Design method of numerical function generators based on polynomial approximation for FPGA implementation
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Authors
Nagayama, Shinobu
Sasao, Tsutomu
Butler, Jon T.
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Date of Issue
2007-08
Date
August 27 - 31, 2007
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Abstract
This paper focuses on numerical function generators
(NFGs) based on k-th order polynomial approximations.
We show that increasing the polynomial order k reduces
signicantly the NFG's memory size. However, larger k
requires more logic elements and multipliers.numerical function generators
(NFGs) based on k-th order polynomial approximations.
We show that increasing the polynomial order k reduces
signicantly the NFG's memory size. However, larger k
requires more logic elements and multipliers. To quantify this tradeoff, we introduce the FPGA utilization measure, and then determine the optimum polynomial order k. Experimental results show that: 1) for low accuracies (up to 17 bits), 1st order polynomial approximations produce the most efficient implementations; and 2) for higher accuracies (18 to 24 bits), 2nd-order polynomial approximations produce the most efficient implementations.
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Article
Description
DSD 2007, 10th EUROMICRO Conference on Digital System Design, Architectures, Methods and Tools, Aug. 27 - 31, 2007, Lubeck, Germany, pp. 280-287.
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. As such, it is in the public domain, and under the provisions of Title 17, United States Code, Section 105, may not be copyrighted.
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Department of Electrical and Computer Engineering
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Citation
S. Nagayama, T. Sasao, and J. T. Butler, "Design method of numerical function generators based on polynomial approximation for FPGA implementation," DSD 2007, 10th EUROMICRO Conference on Digital System Design, Architectures, Methods and Tools, Aug. 27 - 31, 2007, Lubeck, Germany, pp. 280-287.