{"title":"在中等精度下更快的fft","authors":"J. Hoeven, Grégoire Lecerf","doi":"10.1109/ARITH.2015.10","DOIUrl":null,"url":null,"abstract":"In this paper, we show how to speed up the computation of fast Fourier transforms over complex numbers for \"medium\" precisions, typically in the range from 100 until 400 bits. On the one hand, such precisions are usually not supported by hardware. On the other hand, asymptotically fast algorithms for multiple precision arithmetic do not pay off yet. The main idea behind our algorithms is to develop efficient vectorial multiple precision fixed point arithmetic, capable of exploiting SIMD instructions in modern processors.","PeriodicalId":6526,"journal":{"name":"2015 IEEE 22nd Symposium on Computer Arithmetic","volume":"55 1","pages":"75-82"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Faster FFTs in Medium Precision\",\"authors\":\"J. Hoeven, Grégoire Lecerf\",\"doi\":\"10.1109/ARITH.2015.10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we show how to speed up the computation of fast Fourier transforms over complex numbers for \\\"medium\\\" precisions, typically in the range from 100 until 400 bits. On the one hand, such precisions are usually not supported by hardware. On the other hand, asymptotically fast algorithms for multiple precision arithmetic do not pay off yet. The main idea behind our algorithms is to develop efficient vectorial multiple precision fixed point arithmetic, capable of exploiting SIMD instructions in modern processors.\",\"PeriodicalId\":6526,\"journal\":{\"name\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"volume\":\"55 1\",\"pages\":\"75-82\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2015 IEEE 22nd Symposium on Computer Arithmetic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.2015.10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2015 IEEE 22nd Symposium on Computer Arithmetic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.2015.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper, we show how to speed up the computation of fast Fourier transforms over complex numbers for "medium" precisions, typically in the range from 100 until 400 bits. On the one hand, such precisions are usually not supported by hardware. On the other hand, asymptotically fast algorithms for multiple precision arithmetic do not pay off yet. The main idea behind our algorithms is to develop efficient vectorial multiple precision fixed point arithmetic, capable of exploiting SIMD instructions in modern processors.
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