DLMF Tables


The DLMF Standard Reference Tables web service (DLMF Tables) is the result of a collaboration between the NIST Applied and Computational Mathematics Division (ACMD) and the University of Antwerp Computational Mathematics (CMA) Research Group. The goal of DLMF Tables is to provide a platform for computing numerical values of special functions to very high precision with guaranteed error bounds. Its most important application is to provide a standard of comparison for testing numerical software.

Currently DLMF Tables uses a multiple-precision floating-point library called MpIeee. MpIeee has been carefully constructed and tested at the University of Antwerp. The library already covers a substantial subset of special functions, for real variables only, and the university is actively working to expand its coverage to more functions and eventually to complex variables. It uses algorithms based on series and continued fraction representations, in conjunction with a detailed analysis of the rounding errors that allows results to be computed so as to lie within an arbitrarily prescribed relative error. For more details, see:

  • [1

    ] F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun and D. Lozier, Validated Evaluation of Special Mathematical Functions, Science of Computer Programming, May 2013, http://dx.doi.org/10.1016/j.scico.2013.05.006.

  • [2

    ] A. Cuyt, V. Brevik Petersen, B. Verdonk, H. Waadeland, W. Jones, Handbook of Continued Fractions for Special Functions, Springer Verlag, 2008.

  • [3

    ] A. Cuyt, B. Verdonk, H. Waadeland, Efficient and Reliable Multiprecision Implementation of Elementary and Special Functions, SIAM J. Sci. Comput. 28 (2006) 1437-1462.

  • [4

    ] M. Colman, A. Cuyt and J. Van Deun, Validated Computation of Certain Hypergeometric Functions, ACM Trans. Math. Software 38 (2011), http://dx.doi.org/10.1145/2049673.2049675.