Generic design of Chinese remaindering schemes

TL;DR

This paper introduces a flexible, modular framework for Chinese remainder algorithms, featuring a novel radix ladder data structure, enabling various forms of remaindering and parallel implementations with improved efficiency.

Contribution

It presents a generic, structured design for Chinese remaindering algorithms, including a new radix ladder data structure and modular components for enhanced flexibility and parallelism.

Findings

Supports multiple remaindering variants like deterministic and early terminated

Enables easy comparison of different Chinese remaindering methods

Facilitates user-transparent parallelism at various levels

Abstract

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a radix ladder, for the intermediate storage and computations. Our design is structured into three main modules: a black box residue computation in charge of computing each residue; a Chinese remaindering controller in charge of launching the computation and of the termination decision; an integer builder in charge of the reconstruction computation. We then show that this design enables many different forms of Chinese remaindering (e.g. deterministic, early terminated, distributed, etc.), easy comparisons between these forms and e.g. user-transparent parallelism at different parallel grains.