Information Technology Laboratory, Applied and Computational Mathematics Division
We are developing an online system for generating validated tables of special function values with an error certification computed to user-specified precision. A typical user might be a researcher or software developer testing his own code or confirming the accuracy of results obtained from a commercial or publicly available package. The goal is to create a standalone system, but also link to and from the NIST Digital Library of Mathematical Functions (DLMF).
The project, DLMF Standard Reference Tables on Demand (DLMF Tables), is a collaborative effort with the University of Antwerp Computational Mathematics Research Group (CMA) led by Annie Cuyt. A beta site based on CMA’s MpIeee, a multiprecision IEEE 754/854 compliant C++ floating point arithmetic library, is already available at http://dlmftables.uantwerpen.be/. The successful candidate will have the opportunity to advance our current efforts in the field of validated computing through the continued research and development of multiple precision function software providing guaranteed error bounds at arbitrary precision. The associate will also help expand DLMF Tables into a full-fledged site, as well as investigate the enhancement of existing multiprecision libraries for possible inclusion in DLMF Tables.
NIST Digital Library of Mathematical Functions. http://dlmf.nist.gov/, Release 1.0.22 of 2019-03-15. F. W. J. Olver, A. B. Olde Daalhuis, D. W. Lozier, B. I. Schneider, R. F. Boisvert, C. W. Clark, B. R. Miller, and B. V. Saunders, eds.
B. I. Schneider, B. R. Miller, and B. V. Saunders. NIST’s Digital Library of Mathematical Functions. Physics Today 71:2 (2018), 48. DOI: 10.1063/PT.3.3846.
F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun, and D. Lozier. Validated Evaluation of Special Mathematical Functions. Science of Computer Programming 90 (2014), 2-20. https://doi.org/10.1016/j.scico.2013.05.006 .
Validated software; Special functions; Multiple precision; Floating point arithmetic; Correct rounding