Are +0 and -0 the same?

Question

JavaScript uses IEEE 754 standard to represent numbers. From Wikipedia:

Signed zero is zero with an associated sign. In ordinary arithmetic, −0 = +0 = 0. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero). This occurs in some signed number representations for integers, and in most floating point number representations. The number 0 is usually encoded as +0, but can be represented by either +0 or −0.

The IEEE 754 standard for floating point arithmetic (presently used by most computers and programming languages that support floating point numbers) requires both +0 and −0. The zeroes can be considered as a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞, division by zero is only undefined for ±0/±0 and ±∞/±∞.

The article contains further information about the different representations.

So this is the reason why, technically, both zeros have to be distinguished.

However, +0 === -0 evaluates to true. Why is that (...) ?

This behaviour is explicitly defined in section 11.9.6, the Strict Equality Comparison Algorithm (emphasis partly mine):

The comparison x === y, where x and y are values, produces true or false. Such a comparison is performed as follows:

(...)

• If Type(x) is Number, then

  1. If x is NaN, return false.
  2. If y is NaN, return false.
  3. If x is the same Number value as y, return true.
  4. If x is +0 and y is −0, return true.
  5. If x is −0 and y is +0, return true.
  6. Return false.

(...)

(The same holds for +0 == -0 btw.)

It seems logically to treat +0 and -0 as equal. Otherwise we would have to take this into account in our code and I, personally, don't want to do that ;)

---

Note:

ES2015 introduces a new comparison method, Object.is. Object.is explicitly distinguishes between -0 and +0:

Object.is(-0, +0); // false

I'll add this as an answer because I overlooked @user113716's comment.

You can test for -0 by doing this:

function isMinusZero(value) {
  return 1/value === -Infinity;
}

isMinusZero(0); // false
isMinusZero(-0); // true

I just came across an example where +0 and -0 behave very differently indeed:

Math.atan2(0, 0);  //returns 0
Math.atan2(0, -0); //returns Pi

Be careful: even when using Math.round on a negative number like -0.0001, it will actually be -0 and can screw up some subsequent calculations as shown above.

Quick and dirty way to fix this is to do smth like:

if (x==0) x=0;

or just:

x+=0;

This converts the number to +0 in case it was -0.

In the IEEE 754 standard used to represent the Number type in JavaScript, the sign is represented by a bit (a 1 indicates a negative number).

As a result, there exists both a negative and a positive value for each representable number, including 0.

This is why both -0 and +0 exist.

Answering the original title Are +0 and -0 the same?:

brainslugs83 (in comments of answer by Spudley) pointed out an important case in which +0 and -0 in JS are not the same - implemented as function:

var sign = function(x) {
    return 1 / x === 1 / Math.abs(x);
}

This will, other than the standard Math.sign return the correct sign of +0 and -0.