GoKawiilNew tool preprocesses polynomial coefficients to halve multiplication count
A Show HN project introduces a web tool that applies a coefficient preprocessing technique to evaluate polynomials using roughly half the multiplications required by the standard Horner's method. Users can enter a polynomial, choose a mathematical field, and the tool computes an optimized evaluation scheme, needing about floor(n/2)+1 multiplications for monic polynomials.
GoKawiil's interpretation of the reporting above, not reported fact.
Polynomial evaluation is a core operation underlying function approximation (like exp, sin, cos), cryptographic computations, hashing, and coding theory, so speeding it up can have wide-ranging performance benefits in software and hardware implementations. Making this optimization technique accessible via a simple online tool lowers the barrier for developers and researchers to apply it without manually deriving the preprocessing steps themselves.
- The tool cuts multiplications needed to evaluate polynomials to about half of Horner's method.
- It works for monic polynomials with floor(n/2)+1 multiplications and general ones with one more.
- Applications include function approximation, cryptography, hashing, and coding theory.
Knuth The Art of Computer Programming Vol. 2 — The polynomial preprocessing trick that beats Horner's method is classic Knuth territory вolume 2 covers polynomial evaluation and arithmetic in depth. If this Show HN made you want the underlying theory rather than just the web tool, it's the reference to keep on the desk.
See Knuth The Art of Computer Programming Vol. 2 on Amazon → Affiliate link — we may earn a commission on purchases, at no extra cost to you. Product picked by AI based on this article; it is not a tested recommendation.Source: thomasahle.com, 2026-09-09
Published there as: “Show HN: Compute polynomials twice as fast”
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