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Fused Three-Input SORN Arithmetic

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Next Generation Arithmetic (CoNGA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13851))

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Abstract

The Sets-of-Real-Numbers (SORN) format for digital arithmetic and signal processing represents real numbers with small sets of exact values and intervals, enabling low-complex and fast computing of arithmetic operations. The format derives from the universal numbers (unum) and has already proven to be a valuable alternative to legacy formats like fixed point or floating point.

The main challenge of SORN arithmetic is degenerating accuracy due to increasing intervals widths, which is tackled in this work with the proposal of fused SORN arithmetic for the three-input operations addition, multiplication and multiply-add, as well as the three-input hypot function. Evaluations on accuracy and hardware performance for different SORN datatypes show that accuracy improvements of up to \(60\%\) can be achieved, along with moderate to high hardware complexity increases. In some cases even improvements for both accuracy and hardware performance can be achieved.

The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the project “Open6GHub” (grant number: 16KISK016).

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Notes

  1. 1.

    The term accuracy within the context of interval-based SORN arithmetic is discussed in Sect. 3.1.

References

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Authors and Affiliations

  1. Institute of Electrodynamics and Microelectronics (ITEM.me), Bermen, Germany

    Moritz Bärthel, Nils Hülsmeier & Steffen Paul

  2. University of Bremen, Bremen, Germany

    Moritz Bärthel, Chen Yuxing, Nils Hülsmeier & Steffen Paul

  3. DSI Aerospace Technologie GmbH, Bremen, Germany

    Jochen Rust

Authors
  1. Moritz Bärthel
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  2. Chen Yuxing
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  3. Nils Hülsmeier
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  4. Jochen Rust
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  5. Steffen Paul
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Corresponding author

Correspondence to Moritz Bärthel .

Editor information

Editors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    John Gustafson

  2. Swiss National Supercomputing Centre, ETH Zurich, Lugano, Switzerland

    Siew Hoon Leong

  3. National Supercomputing Centre, Singapore, Singapore

    Marek Michalewicz

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Bärthel, M., Yuxing, C., Hülsmeier, N., Rust, J., Paul, S. (2023). Fused Three-Input SORN Arithmetic. In: Gustafson, J., Leong, S.H., Michalewicz, M. (eds) Next Generation Arithmetic. CoNGA 2023. Lecture Notes in Computer Science, vol 13851. Springer, Cham. https://doi.org/10.1007/978-3-031-32180-1_7

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  • DOI: https://doi.org/10.1007/978-3-031-32180-1_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32179-5

  • Online ISBN: 978-3-031-32180-1

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