Essential issues of modern floating point arithmetic

R.A. Iushchenko

Abstract


An overview of modern floating point arithmetic is presented. Aspects that differ from real numbers arithmetic and thus being the source of many numeric problems are emphasized. These problems scale drastically given volume of a data is large and computations being parallel. Nevertheless, it is possible to minimize and even guarantee a certain precision of the results even without considerable loss of performance.


Keywords


Floating point arithmetic

Full Text:

PDF (Russian)

References


Молчанов И.Н. Машинная математика. Проблемы и перспективы // Кибернетика и систем. анализ. – 2004. – № 6. — С. 65-72.

Молчанов И.Н., Перевозчикова О.Л., Химич А.Н. Опыт разработки семейства кластерных комплексов Инпарком // Кибернетика и систем. анализ. – 2009, № 6. – С. 88-96.

http://www.cs.unc.edu/~ibr/projects/paranoia/.

http://software.intel.com/en-us/videos/tim-mattson-floating-points-arent-real/.

Goldberg D., What Every Computer Sci-entist Should Know About Floating-Point Arithmetic // ACM Computing Surveys. – 1991. – N. 23, Vol 1. – P. 5-48.

Severance, C. An Interview with the Old Man of Floating-Point // IEEE Computer. – 1998. – N. 1. – P. 114-115.

IEEE 754-2008 Standard for Floating-Point Arithmetic

Bjørndalen J. M., Anshus O. J. Trusting floating point benchmarks - are your benchmarks really data independent?, Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing, June 18-21, 2006, Umeå, Sweden.

Higham N. Accuracy and Stability of Numerical Algorithms.

Bruce Dawson, http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm

http://software.intel.com/en-us/videos/tim-mattson-floating-points-arent-real/

Kahan W. Implementation of algorithms. Technical Report 20, Department of Computer Science, University of California, Berkeley, CA, USA, 1973.

Buttari A., Dongarra J., Kurzak J., Luszczek P., Tomov S. "Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy," ACM Transactions on Mathematical Software, Vol 34, Number 4, pp. 17-22, 2008.

Николаевская Е.А., Чистякова Т.В. Программно-алгоритмические методы повышения точности компьютерных решений // Кибернетика и системный анализ. – 2009. – № 6. – С. 172-176.

http://www.cs.unc.edu/~ibr/projects/paranoia/


Refbacks

  • There are currently no refbacks.