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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Shrnutí: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].
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2008.209