Usage

In node:

$ npm install frac

In the browser:

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

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 (default); if false, improper

The return value is an array of the form [quot, num, den] where quot==0 for improper fractions.

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


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)" alpha

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