Why does this Fibonacci number function return infinity for the 4000th value?

Question

function fibo() {
var first,second,add;
for(var i=0;i<4000;i++){
    if(i === 0){
        first = 1;
        second = 2;
    }
    add = first + second;
    first         


        

Answer 1

Although already accepted, I think I can offer a simpler solution. Just store numbers in arrays, one digit per element, and perform addition like you did in elementary school - "in columns". It goes like this:

function add(a, b) {
    while (a.length < b.length) a.unshift(0);
    while (a.length > b.length) b.unshift(0);
    var carry = 0, sum = []
    for (var i = a.length - 1; i >= 0; i--) {
        var s = a[i] + b[i] + carry;
        if (s >= 10) {
            s = s - 10;
            carry = 1;
        } else {
            carry = 0;
        }
        sum.unshift(s);
    }
    if (carry)
        sum.unshift(carry);
    return sum;
}

And the fibonacci function is like this:

function fib(n) {
    var f1 = [0];
    var f2 = [1];

    while (n--) {
        var f3 = add(f1, f2)
        f1 = f2;
        f2 = f3;
    }
    return f1.join("");
}

Seems totally ineffective, but only takes fractions of second to get fib(4000) on a 2.3GHz macbook.

Answer 2

Because Number.MAX_VALUE + Number.MAX_VALUE === Infinity

The issue is that sum exceeds JavaScripts capabilities for storing numeric values.