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

Sebastian Vogel, Martin D.F. Wong

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

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 script P sign(x) and its derivative script P sign'(x).

Original languageEnglish (US)
Title of host publicationProceedings of the ASP-DAC 2006
Subtitle of host publicationAsia and South Pacific Design Automation Conference 2006
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages315-319
Number of pages5
ISBN (Print)0780394518, 9780780394513
DOIs
StatePublished - Jan 1 2006
EventASP-DAC 2006: Asia and South Pacific Design Automation Conference 2006 - Yokohama, Japan
Duration: Jan 24 2006Jan 27 2006

Publication series

NameProceedings of the Asia and South Pacific Design Automation Conference, ASP-DAC
Volume2006

Other

OtherASP-DAC 2006: Asia and South Pacific Design Automation Conference 2006
CountryJapan
CityYokohama
Period1/24/061/27/06

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering

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