Accurate Complex Multiplication in Floating-Point Arithmetic

Vincent Lefèvre (1) , Jean-Michel Muller (1, 2)

1 ARIC - Arithmetic and Computing
2 CNRS - Centre National de la Recherche Scientifique

We deal with accurate complex multiplication in binary floating-point arithmetic, with an emphasis on the case where one of the operands in a "double-word" number. We provide an algorithm that returns a complex product with normwise relative error bound close to the best possible one, i.e., the rounding unit u.

Mots clés: Floating-point arithmetic; Complex multiplication; Rounding error analysis

Domaines: Autre [cs.OH]; Arithmétique des ordinateurs

Vincent Lefèvre, Jean-Michel Muller. Accurate Complex Multiplication in Floating-Point Arithmetic. 2019. ⟨hal-02001080v1⟩