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Karatsuba with Rectangular Multipliers for FPGAs
University of Kassel, Digital Technology Group, Germany.
Linköping University, Department of Electrical Engineering, Computer Engineering. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-3470-3911
Univ Lyon, INSA Lyon, Inria, CITI, France.
University of Kassel, Digital Technology Group, Germany.
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2018 (English)In: 2018 IEEE 25TH SYMPOSIUM ON COMPUTER ARITHMETIC (ARITH), IEEE, 2018, p. 13-20Conference paper, Published paper (Refereed)
Abstract [en]

This work presents an extension of Karatsuba's method to efficiently use rectangular multipliers as a base for larger multipliers. The rectangular multipliers that motivate this work are the embedded 18x25-bit signed multipliers found in the DSP blocks of recent Xilinx FPGAs: The traditional Karatsuba approach must under-use them as square 18x18 ones. This work shows that rectangular multipliers can be efficiently exploited in a modified Karatsuba method if their input word sizes have a large greatest common divider. In the Xilinx FPGA case, this can be obtained by using the embedded multipliers as 16x24 unsigned and as 17x25 signed ones.The obtained architectures are implemented with due detail to architectural features such as the pre-adders and post-adders available in Xilinx DSP blocks. They are synthesized and compared with traditional Karatsuba, but also with (non-Karatsuba) state-of-the-art tiling techniques that make use of the full rectangular multipliers. The proposed technique improves resource consumption and performance for multipliers of numbers larger than 64 bits.

Place, publisher, year, edition, pages
IEEE, 2018. p. 13-20
Series
International Symposium on Computer Arithmetic, ISSN 1063-6889
National Category
Computer Systems Embedded Systems Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-150920DOI: 10.1109/ARITH.2018.8464809ISI: 000454795600003ISBN: 978-1-5386-2613-9 (electronic)OAI: oai:DiVA.org:liu-150920DiVA, id: diva2:1245437
Conference
25th International Symposium on Computer Arithmetic, Amherst, MA, USA, June 25-27, 2018
Available from: 2018-09-05 Created: 2018-09-05 Last updated: 2019-01-21Bibliographically approved

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Gustafsson, Oscar

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
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  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
  • html
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  • asciidoc
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