Asger Munk Nielsen

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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)
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)
ÐThis 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)
This paper presents the foundations for a packet forwarding Jloating point format and the design of a rounder ensuring compatibility between packet forwarding format and the standard binary IEEE 754 jloating point format. The packet forwarding format and related addition and multiplication algorithms described in this series propose a new ALU pipeline(More)
We develop a formal account of digit serial number representations by describing them as strings from a language. A pre x 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)
David P. Lusch,∗ Kristy E. Stanley,† Randall J. Schaetzl,∗ Anthony D. Kendall,‡ Remke L. Van Dam,‡ Asger Nielsen,§ Bradley E. Blumer,∗ Trevor C. Hobbs,∗ Jonathan K. Archer,∗ Jennifer L. F. Holmstadt,∗ and Christopher L. May‡ ∗Department of Geography, Michigan State University †Department of Geography, University of Wisconsin–Madison ‡Department of(More)