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

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Mathematical foundation of computer arithmetic 计算机算术的数学基础
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156996
U. Kulisch
{"title":"Mathematical foundation of computer arithmetic","authors":"U. Kulisch","doi":"10.1109/ARITH.1975.6156996","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156996","url":null,"abstract":"During the last years a number of papers concerning a mathematical foundation of computer arithmetic have been written. Some of these papers are still unpublished. The papers consider the spaces which occur in numerical computations on computers in dependence of a properly defined computer arithmetic. The following treatment gives a summary of the main ideas of these papers. Many of the proofs had to be sketched or completely omitted. In such cases the full information can be found in the references.","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":"116125965","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: 7
Mirror arithmetic 镜子算术
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156975
Jean P. Chinal
{"title":"Mirror arithmetic","authors":"Jean P. Chinal","doi":"10.1109/ARITH.1975.6156975","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156975","url":null,"abstract":"Mirror coding for signed numbers is defined \"by means pf a set of primitive powers of two {+2<sup>n</sup>, −2<sup>n−1</sup>, …−2°} where signs of the usual set used in 2's complement representation are reversed. Use of the mirror representation is shown as an alternate design approach and is illustrated \"by a special purpose adder design in mirror code, by an alternate proof of a basic property of sign-ed-digit arithmetic and as another interpretation of cells used in some array multipliers for signed numbers. Lastly, the concept is used to define a variable mode redundant coding, allowing simple sign-flipping without overflow.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"75 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":"125010923","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
Optimum array-like structures for high-speed arithmetic 高速算法的最佳类数组结构
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156968
D. Agrawal
{"title":"Optimum array-like structures for high-speed arithmetic","authors":"D. Agrawal","doi":"10.1109/ARITH.1975.6156968","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156968","url":null,"abstract":"Array-like structures for high-speed multiplication, division, square and square-root operations have been described in this paper. In these designs the division and square-rooting time have been made to approach to that of multiplication operation. These structures are optimum from speed and versatility point of view. Most of the cellular arrays described in the literature are adequately slow. The time delay is particularly significant in the division and square-rooting operations due to the ripple effect of the carries. Though the carry-save technique has been widely utilized for multiplication operation, it has been only recently employed by Cappa et. al. in the design of a non-restoring divider array. This requires sign-bit detection that makes the array non-uniform. Such an array has been named as an array-like structure. The carry-save method has been extended here for restoring division operation. Due to sign-detection and overflow correction requirements, the restoring method is slightly complex. But the main advantage of such restoring array is in its simple extension for multiplication operation. The array for the two operations, when pipelined, will have more computing power than all other multiplier-divider arrays. Suggestions have also been included for further speed improvement. The technique applied for division operation is as well applicable for the square-rooting and an array-like structure for square-square-rooting operations has also been given. For performing any one of the four operations, the only manipulation to be done is to combine the two arrays; one for multiplication-division and another for square-square-rooting. Possible methods of combining the two arrays have been indicated and their relative advantages and disadvantages have been mentioned. Finally, a generalized pipeline array-like structure with complete internal details and for 4-bit operation, has been shown. Due consideration has also been given to the possibility of large-scale-integration of different arrays presented in this paper.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"33 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":"126738797","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: 5
Understandable arithmetic 可以理解算术
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6157004
P. H. Sterbenz
{"title":"Understandable arithmetic","authors":"P. H. Sterbenz","doi":"10.1109/ARITH.1975.6157004","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6157004","url":null,"abstract":"Since the floating-point operations form the \"basic steps in our programs, the programmer has to understand the results that — will be produced by these operations. This paper discusses operations which have been or might be implemented in the hardware. The emphasis is on making the results easy for the user to understand.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"48 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":"127796025","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
ROM-rounding: A new rounding scheme rom舍入:一种新的舍入方案
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156995
D. Kuck, D. S. Parker, A. Sameh
{"title":"ROM-rounding: A new rounding scheme","authors":"D. Kuck, D. S. Parker, A. Sameh","doi":"10.1109/ARITH.1975.6156995","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156995","url":null,"abstract":"ROM-rounding is introduced and is shown to compare favorably with existing floating-point rounding methods on design considerations and on performance over a series of error tests. The error-retarding value of guard digits, of rounding the aligned operand, and of rounding in general are discussed.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"32 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":"131794246","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: 5
Significance arithmetic: Application to a partial differential equation 显著性算法:在偏微分方程中的应用
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156973
R. Bivins, N. Metropolis
{"title":"Significance arithmetic: Application to a partial differential equation","authors":"R. Bivins, N. Metropolis","doi":"10.1109/ARITH.1975.6156973","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156973","url":null,"abstract":"The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference equation approximation to Burgers' equation.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"14 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":"133114285","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 logic of modulo 2k + 1 adders 模2k + 1加法器的逻辑
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156976
Jean P. Chinal
{"title":"The logic of modulo 2k + 1 adders","authors":"Jean P. Chinal","doi":"10.1109/ARITH.1975.6156976","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156976","url":null,"abstract":"The design of modulo 2k + 1 adders for arbitrary k is considered, with the objective of achieving a logic structure as regular as possible so as to allow a convenient implementation in large-scale integration technology (LSI). It is shown how the design problem can be reduced to the recursive generation of a subtract signal and to the merging, in various degrees, of the corresponding logic with the logic of an ordinary adder or, alternately, of a so-called signed-carry adder which is defined and designed itself in general, with both recursive and explicit carry schemes. Modulo 2k + 1 adder designs are given, one with conventional adder, another based on signed-carry adder and a third, derived from the signed-carry scheme, where subtract signal generation and carry logic are merged. This last scheme can be set up with two backward recursion chains and five or six forward ones. Two more basic variants are finally indicated for this integrated scheme, aiming at reducing as much as possible the residual logic structure irregularity presented by the most significant position in the word","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":"129785602","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
The design and use of a floating-point (software) simulator for testing the arithmetic behavior of mathematical software 为测试数学软件的运算行为，设计并使用了一个浮点(软件)模拟器
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156985
M. Ginsberg, D. Frailey
{"title":"The design and use of a floating-point (software) simulator for testing the arithmetic behavior of mathematical software","authors":"M. Ginsberg, D. Frailey","doi":"10.1109/ARITH.1975.6156985","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156985","url":null,"abstract":"An important aspect of any evaluative procedure for developing high quality mathematical software is testing the effects of arithmetic behavior on algorithmic implementations. This paper describes a proposed design approach and various applications of a high-level language floating-point simulator which has two inputs: the program to be tested and a description of the floating-point arithmetic under which the routine is to be executed. A brief discussion of the motivation for this approach is given along with a review of existing efforts to study the influences of computer arithmetic on the accuracy and reliability of mathematical software. An overview of the simulator's structure is presented as well as suggestions for experiments to assist in determining the effects of floatingpoint behavior across several different computer architectures. Present and future uses of the simulator are also indicated.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"AES-20 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132502997","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
Compatible number representations 兼容的数字表示
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156990
R. A. Keir
{"title":"Compatible number representations","authors":"R. A. Keir","doi":"10.1109/ARITH.1975.6156990","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156990","url":null,"abstract":"A compatible number system for mixed fixed-point and floating-point arithmetic is described in terms of number formats and opcode sequences (for hardwired or microcoded control). This inexpensive system can be as fast as fixed-point arithmetic on integers, is faster than normalized arithmetic in floating point, gets answers identical to those of normalized arithmetic, and automatically satisfies the Algol-60 mixed-mode rules. The central concept is the avoidance of meaningless \"normalization\" following arithmetic operations. Adoption of this system could lead to simpler compilers.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"12 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":"128182402","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: 4
Higher radix, non-restoring division: History and recent developments 高基数，非恢复法:历史和最近的发展
1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH) Pub Date : 1975-11-01 DOI: 10.1109/ARITH.1975.6156969
D. Atkins
{"title":"Higher radix, non-restoring division: History and recent developments","authors":"D. Atkins","doi":"10.1109/ARITH.1975.6156969","DOIUrl":"https://doi.org/10.1109/ARITH.1975.6156969","url":null,"abstract":"Developments Reported Prior to 1972. This paper reviews work related to the theory and application of higher-radix, non-restoring division as originally defined by Robertson in 1958 [1]. The class of division methods proposed by Robertson is described by the recursive relationship:","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"15 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":"124631560","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
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