The recently proposed O(n log n) integer multiplication algorithm [pdf]

A researcher has proposed a new integer multiplication algorithm that has a time complexity of O(n log n), which is a significant improvement over the previous best known bound of O(n log n log log n). The new algorithm, called the 'Harvey algorithm', is based on the Fast Fourier Transform (FFT) and uses a new technique called 'grouping' to reduce the number of multiplications required. The algorithm has been implemented and tested on various inputs, and the results show that it is faster and more efficient than the previous best known algorithm.