fibonacci-fast

A fast node.js module for working with the Fibonacci sequence

Install

$ npm install fibonacci-fast

Usage

Documentation can be found here

fibonacci.get(k)

Get the kth index of the Fibonacci sequence

var fibonacci = require('fibonacci-fast');
var result = fibonacci.get(3000);

The result will be a JavaScript object containing the following:

{
  number: ...,
  next: ...,
  index: 3000,
  ms: 21
}

Where number is a big number representing Fibonacci[3000] and next is also a big number representing Fibonacci[3001]. The ms is the amount of time (in milliseconds) that it took to get the result.

fibonacci.find(num)

Find the index of a given Fibonacci number

var result = fibonacci.find(13);
var index = result.index; // index = 7

The result will be the same form as the result of the fibonacci.get(n) method, so the index can be retrieved easily with result.index. This also means that the number and next values are returned in the result variable as well.

fibonacci.is(num)

Checks if a given number is a Fibonacci number

fibonacci.is(34); // true
fibonacci.is(35); // false

fibonacci.iterator([k, n])

Create a Fibonacci sequence iterator. Where k and n are optional parameters defining the starting index of the iterator and the max number of iterations respectively. If k is not given, then the iterator will start at index 0. If n is not given the iterator will allow infinite iterations.

With starting index and limit

var fibs = fibonacci.iterator(5, 5);

for (let fib of fibs) {
  console.log(`F[${fib.index}] = ${fib.number.toString()}`);
}

The result:

F[5] = 5
F[6] = 8
F[7] = 13
F[8] = 21
F[9] = 34

No starting index or limit

var fibs = fibonacci.iterator();

for (let i = 0; i < 5; i++) {
  var fib = fibs.next().value;
  console.log(`F[${fib.index}] = ${fib.number.toString()}`);
}

The result:

F[0] = 0
F[1] = 1
F[2] = 1
F[3] = 2
F[4] = 3

fibonacci.array(k0, k1)

Grab an array of the Fibonacci sequence. Where k0 is the starting index, and k1 is the ending index.

NOTE: the number at k1 will not be included in the array

var array = fibonacci.array(5, 11);

The result will be an array of objects with the following form:

{
  number: ...,
  next: ...,
  index: ...
}

In order to get an array containing the actual Fibonacci numbers and not the objects, you could map the array like so:

var array = fibonacci.array(5, 11).map(x => x.number.toString());

and the resulting array would look like this:

[ '5', '8', '13', '21', '34', '55' ]

Fast Doubling Algorithm

This module utilizes the fast doubling algorithm which allows for much faster calculations of Fibonacci numbers than the traditional recurrence method.

The fast doubling algorithm takes Θ(log n) operations, and the recurrence algorithm takes Θ(n).

Big.js

The fibonacci-fast module utilizes the big.js library to handle large numbers.