How large can integers be in Javascript before roundoff error?

Question

The code below:

function lookForMatches()
{
    for (var a=1;a<=2000;a++)
    {
        for (var b=1;b<=a;b++)
        {
            c=a*a*a+b*b*b;
            d=5*c*c;
            e=d-4;
            f=d+4;
            g=Math.floor(Math.sqrt(e))*Math.floor(Math.sqrt(e))
            h=Math.floor(Math.sqrt(f))*Math.floor(Math.sqrt(f))
            if (g==e||h==f)
                document.getElementById("matches").innerHTML+=c+" ";
        }
    }
    document.getElementById("matches").innerHTML+="Done."
}

is supposed to check for Fibonacci numbers in the sequence of the sums of positive cubes, but the output is:

2 5075441272 2976917960 7114243176 Done.

I ran the Fibonacci test manually in Windows Calculator, and although the square root of (5*5075441272²±4) is extremely close to an integer value, it's definitely not an integer! I'm not even certain if the number 5075441272 is actually a valid sum of cubes. How large can integer values be in Javascript without introducing roundoff error?

In JavaScript, all numbers are `double`s (double-precision binary floating-point numbers). It has 53 bits of precision. — The Paramagnetic Croissant, May 28 '14 at 20:15
what do you mean by round-off for an integer? round to what? — Christian Fritz, May 28 '14 at 20:16
@ChristianFritz In JavaScript there are no true int values. All numbers are type Number, so some sort of internal rounding must be occurring. — Brian J. Fink, May 28 '14 at 20:21
@michael_n Largest value error-free is not the same as max value. SO NOT A DUPLICATE! — Brian J. Fink, May 28 '14 at 20:25
@Samuel Number.MAX_VALUE returns 1.7976931348623157e+308 so it's not useful to me. — Brian J. Fink, May 28 '14 at 21:01
@michael_n I was mistaken. I guess my question is a duplicate after all. — Brian J. Fink, May 28 '14 at 21:15
@ChristianFritz Sorry, I put your name on the comment about the "duplicate" controversy by mistake, so please disregard it. — Brian J. Fink, May 28 '14 at 21:17

score 1 · Accepted Answer · edited May 23 '17 at 10:26

1

The max size is +/- 9007199254740992

ECMA SPEC

Also it appears that this has been answered here as well : What is JavaScript's highest integer value that a Number can go to without losing precision?

edited May 23 '17 at 10:26

Community

1
1

answered May 28 '14 at 20:21

ckruszynsky

533
3
7

That explains the error I experienced! – Brian J. Fink May 28 '14 at 20:30
New output: `2 Done.` – Brian J. Fink May 28 '14 at 20:38

How large can integers be in Javascript before roundoff error?

1 Answers1