Division by two

Abstract: In this paper, on-line algorithms for division and multiplication are developed. It is assumed that the operands as well as the result flow through the arithmetic unit in a digit-by-digit, most significant digit first fashion. The use of a redundant digit set, at least for the digits of the result, is required.

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].

Abstract: This paper describes the design of an arithmetic unit called CADAC (clean arithmetic with decimal base and controlled precision). Programming language specifications for carrying out "ideal" floating-point arithmetic are described first. These specifications include detailed requirements for dynamic precision control and exception handling, along with both complex and interval arithmetic at the level of a programming language such as Fortran or PL/I.

Abstract: Even though decimal arithmetic is pervasive in financial and commercial transactions, computers are still implementing almost all arithmetic calculations using binary arithmetic. As chip real estate becomes cheaper it is becoming likely that more computer manufacturers will provide processors with decimal arithmetic engines. Programming languages and databases are expanding the decimal data types available while there has been little change in the base hardware. As a result, each language and application is defining a different arithmetic and few have considered the efficiency of hardware implementations when setting requirements. We propose a decimal format which meets the requirements of existing standards for decimal arithmetic and is efficient for hardware implementation. We propose this specification in the hope that designers will consider providing decimal arithmetic in future microprocessors and that future decimal software specifications will consider hardware efficiencies.