This paper discusses CELEFUNT, a pakage of Fortran programs for testing complex elementary functions.

SPECFUN is a package containing transportable FORTRAN special function programs for real arguments and accompanying test drivers. Components include Bessel functions, exponential integrals, error functions and related functions, and gamma functions and related functions.

This paper describes C programs for the support functions copysign(x,y), logb(x), scalb(x,n), nextafter(x,y), finite(x), and isnan(x) recommended in the Appendix to the IEEE Standard for Binary Floating-Point Arithmetic. In the case of logb , the modified definition given in the later IEEE Standard for Radix-Independent Floating-Point Arithmetic is followed. These programs should run without modification on most systems conforming to the binary standard.

Methods are presented for evaluating the performance of programs for the functions Γ( x ), ln Γ( x ), and ψ( x ). Accuracy estimates are based on comparisons using the manipulation theorem. Ideas for checking robustness are also given, and details on specific implementations of test programs are included.

This paper discusses the use of local Taylor series expansions for determining the accuracy of computer programs for special functions. The main example is testing of programs for exponential integrals. Additional applicaitons include testing of programs for certain Bessel functions, Dawson's integral, and error functions.

This paper presents methods for performance evaluation of computer programs for the functions erf( x ), erfc( x ), and e x 2 erfc( x ). Accuracy estimates are based on comparisons using power series expansions and an expansion in the repeated integrals of erfc( x ). Some suggestions for checking robustness are also given. Details of a specific implementation of a test program are included.

This paper presents methods for performance evaluation of the K Bessel functions. Accuracy estimates are based on comparisons involving the multiplication theorem. Some ideas for checking robustness are also given. The techniques used here are easily extended to the Y Bessel functions and, with a little more effort, to the I and J functions. Details on a specific implementation for testing the K Bessel functions are included.

Numerical software written in high-level languages often relies on machine-dependent parameters to improve portability. MACHAR is an evolving FORTRAN subroutine for dynamically determining thirteen fundamental parameters associated with a floating-point arithmetic system. The version presented here operates correctly on a large number of different floating-point systems, including those implementing the new IEEE Floating-Point Standard.

subroutine calculates sequences of modified Bessel functions of the first kind, I,+,(x), n = 0, 1 .... , NB -1 or e-Xln+,(x), n = O, 1 .....

article Free Access Share on The Computation of Real Fractional Order Bessel Functions of the Second Kind Authors: W. J. Cody Argonne National Laboratory, 9700 S. Cass Ave, Argonne, IL Argonne National Laboratory, 9700 S. Cass Ave, Argonne, ILView Profile , Rose M. Motley Argonne National Laboratory, 9700 S. Cass Ave, Argonne, IL Argonne National Laboratory, 9700 S. Cass Ave, Argonne, ILView Profile , L. Wayne Fullerton Los Alamos Scientific Laboratory, Los Alamos, NM Los Alamos Scientific Laboratory, Los Alamos, NMView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 3Issue 3Sept. 1977 pp 232–239https://doi.org/10.1145/355744.355747Published:01 September 1977Publication History 5citation660DownloadsMetricsTotal Citations5Total Downloads660Last 12 Months21Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

article The FUNPACK Package of Special Function Subroutines Share on Author: W. J. Cody Applied Mathematics Division, Argonne National Laboratory, 9700 Cass Ave., Argonne, IL Applied Mathematics Division, Argonne National Laboratory, 9700 Cass Ave., Argonne, ILView Profile Authors Info & Claims ACM Transactions on Mathematical SoftwareVolume 1Issue 1March 1975 pp 13–25https://doi.org/10.1145/355626.355631Online:01 March 1975Publication History 34citation643DownloadsMetricsTotal Citations34Total Downloads643Last 12 Months10Last 6 weeks4 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

The appearance of hexadecimal floating-point arithmetic systems has prompted a continuing discourse on the relative numerical merits of various choices of base. Until lately this discourse has centered around the static properties of the floating-point representation of numbers, and has primarily concerned only binary and hexadecimal representations. Recent events may change this discourse considerably. A third numerically attractive alternative for the choice of base has been proposed, and a comparison of the dynamic numerical properties of floating-point arithmetic systems has been completed. This paper surveys these recent events and summarizes our current knowledge of the numerical characteristics of floating-point arithmetic systems.

The appearance of hexadecimal floating point arithmetic systems has prompted a continuing discourse on the relative numerical merits of various choices of base. Until lately this discourse has centered around the static properties of the floating point representation of numbers, and has primarily concerned only binary and hexadecimal representations. Recent events may change this discourse considerably. A third numerically attractive alternative for the choice of base has been proposed, and a comparison of the dynamic numerical properties of floating point arithmetic systems has been completed. This paper surveys these recent events and summarizes our current knowledge of the numerical characteristics of floating point arithmetic systems.