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Comment by jonstewart | Hacker News Reader

The most unhinged AVX-512 instruction is GF2P8AFFINEQB.

From my 1980s 8-bit CPU perspective, the instruction is unhinged based solely on the number of letters. Compared to LDA, STA, RTS, that's not an assembler mnemonic, it's a novel. :-)

"Load accumulator" (LDA)

"Galois Field 2^8 affine transform on quad binary words" (GF2P8AFFINEQB)

The compression factor isn't quite the same on character count, but it's still abbreviated. :)

Incidentally, how is it a GF(2^8) affine transform? As best as I can tell, it’s a GF(2)^8 affine transform, i.e. an affine transform of vectors of bits with normal XOR addition and AND multiplication, and the polynomial defining GF(2^8) just does not enter anywhere. It does enter into GF2P8AFFINEINVQB, but I’m having difficulties finding a geometric description for that one at all.

I believe that the polynomial for GF2P8AFFINEQB is user-defined. One argument is an 8x8 matrix in GF(2) and the result is [A.x + b] in GF(2)^8 for each 8-bit section. Don't quote me on this, but I believe that matrix multiply in GF(2)^8 gets you a transform in GF(2^8).

There's a pretty good list of weird off-label uses for the Galois Field instructions here: https://gist.github.com/animetosho/d3ca95da2131b5813e16b5bb1...

I think I actually need that instruction and have a use case for it, and it does something with a matrix transpose so I might finally find a real world useful demonstration of a matrix operation I can cite to people who don't know what those mean.

Here is Knuth introducing the MMIX instruction MXOR, which Intel later defined on vector registers under the name vgf2p8affineqb.

https://www.youtube.com/watch?v=r_pPF5npnio&t=3300 (55:00)

"This is an instruction that doesn't exist in any computer right now, so why should I put it in a machine, if it's supposed to be realistic? Well, it's because it's ahead of time."

MMIX? Now that's something I haven't heard in a long time...

What about GF2P8AFFINEINVQB?

potato, potato, tomato, tomato

It has a fixed polynomial, so not really that useful for anything but AES

The only case where I've had use of GF(2^8) inverses is in FEC algorithms (Forney's algorithm) and then you need some kind of weird polynomial. But all of those needs are rarely in the hot-path, and the FEC algo's are way outdated

I think the AFFINE and AFFINEINV instructions are specifically for FEC and maybe compression algorithms. I also think they smell like something requested by one of the big customers of Intel (e.g. the government).

Hmm of course erasure codes would always need to solve these problems. Not sure what modern applications need that in the X86 world

I really think it's only AES since thats the only place I've seen that polynomial used. But of course maybe there's an obscure tape backup FEC algo used somewhere in datacenters?

The forward affine matrix is useful for all sorts of bit manipulation, e.g. something as simple as a bit reversal.

Sometimes I read through the instrinsics guide just to play the game of spotting instructions defined primarily because certain cryptologic agencies asked for it.

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