Generic design of Chinese remaindering schemes

Jean-Guillaume Dumas 1 Thierry Gautier 2 Jean-Louis Roch 2
2 MOAIS - PrograMming and scheduling design fOr Applications in Interactive Simulation
Inria Grenoble - Rhône-Alpes, LIG - Laboratoire d'Informatique de Grenoble
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.
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Submitted on : Tuesday, May 4, 2010 - 12:07:43 PM
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Jean-Guillaume Dumas, Thierry Gautier, Jean-Louis Roch. Generic design of Chinese remaindering schemes. PASCO '10 - 4th International Symposium on Parallel Symbolic Computation, Jul 2010, Grenoble, France. pp.26-34, ⟨10.1145/1837210.1837218⟩. ⟨hal-00449864v2⟩

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