{"title":"用间接二部表查找法求非线性函数的乘积","authors":"D. Matula, A. Fit-Florea, L. McFearin","doi":"10.1109/ASAP.2002.1030710","DOIUrl":null,"url":null,"abstract":"Many function approximation procedures can obtain enhanced accuracy by an efficient table lookup of a product z=f(x)g(y). Both x and y are represented by indices of i leading bits (typically 7<i<16) for arguments normalized to [0, 1] or [1, 2]. Direct bipartite lookup employs 1/2 bits each of x and y yielding roughly an 1/2 bit result which can lose 2 to 3 bits of accuracy when f and g are nonlinear. Indirect bipartite lookup first generates i/2 bit interval index values for f(x) and g(y) using separate j-bits-in 1/2bits-out tables for f(x) and g(y) where i/2<j<i and is chosen large enough to substantially reduce the effect of nonlinearity in f(x) and g(y). The separate tables readily compensate for the high nonlinearity in f and/or g and generate interval index values representing intervals that can be tailored to minimize the maximum error of the product z=f(x)g(y) determined by an interval product table with the concatenated interval indices as the i bit input. We describe several variations in interval index generation methodology and in the design of the interval product table lookup architecture so as to obtain accuracy of 1/2 bits (or better) in output in 2-3 cycles of table lookup latency.","PeriodicalId":424082,"journal":{"name":"Proceedings IEEE International Conference on Application- Specific Systems, Architectures, and Processors","volume":"58 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2002-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Evaluating products of nonlinear functions by indirect bipartite table lookup\",\"authors\":\"D. Matula, A. Fit-Florea, L. McFearin\",\"doi\":\"10.1109/ASAP.2002.1030710\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many function approximation procedures can obtain enhanced accuracy by an efficient table lookup of a product z=f(x)g(y). Both x and y are represented by indices of i leading bits (typically 7<i<16) for arguments normalized to [0, 1] or [1, 2]. Direct bipartite lookup employs 1/2 bits each of x and y yielding roughly an 1/2 bit result which can lose 2 to 3 bits of accuracy when f and g are nonlinear. Indirect bipartite lookup first generates i/2 bit interval index values for f(x) and g(y) using separate j-bits-in 1/2bits-out tables for f(x) and g(y) where i/2<j<i and is chosen large enough to substantially reduce the effect of nonlinearity in f(x) and g(y). The separate tables readily compensate for the high nonlinearity in f and/or g and generate interval index values representing intervals that can be tailored to minimize the maximum error of the product z=f(x)g(y) determined by an interval product table with the concatenated interval indices as the i bit input. We describe several variations in interval index generation methodology and in the design of the interval product table lookup architecture so as to obtain accuracy of 1/2 bits (or better) in output in 2-3 cycles of table lookup latency.\",\"PeriodicalId\":424082,\"journal\":{\"name\":\"Proceedings IEEE International Conference on Application- Specific Systems, Architectures, and Processors\",\"volume\":\"58 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2002-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings IEEE International Conference on Application- Specific Systems, Architectures, and Processors\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ASAP.2002.1030710\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings IEEE International Conference on Application- Specific Systems, Architectures, and Processors","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ASAP.2002.1030710","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Evaluating products of nonlinear functions by indirect bipartite table lookup
Many function approximation procedures can obtain enhanced accuracy by an efficient table lookup of a product z=f(x)g(y). Both x and y are represented by indices of i leading bits (typically 7
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