Program Verification in the presence of complex numbers, functions with branch cuts etc

James Davenport, Russell Bradford, Matthew England, David Wilson

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

25 Citations (Scopus)
110 Downloads (Pure)

Abstract

In considering the reliability of numerical programs,
it is normal to “limit our study to the semantics
dealing with numerical precision” (Martel, 2005). On the other
hand, there is a great deal of work on the reliability of
programs that essentially ignores the numerics. The thesis
of this paper is that there is a class of problems that fall
between these two, which could be described as “does the lowlevel
arithmetic implement the high-level mathematics”. Many
of these problems arise because mathematics, particularly
the mathematics of the complex numbers, is more difficult
than expected: for example the complex function log is not
continuous, writing down a program to compute an inverse
function is more complicated than just solving an equation,
and many algebraic simplification rules are not universally
valid.
The good news is that these problems are theoretically
capable of being solved, and are practically close to being solved,
but not yet solved, in several real-world examples. However,
there is still a long way to go
Original languageEnglish
Title of host publicationProceedings of SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Place of PublicationPiscataway
PublisherIEEE
Pages83-88
Number of pages6
ISBN (Print)9781467350266
DOIs
Publication statusPublished - 2012
EventSYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing - Timisoara, Romania
Duration: 25 Sep 201228 Sep 2012

Conference

ConferenceSYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
CountryRomania
CityTimisoara
Period25/09/1228/09/12

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    Davenport, J., Bradford, R., England, M., & Wilson, D. (2012). Program Verification in the presence of complex numbers, functions with branch cuts etc. In Proceedings of SYNASC 2012: 14th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (pp. 83-88). IEEE. https://doi.org/10.1109/SYNASC.2012.68