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BigInt.doccarchive/data/documentation/bigint/aboutbfraction.json
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{"variants":[{"traits":[{"interfaceLanguage":"swift"}],"paths":["\/documentation\/bigint\/aboutcrt"]}],"abstract":[{"text":"Chinese Remainder Theorem","type":"text"}],"kind":"article","metadata":{"modules":[{"name":"BigInt"}],"roleHeading":"Article","title":"About CRT","role":"article"},"identifier":{"url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutCRT","interfaceLanguage":"swift"},"primaryContentSections":[{"kind":"content","content":[{"text":"Overview","anchor":"Overview","type":"heading","level":2},{"inlineContent":[{"type":"text","text":"Create a CRT instance from a given set of moduli which fullfill the following conditions:"}],"type":"paragraph"},{"type":"unorderedList","items":[{"content":[{"inlineContent":[{"type":"text","text":"at least two moduli"}],"type":"paragraph"}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"all moduli are positive"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"the moduli are pairwise coprime"}]}]}]},{"inlineContent":[{"text":"Then use the ","type":"text"},{"code":"compute","type":"codeVoice"},{"text":" method to compute the CRT value for a given set of residues.","type":"text"}],"type":"paragraph"},{"inlineContent":[{"text":"The same CRT instance can be used for different inputs, as long as the moduli are the same.","type":"text"}],"type":"paragraph"},{"type":"heading","level":3,"text":"Example","anchor":"Example"},{"syntax":"swift","code":["let moduli = [3, 5, 7]","let crt = CRT(moduli)!","","let residues = [2, 2, 6]","print(\"CRT value:\", crt.compute(residues))"],"type":"codeListing"},{"type":"paragraph","inlineContent":[{"type":"text","text":"giving:"}]},{"code":["CRT value: 62"],"type":"codeListing","syntax":"swift"}]}],"sections":[],"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt"]]},"schemaVersion":{"minor":3,"patch":0,"major":0},"seeAlsoSections":[{"anchor":"Articles","identifiers":["doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBInt","doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBFraction","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Performance","doc:\/\/bigint.BigInt\/documentation\/BigInt\/References","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Algorithms","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Protocols"],"title":"Articles","generated":true}],"references":{"doc://bigint.BigInt/documentation/BigInt":{"title":"BigInt","abstract":[{"text":"Signed integers and fractions of unbounded size","type":"text"}],"kind":"symbol","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt","role":"collection","type":"topic","url":"\/documentation\/bigint"},"doc://bigint.BigInt/documentation/BigInt/AboutBFraction":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBFraction","url":"\/documentation\/bigint\/aboutbfraction","type":"topic","role":"article","kind":"article","abstract":[{"type":"text","text":"Signed fractions with numerator and denominator of unbounded size"}],"title":"About BFraction"},"doc://bigint.BigInt/documentation/BigInt/Algorithms":{"kind":"article","title":"Algorithms","role":"article","type":"topic","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Algorithms","url":"\/documentation\/bigint\/algorithms","abstract":[{"type":"text","text":"Some of the algorithms used in BigInt are described below"}]},"doc://bigint.BigInt/documentation/BigInt/Performance":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Performance","url":"\/documentation\/bigint\/performance","type":"topic","role":"article","kind":"article","abstract":[{"text":"Execution times for certain BigInt operations","type":"text"}],"title":"Performance"},"doc://bigint.BigInt/documentation/BigInt/References":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/References","kind":"article","type":"topic","url":"\/documentation\/bigint\/references","title":"References","role":"article","abstract":[{"text":"Algorithms from the following books and papers have been used in the implementation","type":"text"}]},"doc://bigint.BigInt/documentation/BigInt/AboutBInt":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBInt","kind":"article","type":"topic","url":"\/documentation\/bigint\/aboutbint","title":"About BInt","role":"article","abstract":[{"type":"text","text":"Signed integers of unbounded size"}]},"doc://bigint.BigInt/documentation/BigInt/Protocols":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Protocols","url":"\/documentation\/bigint\/protocols","type":"topic","role":"article","kind":"article","abstract":[{"type":"text","text":"BigInt supports Apple’s "},{"type":"codeVoice","code":"SignedInteger"},{"text":", ","type":"text"},{"type":"codeVoice","code":"BinaryInteger"},{"type":"text","text":", "},{"type":"codeVoice","code":"Codable"},{"text":", and ","type":"text"},{"type":"codeVoice","code":"Numeric"},{"text":" protocols.","type":"text"}],"title":"Protocols and Additions"}}} | ||
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BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-1yd5f.json
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BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-608h1.json
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