Pub Date : 1972-05-15DOI: 10.1109/ARITH.1972.6153918
Alan B. Marcovitz
A set of standards for the design of the arithmetic unit of all general purpose digital computers has been proposed. This paper discusses that proposal and suggests that such standards are not now in the best interest of either the computer industry or the computer user.
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Pub Date : 1972-05-01DOI: 10.1109/ARITH.1972.6153916
J. Yohe
In this paper we discuss directed roundings and indicate how hardware might be designed to produce proper upward-directed, downward-directed, and certain commonly used symmetric roundings. Algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori error analysis of these algorithms are presented. Some of the basic applications of directed roundings are surveyed.
{"title":"Roundings in floating point arithmetic","authors":"J. Yohe","doi":"10.1109/ARITH.1972.6153916","DOIUrl":"https://doi.org/10.1109/ARITH.1972.6153916","url":null,"abstract":"In this paper we discuss directed roundings and indicate how hardware might be designed to produce proper upward-directed, downward-directed, and certain commonly used symmetric roundings. Algorithms for the four binary arithmetic operations and for rounding are presented, together with proofs of their correctness; appropriate formulas for a priori error analysis of these algorithms are presented. Some of the basic applications of directed roundings are surveyed.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"PC-26 1","pages":"1-36"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84855139","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}
Pub Date : 1972-05-01DOI: 10.1109/ARITH.1972.6153913
W. Cody
The appearance of hexadecimal floating point arithmetic systems has prompted a continuing discourse on the relative numerical merits of various choices of base. Until lately this discourse has centered around the static properties of the floating point representation of numbers, and has primarily concerned only binary and hexadecimal representations. Recent events may change this discourse considerably. A third numerically attractive alternative for the choice of base has been proposed, and a comparison of the dynamic numerical properties of floating point arithmetic systems has been completed. This paper surveys these recent events and summarizes our current knowledge of the numerical characteristics of floating point arithmetic systems.
{"title":"Static and dynamic numerical characteristic of floating point arithmetic","authors":"W. Cody","doi":"10.1109/ARITH.1972.6153913","DOIUrl":"https://doi.org/10.1109/ARITH.1972.6153913","url":null,"abstract":"The appearance of hexadecimal floating point arithmetic systems has prompted a continuing discourse on the relative numerical merits of various choices of base. Until lately this discourse has centered around the static properties of the floating point representation of numbers, and has primarily concerned only binary and hexadecimal representations. Recent events may change this discourse considerably. A third numerically attractive alternative for the choice of base has been proposed, and a comparison of the dynamic numerical properties of floating point arithmetic systems has been completed. This paper surveys these recent events and summarizes our current knowledge of the numerical characteristics of floating point arithmetic systems.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"136 1","pages":"1-15"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76389906","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}
Pub Date : 1972-05-01DOI: 10.1109/ARITH.1972.6153909
M. Schmookler
New applications and new technologies will make high speed decimal arithmetic an attractive alternative to binary arithmetic. This new environment will be characterized by fewer computations for each item of data. Emphasis on binary arithmetic has resulted in techniques permitting great improvements in performance. Similar improvements are needed for decimal. Various forms of LSI arrays will permit new approaches to implementing arithmetic units. ROM arrays used as complex logic blocks permit practical designs of simultaneous multipliers and batch adders, with essentially the same cost and performance for BCD operands as for binary operands of the same word size.
{"title":"Considerations in the design of a high speed decimal unit","authors":"M. Schmookler","doi":"10.1109/ARITH.1972.6153909","DOIUrl":"https://doi.org/10.1109/ARITH.1972.6153909","url":null,"abstract":"New applications and new technologies will make high speed decimal arithmetic an attractive alternative to binary arithmetic. This new environment will be characterized by fewer computations for each item of data. Emphasis on binary arithmetic has resulted in techniques permitting great improvements in performance. Similar improvements are needed for decimal. Various forms of LSI arrays will permit new approaches to implementing arithmetic units. ROM arrays used as complex logic blocks permit practical designs of simultaneous multipliers and batch adders, with essentially the same cost and performance for BCD operands as for binary operands of the same word size.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"6 1","pages":"1-10"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75308601","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}
Pub Date : 1972-05-01DOI: 10.1109/ARITH.1972.6153917
L. R. Turner
A mode of implementation of the basic floating-point operations of multiplication and addition (subtraction) is discussed which permits the exec-ution of multiple precision floating-point arithmetic with the aid of a single algorithm for multiple precision addition. Speed cannot compete with explicit implementations in hardware but the time consuming overhead of most software implementations is avoided to advantage.
{"title":"Hardware provisions for extended precision floating-point arithmetic","authors":"L. R. Turner","doi":"10.1109/ARITH.1972.6153917","DOIUrl":"https://doi.org/10.1109/ARITH.1972.6153917","url":null,"abstract":"A mode of implementation of the basic floating-point operations of multiplication and addition (subtraction) is discussed which permits the exec-ution of multiple precision floating-point arithmetic with the aid of a single algorithm for multiple precision addition. Speed cannot compete with explicit implementations in hardware but the time consuming overhead of most software implementations is avoided to advantage.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"242 1","pages":"1-5"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82890937","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}
Pub Date : 1972-05-01DOI: 10.1109/ARITH.1972.6153911
D. Atkins
The work to date has provided analytic tools to help answer design questions about table look-up type quotient selectors, and also a means for computer-aided design of any particular version deemed feasible. Reference 4 describes the application of a quotient selector in the arithmetic units of ILLIAC III.
{"title":"The analysis and design of a class of quotient digit selectors","authors":"D. Atkins","doi":"10.1109/ARITH.1972.6153911","DOIUrl":"https://doi.org/10.1109/ARITH.1972.6153911","url":null,"abstract":"The work to date has provided analytic tools to help answer design questions about table look-up type quotient selectors, and also a means for computer-aided design of any particular version deemed feasible. Reference 4 describes the application of a quotient selector in the arithmetic units of ILLIAC III.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"100 1","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76777889","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}
Pub Date : 1972-05-01DOI: 10.1109/ARITH.1972.6153888
R. O. Whitaker
About the time that Athens and Sparta were destroying each other, the Romans developed a numbering system which was to be used by the entire civilized world for the next thousand years. It served well for counting. Addition and subtraction were performed with some difficulty. Multiplication and division were impossible.
{"title":"Changing from the Arabic-decimal system to the \"Assembler Digit-Base-16\" system","authors":"R. O. Whitaker","doi":"10.1109/ARITH.1972.6153888","DOIUrl":"https://doi.org/10.1109/ARITH.1972.6153888","url":null,"abstract":"About the time that Athens and Sparta were destroying each other, the Romans developed a numbering system which was to be used by the entire civilized world for the next thousand years. It served well for counting. Addition and subtraction were performed with some difficulty. Multiplication and division were impossible.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"68 1","pages":"1-14"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78644760","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}
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