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I have another one. Afaik you can calculate the Number Theoretic Transform in GF2 using clmul. This gives you most of the goodies a FFT will, but without ever running into roundig Errors. You can use this for example to do fast bignum multiplications.
Do you have a reference for this? (Googled a bit but didn't find something that looks like that, maybe I just used the wrong search terms? I guess the fast bignum part refers to the Schoenhage-Strassen algorithm. But I can't seem to find anything specifically re NTT using CLMUL.)
Here is a paper using NTT over a Galois Field doing image filtering: https://www.computer.org/csdl/trans/tc/1977/09/01674935.pdf … They don't use GF(2) which clmul does natively, but GF(45 X 229 + 1) instead. I'm pretty sure that clmul can be used to compute these, but it's not exactly my area of expertise :-)
Ah, no. dug a bit deeper. You can't use clmul for that. It's plain modulo-prime arithmetic that they are using. :-/
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