Big Integer and Javascript

The other day I was testing the graphics library D3.js and wanted to represent the Fibonacci series.

So I did a quick program in Node.js:

var fibonacci = [ 0, 1 ];

var position=2;

var sum=0;

while (position<100) {

	fibonacci[position]=fibonacci[position-1]+fibonacci[position-2];
	position++;
	
}

console.log(JSON.stringify(fibonacci));

This program return first 100 positions.

Doing mental arithmetic I realized that in the 79 position of the array (the sum of the position 77 and 78) was wrong!

 5527939700884757
 8944394323791464 
14472334024676220!!!

I read a little on the internet and the largest number that is represented as an integer in JavaScript is 2 ^ 53.

Let’s do a little sample.

var big=Math.pow(2, 53);
var big2=big+1;

console.log('big: '+big);
console.log('big2: '+big2);

OMG it’s true!

So I changed initial program by this:

var limit=Math.pow(2, 53);

var fibonacci = [ 0, 1 ];

var position=2;

var controller=0;
var sum=0;

while (controller==0) {

	sum=fibonacci[position-1]+fibonacci[position-2];

	if (sum>limit) {
		controller=1;
	} else {
		fibonacci[position]=sum;	
		position++;
	}
	
}

position--;

console.log('The last right position is: ' + position);
console.log(JSON.stringify(fibonacci));

So the last right position is 78 because 14472334024676221 > 9007199254740992 :-)

Be careful with this. Next week I’ll try this library big-integer.