ÐThis paper presents a floating-point addition algorithm and adder pipeline design employing a packet forwarding pipeline paradigm. The packet forwarding format and the proposed algorithms constitute a new paradigm for handling data hazards in deeply pipelined floating-point pipelines. The addition and rounding algorithms employ a four stage execution phase… (More)
We develop a formal account of digit serial number representations by describing them as strings from a language. A preex of a string represents an interval approximating a number by enclosure. Standard on-line representations are shown to be a special case of the general digit serial representations. Matrices are introduced as representations of intervals… (More)
This paper presents a thorough analysis of radix representations of elements from general rings, in particular we study the questions of redundancy, completeness and mappings into such representations. After a brief description of the more usual representations of integers, a more detailed analysis of various complex number systems is performed. This… (More)
This paper presents an analysis of radix representations of elements from general rings, in particular we study the questions of redundancy and completeness in such representations. Mappings into radix representations as well as conversions between such are discussed, in particular where the target system is redundant. Results are shown valid for normed… (More)
We propose a new on-line algorithm for fast evaluation of logarithms and exponentials. This algorithm is derived from the widely studied Briggs-De Lugish iteration. We examine various compromises between the on-line delay and the size of the required comparison constants.