Low Precision Table Based Complex Reciprocal Approximation

Jean-Michel Muller (1) , Pouya Dormiani (2) , Milos Ercegovac (2)

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

A recently proposed complex valued division algorithm designed for efficient hardware implementations requires a prescaling step by a constant factor. Techniques for obtaining this prescaling factor have been mentioned by the authors, which serves to justify the feasibility of the algorithm but is inadequate for obtaining efficient implementations. Table based solutions are formulated in this paper for obtaining the prescaling factor, a low precision reciprocal approximation for a complex value, using techniques adopted from univariate function approximations. Two separate designs are proposed, one using a single table (a reference design) and another using generalized multipartite tables. The main contribution of this work is the extension of generalized multipartite table methods to a function of two variables. The multipartite tables derived were up to 67% more memory efficient than their single table counterparts.

Mots clés: computer arithmetic; complex arithmetic; division; digit-recurrence algorithms; prescaling

Domaines: Autre [cs.OH]

Jean-Michel Muller, Pouya Dormiani, Milos Ercegovac. Low Precision Table Based Complex Reciprocal Approximation. 43rd Asilomar Conference on signals, systems and computers, Nov 2009, Pacific Grove, California, United States. ⟨ensl-00436329v1⟩