What's the fastest way to square a number in JavaScript?

Question

What's the fastest way to square a number in JavaScript?

function squareIt(number) {
   return Math.pow(number,2);
}

function squareIt(number) {
   return number * number;
}

Or some other method that I don't know about. I'm not looking for a golfed answer, but the answer that's likely to be shortest in the compiler, on the average.

Edit: I saw Why is squaring a number faster than multiplying two random numbers? which seemed to indicate that squaring is faster than multiplying two random numbers, and presumed that n*n wouldn't take advantage of this but that Math.pow(n,2) would. As jfriend00 pointed out in the comments, and then later in an answer, http://jsperf.com/math-pow-vs-simple-multiplication/10 seems to suggest that straight multiplication is faster in everything but Firefox (where both ways are similarly fast).

Answer 1

Note: Questions like this change over time as browser engines change how their optimizations work. For a recent look comparing:

Math.pow(x1, 2)
x1 * x1
x1 ** 2                  // ES6 syntax

See this revised performance test and run it in the browsers you care about: https://jsperf.com/math-pow-vs-simple-multiplication/32.

As of April 2020, Chrome, Edge and Firefox show less than 1% difference between all three of the above methods.

If the jsperf link is not working (it seems to be occasionally down), then you can try this perf.link test case.

Original Answer from 2014:

All performance questions should be answered by measurement because specifics of the browser implementation and the particular scenario you care about are often what determine the outcome (thus a theoretical discussion is not always right).

In this case, performance varies greatly by browser implementation. Here are are results from a number of different browsers in this jsperf test: http://jsperf.com/math-pow-vs-simple-multiplication/10 which compares:

Math.pow(x1, 2)
x1 * x1

Longer bars are faster (greater ops/sec). You can see that Firefox optimizes both operations to be pretty much the same. In other browsers, the multiplication is significantly faster. IE is both the slowest and shows the greatest percentage difference between the two methods. Firefox is the fastest and shows the least difference between the two.

Answer 2

In ES6 you can do the following with Exponentiation (x ** y), which produces the same result as Math.pow(x,y):

function squareIt(number) {
  return number ** 2;
}

console.log(squareIt(5));

or you can use a JavaScript library called BigInteger.js for the purpose.

alert(bigInt(5).square());

<script src="https://cdnjs.cloudflare.com/ajax/libs/big-integer/1.6.40/BigInteger.min.js"></script>

Answer 3

In general, x * x is either much faster than or about the same as a pow() call in any language. pow() is a general exponential designed to work with floating point arguments, and it usually uses a calculation that has a lot more operations than a single multiplication. It's notoriously slow. Some pow() implementations will helpfully filter out integer powers for special evaluations, like for x^4 it might do x2=x * x, x4=x2 * x2, but adding special conditions like that can slow down the general implementation, and the x * x vs. pow() rule is so well known among programmers you can't really count on the library implementation to help you out. This is standard advice in numerical analysis: never use pow() for x^2 (or x^.5). At best, it's no slower than the pow implementation, if it's optimized out as x * x at compile time, and at worst, it's horribly slower (and probably not as accurate either). You could go and test it on every possible platform you expect your code to run on, but in real life, there's no good reason to use pow() for squares. There can be good reasons to write a convenience function that does x * x, but if the language allows it, it's a good idea to make sure that it's marked up so that there's no actual function call going on at the machine level. Unfortunately, I don't think Javascript has anything like that, but I suspect that the JIT compilers are usually smart enough to render short functions like that without a jump.

Regarding the issue of x * x vs. x * y, the former would often be faster simply because it avoids a MOV at the machine level (aside from the considerations in the post you referenced), but it's pretty certain that the JS engine is smart enough not to do an extra MOV if the operand is already in a register. It's not going to load x from memory and then load it from memory again, or move it from one register into another. That's a basic behavior of optimizing compilers. You have to keep in mind that the compiler is going to do a lot of rearranging and consolidation of algebraic operations, so when you write x * x, a lot of things could be going on depending on what happened to x previously or happens to it later. This is another reason to avoid pow(), since the optimizer can do a lot of tricks with x * x that may not be available if it does a pow() call instead. Again, you can hope that it intelligently inlines pow(x,2) to x * x, but don't count on it.