Fast Polynomials

Learning and science

algorithms reference

SHOW HN2026

139points
42comments
#467of 4,366 in 2026
Top 11%of 2026 by points

How HN took it

CuriousMostly questions and neutral comments

3 positive, 8 neutral or asking, 1 mixed, 4 critical, out of 16 comments about the project. Thread score -0.03.

Performance: 0 for, 3 againstDesign: 1 for, 1 againstIdea: 2 for, 0 against

The thread, comment by comment

Each row is a top-level comment and its replies, in HN's order. Select a cell to open that comment on HN.

positive neutral or mixed critical about another commenter or something else the maker

What HN said

What people liked

  • Interactive demo is useful for learning evaluation methods.

    From 1 comment
    • This is super cool. I learned a lot playing with the demo. I only knew Horner and Estrin, but I think I've gotten a grasp on most of them. One small change I'd recommend is for…
      pvillano on HN
  • Lean proof makes the bound trustworthy.

    From 1 comment
    • The Lean proof is the interesting part. A 100-page construction nobody's sure about becomes something you can trust when the multiplication-count bound is machine-checked.
      lee_ward on HN

Objections

  • Preprocessing cost may outweigh gains for hashing.

    From 1 comment
    • It is applicable, but it is not useful. Universal hashes use the input text as the set of coefficients. This method requires additional preprocessing of the coefficients, before…
      adrian_b on HN
  • Heuristic hashes like xxh3 may still be faster.

    From 1 comment
    • You benchmarked a really old heuristic hash in Murmur and xxh64. xxh3 is ~1.6x to 1.8x faster than xxh64 - extrapolating that to 5.7 in your paper puts it at ~18-27% faster.…
      vlovich123 on HN

Requests

  • Separate source nodes for x, x^2, x^4 in the graph view.

    From 1 comment
    • This is super cool. I learned a lot playing with the demo. I only knew Horner and Estrin, but I think I've gotten a grasp on most of them. One small change I'd recommend is for…
      pvillano on HN
  • Fix the monic toggle that resets when switching methods.

    From 1 comment
    • 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…
      voxelghost on HN

Questions

  • Tradeoff between multiplication and addition cost.

    From 1 comment
    • What is the tradeoff between multiplication and addition?
      gowld on HN
  • Why not use FFT for multipoint evaluation.

    From 1 comment
    • If you're going to preprocess the polynomial, maybe you want to evaluate it at many different points. But then why not use the FFT?
      throwaway81523 on HN

Alternatives named

  • Horner's method

    From 1 comment
    • This is super cool. I learned a lot playing with the demo. I only knew Horner and Estrin, but I think I've gotten a grasp on most of them. One small change I'd recommend is for…
      pvillano on HN
  • Estrin's method

    From 1 comment
    • If you are working over floating point, you probably with to use Estrin's method (see https://en.wikipedia.org/wiki/Estrin%27s_scheme - also tab 3 on the website.) It takes…
      thomasahle on HN
  • Rabin-Winograd

    From 1 comment
    • Thank you! It was a lot of fun to make the website and see all the methods in practice after having just looked at the theory for a long time :D > have a separate source node for…
      thomasahle on HN
  • xxh3 and wyhash

    From 1 comment
    • Would this be applicable to fast hashes like WyHash and xxh3 or are those not using polynomials? Is this mainly for faster cryptographic hashes?
      vlovich123 on HN

Category, keywords, summaries and labels on this page were made by AI (Thread Reader v2) and not checked by hand. Each point links to the comments it came from.

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