Hypergeometric functions in Exact Geometric Computation

Zilin Du, Maria Eleftheriou, José E. Moreira, Chee Yap

Research output: Contribution to journalConference article

Abstract

Most problems in computational geometry are algebraic. A general approach to address nonrobustness in such problems is Exact Geometric Computation (EGC). There are now general libraries that support EGC for the general programmer (e.g., Core Library, LEDA Real). Many applications require non-algebraic functions as well. In this paper, we describe how to provide non-algebraic functions in the context of other EGC capabilities. We implemented a multiprecision hypergeometric series package which can be used to evaluate common elementary math functions to an arbitrary precision. This can be achieved relatively easily using the Core Library which supports a guaranteed precision level of accuracy. We address several issues of efficiency in such a hypergeometric package: automatic error analysis, argument reduction, preprocessing of hypergeometric parameters, and precomputed constants. Some preliminary experimental results are reported.

Original languageEnglish (US)
Pages (from-to)53-64
Number of pages12
JournalElectronic Notes in Theoretical Computer Science
Volume66
DOIs
StatePublished - Jul 2002
EventCCA 2002, Computability and Complexity in Analysis (ICALP 2002 Satellite Workshop) - Malaga, Spain
Duration: Jul 12 2002Jul 13 2002

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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