A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format

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...

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Vydáno v:	IEEE transactions on computers Ročník 58; číslo 2; s. 148 - 162
Hlavní autoři:	Cornea, M., Harrison, J., Anderson, C., Tang, P., Schneider, E., Gvozdev, E.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York IEEE 01.02.2009 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Accuracy Algorithms Approximation methods Arithmetic binary-decimal conversion Computer arithmetic Computer programs correct rounding decimal floating-point Decimals Encoding Floating point arithmetic Format Hardware Mathematical analysis multiple-precision arithmetic Software Table lookup General Software libraries Numerical Algorithms and Problems Standards
ISSN:	0018-9340, 1557-9956
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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].
AbstractList	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]. 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 [abstract truncated by publisher]. 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.
Author	Schneider, E. Harrison, J. Anderson, C. Cornea, M. Tang, P. Gvozdev, E.
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Cites_doi	10.1109/ARITH.2007.7 10.1109/ACSSC.2002.1196949 10.1109/40.768506 10.1109/ieeestd.1985.82928 10.1147/rd.511.0217 10.1109/ARITH.2003.1207666 10.1145/103162.103163 10.1109/ASAP.2003.1212858 10.1145/221332.221334 10.1145/368518.368529 10.3403/00836057 10.1109/ACSSC.2001.987708 10.1049/ip-cdt:20020407 10.1109/TC.1983.1676238
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References	ref12 ref15 ref14 Gray (ref16) 2001; 2 ref11 (ref23) 2008 (ref20) 2006 (ref25) 2004 ref17 ref19 Boldo (ref2) Duale (ref10) 2007 Wang (ref26) (ref22) 2005 Bohlender (ref1) 1987 ref21 Tang (ref24) (ref18) 1998 Weik (ref27) 2007 ref8 ref7 ref4 (ref13) 1998 ref3 ref6 ref5 Cowlishaw (ref9) 2006
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SubjectTerms	Accuracy Algorithms Approximation methods Arithmetic binary-decimal conversion Computer arithmetic Computer programs correct rounding decimal floating-point Decimals Encoding Floating point arithmetic Format Hardware Mathematical analysis multiple-precision arithmetic Software Table lookup
Title	A Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic Using the Binary Encoding Format
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