SRT Division Algorithms as Dynamical Systems

نویسندگان

  • Mark McCann
  • Nicholas Pippenger
چکیده

Sweeney–Robertson–Tocher (SRT) division, as it was discovered in the late 1950s, represented an important improvement in the speed of division algorithms for computers at the time. A variant of SRT division is still commonly implemented in computers today. Although some bounds on the performance of the original SRT division method were obtained, a great many questions remained unanswered. In this paper, the original version of SRT division is described as a dynamical system. This enables us to bring modern dynamical systems theory, a relatively new development in mathematics, to bear on an older problem. In doing so, we are able to show that SRT division is ergodic, and is even Bernoulli, for all real divisors and dividends. With the Bernoulli property, we are able to use entropy to prove that the natural extensions of SRT division are isomorphic by way of the Kolmogorov–Ornstein theorem. We demonstrate how our methods and results can be applied to a much larger class of division algorithms.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

An Approximate Sign Detection Method for Residue Numbers and its Application to RNS Division

we present new division algorithms for Residue Number System (RNS). The algorithms are based on a sign estimation procedure that computes the sign of a residue number to be positive, negative, or indeterminate. In the last case, magnitude of the number is guaranteed to be in a limited interval whose size is related to the cost of the sign estimation process. Our division algorithms resemble SRT...

متن کامل

The Design and Implementation of a High-performance Floating-point Divider

The increasing computation requirements of modern computer applications have stimulated a large interest in developing extremely high-performance floating-point dividers. A variety of division algorithms are available, with SRT being utilized in many computer systems. A careful analysis of SRT divider topologies has demonstrated that a relatively simple divider designed in an aggressive circuit...

متن کامل

SRT Division Diagrams and Their Usage in Designing Custom Integrated Circuits for Division

This paper describes the construction and analysis of several diagrams which depict SRT division al orithms. These diagrams yield insight into the operation of the algorithms and the many imp ementation tradeoffs available in custom circuit desi n. B radix diagrams are shown, as well as tables for higher radices. Ig Examples of simple low he tables were enerated by a program which can create an...

متن کامل

Atomic Objects for Real-Time Distributed Systems with Mixed Time Constraints

Two types of applications are considered: Hard Real-Time (HRT) and Soft Real-Time (SRT). HRT applications need to meet their deadlines under all circumstances; deadlines of SRT applications may occasionally be missed. Both applications are constructed from objects. HRT and SRT applications coexist on the same set of processors and share objects to allow a consistent exchange of data via transac...

متن کامل

Capturing Outlines of Planar Generic Images by Simultaneous Curve Fitting and Sub-division

In this paper, a new technique has been designed to capture the outline of 2D shapes using cubic B´ezier curves. The proposed technique avoids the traditional method of optimizing the global squared fitting error and emphasizes the local control of data points. A maximum error has been determined to preserve the absolute fitting error less than a criterion and it administers the process of curv...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Comput.

دوره 34  شماره 

صفحات  -

تاریخ انتشار 2003