Vol 15, No 1 (2011) > Articles >

Are IEEE 754 32-Bit and 64-Bit Binary Floating-Point Accurate Enough?

Bernaridho Hutabarat 1 , I Ketut Purnama 1 , Mochamad Hariadi 1 , Mauridhi Purnomo 1


  1. Department of Electrical Engineering, Faculty of Industrial Engineering, Institut Teknologi Sepuluh Nopember, Sukolilo, Surabaya 60111, Indonesia


Abstract: This paper describes a research toward the accuracy of floating-point values, and effort to reveal the real accuracy. The methods used in this research paper are assignment of values, assignment of value of arithmetic expressions, and output the values using floating-point value format that helps reveal the accuracy. The programming-tool used are Visual C# 9, Visual  C++  9,  Java  5,  and  Visual  BASIC  9.  These  tools  run  on  top  of  Intel 80x 86  hardware.  The  results  show  that 1*10-x cannot be accurately represented, and the approximate accuracy ranges only from 7 to 16 decimal digits.
Keywords: accuracy, binary, floating-point, IEEE 754
Published at: Vol 15, No 1 (2011) pages: 68-74

Access Counter: 1228 views, 632 PDF downloads, .

Full PDF Download


W. Kahan, Intel and Floating Point, 2008, in www.intel.com/standards/floatingpoint.pdf.

D. Goldberg, ACM Computing Surveys 23/1 (1991) 5.

W. Stalling, Computer Organization and Architecture, 7th ed, Pearson Education, 2006, p.750.

A.S. Tanenbaum, Structured Computer Organization, 5th ed, Pearson Prentice Hall, Boston, 2006, p.777.

W.D. Clinger, Conference on Programming Language Design and Implementation, Utah, USA, 2003, p.360.

M.F. Cowlishaw, Proceedings 16th IEEE Symp. Comput. Arithmetic. Washington DC, USA, 2003, p.104.

J.J. Fernández, I. Garc´ıa, E.M. Garzón, Future Generation Computer Systems, Elsevier, 19/8 (2003) 1321.

H.M. Deitel, P.J. Deitel, Visual BASIC 2008 How To Program, Pearson Education, New Jersey, 2009, p.1452.

P.J. Deitel, H.M. Deitel, Java: How to Program, 5th Edition, Pearson, New Jersey, 2006, p.1546.

ECMA International, Standard ECMA-334 C# Language Specification, 4th ed, ECMA International, Geneva, 2006, p.553.

ECMA International, Standard ECMA-335 C# Common Language Infrastructure, 4th ed, ECMA International, Geneva, 2006, p.558.

M. Cornea, 19th IEEE International Symposium on Computer Arithmetic, Portland, Oregon, USA, 2009, p.225.

IEEE, IEEE 754 Standard for Floating-Point Arithmetic, IEEE Xplore Digital Library, http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4610935, 2008.

K. Karuri, R. Leupers, G. Ascheid, H. Meyr, M. Kedia, Proceeding of Conference on Design, European Design and Automation Association 3001 Leuven, Belgium, Belgium, 2006, p.221.

A.P. Stamatakis, H. Meier, T. Ludwig, Proceedings of 18th IEEE/ACM International Parallel/Distributed Processing, New York, USA, 2004, p.456.

M.A. Erle, M.J. Schulte, B.J. Hickmann, IEEE Symposium on Computer Arithmetic, Montpellier, France, 2007, p.46-55.

M. Cornea, C. Anderson, J. Harrison, P. Tang, E. Schneider, E. Gvozdev, C. Tsen. Proceedings of the 18th IEEE Symposium on Computer Arithmetic, Montpellier, France, 2007, p.29.

T. Lang, A. Nannarelli, IEEE Trans. Comput. 56/6 (2007) 727.

M. Burtscher, P. Ratanaworabhan. IEEE Trans. Comput. 58/1 (2009) 18.

S. Graillat, V. Ménissier-Morain, Proceedings of the 21st International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, 2007, p.341.

M. Hiromoto, H. Ochi, Y. Nakamura, IPSJ Transactions on System LSI Design Methodology, Information and Media Technologies 4/2 (2009) 250.

A. Kaivani, A.Z. Alhosseini, S. Gorgin, M. Fazlali, Proceeding of the 9th International Conference on Information Technology, IEEE Computer Society, Washington DC, USA, 2006, p.273.

G.R. Morris, V.K. Prasanna, Proceedings of the 9th Annual High Performance Embedded Computing Workshop, Lexington, USA, 2005, p.420.

S. Oishi, K. Tanabe, T. Ogita, S.M. Rump, J. Comput. Appl. Math. 205/1 (2007) 533.

S.M. Rump, P. Zimmermann, S. Boldo, G. Melquiond, BIT Numerical Mathematics 49/2 (2009) 419.

H.B. Shah, C. Gorg, M.J. Harrold, IEEE Transactions on Software Engineering, IEEE Computer Society Digital Library, 2010, p.150. DOI:http://doi.ieeecomputersociety.org/10.1109/TSE.2010.7.

C. Tsen, M.J. Schulte, S.G. Navarro, Proceedings of the IEEE International Conference on Application-Specific Systems, Architecture, and Processors, Montreal, Canada, 2007, p.115.

C. Tsen, M.J. Schulte, S.G. Navarro, Proceedings of the 25th IEEE International Conference on Computer Design, Lake Tahoe, CA, 2007, p.288.

C. Tsen, S.G. Navarro, M. Schulte, B. Hickmann, K. Compton, Proceedings 20th IEEE International Conference on Application-Specific Systems, Architectures and Processors, Boston, USA, 2009, p.8.