Recursive double-size fixed precision arithmetic

Alexis Breust 1 Christophe Chabot 1 Jean-Guillaume Dumas 1 Laurent Fousse 1 Pascal Giorgi 2
2 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This work is a part of the SHIVA (Secured Hardware Immune Versatile Architecture) project whose purpose is to provide a programmable and reconfigurable hardware module with high level of security. We propose a recursive double-size fixed precision arithmetic called RecInt. Our work can be split in two parts. First we developped a C++ software library with performances comparable to GMP ones. Secondly our simple representation of the integers allows an implementation on FPGA. Our idea is to consider sizes that are a power of 2 and to apply doubling techniques to implement them efficiently: we design a recursive data structure where integers of size 2^k, for k>k0 can be stored as two integers of size 2^{k-1}. Obviously for k<=k0 we use machine arithmetic instead (k0 depending on the architecture).
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Alexis Breust, Christophe Chabot, Jean-Guillaume Dumas, Laurent Fousse, Pascal Giorgi. Recursive double-size fixed precision arithmetic. ICMS: International Congress of Mathematical Software, Jul 2016, Berlin, Germany. pp.223--231, ⟨10.1007/978-3-319-42432-3_28⟩. ⟨hal-00582593v2⟩

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