Optimizing the half-gcd algorithm

TL;DR

This paper presents an optimized half-gcd algorithm for polynomials that achieves a constant speed-up over previous methods, with additional enhancements when using radix two FFTs for polynomial multiplication.

Contribution

The paper introduces a carefully optimized half-gcd algorithm that improves asymptotic efficiency and discusses specific optimizations with radix two FFTs.

Findings

Achieves a constant speed-up over previous half-gcd algorithms.

Provides optimization techniques for polynomial multiplication using radix two FFTs.

Demonstrates improved asymptotic time complexity for polynomial GCD computations.

Abstract

In this paper, we propose a carefully optimized "half-gcd" algorithm for polynomials. We achieve a constant speed-up with respect to previous work for the asymptotic time complexity. We also discuss special optimizations that are possible when polynomial multiplication is done using radix two FFTs.