Division and Square Root: Digit-Recurrence Algorithms and Implementations (Hardback)

This text is intended for researchers into division and square root and related operations, as well as for designers of the corresponding arithmetic units, either for general-purpose processors or for special purpose components of systems for applications such as signal and image processing. The book can also be used in graduate courses on arithmetic algorithms and processors. As the capabilities of IC technologies improve, hardware implementation of all basic arithmetic operations is becoming common in the design of processors. While the design of fast and efficient adders and multipliers is well understood, division and square root remain a serious design challenge. The reasons are the intrinsic dependence among the iteration steps and the complexity of the result-digit generation function. To limit the effect of these on the execution time, an extensive theory has been developed, based on concepts such as redundant number representations, prediction of result digits, and operand scaling. The authors give a unified presentation of the most relevant aspects of this theory. This can serve as the basis of specific implementations, as well as the foundations for further research. This work integrates a wealth of research. The authors have drawn on results of many researchers as well as on their own work. A comprehensive bibliography is provided, as well as bibliographical notes after each chapter.