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[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic最新文献

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New redundant representations of complex numbers and vectors 复数和向量的新冗余表示
[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic Pub Date : 1991-06-26 DOI: 10.1109/ARITH.1991.145526
J. Duprat, Yvan Herreros, Sylvanus Kla
{"title":"New redundant representations of complex numbers and vectors","authors":"J. Duprat, Yvan Herreros, Sylvanus Kla","doi":"10.1109/ARITH.1991.145526","DOIUrl":"https://doi.org/10.1109/ARITH.1991.145526","url":null,"abstract":"A new redundant representation for complex numbers, called polygonal representation, is presented. This representation enables fast carry-free addition (in a way quite similar to the carry-free addition in signed-digits number systems), and is convenient for multiplication. In addition, the technique is extended to handle n-dimensional vectors.<<ETX>>","PeriodicalId":190650,"journal":{"name":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124932764","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: 23
Analysis of arithmetic algorithms: a statistical study 算术算法分析:统计学研究
[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic Pub Date : 1991-06-26 DOI: 10.1109/ARITH.1991.145527
F. Chaitin-Chatelin, V. Frayssé
{"title":"Analysis of arithmetic algorithms: a statistical study","authors":"F. Chaitin-Chatelin, V. Frayssé","doi":"10.1109/ARITH.1991.145527","DOIUrl":"https://doi.org/10.1109/ARITH.1991.145527","url":null,"abstract":"In order to get insight into the perturbations generated by running algorithms on a computer, one may simulate them by random perturbations on the data. For linear systems, it is found that such a statistical estimation gives results which compare favorably with those given by the backward analysis of J.H. Wilkinson (1961) and R.D. Skeel (1979). The objective is to use such a technique mainly for nonlinear problems when no theoretical analysis is available.<<ETX>>","PeriodicalId":190650,"journal":{"name":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128617729","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
Integer division using reciprocals 使用倒数进行整数除法
[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic Pub Date : 1991-06-26 DOI: 10.1109/ARITH.1991.145558
Robert Alverson
{"title":"Integer division using reciprocals","authors":"Robert Alverson","doi":"10.1109/ARITH.1991.145558","DOIUrl":"https://doi.org/10.1109/ARITH.1991.145558","url":null,"abstract":"By using a reciprocal approximation, integer division can be synthesized from a multiply followed by a shift. Without carefully selecting the reciprocal, however, the quotient obtained often suffers from off-by-one errors, requiring a correction step. The author describes the design decisions made when designing integer division for a new 64-b machine. The result is a fast and economical scheme for computing both unsigned and signed integer quotients which guarantees an exact answer without any correction. The reciprocal computation is fast enough, with one table lookup and five multiplies, so that this scheme is competitive with a dedicated divider, while requiring much less hardware specific to division. The real strength of the proposed method is division by a constant, which takes only a single multiply and shift, one operation on the machine considered. The analysis shows that the computed quotient is always exact: no adjustment or correction is necessary.<<ETX>>","PeriodicalId":190650,"journal":{"name":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130611457","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: 30
Arithmetic for digital neural networks 数字神经网络的算法
[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic Pub Date : 1991-06-26 DOI: 10.1109/ARITH.1991.145534
Dapeng Zhang, G. Jullien, W. Miller, E. Swartzlander
{"title":"Arithmetic for digital neural networks","authors":"Dapeng Zhang, G. Jullien, W. Miller, E. Swartzlander","doi":"10.1109/ARITH.1991.145534","DOIUrl":"https://doi.org/10.1109/ARITH.1991.145534","url":null,"abstract":"The implementation of large input digital neurons using designs based on parallel counters is described. The implementation of the design uses a two-cell library, in which each cell is implemented using switching trees which are pipelined binary trees of n-channel transistors. Results obtained from initial switching trees realized with a 3- mu m CMOS process indicate that the design is capable of being pipelined at 40 MHz sample rates, with better performance expected for more advanced technologies. It appears feasible to develop a wafer-scale implementation with 2000 neurons (each with 1000 inputs) that would perform 3*10/sup 12/ additions/s.<<ETX>>","PeriodicalId":190650,"journal":{"name":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126158290","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: 23
Exact accumulation of floating-point numbers 浮点数的精确累加
[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic Pub Date : 1900-01-01 DOI: 10.1109/ARITH.1991.145535
M. Muller, C. Rub, W. Rulling
{"title":"Exact accumulation of floating-point numbers","authors":"M. Muller, C. Rub, W. Rulling","doi":"10.1109/ARITH.1991.145535","DOIUrl":"https://doi.org/10.1109/ARITH.1991.145535","url":null,"abstract":"The authors present a new idea for designing a chip which computes the exact sum of arbitrarily many floating-point numbers, i.e. it can accumulate the floating-point numbers without cancellation. Such a chip is needed to provide a fast implementation of Kulisch arithmetic. This is a new theory of floating-point arithmetic which makes it possible to compute least significant bit accurate solutions to even ill-conditioned numerical problems. The proposed approach avoids the disadvantages of previously suggested designs which are too large, too slow, or consume too much power. The crucial point is a technique for a fast carry resolution in a long accumulator. It can also be implemented in software.<<ETX>>","PeriodicalId":190650,"journal":{"name":"[1991] Proceedings 10th IEEE Symposium on Computer Arithmetic","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124385257","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: 18
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