# frac

Rational approximation with bounded denominator

``npm install frac``

# frac

Rational approximation to a floating point number with bounded denominator.

Uses the Mediant Method https://en.wikipedia.org/wiki/Mediant_(mathematics)

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

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)"

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