Cristina S. Anderson

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 [1] was revised [2], and an important addition is the definition of decimal floating-point arithmetic. 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. 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 floatingpoint arithmetic, with emphasis on using binary operations efficiently. The focus is on rounding techniques for decimal values stored in binary format, but algorithms for the more important or interesting operations of addition, multiplication, division, and conversions between binary and decimal floating-point formats are also outlined. 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.

Software Implementation of the IEEE 754R Decimal Floating-Point Arithmetic

The IEEE Standard 754-1985 for Binary Floating-Point Arithmetic [1] is being revised [2], and an important addition to the current text is the definition of decimal floating-point arithmetic [3]. 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 [2] 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 [2].