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.

jfriend00 · Accepted Answer · 2018-07-14T15:53:29.100

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>

I tried with -Number.MAX_VALUE and they are also the same. So no going back to minimum and maximum.... — Jérôme Verstrynge, Sep 27 '13 at 15:58
Yet `Number.MAX_VALUE * 2` results in `Infinity`. "Go figure" as they say. — Bernhard Hofmann, Apr 15 '14 at 15:03
With floating point numbers addition of a `x` small number with with a much bigger number `(2^54*x)` is simply ignored due to rounding, while multiplication is can always be executed (until the exponent overflows). For anyone left wondering of bernhard result. — HopefullyHelpful, Jan 26 '16 at 22:00
`1.7976931348623157e+308 + 0.0000000000000001e+308 == Infinity` — Isaac, Jan 15 '18 at 23:32

score 4 · Answer 2 · edited Oct 26 '20 at 08:25

4

The maximum and minimum is +/- 9007199254740992

Try these Number type properties:

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

From the ECMAScript 2020 language specification, section "The Number Type":

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

Test:

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

edited Oct 26 '20 at 08:25

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answered Sep 27 '13 at 15:46

Rahul Tripathi

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Ok, but how does JS handle overflow and underflows? – Jérôme Verstrynge Sep 27 '13 at 15:47
6

I don't think this actually answers the OP's question. – jfriend00 Sep 27 '13 at 15:47
@jfriend00:- Updated my answer with a link which can help. Do correct me if I am completely missing the obvious!!! :) – Rahul Tripathi Sep 27 '13 at 15:51
Rahul, did you actually run alert([Number.MAX_VALUE, Number.MIN_VALUE]); in JsFiddle? I don't think Number.MIN_VALUE is what you think... – Jérôme Verstrynge Sep 27 '13 at 15:57
@JVerstry:- I have just given an idea of showing that in JsFiddle..Is that making a wrong sense?? – Rahul Tripathi Sep 27 '13 at 15:58
3

Link in the answer is SPAM – MonteCristo Mar 04 '20 at 23:59

tsh · Answer 3 · 2022-09-29T03:06:35.030

`Number`

In JavaScript, number type is 64 bit IEEE 754 floating point number which is not an integer. So it don't follow common patterns of integer overflow / underflow behavior in other languages.

As the floating point number use 53 bits for base part. It may represent numbers in range Number.MIN_SAFE_INTEGER to Number.MAX_SAFE_INTEGER (-2⁵³+1 to 2⁵³-1) without floating point errors. For numbers out of this range, it may be rounded to nearest number available, or may be Infinity if it is too large.

Bit-wise operator

Bit-wise operator treat operand 32 bit integers. And common integer overflow may happened as in other languages. Only last 32 bits may be kept after calculate. For example, 3<<31 would results -2147483648.

>>> treat operand as unsigned 32 bit integers. All other operator treat operand as signed 32 bit integers. If you want to convert signed integer to unsigned, you may write value >>> 0 to do the trick. To convert back, use value | 0.

If you want to shift an integer with 33, it will actually be shifted with 1.

`BigInt`

Just like Java's java.math.BigInteger, BigInt supports unbounded integers (still bound by your memory limit though). So integer overflow may never happen here.

TypedArray

For most TypedArray types, when an integer out of supported range assigned, it got truncated as what other languages do when converting integers, by keeping least significant bits. For example new Int8Array([1000])[0] got -24.

Uint8ClampedArray is a bit different from other TypedArray's. Uint8ClampedArray supports integers in range 0 ~ 255. When numbers out of range is used, 0 or 255 will be set instead.

asm.js

The same rules for bit-wise operator applied here. The value would be trucked back as what | 0 or >>> 0 do.

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

3 Answers3

`Number`

Bit-wise operator

`BigInt`

TypedArray

asm.js

Linked

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