{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T11:25:17Z","timestamp":1763724317149,"version":"3.41.0"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2015,9,24]],"date-time":"2015-09-24T00:00:00Z","timestamp":1443052800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Reconfigurable Technol. Syst."],"published-print":{"date-parts":[[2015,10]]},"abstract":"<jats:p>Gaussian random number generators (GRNGs) are an important component in parallel Monte Carlo simulations using FPGAs, where tens or hundreds of high-quality Gaussian samples must be generated per cycle using very few logic resources. This article describes the Table-Hadamard generator, which is a GRNG designed to generate multiple streams of random numbers in parallel. It uses discrete table distributions to generate pseudo-Gaussian base samples, then a parallel Hadamard transform to efficiently apply the central limit theorem. When generating 64 output samples, the Table-Hadamard requires just 130 slices per generated sample, which is a third of the resources needed by the next best technique, while still providing higher statistical quality.<\/jats:p>","DOI":"10.1145\/2629607","type":"journal-article","created":{"date-parts":[[2015,9,29]],"date-time":"2015-09-29T19:22:29Z","timestamp":1443554549000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["The Table-Hadamard GRNG"],"prefix":"10.1145","volume":"8","author":[{"given":"David B.","family":"Thomas","sequence":"first","affiliation":[{"name":"Imperial College London, London, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,9,24]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2008.917552"},{"volume-title":"Proceedings of the Conference on Military and Aerospace Applications of Programmable Devices and Technologies.","author":"Ray","key":"e_1_2_1_2_1","unstructured":"Ray J. 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Generating high tail accuracy Gaussian random numbers in hardware using central limit theorem . In Proceedings of the 2011 IEEE\/IFIP 19th International Conference on VLSI and System-on-Chip (VLSI-SoC\u201911) . 60--65. Jamshaid Sarwar Malik, Jameel Nawaz Malik, Ahmed Hemani, and Nasir D. Gohar. 2011. Generating high tail accuracy Gaussian random numbers in hardware using central limit theorem. In Proceedings of the 2011 IEEE\/IFIP 19th International Conference on VLSI and System-on-Chip (VLSI-SoC\u201911). 60--65."},{"key":"e_1_2_1_10_1","volume-title":"Retrieved","author":"O\u2019Connor Sean","year":"2006","unstructured":"Sean O\u2019Connor . 2006 . The Hadamard Transform Fact Sheet . Retrieved August 24, 2015, from http:\/\/www.dsprelated.com\/showmessage\/65499\/1.php. Sean O\u2019Connor. 2006. The Hadamard Transform Fact Sheet. Retrieved August 24, 2015, from http:\/\/www.dsprelated.com\/showmessage\/65499\/1.php."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11265-006-0014-9"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cdt:20060188"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/FPL.2010.25"},{"volume-title":"Proceedings of the 21st IEEE International Conference on Application-Specific Systems, Architectures, and Processors. 208--215","author":"David","key":"e_1_2_1_14_1","unstructured":"David B. Thomas and Wayne Luk. 2010b. An FPGA-specific algorithm for direct generation of multi-variate gaussian random numbers . In Proceedings of the 21st IEEE International Conference on Application-Specific Systems, Architectures, and Processors. 208--215 . David B. Thomas and Wayne Luk. 2010b. An FPGA-specific algorithm for direct generation of multi-variate gaussian random numbers. In Proceedings of the 21st IEEE International Conference on Application-Specific Systems, Architectures, and Processors. 208--215."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/1926367.1926371"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.2307\/2347330"},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the International Conference on Field Programmable Logic and Applications. IEEE","author":"Zhang Guanglie L.","year":"2005","unstructured":"Guanglie L. Zhang , Philip H. W. Leong , Dong- U Lee , John D. Villasenor , Ray C. C. Cheung , and Wayne Luk . 2005 . Ziggurat-based hardware Gaussian random number generator . In Proceedings of the International Conference on Field Programmable Logic and Applications. IEEE , Los Alamitos, CA, 275--280. Guanglie L. Zhang, Philip H. W. Leong, Dong-U Lee, John D. Villasenor, Ray C. C. Cheung, and Wayne Luk. 2005. Ziggurat-based hardware Gaussian random number generator. 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