Does Javascript handle integer overflow and underflow? If yes, how?

Question

We know that Java does not handle underflows and overflows, but how does Javascript handle these for integers?

Does it go back to a minimum/maximum? If yes, which minimum/maximum?

I need to split a string and compute a hash value based on its characters.

Answer 1

In a simple test, when I try this:

var max = Number.MAX_VALUE;
var x = max + 10;

var min = Number.MIN_VALUE;
var y = min / 10;

I find that x and max have the same value (in Chrome, IE and Firefox) so it appears that some overflows are just pegged to the max value. And, y gets pegged to 0 so some underflows seem to go to zero.

Ahhh, but it is not quite that simple. Not all overflows go to Number.MAX_VALUE and not all underflows go to Number.MIN_VALUE. If you do this:

var max = Number.MAX_VALUE;
var z = max * 2;

Then, z will be Infinity.

It turns out that it depends upon how far you overflow/underflow. If you go too far, you will get INFINITY instead. This is because of the use of IEEE 754 round-to-nearest mode where the max value can be considered nearer than infinity. See Adding to Number.MAX_VALUE for more detail. Per that answer, values of 1.7976931348623158 × 10³⁰⁸ or greater round to infinity. Values between Number.MAX_VALUE and that will round to Number.MAX_VALUE.

To, make things even more complicated, there is also something as gradual underflow which Javascript supports. This is where the mantissa of the floating point value has leading zeroes in it. Gradual underflow allows floating point to represent some smaller numbers that it could not represent without that, but they are represented at a reduced precision.

You can see exactly where the limits are:

>>> Number.MAX_VALUE + 9.979201e291
1.7976931348623157e+308
>>> Number.MAX_VALUE + 9.979202e291
Infinity

Here's a runnable snippet you can try in any browser:

var max = Number.MAX_VALUE;
var x = max + 10;

var min = Number.MIN_VALUE;
var y = min / 10;

var z = max * 2;

document.getElementById("max").innerHTML = max;
document.getElementById("max10").innerHTML = x;
document.getElementById("min").innerHTML = min;
document.getElementById("min10").innerHTML = y;
document.getElementById("times2").innerHTML = z;

body {
    font-family: "Courier New"; 
    white-space:nowrap;
}

Number.MAX_VALUE &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= <span id="max"></span><br>
Number.MAX_VALUE + 10 = <span id="max10"></span><br>
<br>
Number.MIN_VALUE &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= <span id="min"></span><br>
Number.MIN_VALUE / 10 = <span id="min10"></span><br>  
<br>
Number.MAX_VALUE * 2 &nbsp;= <span id="times2"></span><br>

Answer 2

The maximum and minimum is +/- 9007199254740992

Try this:

alert([Number.MAX_VALUE, Number.MIN_VALUE]);

From here:-

Note that all the positive and negative integers whose magnitude is no greater than 2⁵³ are representable in the Number type (indeed, the integer 0 has two representations, +0 and −0).

Test this:-

var x = 9007199254740992;
var y = -x;
x == x + 1; // true !
y == y - 1; // also true !