Generic design of Chinese remaindering schemes

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.

Fifteen years after DSC and WLSS2 what parallel computations I do today

“…We could verify that for at least 2 processes the memory contention problem was solved. In addition, the authors of [16] report avoidance of bus contention by using Google's cached heap allocation scheme TCmalloc. Perhaps symbolic computation system vendors should also offer software compiled with such malloc schemes.…”

LinBox Founding Scope Allocation, Parallel Building Blocks, and Separate Compilation

“…We used dynamic libraries to exchange allocators for the experiments, but one can use them together in the Lin-Box library if needed [8, §7]. Preliminary experiments on early terminated Chinese remaindering, not the easiest to parallelize, have demonstrated the advantage, in our setting, of TCMalloc over the others [3]. One of the main reasons for that fact is that our problems required many temporary allocations.…”

“…For instance, this is used in Chinese Remaindering algorithms. The computation is performed modulo a sequence of (co)prime numbers and the result is built from a sequence of residues, until a condition is satisfied [3]. The termination of the algorithm depends on the accumulated result.…”