Low-Latency Low-Cost Architecture for Square and Cube Roots

Jihyuck JO  In-Cheol PARK  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.9   pp.1951-1955
Publication Date: 2017/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E100.A.1951
Type of Manuscript: PAPER
Category: Digital Signal Processing
computer arithmetic,  cube roots,  square roots,  non-iterative root calculation,  

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This paper presents a low-latency, low-cost architecture for computing square and cube roots in the fixed-point format. The proposed architecture is designed based on a non-iterative root calculation scheme to achieve fast computations. While previous non-iterative root calculators are restricted to a square-root operation due to the limitation of their mathematical property, the root computation is generalized in this paper to apply an approximation method to the non-iterative scheme. On top of that, a recurrent method is proposed to select parameters, which enables us to reduce the table size while keeping the maximum relative error value low. Consequently, the proposed root calculator can support both square and cube roots at the expense of small delay and low area overheads. This extension can be generalized to compute the nth roots, where n is a positive integer.