Pub Date : 1988-11-14DOI: 10.1109/SUPERC.1988.74134
Y. Abe
The computer center of the Institute of Plasma Physics installed a supercomputer, and almost all computation time is used for simulation studies of plasmas. The status of the simulation is reported. Although particle simulation codes are used to study microscopic phenomena of plasma, they contain a charge-assignment portion that cannot be vectorized because of the recurrence of data. The author proposes an algorithm to vectorize the charge-assignment routine.<>
{"title":"Present status of computer simulation at IPP","authors":"Y. Abe","doi":"10.1109/SUPERC.1988.74134","DOIUrl":"https://doi.org/10.1109/SUPERC.1988.74134","url":null,"abstract":"The computer center of the Institute of Plasma Physics installed a supercomputer, and almost all computation time is used for simulation studies of plasmas. The status of the simulation is reported. Although particle simulation codes are used to study microscopic phenomena of plasma, they contain a charge-assignment portion that cannot be vectorized because of the recurrence of data. The author proposes an algorithm to vectorize the charge-assignment routine.<<ETX>>","PeriodicalId":103561,"journal":{"name":"Proceedings Supercomputing Vol.II: Science and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125198440","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 : 1988-11-14DOI: 10.1109/SUPERC.1988.74138
R. Frye
The smallest counterexample to Euler's generalization of Fermat's Last theorem is 95800/sup 4/+217519/sup 4/+414560/sup 4/=422481/sup 4/. The author explains how this solution was found by an exhaustive data-parallel search on several Connection Machine systems. An outline of the history of the problem and the architecture of the data-parallel Connection Machine system are presented along with the parallel algorithm.<>
{"title":"Finding 95800/sup 4/+217519/sup 4/+414560/sup 4/=422481/sup 4/ on the Connection Machine","authors":"R. Frye","doi":"10.1109/SUPERC.1988.74138","DOIUrl":"https://doi.org/10.1109/SUPERC.1988.74138","url":null,"abstract":"The smallest counterexample to Euler's generalization of Fermat's Last theorem is 95800/sup 4/+217519/sup 4/+414560/sup 4/=422481/sup 4/. The author explains how this solution was found by an exhaustive data-parallel search on several Connection Machine systems. An outline of the history of the problem and the architecture of the data-parallel Connection Machine system are presented along with the parallel algorithm.<<ETX>>","PeriodicalId":103561,"journal":{"name":"Proceedings Supercomputing Vol.II: Science and Applications","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114395036","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 : 1988-11-14DOI: 10.1109/SUPERC.1988.74139
Y. Kanada
More than 200 million decimal places of pi were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R.P. Brent in 1976. Correctness of the calculation was verified through Borwein's quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer. Two programs generated values up to 3*2/sup 26/, about 201 million. The two results agreed except for the last 21 digits. The results also agree with the 133,554,000-place calculation of pi that was done by the author in January 1987. Compared to the record in 1987, 50% more decimal digits were calculated with about 1/6 of CPU time. The computation was performed with a real-arithmetic-based vectorized fast Fourier transform (FFT) multiplier and vectorized multiple-precision add, subtract, and (single-word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820.<>
{"title":"Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation","authors":"Y. Kanada","doi":"10.1109/SUPERC.1988.74139","DOIUrl":"https://doi.org/10.1109/SUPERC.1988.74139","url":null,"abstract":"More than 200 million decimal places of pi were calculated using an arithmetic geometric mean formula independently discovered by E. Salamin and R.P. Brent in 1976. Correctness of the calculation was verified through Borwein's quartic convergent formula developed in 1983. The computation took CPU times of 5 hours 57 minutes for the main calculation and 7 hours 30 minutes for the verification calculation on the HITAC S-820 model 80 supercomputer. Two programs generated values up to 3*2/sup 26/, about 201 million. The two results agreed except for the last 21 digits. The results also agree with the 133,554,000-place calculation of pi that was done by the author in January 1987. Compared to the record in 1987, 50% more decimal digits were calculated with about 1/6 of CPU time. The computation was performed with a real-arithmetic-based vectorized fast Fourier transform (FFT) multiplier and vectorized multiple-precision add, subtract, and (single-word) constant multiplication programs. Vectorizations for the later cases were realized through first order linear recurrence vector instruction on the S-820.<<ETX>>","PeriodicalId":103561,"journal":{"name":"Proceedings Supercomputing Vol.II: Science and Applications","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127824237","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：