{"id":396344,"date":"2019-01-17T09:56:08","date_gmt":"2019-01-17T17:56:08","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=396344"},"modified":"2019-01-17T09:56:08","modified_gmt":"2019-01-17T17:56:08","slug":"efficient-rational-number-reconstruction","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/efficient-rational-number-reconstruction\/","title":{"rendered":"Efficient Rational Number Reconstruction"},"content":{"rendered":"<div class=\"Abstracts\">\n<div id=\"aep-abstract-id4\" class=\"abstract author\">\n<div id=\"aep-abstract-sec-id5\">\n<p>An efficient algorithm is presented for reconstructing a rational number from its residue modulo a given integer. The algorithm is based on a double-digit version of Lehmer&#8217;s multiprecision extended Euclidean algorithm. While asymptotic complexity remains quadratic in the length of the input, experiments with an implementation show that for small inputs the new algorithm is more than 3 times faster than the algorithm in common use, and is more than 7 times faster for inputs that are 100 words long.<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>An efficient algorithm is presented for reconstructing a rational number from its residue modulo a given integer. The algorithm is based on a double-digit version of Lehmer&#8217;s multiprecision extended Euclidean algorithm. While asymptotic complexity remains quadratic in the length of the input, experiments with an implementation show that for small inputs the new algorithm is [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13561],"msr-publication-type":[193715],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-396344","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-locale-en_us"],"msr_publishername":"Academic Press","msr_edition":"","msr_affiliation":"","msr_published_date":"1995-09-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"287-297","msr_chapter":"","msr_isbn":"","msr_journal":"Journal of Symbolic Computation, Issue 3","msr_volume":"20","msr_number":"","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"396350","msr_publicationurl":"","msr_doi":"https:\/\/doi.org\/10.1006\https://www.microsoft.com/jsco.1995.1051","msr_publication_uploader":[{"type":"file","title":"1-s2.0-S0747717185710516-main","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2017\/07\/1-s2.0-S0747717185710516-main-1.pdf","id":396350,"label_id":0},{"type":"doi","title":"https:\/\/doi.org\/10.1006\https://www.microsoft.com/jsco.1995.1051","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"text","value":"George E. 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