Towards quantitative comparison of computer number systems

1981 IEEE 5th Symposium on Computer Arithmetic (ARITH) Pub Date : 1981-05-16 DOI:10.1109/ARITH.1981.6159284

S. Ong, D. Atkins

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引用次数: 1

Abstract

This paper describes an evolving Arithmetic Design System (ADS) to support the quantitative evaluation of alternate number systems with respect to a given application and realization technology. In computer arithmetic we are concerned with establishing a correspondence between abstract quantities (numbers) and some physical representation (symbols), and with simulating the operations on these symbols. The ADS is intended to help study the cost and performance of alternate simulations. A finite number system is a triple consisting of a symbol set (elements are called "digit-vectors"), an interpretation set, a mapping between these two sets, and a set of operators (digit-vector algorithms) defined on its symbol set. A set of these digit vector algorithms are proposed for conducting arithmetic design. A number system matrix defines the digit vector algorithm for numerous number systems and a method for computing time and space complexity of compositions of these algorithms is proposed. An example of how the system could be used to compare addition, with and without overflow detection, for three number systems is given.

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计算机数字系统的定量比较

本文描述了一种进化的算法设计系统(ADS)，以支持相对于给定的应用和实现技术的替代数系统的定量评估。在计算机算术中，我们关心的是建立抽象数量(数字)和某些物理表示(符号)之间的对应关系，并模拟对这些符号的运算。ADS旨在帮助研究替代模拟的成本和性能。有限数系统是由一个符号集(元素称为“数字向量”)、一个解释集、这两个集合之间的映射以及在其符号集上定义的一组操作符(数字向量算法)组成的三元组。提出了一套数字矢量算法，用于进行算法设计。一个数系矩阵定义了数系的数字向量算法，并提出了计算这些算法组合的时间和空间复杂度的方法。给出了一个例子，说明了该系统如何用于比较三个数字系统在有无溢出检测的情况下的加法运算。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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1981 IEEE 5th Symposium on Computer Arithmetic (ARITH)

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