Abstract
The article concerns problems of formulating standard requirements to implementations of mathematical functions working with floating-point numbers and conformance test development for them. Inconsistency and incompleteness of available standards in the domain is demonstrated. Correct rounding requirement is suggested to guarantee preservation of all important properties of functions and to support high level of interoperability between different mathematical libraries and software using them. Conformance test construction method is proposed based on different sources of test data: numbers satisfying specific patterns, boundaries of intervals of uniform function behavior, and points where correct rounding needs much higher precision than in average. Analysis of test results obtained on various implementations of POSIX mathematical library is also presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
IEEE 754-2008. IEEE Standard for Binary Floating-Point Arithmetic. NY, IEEE (2008)
Kuliamin, V.: Standardization and Testing of Implementations of Mathematical Functions in Floating Point Numbers. Programming and Computer Software 33(3), 154–173 (2007)
Kuliamin, V.: Test Construction for Mathematical Functions. In: Suzuki, K., Higashino, T., Ulrich, A., Hasegawa, T. (eds.) TestCom/FATES 2008. LNCS, vol. 5047, pp. 23–37. Springer, Heidelberg (2008)
ISO/IEC 9899. Programming Languages - C. Geneve: ISO (1999)
IEEE 1003.1-2004. Information Technology - Portable Operating System Interface (POSIX). NY, IEEE (2004)
ISO/IEC 10967-2. Information Technology - Language Independent Arithmetic - Part 2: Elementary Numerical Functions. Geneve, ISO (2002)
Goldberg, D.: What Every Computer Scientist Should Know about Floating-Point Arithmetic. ACM Computing Surveys 23(1), 5–48 (1991)
Defour, D., Hanrot, G., Lefevre, V., Muller, J.-M., Revol, N., Zimmermann, P.: Proposal for a standardization of mathematical function implementation in floating-point arithmetic. Numerical Algorithms 37(1-4), 367–375 (2004)
Ng, K.C.: Arguments Reduction for Huge Arguments: Good to the Last Bit (1992), http://www.validlab.com/arg.pdf
Kahan, W.: Minimizing q*m − n. (1983) (unpublished), http://http.cs.berkeley.edu/~wkahan/testpi/nearpi.c
de Dinechin, F., Ershov, A., Gast, N.: Towards the post-ultimate libm. In: Proc. of 17th Symposium on Computer Arithmetic, June 2005. IEEE Computer Society Press, Los Alamitos (2005)
Lefèvre, V., Muller, J.-M., Tisserand, A.: The Table Maker’s Dilemma. INRIA Research Report 98-12 (1998)
Lefèvre, V., Muller, J.-M.: Worst Cases for Correct Rounding of the Elementary Functions in Double Precision. In: Proc. of 15th IEEE Symposium on Computer Arithmetic, Vail, Colorado, USA, June (2001)
Edelman, A.: The Mathematics of the Pentium Division Bug. SIAM Review 39(1), 54–67 (1997)
Ziv, A., Aharoni, M., Asaf, S.: Solving Range Constraints for Binary Floating-Point Instructions. In: Proc. of 16th IEEE Symposium on Computer Arithmetic (ARITH-16 2003), pp. 158–163 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kuliamin, V. (2010). Standardization and Testing of Mathematical Functions. In: Pnueli, A., Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2009. Lecture Notes in Computer Science, vol 5947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11486-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-642-11486-1_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11485-4
Online ISBN: 978-3-642-11486-1
eBook Packages: Computer ScienceComputer Science (R0)