Modular Representation of Rational Fractions

Q4 Materials Science

Radioelektronika, Nanosistemy, Informacionnye Tehnologii Pub Date : 2023-08-21 DOI:10.17587/it.29.406-413

S. A. Inyutin

引用次数: 0

Abstract

The computer is designed to perform calculations, therefore it is a device for automatically processing machine data formats that display structured information. In machine data formats, the digit grid of typical and specialized computers displays numerical values on which calculations are performed in various number systems. A new modular packed representation of numerical values by rational fractions with fixed denominators, previously unknown, is introduced. For such modular representations of numerical quantities, a basic algorithm for the formation of vector components of types of representations is given with an estimate of complexity. A method of optimal approximation by packed modular representations of arbitrary irregular fractions has been found. The features of algorithms for performing additive and multiplicative operations for packed representations in a modular processor are analyzed.

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有理分数的模表示

计算机是为执行计算而设计的，因此它是自动处理显示结构化信息的机器数据格式的设备。在机器数据格式中，典型和专用计算机的数字网格显示在各种数字系统中执行计算的数值。引入了一种新的用固定分母的有理数分式表示数值的模填充形式，这是以前未知的。对于这种数值量的模表示，给出了表示类型的向量分量形成的基本算法，并给出了复杂度的估计。提出了一种用任意不规则分数的填充模表示的最优逼近方法。分析了在模块化处理器中对封装表示进行加法和乘法运算的算法特点。

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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来源期刊

Radioelektronika, Nanosistemy, Informacionnye Tehnologii Materials Science-Materials Science (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Journal “Radioelectronics. Nanosystems. Information Technologies” (abbr RENSIT) publishes original articles, reviews and brief reports, not previously published, on topical problems in radioelectronics (including biomedical) and fundamentals of information, nano- and biotechnologies and adjacent areas of physics and mathematics. The authors of the journal are academicians, corresponding members and foreign members of the Russian Academy of Natural Sciences (RANS) and their colleagues, as well as other russian and foreign authors on the proposal of the members of RANS, which can be obtained by the author before sending articles to the editor or after its arrival on the recommendation of a member of the editorial board or another member of the RANS, who gave the opinion on the article at the request of the editior. The editors will accept articles in both Russian and English languages. Articles are internally peer reviewed (double-blind peer review) by members of the Editorial Board. Some articles undergo external review, if necessary. Designed for researchers, graduate students, physics students of senior courses and teachers. It turns out 2 times a year (that includes 2 rooms)