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LNS with Co-Transformation Competes with Floating-Point

Lookup NU author(s): Dr Nick Coleman



This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).


The logarithmic number system has been proposed as an alternative to floating-point arithmetic. Multiplication, division and square-root operations are accomplished with inexpensive fixed-point methods, but addition and subtraction are considerably more challenging. Recent work has demonstrated that these operations too can be done with similar speed and accuracy to their FP equivalents, but the necessary circuitry is complex. In particular, it is dominated by the need for large ROM tables for the storage and interpolation of non-linear functions. We describe a new co-transformation procedure that eliminates much of the ROM space and allows the easy synthesis of the remainder in logic, and we then evaluate several interpolation methods that might benefit from it. Synthesised 32-bit implementations are compared with floating-point units, and show substantial reductions in delay, with equivalent accuracy and area.

Publication metadata

Author(s): Coleman JN, Ismail RC

Publication type: Article

Publication status: Published

Journal: IEEE Transactions on Computer

Year: 2016

Volume: 65

Issue: 1

Pages: 136-146

Print publication date: 01/01/2016

Online publication date: 09/03/2015

Acceptance date: 23/12/2014

Date deposited: 04/02/2016

ISSN (print): 0018-9340

ISSN (electronic): 1557-9956

Publisher: IEEE


DOI: 10.1109/TC.2015.2409059


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