{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T05:38:17Z","timestamp":1740116297134,"version":"3.37.3"},"reference-count":31,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["16-37-60003 mol_a_dk"],"award-info":[{"award-number":["16-37-60003 mol_a_dk"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J CIRCUIT SYST COMP"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p> Residue number system (RNS), due to its carry-free nature, is popular in many applications of high-speed computer arithmetic, especially in digital signal processing and cryptography. However, the main limiting factor of RNS is a high complexity of such operations as magnitude comparison, sign determination and overflow detection. These operations have, for many years, been a major obstacle to more widespread use of parallel residue arithmetic. This paper presents a new efficient method to perform these operations, which is based on computation and analysis of the interval estimation for the relative value of an RNS number. The estimation, which is called the interval floating-point characteristic (IFC), is represented by two directed rounded bounds that are fixed-precision numbers. Generally, the time complexities of serial and parallel computations of IFC are linear and logarithmic functions of the size of the moduli set, respectively. The new method requires only small-integer and fixed-precision floating-point operations and focuses on arbitrary moduli sets with large dynamic ranges ([Formula: see text]). Experiments indicate that the performance of the proposed method is significantly higher than that of methods based on Mixed-Radix Conversion. <\/jats:p>","DOI":"10.1142\/s0218126618500044","type":"journal-article","created":{"date-parts":[[2017,6,12]],"date-time":"2017-06-12T04:09:20Z","timestamp":1497240560000},"page":"1850004","source":"Crossref","is-referenced-by-count":13,"title":["Interval Estimation of Relative Values in Residue Number System"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0239-0404","authenticated-orcid":false,"given":"Konstantin","family":"Isupov","sequence":"first","affiliation":[{"name":"Department of Electronic Computing Machines, Vyatka State University, Kirov 610000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladimir","family":"Knyazkov","sequence":"additional","affiliation":[{"name":"Department of Electronic Computing Machines, Vyatka State University, Kirov 610000, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2017,8,23]]},"reference":[{"key":"S0218126618500044BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/TEC.1959.5219515"},{"volume-title":"Computer Arithmetic: Algorithms and Hardware Designs","year":"2000","author":"Parhami B.","key":"S0218126618500044BIB002"},{"volume-title":"Residue Arithmetic and Its Application to Computer Technology","year":"1967","author":"Szabo N. 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