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

Jihyuck JO; In-Cheol PARK

doi:10.1587/transfun.E100.A.1951

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

Jihyuck JO, In-Cheol PARK

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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 n^th roots, where n is a positive integer.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.9 pp.1951-1955

Publication Date: 2017/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E100.A.1951

Type of Manuscript: PAPER

Category: Digital Signal Processing

Authors

Jihyuck JO
Korea Advanced Institute of Science and Technology (KAIST)
In-Cheol PARK
Korea Advanced Institute of Science and Technology (KAIST)

Keyword

computer arithmetic, cube roots, square roots, non-iterative root calculation

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Jihyuck JO, In-Cheol PARK, "Low-Latency Low-Cost Architecture for Square and Cube Roots" in IEICE TRANSACTIONS on Fundamentals, vol. E100-A, no. 9, pp. 1951-1955, September 2017, doi: 10.1587/transfun.E100.A.1951.
Abstract: 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 n^th roots, where n is a positive integer.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1951/_p

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@ARTICLE{e100-a_9_1951,
author={Jihyuck JO, In-Cheol PARK, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Low-Latency Low-Cost Architecture for Square and Cube Roots},
year={2017},
volume={E100-A},
number={9},
pages={1951-1955},
abstract={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 n^th roots, where n is a positive integer.},
keywords={},
doi={10.1587/transfun.E100.A.1951},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - Low-Latency Low-Cost Architecture for Square and Cube Roots
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1951
EP - 1955
AU - Jihyuck JO
AU - In-Cheol PARK
PY - 2017
DO - 10.1587/transfun.E100.A.1951
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2017
AB - 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 n^th roots, where n is a positive integer.
ER -