{"id":184505,"date":"2004-04-21T00:00:00","date_gmt":"2009-10-31T13:49:51","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/complex-arithmetic-for-hardware-implementation-division-and-square-root\/"},"modified":"2018-07-19T09:03:19","modified_gmt":"2018-07-19T16:03:19","slug":"complex-arithmetic-for-hardware-implementation-division-and-square-root","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/complex-arithmetic-for-hardware-implementation-division-and-square-root\/","title":{"rendered":"Complex Arithmetic for Hardware Implementation: Division and Square Root"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We adapt the radix-r digit-recurrence division algorithm to complex division and square root. By prescaling the operands, we make the selection of result digits practical. This leads to a simple hardware implementation, comparable in delay and cost to implementation of a conventional division and similar to a conventional square root. Moreover, this approach allows correct rounding of complex results. The prescaling uses the same table lookup for both operations making a combined design attractive. To reduce large prescaling tables required for higher radices, we adapt the bipartite-table method to multi-variable functions. We present our scheme and discus its implementation a hardware level. We also comment on the power of operands scaling in other hardware-oriented arithmetic algorithms.<\/p>\n<p>+ Joint work with Jean-Michel Muller, CNRS-Laboratoire CNRS-ENSL-INRIA-UCBL LIP, Ecole Normale Superieure de Lyon, France.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We adapt the radix-r digit-recurrence division algorithm to complex division and square root. By prescaling the operands, we make the selection of result digits practical. This leads to a simple hardware implementation, comparable in delay and cost to implementation of a conventional division and similar to a conventional square root. Moreover, this approach allows correct [&hellip;]<\/p>\n","protected":false},"featured_media":195459,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[13558],"msr-video-type":[],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-184505","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-research-area-security-privacy-cryptography","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/KZcWX6rA7-c","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184505"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184505\/revisions"}],"predecessor-version":[{"id":496202,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/184505\/revisions\/496202"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/195459"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=184505"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=184505"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=184505"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=184505"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=184505"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=184505"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}