Closed form solution for optimal buffer sizing using the Weierstrass elliptic function

S. Vogel; M. D. F. Wong

doi:10.1109/ASPDAC.2006.1594701

Closed form solution for optimal buffer sizing using the Weierstrass elliptic function

S. Vogel, M. D. F. Wong

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Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

Abstract

This paper presents a fundamental result on buffer sizing. Given an interconnection wire with n buffers evenly spaced along the wire, we would like to size all buffers such that the Elmore delay is minimized. It is well known that the problem can be solved by an iterative algorithm which sizes one buffer at a time. However, no closed form solution has ever been reported. In this paper, we derive a closed form buffer sizing function f(x) where f(x) gives the optimal buffer size for the buffer at position x. We show that f(x) can be expressed in terms of the Weierstrass elliptic function p(x) and its derivative p'(x).

Original language	English
Title of host publication	Proceedings of The 11th Asia and South Pacific Conference on Design Automation, ASP-DAC 2006
Publisher	IEEE
Number of pages	5
ISBN (Print)	9780780394513, 0780394518
DOIs	https://doi.org/10.1109/ASPDAC.2006.1594701 https://doi.org/10.1145/1118299.1118378
Publication status	Published - 25 Jan 2006
Event	11th Asia and South Pacific Design Automation Conference, ASP-DAC 2006 - Pacifico Yokohama, Yokohama, Japan Duration: 24 Jan 2006 → 27 Jan 2006 https://www.aspdac.com/aspdac2006/ (Conference website) https://www.aspdac.com/aspdac2006/tpc/pdf/finalprogprint_nosign.pdf (Conference programme ) https://ieeexplore.ieee.org/xpl/conhome/10626/proceeding (Conference proceedings)

Publication series

Name	Proceedings of The Asia and South Pacific Conference on Design Automation, ASP-DAC
Volume	2006

Conference

Conference	11th Asia and South Pacific Design Automation Conference, ASP-DAC 2006
Country/Territory	Japan
City	Yokohama
Period	24/01/06 → 27/01/06
Internet address	https://www.aspdac.com/aspdac2006/ (Conference website) https://www.aspdac.com/aspdac2006/tpc/pdf/finalprogprint_nosign.pdf (Conference programme ) https://ieeexplore.ieee.org/xpl/conhome/10626/proceeding (Conference proceedings)

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Vogel, S., & Wong, M. D. F. (2006). Closed form solution for optimal buffer sizing using the Weierstrass elliptic function. In Proceedings of The 11th Asia and South Pacific Conference on Design Automation, ASP-DAC 2006 Article 1594701 (Proceedings of The Asia and South Pacific Conference on Design Automation, ASP-DAC; Vol. 2006). IEEE. https://doi.org/10.1109/ASPDAC.2006.1594701, https://doi.org/10.1145/1118299.1118378

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abstract = "This paper presents a fundamental result on buffer sizing. Given an interconnection wire with n buffers evenly spaced along the wire, we would like to size all buffers such that the Elmore delay is minimized. It is well known that the problem can be solved by an iterative algorithm which sizes one buffer at a time. However, no closed form solution has ever been reported. In this paper, we derive a closed form buffer sizing function f(x) where f(x) gives the optimal buffer size for the buffer at position x. We show that f(x) can be expressed in terms of the Weierstrass elliptic function p(x) and its derivative p'(x).",

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Vogel, S & Wong, MDF 2006, Closed form solution for optimal buffer sizing using the Weierstrass elliptic function. in Proceedings of The 11th Asia and South Pacific Conference on Design Automation, ASP-DAC 2006., 1594701, Proceedings of The Asia and South Pacific Conference on Design Automation, ASP-DAC, vol. 2006, IEEE, 11th Asia and South Pacific Design Automation Conference, ASP-DAC 2006, Yokohama, Japan, 24/01/06. https://doi.org/10.1109/ASPDAC.2006.1594701, https://doi.org/10.1145/1118299.1118378

Closed form solution for optimal buffer sizing using the Weierstrass elliptic function. / Vogel, S.; Wong, M. D. F.
Proceedings of The 11th Asia and South Pacific Conference on Design Automation, ASP-DAC 2006. IEEE, 2006. 1594701 (Proceedings of The Asia and South Pacific Conference on Design Automation, ASP-DAC; Vol. 2006).

Research output: Chapter in book/report/conference proceeding › Conference proceeding › peer-review

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Closed form solution for optimal buffer sizing using the Weierstrass elliptic function

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