Issue No. 02 - February (2009 vol. 58)

ISSN: 0018-9340

pp: 148-162

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/TC.2008.209

Evgeny Gvozdev , Intel Corporation, Hillsboro

Marius Cornea , Intel Corporation, Hillsboro

Ping Tak Peter Tang , Intel Corporation, Hillsboro

Cristina Anderson , Intel Corporation, Hillsboro

John Harrison , Intel Corporation, Hillsboro

Eric Schneider , Intel Corporation, Hillsboro

ABSTRACT

The IEEE Standard 754-1985 for Binary Floating-Point Arithmetic [19] was revised [20], and an important addition is the definition of decimal floating-point arithmetic [8], [24]. This is intended mainly to provide a robust reliable framework for financial applications that are often subject to legal requirements concerning rounding and precision of the results, because the binary floating-point arithmetic may introduce small but unacceptable errors. Using binary floating-point calculations to emulate decimal calculations in order to correct this issue has led to the existence of numerous proprietary software packages, each with its own characteristics and capabilities. The IEEE 754R decimal arithmetic should unify the ways decimal floating-point calculations are carried out on various platforms. New algorithms and properties are presented in this paper, which are used in a software implementation of the IEEE 754R decimal floating-point arithmetic, with emphasis on using binary operations efficiently. The focus is on rounding techniques for decimal values stored in binary format, but algorithms are outlined for the more important or interesting operations of addition, multiplication, and division, including the case of nonhomogeneous operands, as well as conversions between binary and decimal floating-point formats. Performance results are included for a wider range of operations, showing promise that our approach is viable for applications that require decimal floating-point calculations. This paper extends an earlier publication [6].

INDEX TERMS

Computer arithmetic, multiple-precision arithmetic, floating-point arithmetic, decimal floating-point, computer arithmetic, correct rounding, binary-decimal conversion.

CITATION

Evgeny Gvozdev, Marius Cornea, Ping Tak Peter Tang, Cristina Anderson, John Harrison, Eric Schneider, "A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format",

*IEEE Transactions on Computers*, vol. 58, no. , pp. 148-162, February 2009, doi:10.1109/TC.2008.209SEARCH