Further Comments on "Residue-to-Binary Converters Based on New Chinese Remainder Theorems"

TL;DR

This paper clarifies the origins of Wang's New Chinese Remainder Theorem, demonstrating it is essentially a rephrasing of an earlier algorithm by Hitz and Kaltofen, and corrects misconceptions about its derivation.

Contribution

The paper corrects the attribution of Wang's New CRT I, showing it is based on prior work by Hitz and Kaltofen, and refutes Ananda Mohan's erroneous proof.

Findings

Wang's New CRT I is a rephrasing of Hitz and Kaltofen's algorithm.

Ananda Mohan's proof claiming derivation from the constructive CRT is incorrect.

The paper clarifies the true origins of Wang's New CRT I.

Abstract

Ananda Mohan suggested that the first New Chinese Remainder Theorem introduced by Wang can be derived from the constructive proof of the well-known Chinese Remainder Theorem (CRT) and claimed that Wang's approach is the same as the one proposed earlier by Huang. Ananda Mohan's proof is however erroneous and we show here that Wang's New CRT I is a rewriting of an algorithm previously sketched by Hitz and Kaltofen.