-
Notifications
You must be signed in to change notification settings - Fork 18
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
1 parent
26f8c3f
commit afb70a0
Showing
585 changed files
with
762 additions
and
691 deletions.
There are no files selected for viewing
Large diffs are not rendered by default.
Oops, something went wrong.
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/aboutbfraction.json
Large diffs are not rendered by default.
Oops, something went wrong.
Large diffs are not rendered by default.
Oops, something went wrong.
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1 +1 @@ | ||
{"abstract":[{"text":"Chinese Remainder Theorem","type":"text"}],"primaryContentSections":[{"content":[{"text":"Overview","anchor":"Overview","level":2,"type":"heading"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Create a "},{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/CRT","type":"reference","isActive":true},{"type":"text","text":" instance from a given set of moduli which fullfill the following conditions:"}]},{"type":"unorderedList","items":[{"content":[{"type":"paragraph","inlineContent":[{"text":"at least two moduli","type":"text"}]}]},{"content":[{"inlineContent":[{"type":"text","text":"all moduli are positive"}],"type":"paragraph"}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"the moduli are pairwise coprime"}]}]}]},{"inlineContent":[{"type":"text","text":"Then use the "},{"type":"codeVoice","code":"compute"},{"text":" method to compute the CRT value for a given set of residues.","type":"text"}],"type":"paragraph"},{"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":"heading","anchor":"Example","text":"Example","level":3},{"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"},{"inlineContent":[{"text":"giving:","type":"text"}],"type":"paragraph"},{"code":["CRT value: 62"],"type":"codeListing","syntax":"swift"}],"kind":"content"}],"variants":[{"paths":["\/documentation\/bigint\/aboutcrt"],"traits":[{"interfaceLanguage":"swift"}]}],"kind":"article","identifier":{"url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutCRT","interfaceLanguage":"swift"},"sections":[],"seeAlsoSections":[{"anchor":"Articles","generated":true,"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"],"title":"Articles"}],"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt"]]},"schemaVersion":{"minor":3,"major":0,"patch":0},"metadata":{"roleHeading":"Article","role":"article","modules":[{"name":"BigInt"}],"title":"About CRT"},"references":{"doc://bigint.BigInt/documentation/BigInt/AboutBFraction":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBFraction","abstract":[{"type":"text","text":"Signed fractions with numerator and denominator of unbounded size"}],"kind":"article","title":"About BFraction","url":"\/documentation\/bigint\/aboutbfraction","type":"topic","role":"article"},"doc://bigint.BigInt/documentation/BigInt/References":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/References","abstract":[{"type":"text","text":"Algorithms from the following books and papers have been used in the implementation"}],"url":"\/documentation\/bigint\/references","kind":"article","type":"topic","role":"article","title":"References"},"doc://bigint.BigInt/documentation/BigInt/Algorithms":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Algorithms","abstract":[{"type":"text","text":"Some of the algorithms used in BigInt are described below"}],"kind":"article","title":"Algorithms","url":"\/documentation\/bigint\/algorithms","type":"topic","role":"article"},"doc://bigint.BigInt/documentation/BigInt/Performance":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Performance","abstract":[{"type":"text","text":"Execution times for certain BigInt operations"}],"url":"\/documentation\/bigint\/performance","kind":"article","type":"topic","role":"article","title":"Performance"},"doc://bigint.BigInt/documentation/BigInt":{"role":"collection","url":"\/documentation\/bigint","type":"topic","kind":"symbol","abstract":[{"type":"text","text":"Signed integers and fractions of unbounded size"}],"title":"BigInt","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt"},"doc://bigint.BigInt/documentation/BigInt/AboutBInt":{"title":"About BInt","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBInt","kind":"article","type":"topic","role":"article","url":"\/documentation\/bigint\/aboutbint","abstract":[{"type":"text","text":"Signed integers of unbounded size"}]},"doc://bigint.BigInt/documentation/BigInt/CRT":{"role":"symbol","navigatorTitle":[{"text":"CRT","kind":"identifier"}],"kind":"symbol","abstract":[{"type":"text","text":"The CRT structure"}],"fragments":[{"text":"struct","kind":"keyword"},{"text":" ","kind":"text"},{"text":"CRT","kind":"identifier"}],"title":"CRT","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/CRT","url":"\/documentation\/bigint\/crt","type":"topic"}}} | ||
{"identifier":{"url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutCRT","interfaceLanguage":"swift"},"sections":[],"schemaVersion":{"patch":0,"major":0,"minor":3},"metadata":{"modules":[{"name":"BigInt"}],"role":"article","roleHeading":"Article","title":"About CRT"},"seeAlsoSections":[{"anchor":"Articles","title":"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"],"generated":true}],"primaryContentSections":[{"kind":"content","content":[{"anchor":"Overview","type":"heading","level":2,"text":"Overview"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Create a "},{"type":"reference","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/CRT","isActive":true},{"type":"text","text":" instance from a given set of moduli which fullfill the following conditions:"}]},{"items":[{"content":[{"type":"paragraph","inlineContent":[{"type":"text","text":"at least two moduli"}]}]},{"content":[{"inlineContent":[{"text":"all moduli are positive","type":"text"}],"type":"paragraph"}]},{"content":[{"type":"paragraph","inlineContent":[{"text":"the moduli are pairwise coprime","type":"text"}]}]}],"type":"unorderedList"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Then use the "},{"type":"codeVoice","code":"compute"},{"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"}]},{"anchor":"Example","level":3,"type":"heading","text":"Example"},{"syntax":"swift","type":"codeListing","code":["let moduli = [3, 5, 7]","let crt = CRT(moduli)!","","let residues = [2, 2, 6]","print(\"CRT value:\", crt.compute(residues))"]},{"type":"paragraph","inlineContent":[{"type":"text","text":"giving:"}]},{"code":["CRT value: 62"],"syntax":"swift","type":"codeListing"}]}],"variants":[{"traits":[{"interfaceLanguage":"swift"}],"paths":["\/documentation\/bigint\/aboutcrt"]}],"abstract":[{"type":"text","text":"Chinese Remainder Theorem"}],"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt"]]},"kind":"article","references":{"doc://bigint.BigInt/documentation/BigInt/Algorithms":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Algorithms","role":"article","kind":"article","abstract":[{"text":"Some of the algorithms used in BigInt are described below","type":"text"}],"title":"Algorithms","url":"\/documentation\/bigint\/algorithms","type":"topic"},"doc://bigint.BigInt/documentation/BigInt/References":{"type":"topic","title":"References","url":"\/documentation\/bigint\/references","role":"article","abstract":[{"text":"Algorithms from the following books and papers have been used in the implementation","type":"text"}],"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/References","kind":"article"},"doc://bigint.BigInt/documentation/BigInt/CRT":{"title":"CRT","url":"\/documentation\/bigint\/crt","type":"topic","kind":"symbol","fragments":[{"text":"struct","kind":"keyword"},{"text":" ","kind":"text"},{"kind":"identifier","text":"CRT"}],"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/CRT","navigatorTitle":[{"text":"CRT","kind":"identifier"}],"abstract":[{"type":"text","text":"The CRT structure"}],"role":"symbol"},"doc://bigint.BigInt/documentation/BigInt/AboutBInt":{"type":"topic","url":"\/documentation\/bigint\/aboutbint","title":"About BInt","role":"article","abstract":[{"text":"Signed integers of unbounded size","type":"text"}],"kind":"article","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBInt"},"doc://bigint.BigInt/documentation/BigInt":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt","url":"\/documentation\/bigint","kind":"symbol","title":"BigInt","abstract":[{"type":"text","text":"Signed integers and fractions of unbounded size"}],"role":"collection","type":"topic"},"doc://bigint.BigInt/documentation/BigInt/Performance":{"type":"topic","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Performance","kind":"article","abstract":[{"text":"Execution times for certain BigInt operations","type":"text"}],"title":"Performance","url":"\/documentation\/bigint\/performance","role":"article"},"doc://bigint.BigInt/documentation/BigInt/AboutBFraction":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBFraction","abstract":[{"text":"Signed fractions with numerator and denominator of unbounded size","type":"text"}],"url":"\/documentation\/bigint\/aboutbfraction","type":"topic","role":"article","title":"About BFraction","kind":"article"}}} |
Large diffs are not rendered by default.
Oops, something went wrong.
Large diffs are not rendered by default.
Oops, something went wrong.
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-1yd5f.json
Large diffs are not rendered by default.
Oops, something went wrong.
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-21ytn.json
Large diffs are not rendered by default.
Oops, something went wrong.
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-25fz4.json
Large diffs are not rendered by default.
Oops, something went wrong.
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-608h1.json
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -1 +1 @@ | ||
{"sections":[],"abstract":[{"type":"text","text":"Inherited from "},{"type":"codeVoice","code":"Equatable.!=(_:_:)"},{"type":"text","text":"."}],"primaryContentSections":[{"kind":"declarations","declarations":[{"tokens":[{"kind":"keyword","text":"static"},{"kind":"text","text":" "},{"kind":"keyword","text":"func"},{"kind":"text","text":" "},{"kind":"identifier","text":"!="},{"kind":"text","text":" "},{"text":"(","kind":"text"},{"kind":"internalParam","text":"lhs"},{"text":": ","kind":"text"},{"kind":"typeIdentifier","text":"Self"},{"text":", ","kind":"text"},{"kind":"internalParam","text":"rhs"},{"text":": ","kind":"text"},{"kind":"typeIdentifier","text":"Self"},{"kind":"text","text":") -> "},{"preciseIdentifier":"s:Sb","text":"Bool","kind":"typeIdentifier"}],"platforms":["macOS"],"languages":["swift"]}]}],"kind":"symbol","schemaVersion":{"minor":3,"patch":0,"major":0},"variants":[{"traits":[{"interfaceLanguage":"swift"}],"paths":["\/documentation\/bigint\/bfraction\/!=(_:_:)-608h1"]}],"identifier":{"interfaceLanguage":"swift","url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/!=(_:_:)-608h1"},"metadata":{"fragments":[{"kind":"keyword","text":"static"},{"kind":"text","text":" "},{"text":"func","kind":"keyword"},{"text":" ","kind":"text"},{"kind":"identifier","text":"!="},{"text":" ","kind":"text"},{"kind":"text","text":"("},{"text":"Self","kind":"typeIdentifier"},{"kind":"text","text":", "},{"kind":"typeIdentifier","text":"Self"},{"text":") -> ","kind":"text"},{"kind":"typeIdentifier","text":"Bool","preciseIdentifier":"s:Sb"}],"role":"symbol","title":"!=(_:_:)","symbolKind":"op","externalID":"s:SQsE2neoiySbx_xtFZ::SYNTHESIZED::s:6BigInt9BFractionV","modules":[{"relatedModules":["Swift"],"name":"BigInt"}],"extendedModule":"Swift","roleHeading":"Operator"},"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt","doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction","doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/Equatable-Implementations"]]},"references":{"doc://bigint.BigInt/documentation/BigInt":{"role":"collection","url":"\/documentation\/bigint","type":"topic","kind":"symbol","abstract":[{"type":"text","text":"Signed integers and fractions of unbounded size"}],"title":"BigInt","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt"},"doc://bigint.BigInt/documentation/BigInt/BFraction/Equatable-Implementations":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/Equatable-Implementations","type":"topic","url":"\/documentation\/bigint\/bfraction\/equatable-implementations","kind":"article","abstract":[],"role":"collectionGroup","title":"Equatable Implementations"},"doc://bigint.BigInt/documentation/BigInt/BFraction":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction","role":"symbol","abstract":[{"type":"text","text":"The BFraction structure"}],"navigatorTitle":[{"text":"BFraction","kind":"identifier"}],"kind":"symbol","title":"BFraction","url":"\/documentation\/bigint\/bfraction","fragments":[{"kind":"keyword","text":"struct"},{"text":" ","kind":"text"},{"kind":"identifier","text":"BFraction"}],"type":"topic"},"doc://bigint.BigInt/documentation/BigInt/BFraction/!=(_:_:)-608h1":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/!=(_:_:)-608h1","fragments":[{"text":"static","kind":"keyword"},{"kind":"text","text":" "},{"text":"func","kind":"keyword"},{"kind":"text","text":" "},{"kind":"identifier","text":"!="},{"text":" ","kind":"text"},{"kind":"text","text":"("},{"text":"Self","kind":"typeIdentifier"},{"kind":"text","text":", "},{"text":"Self","kind":"typeIdentifier"},{"text":") -> ","kind":"text"},{"kind":"typeIdentifier","preciseIdentifier":"s:Sb","text":"Bool"}],"type":"topic","kind":"symbol","role":"symbol","abstract":[],"title":"!=(_:_:)","url":"\/documentation\/bigint\/bfraction\/!=(_:_:)-608h1"}}} | ||
{"abstract":[{"text":"Inherited from ","type":"text"},{"code":"Equatable.!=(_:_:)","type":"codeVoice"},{"type":"text","text":"."}],"metadata":{"extendedModule":"Swift","externalID":"s:SQsE2neoiySbx_xtFZ::SYNTHESIZED::s:6BigInt9BFractionV","symbolKind":"op","role":"symbol","title":"!=(_:_:)","roleHeading":"Operator","fragments":[{"text":"static","kind":"keyword"},{"text":" ","kind":"text"},{"text":"func","kind":"keyword"},{"text":" ","kind":"text"},{"text":"!=","kind":"identifier"},{"kind":"text","text":" "},{"text":"(","kind":"text"},{"text":"Self","kind":"typeIdentifier"},{"text":", ","kind":"text"},{"kind":"typeIdentifier","text":"Self"},{"text":") -> ","kind":"text"},{"preciseIdentifier":"s:Sb","text":"Bool","kind":"typeIdentifier"}],"modules":[{"name":"BigInt","relatedModules":["Swift"]}]},"identifier":{"url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/!=(_:_:)-608h1","interfaceLanguage":"swift"},"variants":[{"paths":["\/documentation\/bigint\/bfraction\/!=(_:_:)-608h1"],"traits":[{"interfaceLanguage":"swift"}]}],"primaryContentSections":[{"declarations":[{"platforms":["macOS"],"languages":["swift"],"tokens":[{"kind":"keyword","text":"static"},{"text":" ","kind":"text"},{"text":"func","kind":"keyword"},{"text":" ","kind":"text"},{"kind":"identifier","text":"!="},{"kind":"text","text":" "},{"text":"(","kind":"text"},{"text":"lhs","kind":"internalParam"},{"text":": ","kind":"text"},{"text":"Self","kind":"typeIdentifier"},{"kind":"text","text":", "},{"text":"rhs","kind":"internalParam"},{"kind":"text","text":": "},{"text":"Self","kind":"typeIdentifier"},{"text":") -> ","kind":"text"},{"text":"Bool","kind":"typeIdentifier","preciseIdentifier":"s:Sb"}]}],"kind":"declarations"}],"kind":"symbol","sections":[],"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt","doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction","doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/Equatable-Implementations"]]},"schemaVersion":{"patch":0,"major":0,"minor":3},"references":{"doc://bigint.BigInt/documentation/BigInt/BFraction":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction","navigatorTitle":[{"text":"BFraction","kind":"identifier"}],"title":"BFraction","fragments":[{"kind":"keyword","text":"struct"},{"kind":"text","text":" "},{"kind":"identifier","text":"BFraction"}],"kind":"symbol","abstract":[{"type":"text","text":"The BFraction structure"}],"role":"symbol","url":"\/documentation\/bigint\/bfraction","type":"topic"},"doc://bigint.BigInt/documentation/BigInt/BFraction/!=(_:_:)-608h1":{"fragments":[{"kind":"keyword","text":"static"},{"text":" ","kind":"text"},{"text":"func","kind":"keyword"},{"text":" ","kind":"text"},{"kind":"identifier","text":"!="},{"text":" ","kind":"text"},{"kind":"text","text":"("},{"text":"Self","kind":"typeIdentifier"},{"kind":"text","text":", "},{"kind":"typeIdentifier","text":"Self"},{"text":") -> ","kind":"text"},{"preciseIdentifier":"s:Sb","text":"Bool","kind":"typeIdentifier"}],"role":"symbol","abstract":[],"url":"\/documentation\/bigint\/bfraction\/!=(_:_:)-608h1","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/!=(_:_:)-608h1","title":"!=(_:_:)","type":"topic","kind":"symbol"},"doc://bigint.BigInt/documentation/BigInt":{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt","url":"\/documentation\/bigint","kind":"symbol","title":"BigInt","abstract":[{"type":"text","text":"Signed integers and fractions of unbounded size"}],"role":"collection","type":"topic"},"doc://bigint.BigInt/documentation/BigInt/BFraction/Equatable-Implementations":{"title":"Equatable Implementations","role":"collectionGroup","kind":"article","url":"\/documentation\/bigint\/bfraction\/equatable-implementations","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction\/Equatable-Implementations","abstract":[],"type":"topic"}}} |
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-6d0go.json
Large diffs are not rendered by default.
Oops, something went wrong.
2 changes: 1 addition & 1 deletion
2
BigInt.doccarchive/data/documentation/bigint/bfraction/!=(_:_:)-7obdp.json
Large diffs are not rendered by default.
Oops, something went wrong.
Oops, something went wrong.