[TinkersW]

You can simplify the 2x sqrts as sqrt(a*b), overall less operations so perhaps more accurate. It would also let you get rid of the funky lane swivels.

As this would only use 1 lane, perhaps if you have multiple of these to normalize, you could vectorize it.

[a_gopher]

my thoughts exactly - crazy to know all these arcane SIMD opcodes but not know basic maths!!

[ashvardanian]

Square root computation can be tricky, often relying on approximations. These approximations tend to perform best for mid-range values, while accuracy can degrade for very large or very small values. With this in mind, a product of roots is generally more accurate than a root of products.

From a SIMD perspective, it’s worth noting that on most platforms, the cost of computing one square root or two is the same. On modern x86 server CPUs, for instance, you can calculate up to 8 double-precision roots in parallel with identical latency. So there’s no additional cost in terms of performance.

I hope this sheds some light on the design of my code.

PS: In a previous life, I did research in Astro- and Plasma Physics. While I don’t claim to remember all the Math, it’s usually more productive to ask for clarification than to assume ignorance ;)

[harry8]

> it’s usually more productive to ask for clarification than to assume ignorance ;)

Good reminder for me and anyone else right there, nicely put.

[nine_k]

Moments like that are enlightening. When you see something really improbable (knowing advanced SIMD while appearing to ignore basic algebra), it's likely the moment you see a gap in your picture of the world. So it's tine to learn something new and likely unexpected (else you could have guessed).