Bug 284631 – Math.hypot() is significantly slower than Math.sqrt()

• Component: JavaScriptCore
• Status: RESOLVED FIXED

[Ashley Gullen]

Created attachment 473562 [details]
Performance benchmark

Steps to reproduce:

Math.hypot() appears to be significantly slower than Math.sqrt(). As it is a more convenient specialized method for calculating the hypotenuse, this makes it easy to write code that is accidentally less performant than expected. This affects our browser-based game engine Construct (https://www.construct.net) as well as third-party math libraries like glMatrix (who eventually realized the same thing and removed uses of Math.hypot(): https://github.com/toji/gl-matrix/commit/8962b2e7727594022e59e48e605049c69403da60)

See attachment for what I believe is a fair benchmark.

Note that optimizing the case where 2 or 3 arguments are passed should be sufficient to optimize the majority of performance-sensitive uses in game engines using 2D and 3D calculations.

Actual results:

On an Apple M1 Pro with Safari 18.1.1, after three runs, the Math.sqrt() benchmark completes in ~39ms, and the Math.hypot() benchmark completes in ~181ms (~4.6x slower).

Expected results:

Both benchmarks should complete in a similar time. If anything perhaps Math.hypot() should be faster, as more of the calculation is completed with a built-in method.

[Yusuke Suzuki]

Right. We should lower Math.hypot into multiplication + sqrt.

[Radar WebKit Bug Importer]

<rdar://problem/141821484>

[Keita Nonaka]

Pull request: https://github.com/WebKit/WebKit/pull/42569

[Ashley Gullen]

That PR looks like it only optimizes for constant parameters - unfortunately that won't bring any real-world performance improvement, as in practice it is always going to be called with non-constant parameters (as per the benchmark).

[Ashley Gullen]

Actually, I'm not so sure. Apologies if I got that wrong! Would be interested to see benchmark results.

[Keita Nonaka]

I dont think hypot() becomes as fast as sqrt() because hypot function has overhead to avoid overflow or underflow. 
sqrt() is faster because it avoids overflow and underflow calculation, so in some cases, sqrt() does not calculate well.
For example, 

```js
console.log(Math.hypot(1e308, 1e308, 1e308))                                               // 1.7320508075688772e+308 
console.log(Math.sqrt(1e308 * 1e308 +  1e308 * 1e308 + 1e308 * 1e308)) // Infinity
```

https://www.typescriptlang.org/play/?#code/MYewdgziA2CmB00QHMAUBZAhgFwBb1wE8AHEbVARlgGYAGADgBoACKup1mhgSm4ChQkGAiRoseeBACOAJ3JsGzAFSd2zANTNVilQvobt+3V3q8gA

[Keita Nonaka]

> NOTE
> Implementations should take care to avoid the loss of precision from overflows and underflows that are prone to occur in naive implementations when this function is called with two or more arguments.

https://tc39.es/ecma262/multipage/numbers-and-dates.html#sec-math.hypot

[EWS]

Committed 292549@main (bdf66e673c2c): <https://commits.webkit.org/292549@main>

Reviewed commits have been landed. Closing PR #42569 and removing active labels.