Implementing decimal floating-point arithmetic through binary: some suggestions

Nicolas Brisebarre (1, 2) , Milos Ercegovac (3, 1, 2) , Nicolas Louvet (1, 2) , Érik Martin-Dorel (1, 2) , Jean-Michel Muller (1, 2) , Adrien Panhaleux (1, 2)

1 ARENAIRE - Computer arithmetic
2 LIP - Laboratoire de l'Informatique du Parallélisme
3 Digital Arithmetic and Reconfigurable Architecture Laboratory

We propose several algorithms and provide some related results that make it possible to implement decimal floating-point arithmetic on a processor that does not have decimal operators, using the available binary floating-point functions. In this preliminary study, we focus on round-to-nearest mode only. We show that several functions in decimal32 and decimal64 arithmetic can be implemented using binary64 and binary128 floating-point arithmetic, respectively. Specifically, we discuss the decimal square root and some transcendental functions. We also consider radix conversion algorithms.

Keywords: Floating-point arithmetic; Decimal floating-point arithmetic; Square root; Transcendental functions; Radix conversion.; Radix conversion

Domains: Computer Science [cs]; Other [cs.OH]

Nicolas Brisebarre, Milos Ercegovac, Nicolas Louvet, Érik Martin-Dorel, Jean-Michel Muller, et al.. Implementing decimal floating-point arithmetic through binary: some suggestions. 21st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP 2010), Jul 2010, Rennes, France. pp.317-320, ⟨10.1109/ASAP.2010.5540969⟩. ⟨ensl-00463353v2⟩