# SOFTWARE IMPLEMENTATION OF THE IEEE 754R DECIMAL FLOATING-POINT ARITHMETIC

### Marius Cornea, Cristina Anderson, Charles Tsen

#### Abstract

The IEEE Standard 754-1985 for Binary Floating-Point Arithmetic (IEEE Std. 754, 1985) is being revised (IEEE Std. 754R Draft, 2006), and an important addition to the current text is the definition of decimal floating-point arithmetic (Cowlishaw, 2003). This is aimed mainly to provide a robust, reliable framework for financial applications that are often subject to legal requirements concerning rounding and precision of the results in the areas of banking, telephone billing, tax calculation, currency conversion, insurance, or accounting in general. Using binary floating-point calculations to approximate decimal calculations has led in the past to the existence of numerous proprietary software packages, each with its own characteristics and capabilities. New algorithms are presented in this paper which were used for a generic implementation in software of the IEEE 754R decimal floating-point arithmetic, but may also be suitable for a hardware implementation. In the absence of hardware to perform IEEE 754R decimal floating-point operations, this new software package that will be fully compliant with the standard proposal should be an attractive option for various financial computations. The library presented in this paper uses the binary encoding method from (IEEE Std. 754R Draft, 2006) for decimal floating-point values. Preliminary performance results show one to two orders of magnitude improvement over a software package currently incorporated in GCC, which operates on values encoded using the decimal method from (IEEE Std. 754R Draft, 2006).

#### References

- IEEE Standard 754-1985 for Binary Floating-Point Arithmetic. IEEE, 1985
- Draft of the Revised IEEE Standard 754-1985, http://754r.ucbtest.org/drafts/754r.pdf
- Michael Cowlishaw, Decimal Floating-Point: Algorism for Computers 2003, 16th IEEE Symposium on Computer Arithmetic.
- M. Erle, E, Schwarz, and M. Schulte, Decimal Multiplication with Efficient Partial Product Generation, 17th Symposium on Computer Arithmetic, 2005
- Peter Tang, BID Format, IEEE 754R Draft http://754r.ucbtest.org/subcommittee/bid.pdf
- Jon Grimm, Decimal Floating-Point Extension for C via decNumber, IBM, GCC Summit, 2005
- (decNumber,2005)http://www.alphaworks.ibm.com/tech/d ecnumber

#### Paper Citation

#### in Harvard Style

Cornea M., Anderson C. and Tsen C. (2006). **SOFTWARE IMPLEMENTATION OF THE IEEE 754R DECIMAL FLOATING-POINT ARITHMETIC** . In *Proceedings of the First International Conference on Software and Data Technologies - Volume 1: ICSOFT,* ISBN 978-972-8865-69-6, pages 13-20. DOI: 10.5220/0001320900130020

#### in Bibtex Style

@conference{icsoft06,

author={Marius Cornea and Cristina Anderson and Charles Tsen},

title={SOFTWARE IMPLEMENTATION OF THE IEEE 754R DECIMAL FLOATING-POINT ARITHMETIC},

booktitle={Proceedings of the First International Conference on Software and Data Technologies - Volume 1: ICSOFT,},

year={2006},

pages={13-20},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001320900130020},

isbn={978-972-8865-69-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Software and Data Technologies - Volume 1: ICSOFT,

TI - SOFTWARE IMPLEMENTATION OF THE IEEE 754R DECIMAL FLOATING-POINT ARITHMETIC

SN - 978-972-8865-69-6

AU - Cornea M.

AU - Anderson C.

AU - Tsen C.

PY - 2006

SP - 13

EP - 20

DO - 10.5220/0001320900130020