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1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)最新文献

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A minicomputer micxoprogrammable, arithmetic processor 一种微型计算机，可编程，算术处理器
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156988
T. Kehl, K. Burkhardt
{"title":"A minicomputer micxoprogrammable, arithmetic processor","authors":"T. Kehl, K. Burkhardt","doi":"10.1109/ARITH.1975.6156988","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156988","url":null,"abstract":"Except for a few notable examples, all computers have been designed as \"adder-central\" architectures. \"Adder-central,\" as used here, refers to an organization which places the Arithmetic Logic Unit (ALU) at that junction of the system through which all data must flow — thus creating a bottleneck. In the early days, when adders were expensive, cost considerations precluded more than one ALU. Nowadays powerful ALU's are available at very low cost and a designer, even of minicomputers, can consider placing more than one ALU in a system.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128335148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Fixed-slash and floating-slash rational arithmetic 固定斜杠和浮动斜杠有理数算术
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156999
D. Matula
{"title":"Fixed-slash and floating-slash rational arithmetic","authors":"D. Matula","doi":"10.1109/ARITH.1975.6156999","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156999","url":null,"abstract":"A finite precision rational number system provides for representation of a collection of rational numbers subject to limitations on numerator and denominator magnitude. In fixed-point and floatingpoint radix number systems only rationals of the form i/βj, where β is the base, can be realized. In contrast, a finite precision rational number system will allow representation of practically all simple fractions encountered in applications. In this preliminary report we first propose two types of finite precision rational number systems which we term fixed-slash and floating-slash systems [2]. We then consider the conversion (rounding) problem, that is, the determination of a number satisfying the numerator and denominator constraints approximating a given non representable real value. We show that the rounding problem is solvable by an efficient procedure, which we term mediant conversion, that derives from the theory of continued fractions.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126684910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
On-line algorithms for division and multiplication 在线除法和乘法算法
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6157007
Kishor S. Trivedi, M. Ercegovac
{"title":"On-line algorithms for division and multiplication","authors":"Kishor S. Trivedi, M. Ercegovac","doi":"10.1109/ARITH.1975.6157007","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6157007","url":null,"abstract":"In this paper we are considering problems of division and multiplication in a computational environment in which all basic arithmetic algorithms satisfy \"on-line\" property: to generate jth digit of the result it is necessary and sufficient to have argument(s) available up to the (j+δ)th digit, where the index difference 6 is a small positive constant. Such an environment, due to its potential to perform a sequence of operations in an overlapped fashion, could conveniently speed up an arithmetic multiprocessor structure or it could be useful in certain real-time applications, with inherent on-line properties. The on-line property implies a left-to-right digit-by-digit type of algorithm and consequently, a redundant representation, at least, of the results. For addition and subtraction such algorithms, satisfying on-line property, can be easily specified. Multiplication requires a somewhat more elaborate approach and there are several possible ways of defining an on-line algorithm. However, the existence of an on-line division algorithm is not obvious and its analysis appears interesting.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122098288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 133
Consequences of a properly implemented computer arithmetic for periodicities of iterative methods 迭代方法周期性的正确实现的计算机算法的结果
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156992
R. Klatte, C. Ullrich
{"title":"Consequences of a properly implemented computer arithmetic for periodicities of iterative methods","authors":"R. Klatte, C. Ullrich","doi":"10.1109/ARITH.1975.6156992","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156992","url":null,"abstract":"In ordered sets it is possible to show under certain assumptions two basic theorems concerning the cycle length of sequences of iterates generated by monotone operators. These results are applied to different iterative methods, where the conclusions are valid for the sequences of iterates produced by the numerical computations only, if the used computer arithmetic is properly implemented.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114191212","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The UNRAU a Unified Numeric Representation Arithmetic Unit UNRAU是统一的数字表示算术单元
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6157001
B. Shriver, Peter Kornerup
{"title":"The UNRAU a Unified Numeric Representation Arithmetic Unit","authors":"B. Shriver, Peter Kornerup","doi":"10.1109/ARITH.1975.6157001","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6157001","url":null,"abstract":"A companion paper entitled, \"A Unified Numeric Data Type in Pascal\", proposes the substitution of the standard data type real of the language Pascal with a unified data representation termed numeric. The numeric data type can represent a variety of arithmetic operands such as integers, normalized floating point numbers, and centered-radius intervals. This paper describes an arithmetic unit which is capable of executing the standard arithmetic operations (addition, subtraction, multiplication, and division) on pairs of operands specified to be of the numeric data type. This arithmetic unit, called the UNRAU — Unified Numeric Representation Arithmetic Unit, supports operations on operands externally represented as 5-tuples (t, a, e, f, r). The UNRAU provides for automatic conversion among the various data types and can also be used to perform an explicit conversion on a single operand. It is intended to implement the UNRAU on a dynamically microprogrammable microprocessor to determine what host facilities are required to efficiently realize such an arithmetic unit and to experiment with the high level language support of such a unit.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115771875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The impact of parallelism on software 并行性对软件的影响
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156977
Gary W. Cobb
{"title":"The impact of parallelism on software","authors":"Gary W. Cobb","doi":"10.1109/ARITH.1975.6156977","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156977","url":null,"abstract":"There seems to be a tug-of-war raging between computer procurement technical evaluation committees, computer designers and scholars of computer science and numerical analysis over the issue of parallelism in computations. Caught in the middle seems to be the user community and the compiler writers. For the scope of this paper, the term \"user community\" will be assumed to be Fortran programmers who are involved in solving problems that require large computer resources, e.g. plasma research, weather prediction, ray tracing, seismic analysis, econometric modeling, weapons research, reactor calculation, etc.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129936133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Matrix processors using p-ADIC arithmetic for exact linear computations 矩阵处理器使用p-ADIC算法进行精确的线性计算
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156994
E. V. Krishnamurtht
{"title":"Matrix processors using p-ADIC arithmetic for exact linear computations","authors":"E. V. Krishnamurtht","doi":"10.1109/ARITH.1975.6156994","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156994","url":null,"abstract":"A unique code (called Hensel's code) is derived for a rational number, by truncating its infinite padic expansion. The four basic arithmetic algorithms for these codes are described and their application to rational matrix computations is demonstrated by solving a system of linear equations exactly, using the Gaussian elimination procedure. A comparative study of the computational complexity involved in this arithmetic and the multiple prime module arithmetic is made with reference to matrix computations. On this basis, a multiple padic scheme is suggested for the design of a highly parallel matrix processor.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114402988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
Minimization methods for macrocellular arithmetic networks 大细胞算法网络的最小化方法
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6157000
R. Mori, M. Elia, A. Serra
{"title":"Minimization methods for macrocellular arithmetic networks","authors":"R. Mori, M. Elia, A. Serra","doi":"10.1109/ARITH.1975.6157000","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6157000","url":null,"abstract":"This paper presents a new method to study arithmetic combinatorial circuits. Using polynomial associated to the input-output sequences and to the systems it is possible to solve the problem of minimization of the number of the component blocks. Particularly, the important case of the multiple outputs elementary units can be treated. Applications of the introduced procedures to multiplier and to fast networks for performing convolution are presented.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131142580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Redundancy in number representations as an aspect of computational complexity of arithmetic functions 数字表示中的冗余是算术函数计算复杂性的一个方面
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156970
A. Avizienis
{"title":"Redundancy in number representations as an aspect of computational complexity of arithmetic functions","authors":"A. Avizienis","doi":"10.1109/ARITH.1975.6156970","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156970","url":null,"abstract":"Introduction Recent research has led to the derivation of bounds for the time required to perform arithmetic operations by means of logical elements with a limited number of inputs [1]–[4]. The model of a (d, r) logical circuit C employed in these studies consists of a set of (d, r) logical elements and a rule of interconnection with designated sets of input and output lines. The (d, r) logical element has r input lines and one output line; these lines can assume one of d distinct states. The (d, r) logical element has a unit time delay; that is, the state of the output line at the time t+1 is a function of the states of the input lines at time t.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130703046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A bibliography on computer arithmetic 计算机算术参考书目
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6157002
B. Shriver, Eric K. Reuter
{"title":"A bibliography on computer arithmetic","authors":"B. Shriver, Eric K. Reuter","doi":"10.1109/ARITH.1975.6157002","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6157002","url":null,"abstract":"This bibliography on computer arithmetic uses, by and large, the format and abbreviations employed by Computing Reviews. It is presented in alphabetical order only and not by individual topics. The topics included, however, span the abstract and implementation problems associated with finite precision computer arithmetics.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131753010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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