From 552de2879203a3e19531a6447ae797f5456539ea Mon Sep 17 00:00:00 2001 From: Michael Griebling Date: Thu, 10 Oct 2024 10:49:14 -0400 Subject: [PATCH] More documentation corrections. --- .../data/documentation/bigint.json | 2 +- .../documentation/bigint/aboutbfraction.json | 2 +- .../data/documentation/bigint/aboutbint.json | 2 +- .../data/documentation/bigint/aboutcrt.json | 2 +- .../data/documentation/bigint/algorithms.json | 2 +- .../data/documentation/bigint/bfraction.json | 2 +- .../bigint/bfraction/!=(_:_:)-1yd5f.json | 2 +- .../bigint/bfraction/!=(_:_:)-21ytn.json | 2 +- .../bigint/bfraction/!=(_:_:)-25fz4.json | 2 +- .../bigint/bfraction/!=(_:_:)-608h1.json | 2 +- .../bigint/bfraction/!=(_:_:)-6d0go.json | 2 +- .../bigint/bfraction/!=(_:_:)-7obdp.json | 2 +- .../bigint/bfraction/'...(_:)-3tvdo.json | 2 +- .../bigint/bfraction/'...(_:)-64tor.json | 2 +- .../bigint/bfraction/'...(_:_:).json | 2 +- .../bigint/bfraction/'.._(_:).json | 2 +- .../bigint/bfraction/'.._(_:_:).json | 2 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b/BigInt.doccarchive/data/documentation/bigint/aboutbfraction.json @@ -1 +1 @@ -{"primaryContentSections":[{"kind":"content","content":[{"anchor":"Overview","level":2,"text":"Overview","type":"heading"},{"type":"paragraph","inlineContent":[{"type":"text","text":"Fractions are represented as "},{"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction","isActive":true,"type":"reference"},{"type":"text","text":" values consisting of a "},{"type":"reference","isActive":true,"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BInt"},{"text":" numerator value and a ","type":"text"},{"type":"reference","isActive":true,"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BInt"},{"text":" denominator value. 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","type":"text"},{"type":"codeVoice","code":"BinaryInteger"},{"text":", ","type":"text"},{"code":"Codable","type":"codeVoice"},{"type":"text","text":", and "},{"type":"codeVoice","code":"Numeric"},{"type":"text","text":" protocols."}],"title":"Protocols and Additions","kind":"article"},"doc://bigint.BigInt/documentation/BigInt/AboutCRT":{"type":"topic","abstract":[{"type":"text","text":"Chinese Remainder Theorem"}],"role":"article","title":"About CRT","url":"\/documentation\/bigint\/aboutcrt","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutCRT","kind":"article"}}} \ No newline at end of file +{"seeAlsoSections":[{"title":"Articles","anchor":"Articles","generated":true,"identifiers":["doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBInt","doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutCRT","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Performance","doc:\/\/bigint.BigInt\/documentation\/BigInt\/References","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Algorithms","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Protocols"]}],"sections":[],"schemaVersion":{"patch":0,"major":0,"minor":3},"kind":"article","abstract":[{"text":"Signed fractions with numerator and denominator of unbounded size","type":"text"}],"variants":[{"paths":["\/documentation\/bigint\/aboutbfraction"],"traits":[{"interfaceLanguage":"swift"}]}],"primaryContentSections":[{"kind":"content","content":[{"type":"heading","level":2,"text":"Overview","anchor":"Overview"},{"inlineContent":[{"type":"text","text":"Fractions are represented as "},{"type":"reference","isActive":true,"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BFraction"},{"text":" values consisting of a ","type":"text"},{"type":"reference","isActive":true,"identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BInt"},{"type":"text","text":" numerator value and a "},{"type":"reference","identifier":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/BInt","isActive":true},{"type":"text","text":" denominator value. The representation is normalized:"}],"type":"paragraph"},{"items":[{"content":[{"type":"paragraph","inlineContent":[{"text":"The numerator and denominator have no common factors except 1","type":"text"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"text":"The denominator is always positive","type":"text"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"text":"Zero is represented as 0\/1","type":"text"}]}]}],"type":"unorderedList"},{"text":"Creating BFraction’s","type":"heading","anchor":"Creating-BFractions","level":3},{"type":"codeListing","code":["\/\/ From its numerator and denominator","let f = BFraction(17, 4)","","\/\/ From its decimal value","let f = BFraction(4.25)","","\/\/ From its string representation","let f = BFraction(\"4.25\")!","\/\/ or equivalently","let f = BFraction(\"425E-2\")!","","\/\/ From a continued fraction","let f = BFraction([3, 4, 12, 4]) \/\/ f = 649 \/ 200"],"syntax":"swift"},{"inlineContent":[{"text":"Defining a fraction by specifying its decimal value might lead to surprises,","type":"text"},{"text":" ","type":"text"},{"type":"text","text":"because not all decimal values can be represented exactly as a floating point number."}],"type":"paragraph"},{"type":"paragraph","inlineContent":[{"type":"text","text":"One might think that "},{"type":"codeVoice","code":"BFraction(0.1)"},{"text":" would equal 1\/10,","type":"text"},{"text":" ","type":"text"},{"text":"but in fact it equals 3602879701896397 \/ 36028797018963968 = 0.1000000000000000055511151231257827021181583404541015625","type":"text"}]},{"inlineContent":[{"text":"On the other hand ","type":"text"},{"code":"BFraction(\"0.1\")!","type":"codeVoice"},{"type":"text","text":" equals 1\/10."}],"type":"paragraph"},{"type":"heading","level":3,"text":"Converting BFraction’s","anchor":"Converting-BFractions"},{"type":"paragraph","inlineContent":[{"type":"text","text":"BFraction values can be converted to String values, to decimal String values, to Double values and to 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multiplication, division, exponentiation, modulus"}]}]},{"content":[{"type":"paragraph","inlineContent":[{"type":"strong","inlineContent":[{"text":"Comparison:","type":"text"}]},{"type":"text","text":" The six standard operations == != < <= > >="}]}]},{"content":[{"type":"paragraph","inlineContent":[{"inlineContent":[{"text":"Rounding:","type":"text"}],"type":"strong"},{"text":" Rounding fractions to integers","type":"text"}]}]},{"content":[{"inlineContent":[{"type":"strong","inlineContent":[{"type":"text","text":"Miscellaneous:"}]},{"type":"text","text":" Bernoulli Numbers, Harmonic Numbers"}],"type":"paragraph"}]}]},{"text":"Bernoulli Numbers","type":"heading","level":3,"anchor":"Bernoulli-Numbers"},{"type":"paragraph","inlineContent":[{"type":"text","text":"The static function"}]},{"code":["let Bn = BFraction.bernoulli(n)"],"syntax":"swift","type":"codeListing"},{"inlineContent":[{"type":"text","text":"computes the n’th (n >= 0) Bernoulli number, which is a rational 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The exception is that the value 0 is represented as a single 64 bit zero Limb and sign "},{"type":"codeVoice","code":"false"}]}]}],"type":"unorderedList"},{"level":3,"anchor":"Creating-BInts","type":"heading","text":"Creating BInt’s"},{"type":"codeListing","syntax":"swift","code":["\/\/ From an integer","let a = BInt(27)","","\/\/ From a decimal value","let x = BInt(1.12345e30) \/\/ x = 1123450000000000064996914495488","","\/\/ From string literals","let b = BInt(\"123456789012345678901234567890\")!","let c = BInt(\"1234567890abcdef1234567890abcdef\", radix: 16)!","","\/\/ From magnitude and sign","let m: Limbs = [1, 2, 3]","let d = BInt(m) \/\/ d = 1020847100762815390427017310442723737601","let e = BInt(m, true) \/\/ e = -1020847100762815390427017310442723737601","","\/\/ From a big-endian 2's complement byte array","let f = BInt(signed: [255, 255, 127]) \/\/ f = -129","","\/\/ From a big-endian magnitude byte array","let g = BInt(magnitude: [255, 255, 127]) \/\/ g = 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","type":"text"},{"code":"BInt","type":"codeVoice"},{"text":" are:","type":"text"}]},{"items":[{"content":[{"inlineContent":[{"type":"strong","inlineContent":[{"type":"text","text":"Arithmetic:"}]},{"text":" addition, subtraction, multiplication, division, exponentiation, remainder and modulus, gcd and lcm","type":"text"}],"type":"paragraph"}]},{"content":[{"inlineContent":[{"inlineContent":[{"text":"Comparison:","type":"text"}],"type":"strong"},{"type":"text","text":" the six standard operations == != < <= > >="}],"type":"paragraph"}]},{"content":[{"inlineContent":[{"type":"strong","inlineContent":[{"text":"Shift Operations:","type":"text"}]},{"text":" logical left- and right shifts","type":"text"}],"type":"paragraph"}]},{"content":[{"inlineContent":[{"inlineContent":[{"text":"Bit Operations:","type":"text"}],"type":"strong"},{"text":" logical and, or, xor, not, bit 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"},{"type":"codeVoice","code":"SecRandomCopyBytes"}]},{"type":"heading","anchor":"Prime-Number-Test","text":"Prime Number Test","level":3},{"inlineContent":[{"text":"Miller-Rabin test","type":"text"}],"type":"paragraph"},{"text":"Prime Number Generation","level":3,"type":"heading","anchor":"Prime-Number-Generation"},{"inlineContent":[{"text":"The algorithm from Java BigInteger translated to Swift","type":"text"}],"type":"paragraph"},{"text":"Factorial","level":3,"anchor":"Factorial","type":"heading"},{"inlineContent":[{"type":"text","text":"The "},{"code":"SplitRecursive","type":"codeVoice"},{"type":"text","text":" algorithm from Peter Luschny: "},{"identifier":"https:\/\/www.luschny.de","isActive":true,"type":"reference"}],"type":"paragraph"},{"level":3,"type":"heading","anchor":"Fibonacci","text":"Fibonacci"},{"inlineContent":[{"text":"The ","type":"text"},{"type":"codeVoice","code":"fastDoubling"},{"text":" algorithm from Project Nayuki: 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uSec"}]}]],[[{"type":"paragraph","inlineContent":[{"type":"text","text":"Square root and remainder"}]}],[{"inlineContent":[{"type":"codeVoice","code":"c2000.sqrtRemainder()"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"text":"13 uSec","type":"text"}]}]],[[{"inlineContent":[{"type":"text","text":"Is perfect square"}],"type":"paragraph"}],[{"inlineContent":[{"code":"(c2000 * c2000).isPerfectSquare()","type":"codeVoice"}],"type":"paragraph"}],[{"inlineContent":[{"type":"text","text":"16 uSec"}],"type":"paragraph"}]],[[{"inlineContent":[{"text":"Square root modulo","type":"text"}],"type":"paragraph"}],[{"inlineContent":[{"type":"codeVoice","code":"b1000.sqrtMod(p1000)"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"text":"1.6 mSec","type":"text"}]}]],[[{"type":"paragraph","inlineContent":[{"text":"Power","type":"text"}]}],[{"inlineContent":[{"type":"codeVoice","code":"c2000 ** 111"}],"type":"paragraph"}],[{"inlineContent":[{"type":"text","text":"1.9 mSec"}],"type":"paragraph"}]],[[{"type":"paragraph","inlineContent":[{"text":"Root","type":"text"}]}],[{"type":"paragraph","inlineContent":[{"code":"c2000.root(111)","type":"codeVoice"}]}],[{"type":"paragraph","inlineContent":[{"text":"15 uSec","type":"text"}]}]],[[{"type":"paragraph","inlineContent":[{"text":"Root and remainder","type":"text"}]}],[{"type":"paragraph","inlineContent":[{"code":"c2000.rootRemainder(111)","type":"codeVoice"}]}],[{"type":"paragraph","inlineContent":[{"type":"text","text":"17 uSec"}]}]],[[{"inlineContent":[{"type":"text","text":"Is perfect root"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"code":"c2000.isPerfectRoot()","type":"codeVoice"}]}],[{"inlineContent":[{"type":"text","text":"13 mSec"}],"type":"paragraph"}]],[[{"inlineContent":[{"type":"text","text":"Jacobi symbol"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"type":"codeVoice","code":"c2000.jacobiSymbol(p1000)"}]}],[{"inlineContent":[{"type":"text","text":"0.15 mSec"}],"type":"paragraph"}]],[[{"inlineContent":[{"text":"Kronecker symbol","type":"text"}],"type":"paragraph"}],[{"inlineContent":[{"type":"codeVoice","code":"c2000.kroneckerSymbol(p1000)"}],"type":"paragraph"}],[{"inlineContent":[{"text":"0.15 mSec","type":"text"}],"type":"paragraph"}]],[[{"inlineContent":[{"type":"text","text":"Bernoulli number"}],"type":"paragraph"}],[{"inlineContent":[{"code":"BFraction.bernoulli(1000)","type":"codeVoice"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"type":"text","text":"83 mSec"}]}]]],"type":"table","header":"row","alignments":["left","left","right"]},{"type":"paragraph","inlineContent":[{"text":"a1000 = 3187705437890850041662973758105262878153514794996698172406519277876060364087986868049465132757493318066301987043192958841748826350731448419937544810921786918975580180410200630645469411588934094075222404396990984350815153163569041641732160380739556436955287671287935796642478260435292021117614349253825","type":"text"}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"b1000 = 9159373012373110951130589007821321098436345855865428979299172149373720601254669552044211236974571462005332583657082428026625366060511329189733296464187785766230514564038057370938741745651937465362625449921195096442684523511715110908407508139315000469851121118117438147266381183636498494901233452870695"}]},{"inlineContent":[{"text":"c2000 = 1190583332681083129323588684910845359379915367459759242106618067261956856381281184752008892106576666833853411939711280970145570546868549934865719229538926506588929417873149597614787608112658086250354719939407543740242931571462165384138560315454455247539461818779966171917173966217706187439870264672508450210272481951994459523586160979759782950984370978171111340529321052541588344733968902238813379990628157732181128074253104347868153860527298911917508606081710893794973605227829729403843750412766366804402629686458092685235454222856584200220355212623917637542398554907364450159627359316156463617143173","type":"text"}],"type":"paragraph"},{"type":"paragraph","inlineContent":[{"text":"p1000 (probably a prime) = 7662841304438384296568220077355872003841475576593385710590818274399706072141018649398767137142090308734613594718593893634649122767374115742644499040193270857876678047220373151142747088797516044505739487695946446362769947024029728822155570722524629197074319602110260674029276185098937139753025851896997","type":"text"}]}]}],"schemaVersion":{"major":0,"patch":0,"minor":3},"identifier":{"url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Performance","interfaceLanguage":"swift"},"abstract":[{"type":"text","text":"Execution times for certain BigInt 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From now on, this BigInt will mirror Ibsen's BigInt changes (more or less) and have addendum files like *BigInt-Extensions.swift* to implement the Apple-centric protocol compliance. diff --git a/Sources/BigInt/BigFrac.swift b/Sources/BigInt/BigFrac.swift index 5a30e43..5795755 100644 --- a/Sources/BigInt/BigFrac.swift +++ b/Sources/BigInt/BigFrac.swift @@ -209,11 +209,11 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { self.init(BInt(n), BInt(d)) } - /// Constructs a BFraction from a decimal value + /// Constructs a BFraction from a floating point value *d* and + /// aborts if *d* is infinite or NaN. /// /// - Parameters: - /// - d: The decimal value - /// - Returns: The BFraction corresponding to `d`, `nil` if `d` is infinite or NaN + /// - d: The floating point value public init?(_ d: Double) { if d.isNaN || d.isInfinite { return nil @@ -229,11 +229,11 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { } } - /// Constructs a BFraction from a String representation + /// Constructs a BFraction from a String representation and aborts + /// if *x* does not represent a valid floating point number. /// /// - Parameters: /// - x: The String representation - /// - Returns: The BFraction represented by `x`, `nil` if `x` does not represent a decimal number /// /// Examples: /// * BFraction("3.1415") = 6283 / 2000 @@ -252,10 +252,10 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { /// Constructs a BFraction from a continued fraction - `BInt` version /// - /// - Precondition: `x` contains at least one element, all elements except possibly the first are positive + /// - Precondition: *x* contains at least one element, all elements + /// except possibly the first are positive /// - Parameters: /// - x: The continued fraction - /// - Returns: The BFraction represented by `x` public init(_ x: [BInt]) { precondition(x.count > 0) var numerator = BInt.ZERO @@ -274,7 +274,6 @@ public struct BFraction: CustomStringConvertible, Comparable, Equatable { /// - Precondition: `x` contains at least one element, all elements except possibly the first are positive /// - Parameters: /// - x: The continued fraction - /// - Returns: The BFraction represented by `x` public init(_ x: [Int]) { var bx = [BInt](repeating: BInt.ZERO, count: x.count) for i in 0 ..< bx.count { diff --git a/Sources/BigInt/BigInt-Extensions.swift b/Sources/BigInt/BigInt-Extensions.swift index 905ced1..22d23e7 100644 --- a/Sources/BigInt/BigInt-Extensions.swift +++ b/Sources/BigInt/BigInt-Extensions.swift @@ -73,7 +73,12 @@ extension BInt : BinaryInteger { } } -extension BInt : ExpressibleByIntegerLiteral { +extension BInt { + + /// Constructs a BInt from a StaticBigInt + /// + /// - Parameters: + /// - value: extended-precision integer literal public init(integerLiteral value: StaticBigInt) { let isNegative = value.signum() < 0 let bitWidth = value.bitWidth diff --git a/Sources/BigInt/BigInt.docc/Extensions/BInt.md b/Sources/BigInt/BigInt.docc/Extensions/BInt.md index 4c713f1..a4c6a91 100644 --- a/Sources/BigInt/BigInt.docc/Extensions/BInt.md +++ b/Sources/BigInt/BigInt.docc/Extensions/BInt.md @@ -152,9 +152,9 @@ Please, see ### Shift Operations - ``<<(_:_:)`` -- ``<<=(_:_:)`` +- ``<<=(_:_:)-9gfzo`` - ``>>(_:_:)`` -- ``>>=(_:_:)`` +- ``>>=(_:_:)-40hci`` ### Bit Operations diff --git a/Sources/BigInt/BigInt.swift b/Sources/BigInt/BigInt.swift index cfadecd..884c7e2 100755 --- a/Sources/BigInt/BigInt.swift +++ b/Sources/BigInt/BigInt.swift @@ -58,7 +58,7 @@ public struct BInt: CustomStringConvertible, Comparable, Codable, Equatable, Has // MARK: - Initializers - /// Constructs a BInt from magnitude and sign + /// Constructs a BInt from magnitude and sign. /// /// - Parameters: /// - magnitude: magnitude of value @@ -75,7 +75,6 @@ public struct BInt: CustomStringConvertible, Comparable, Codable, Equatable, Has /// Constructs a BInt from an Int value /// /// - Parameter x: Int value - /// - Returns: The BInt with value `x` public init(_ x: Int) { if x == Int.min { self.init([0x8000000000000000], true) @@ -86,11 +85,11 @@ public struct BInt: CustomStringConvertible, Comparable, Codable, Equatable, Has } } - /// Constructs a BInt from a decimal value + /// Constructs a BInt from a Double value where *d* is truncated + /// to an integer value and aborts if *d* is infinite or NaN. /// /// - Parameters: /// - d: The decimal value - /// - Returns: The BInt corresponding to `d` truncated to an integer value, `nil` if `d` is infinite or NaN public init?(_ d: Double) { if d.isNaN || d.isInfinite { return nil @@ -105,7 +104,8 @@ public struct BInt: CustomStringConvertible, Comparable, Codable, Equatable, Has } } - /// Constructs a BInt from a String value and radix + /// Constructs a BInt from a String value and radix and aborts + /// if *x* does not designate an integer in the given radix. /// /// Examples: /// * BInt("34111220000000000475892058") @@ -116,7 +116,6 @@ public struct BInt: CustomStringConvertible, Comparable, Codable, Equatable, Has /// - Parameters: /// - x: String value to be converted /// - radix: Radix of x, from 2 to 36 inclusive, default is 10 - /// - Returns: The BInt corresponding to `x`, `nil` if `x` does not designate an integer in the given radix public init?(_ x: String, radix: Int = 10) { if radix < 2 || radix > 36 { return nil @@ -173,11 +172,11 @@ public struct BInt: CustomStringConvertible, Comparable, Codable, Equatable, Has self.init(magnitude, sign) } - /// Constructs a random BInt with a specified number of bits + /// Constructs a uniformly distributed random BInt with a specified + /// number of bits in the range 0 `..<` 2 ^ *bitWidth*. /// /// - Precondition: bitWidth is positive /// - Parameter bitWidth: Number of bits - /// - Returns: A uniformly distributed random BInt in range 0 ..< 2 ^ `bitWidth` public init(bitWidth: Int) { precondition(bitWidth > 0, "Bitwidth must be positive") let (q, r) = bitWidth.quotientAndRemainder(dividingBy: 64) diff --git a/Sources/BigInt/CRT.swift b/Sources/BigInt/CRT.swift index 5e986b4..eb289fb 100644 --- a/Sources/BigInt/CRT.swift +++ b/Sources/BigInt/CRT.swift @@ -27,11 +27,10 @@ public struct CRT { // MARK: - Initializers - /// Constructs a CRT instance from the moduli - `BInt` version + /// Constructs a CRT instance from the moduli and aborts if conditions are not met - `BInt` version /// /// - Parameters: /// - m: The moduli - /// - Returns: The CRT instance for the moduli, `nil` if they do not fullfill the conditions public init?(_ m: [BInt]) { guard m.count > 1 else { return nil @@ -51,11 +50,10 @@ public struct CRT { self.M = self.u[self.u.count - 1] * self.m[self.m.count - 1] } - /// Constructs a CRT instance from the moduli - `Int` version + /// Constructs a CRT instance from the moduli and aborts if conditions are not met - `Int` version /// /// - Parameters: /// - m: The moduli - /// - 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"},{"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"}}} \ No newline at end of file diff --git a/docs/data/documentation/bigint/aboutcrt.json b/docs/data/documentation/bigint/aboutcrt.json index 4a25761..8aa0873 100644 --- a/docs/data/documentation/bigint/aboutcrt.json +++ b/docs/data/documentation/bigint/aboutcrt.json @@ -1 +1 @@ -{"schemaVersion":{"patch":0,"minor":3,"major":0},"kind":"article","primaryContentSections":[{"content":[{"anchor":"Overview","type":"heading","level":2,"text":"Overview"},{"inlineContent":[{"type":"text","text":"Create a CRT instance from a given set of moduli which fullfill the following 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+{"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt"]]},"kind":"article","sections":[],"seeAlsoSections":[{"anchor":"Articles","title":"Articles","generated":true,"identifiers":["doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBInt","doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutBFraction","doc:\/\/bigint.BigInt\/documentation\/BigInt\/AboutCRT","doc:\/\/bigint.BigInt\/documentation\/BigInt\/References","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Algorithms","doc:\/\/bigint.BigInt\/documentation\/BigInt\/Protocols"]}],"primaryContentSections":[{"kind":"content","content":[{"type":"heading","text":"","anchor":"","level":2},{"type":"paragraph","inlineContent":[{"type":"text","text":"To assess the performance of BigInt, the execution times for a number of common operations were measured on an iMac 2021, Apple M1 chip."},{"text":" ","type":"text"},{"type":"text","text":"The results are shown in the table below. It shows the operation being measured and the time it took (in microseconds or milliseconds)."}]},{"type":"aside","style":"note","content":[{"inlineContent":[{"type":"text","text":""},{"text":" ","type":"text"},{"text":"Four large numbers ","type":"text"},{"type":"codeVoice","code":"a1000"},{"text":", ","type":"text"},{"type":"codeVoice","code":"b1000"},{"type":"text","text":", "},{"type":"codeVoice","code":"c2000"},{"type":"text","text":" and "},{"code":"p1000","type":"codeVoice"},{"type":"text","text":" were used throughout the measurements. 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a/docs/data/documentation/bigint/protocols.json b/docs/data/documentation/bigint/protocols.json index 3eb9349..2b22e73 100644 --- a/docs/data/documentation/bigint/protocols.json +++ b/docs/data/documentation/bigint/protocols.json @@ -1 +1 @@ -{"abstract":[{"text":"BigInt supports Apple’s ","type":"text"},{"type":"codeVoice","code":"SignedInteger"},{"type":"text","text":", "},{"code":"BinaryInteger","type":"codeVoice"},{"text":", ","type":"text"},{"code":"Codable","type":"codeVoice"},{"type":"text","text":", and "},{"code":"Numeric","type":"codeVoice"},{"text":" 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