arXiv subjects

Eric B. Olsen

Publications and source records attributed to Eric B. Olsen.

3 recordsLinked to original sources

arXiv2026

Direct Integer Division in RNS and its Hardware Solutions

Residue Number Systems (RNS) offer efficient modular arithmetic and natural parallelism, but direct integer division in RNS remains a difficult and comparatively underdeveloped operation. This paper builds on the type-II division algorithm of Szabo and Tanaka and reformulates it for more efficient hardware implementation. A principal contribution is the introduction of a power-based RNS, in which moduli are selected as powers of natural primes, increasing dynamic range, improving bit efficiency, and providing greater flexibility for scaling during division. The paper further formalizes three decomposition methods required by the division process: multi-factor scaling for modulus-based division, mixed-radix conversion for base extension and comparison, and a new divisor decomposition method introduced in this work. Each method is supported by mathematical development, including analysis of modulus invalidation during computation. These results simplify the hardware structure of the algorithm and improve its scalability. Supported by hardware diagrams and performance tables, the work advances both the theory and practical implementation of direct RNS division.

cs.AR↗

arXiv2017

Proposal for a High Precision Tensor Processing Unit

This whitepaper proposes the design and adoption of a new generation of Tensor Processing Unit which has the performance of Google's TPU, yet performs operations on wide precision data. The new generation TPU is made possible by implementing arithmetic circuits which compute using a new general purpose, fractional arithmetic based on the residue number system.

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arXiv2015

Introduction of the Residue Number Arithmetic Logic Unit With Brief Computational Complexity Analysis

Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several new residue based fractional representations. The result is that fractional arithmetic may be performed without carry. Additionally, fractional operations such as addition, subtraction and multiplication of a fraction by an integer occur in a single clock period, regardless of word size. Fractional multiplication is of the order O(p), where p equals the number of residues. More significantly, complex operations, such as sum of products, may be performed in an extended format, where fractional products are performed and summed using single clock instructions, regardless of word width, and where a normalization operation with an execution time of the order O(p) is performed as a final step.

cs.OH↗