SheetJS
e0b3a1e75c
Note: The Aberth algorithm is sensitive to input errors New tests trigger an infinite loop under old tolerance, work fine with new.
1.5 KiB
1.5 KiB
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:
xthe number we wish to approximateDthe maximum denominatormixedif 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)"