Optimized cubic chebyshev interpolator for elementary function hardware implementations

Masoud Sadeghian, James E. Stine, E. George Walters

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

This paper presents a cubic interpolator for computing elementary functions using truncated-matrix arithmetic units and an optimized number of coefficients bits. The proposed method optimizes the initial coefficient values found using a Chebyshev series approximation, minimizing the maximum absolute error of the interpolator output. The resulting designs can be utilized for approximating any function up to 53-bits of precision (IEEE double precision significand). Area, delay and power estimates are given for 16, 24 and 32-bit cubic interpolators that compute the reciprocal function, targeting a 65nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes than previously proposed methods.

Original languageEnglish (US)
Title of host publication2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1536-1539
Number of pages4
ISBN (Print)9781479934324
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014 - Melbourne, VIC, Australia
Duration: Jun 1 2014Jun 5 2014

Publication series

NameProceedings - IEEE International Symposium on Circuits and Systems
ISSN (Print)0271-4310

Other

Other2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014
CountryAustralia
CityMelbourne, VIC
Period6/1/146/5/14

Fingerprint

Hardware
Table lookup

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Cite this

Sadeghian, M., Stine, J. E., & Walters, E. G. (2014). Optimized cubic chebyshev interpolator for elementary function hardware implementations. In 2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014 (pp. 1536-1539). [6865440] (Proceedings - IEEE International Symposium on Circuits and Systems). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISCAS.2014.6865440
Sadeghian, Masoud ; Stine, James E. ; Walters, E. George. / Optimized cubic chebyshev interpolator for elementary function hardware implementations. 2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 1536-1539 (Proceedings - IEEE International Symposium on Circuits and Systems).
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Sadeghian, M, Stine, JE & Walters, EG 2014, Optimized cubic chebyshev interpolator for elementary function hardware implementations. in 2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014., 6865440, Proceedings - IEEE International Symposium on Circuits and Systems, Institute of Electrical and Electronics Engineers Inc., pp. 1536-1539, 2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014, Melbourne, VIC, Australia, 6/1/14. https://doi.org/10.1109/ISCAS.2014.6865440

Optimized cubic chebyshev interpolator for elementary function hardware implementations. / Sadeghian, Masoud; Stine, James E.; Walters, E. George.

2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1536-1539 6865440 (Proceedings - IEEE International Symposium on Circuits and Systems).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - This paper presents a cubic interpolator for computing elementary functions using truncated-matrix arithmetic units and an optimized number of coefficients bits. The proposed method optimizes the initial coefficient values found using a Chebyshev series approximation, minimizing the maximum absolute error of the interpolator output. The resulting designs can be utilized for approximating any function up to 53-bits of precision (IEEE double precision significand). Area, delay and power estimates are given for 16, 24 and 32-bit cubic interpolators that compute the reciprocal function, targeting a 65nm CMOS technology from IBM. Results indicate the proposed method uses smaller arithmetic units and has reduced lookup table sizes than previously proposed methods.

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Sadeghian M, Stine JE, Walters EG. Optimized cubic chebyshev interpolator for elementary function hardware implementations. In 2014 IEEE International Symposium on Circuits and Systems, ISCAS 2014. Institute of Electrical and Electronics Engineers Inc. 2014. p. 1536-1539. 6865440. (Proceedings - IEEE International Symposium on Circuits and Systems). https://doi.org/10.1109/ISCAS.2014.6865440