Show HN: Compute polynomials twice as fast

tthomasahle about 19 hours ago 9 commentsRead Article on thomasahle.com

HI version is available. Content is displayed in original English for accuracy.

A few years ago my coauthor and I was wondering if we could reduce the number of multiplications used for hashing algorithms. We had a construction and a 100 page proof, but we were not 100% sure it was correct. Now we have a full Lean proof, so we decided to publish it.

I made this website to make it easy for anyone how has polynomials to evaluate to see how it would be done using our method, as well as a number of previous approaches by Knuth and others.

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voxelghost•about 1 hour ago

It keeps flipping back to 'monic' from e.g. 'ln(1+x)' when switching between algorithms, and then seems to lock to 'monic'? (Am I missing something?)

Also I am curious, in your version vs. horner , how do both algorithms map onto number of fmadd operations?

gowld•about 1 hour ago

"monic" is a separate switch from the example functions radio-selector. Enabling "monic" removes the leading coefficient.

vlovich123•about 1 hour ago

Would this be applicable to fast hashes like WyHash and xxh3 or are those not using polynomials? Is this mainly for faster cryptographic hashes?

aetherspawn•about 2 hours ago

I guess it’s not faster than using a table for CRC8?

gowld•about 1 hour ago

From the abstract, a name that many on HN would recognize:

> We also give an injective polynomial construction for universal hashing that uses N multiplications to hash 2N values with a single random key. This improves the best previous construction by Daniel J. Bernstein (this http URL).

gowld•about 1 hour ago

What is the tradeoff between multiplication and addition?

nraynaud•26 minutes ago

Just a few years ago, mults were slower, but I think now (Intel i9) mult, add and fma are the same.

https://stackoverflow.com/a/39135689

gigatexal•about 1 hour ago

I think multiplications are faster to do in computer land than adds? I too am curious.

hyperhello•about 1 hour ago

Also could use analysis of dependencies to see what can happen in parallel. Or for that matter, some real benchmarks.