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Electronics 2016, 5(2), 17; doi:10.3390/electronics5020017

Optimized Linear, Quadratic and Cubic Interpolators for Elementary Function Hardware Implementations

1
Oklahoma State University, Department of Electrical and Computer Engineering, 202 Engineering South, Stillwater, OK 74078, USA
2
Penn State Erie, The Behrend College, Department of Electrical and Computer Engineering, Erie, PA 16563, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Mostafa Bassiouni
Received: 30 December 2015 / Revised: 13 March 2016 / Accepted: 28 March 2016 / Published: 8 April 2016
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Abstract

This paper presents a method for designing linear, quadratic and cubic interpolators that compute elementary functions using truncated multipliers, squarers and cubers. Initial coefficient values are obtained using a Chebyshev series approximation. A direct search algorithm is then used to optimize the quantized coefficient values to meet a user-specified error constraint. The algorithm minimizes coefficient lengths to reduce lookup table requirements, maximizes the number of truncated columns to reduce the area, delay and power of the arithmetic units, and minimizes the maximum absolute error of the interpolator output. The method can be used to design interpolators to approximate any function to a user-specified accuracy, up to and beyond 53-bits of precision (e.g., IEEE double precision significand). Linear, quadratic and cubic interpolator designs that approximate reciprocal, square root, reciprocal square root and sine are presented and analyzed. Area, delay and power estimates are given for 16, 24 and 32-bit interpolators that compute the reciprocal function, targeting a 65 nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes compared to previously proposed methods. The method can be used to optimize coefficients in other systems while accounting for coefficient quantization as well as truncation and rounding effects of multiple arithmetic units. View Full-Text
Keywords: elementary functions; interpolators; table-driven methods elementary functions; interpolators; table-driven methods
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Sadeghian, M.; Stine, J.E.; Walters, E.G. Optimized Linear, Quadratic and Cubic Interpolators for Elementary Function Hardware Implementations. Electronics 2016, 5, 17.

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