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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"}]}]}]},{"level":3,"anchor":"Creating-BInts","text":"Creating BInt’s","type":"heading"},{"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 = 16777087","","\/\/ Random value with specified bitwidth","let h = 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-{"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 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mSec"}],"type":"paragraph"}]],[[{"inlineContent":[{"type":"text","text":"Root"}],"type":"paragraph"}],[{"inlineContent":[{"type":"codeVoice","code":"c2000.root(111)"}],"type":"paragraph"}],[{"inlineContent":[{"type":"text","text":"13 uSec"}],"type":"paragraph"}]],[[{"type":"paragraph","inlineContent":[{"type":"text","text":"Root and remainder"}]}],[{"type":"paragraph","inlineContent":[{"code":"c2000.rootRemainder(111)","type":"codeVoice"}]}],[{"type":"paragraph","inlineContent":[{"type":"text","text":"14 uSec"}]}]],[[{"type":"paragraph","inlineContent":[{"type":"text","text":"Is perfect root"}]}],[{"inlineContent":[{"type":"codeVoice","code":"c2000.isPerfectRoot()"}],"type":"paragraph"}],[{"inlineContent":[{"type":"text","text":"11 mSec"}],"type":"paragraph"}]],[[{"inlineContent":[{"type":"text","text":"Jacobi symbol"}],"type":"paragraph"}],[{"inlineContent":[{"type":"codeVoice","code":"c2000.jacobiSymbol(p1000)"}],"type":"paragraph"}],[{"inlineContent":[{"text":"0.11 mSec","type":"text"}],"type":"paragraph"}]],[[{"inlineContent":[{"text":"Kronecker symbol","type":"text"}],"type":"paragraph"}],[{"inlineContent":[{"code":"c2000.kroneckerSymbol(p1000)","type":"codeVoice"}],"type":"paragraph"}],[{"inlineContent":[{"text":"0.11 mSec","type":"text"}],"type":"paragraph"}]],[[{"inlineContent":[{"type":"text","text":"Bernoulli number"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"code":"BFraction.bernoulli(1000)","type":"codeVoice"}]}],[{"inlineContent":[{"text":"65 mSec","type":"text"}],"type":"paragraph"}]],[[{"type":"paragraph","inlineContent":[{"text":"Harmonic number","type":"text"}]}],[{"type":"paragraph","inlineContent":[{"code":"BFraction.harmonic(10000)","type":"codeVoice"}]}],[{"inlineContent":[{"text":"30 mSec","type":"text"}],"type":"paragraph"}]]],"type":"table"},{"type":"paragraph","inlineContent":[{"type":"text","text":"a1000 = 3187705437890850041662973758105262878153514794996698172406519277876060364087986868049465132757493318066301987043192958841748826350731448419937544810921786918975580180410200630645469411588934094075222404396990984350815153163569041641732160380739556436955287671287935796642478260435292021117614349253825"}]},{"inlineContent":[{"text":"b1000 = 9159373012373110951130589007821321098436345855865428979299172149373720601254669552044211236974571462005332583657082428026625366060511329189733296464187785766230514564038057370938741745651937465362625449921195096442684523511715110908407508139315000469851121118117438147266381183636498494901233452870695","type":"text"}],"type":"paragraph"},{"type":"paragraph","inlineContent":[{"text":"c2000 = 1190583332681083129323588684910845359379915367459759242106618067261956856381281184752008892106576666833853411939711280970145570546868549934865719229538926506588929417873149597614787608112658086250354719939407543740242931571462165384138560315454455247539461818779966171917173966217706187439870264672508450210272481951994459523586160979759782950984370978171111340529321052541588344733968902238813379990628157732181128074253104347868153860527298911917508606081710893794973605227829729403843750412766366804402629686458092685235454222856584200220355212623917637542398554907364450159627359316156463617143173","type":"text"}]},{"type":"paragraph","inlineContent":[{"type":"text","text":"p1000 (probably a prime) = 7662841304438384296568220077355872003841475576593385710590818274399706072141018649398767137142090308734613594718593893634649122767374115742644499040193270857876678047220373151142747088797516044505739487695946446362769947024029728822155570722524629197074319602110260674029276185098937139753025851896997"}]}]}],"abstract":[{"type":"text","text":"Execution times for certain BigInt operations"}],"variants":[{"paths":["\/documentation\/bigint\/performance"],"traits":[{"interfaceLanguage":"swift"}]}],"hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt"]]},"metadata":{"role":"article","modules":[{"name":"BigInt"}],"roleHeading":"Article","title":"Performance"},"sections":[],"references":{"doc://bigint.BigInt/documentation/BigInt/AboutBInt":{"type":"topic","url":"\/documentation\/bigint\/aboutbint","title":"About BInt","role":"article","abstract":[{"text":"Signed integers of unbounded 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Their actual values are shown below the table."}]}],"type":"aside"},{"alignments":["left","left","right"],"header":"row","rows":[[[{"type":"paragraph","inlineContent":[{"type":"text","text":"Operation"}]}],[{"inlineContent":[{"type":"text","text":"Swift code"}],"type":"paragraph"}],[{"inlineContent":[{"text":"Time","type":"text"}],"type":"paragraph"}]],[[{"inlineContent":[{"text":"As string","type":"text"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"type":"codeVoice","code":"c2000.asString()"}]}],[{"inlineContent":[{"type":"text","text":"8.3 uSec"}],"type":"paragraph"}]],[[{"type":"paragraph","inlineContent":[{"text":"As signed bytes","type":"text"}]}],[{"inlineContent":[{"type":"codeVoice","code":"c2000.asSignedBytes()"}],"type":"paragraph"}],[{"inlineContent":[{"type":"text","text":"0.18 uSec"}],"type":"paragraph"}]],[[{"inlineContent":[{"type":"text","text":"Bitwise and"}],"type":"paragraph"}],[{"type":"paragraph","inlineContent":[{"type":"codeVoice","code":"a1000 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Its functionality falls in the following categories: * **Arithmetic:** addition, subtraction, multiplication, division, exponentiation, remainder and modulus, gcd and lcm -* **Comparison:** the six standard operations == != < <= > >= +* **Comparison:** the six standard operations `==`, `!=`, `<`, `<=`, `>`, and `>=` * **Shifting:** logical left shift and rigth shift * **Logical:** bitwise and, or, xor, and not * **Modulo:** normal modulus, inverse modulus, and modular exponentiation -* **Conversion:** to double, to integer, to string, to magnitude byte array, and to 2's complement byte array +* **Conversion:** to/from double, to/from integer, to/from string, to/from a magnitude + byte array, and to/from a 2's complement byte array * **Primes:** prime number testing, probable prime number generation and primorial -* **Miscellaneous:** random number generation, n-th root, square root modulo an odd prime, +* **Miscellaneous:** random number generation, n-th root, square root modulo and odd prime, Jacobi symbol, Kronecker symbol, Factorial function, Binomial function, Fibonacci numbers, Lucas numbers and Bernoulli numbers * **Fractions:** Standard arithmetic on fractions whose numerators and denominators are of unbounded size * **Chinese Remainder Theorem:** Compute the CRT value from given residues and moduli +BigInt requires Swift 5.0. It also requires that the Int and UInt types be 64-bit types. +BigInt has been updated to include Leif Ibsen's changes up to v1.19.0. -BigInt requires Swift 5.0. It also requires that the `Int` and `UInt` types be 64 bit types. - -Its documentation is build with the DocC plugin and published on GitHub Pages at this location: +Its documentation is built with the DocC plugin and published on GitHub Pages at this location: -https://leif-ibsen.github.io/BigInt/documentation/bigint +https://mgriebling.github.io/BigInt/documentation/bigint The documentation is also available in the *BigInt.doccarchive* file. @@ -29,6 +33,23 @@ The documentation is also available in the *BigInt.doccarchive* file. The page you're looking for can't be found. The *BigInt.doccarchive* file contains the correct documentation. - It is emphasized that it is only the documentation that's in error. The operators themselves work correctly. + +From now on, this BigInt variant will mirror Ibsen's BigInt changes (more or less) and have addendum files +like *BigInt-Extensions.swift* to implement the Apple-centric protocol compliance. + +Two changes were required in the original source to support BinaryInteger +compliance: + +1) Renamed `mantissa` to `_mantissa` to avoid conflict with the protocol-required +`mantissa`variable. +2) Added the Codable protocol to the BigInt struct definition. This is a *free* +addition that doesn't require any additional code. Benefits include being able +to read and write JSON files containing BigInts. + +Supporting these protocols greatly simplifies the BigDecimal additions and +makes BigInt a first-class citizen that can interoperate with all the other +integer types. + + diff --git a/Sources/BigInt/BigInt-Extensions.swift b/Sources/BigInt/BigInt-Extensions.swift new file mode 100644 index 0000000..d3e02c1 --- /dev/null +++ b/Sources/BigInt/BigInt-Extensions.swift @@ -0,0 +1,104 @@ +// +// BigInt-Extensions.swift +// +// Created by Mike Griebling on 13.07.2023. +// + +extension BInt : SignedInteger { + public static var isSigned: Bool { true } + + public init(_ source: T) where T : BinaryInteger { + if let int = BInt(exactly: source) { + self = int + } else { + self.init(0) + } + } + + public init(clamping source: T) where T : BinaryInteger { + self.init(source) + } + + public init(truncatingIfNeeded source: T) where T : BinaryInteger { + self.init(source) + } + + public init?(exactly source: T) where T : BinaryInteger { + var isNegative = false + if source.signum() < 0 { + isNegative = true + } + let words = source.words + var bwords = Limbs() + for word in words { + if isNegative { bwords.append(UInt64(~word)) } + else { bwords.append(UInt64(word)) } + } + self.init(bwords, false) + if isNegative { self += 1; self.negate() } + } + + public init?(exactly source: T) where T : BinaryFloatingPoint { + guard source.isFinite else { return nil } + if source.rounded() != source { return nil } + if source.isZero { self.init(0); return } + self.init(source) + } + + public init(_ source: T) where T : BinaryFloatingPoint { + // FIXME: - Support other types of BinaryFloatingPoint + if let bint = BInt(Double(source)) { + self = bint + } else { + self.init(0) + } + } +} + +extension BInt : Numeric { + public var magnitude: BInt { BInt(_magnitude) } +} + +extension BInt : BinaryInteger { + public var words: [UInt] { + _magnitude.map { UInt($0) } + } + + public static func <<= (lhs: inout BInt, rhs: RHS) { + lhs = lhs << Int(rhs) + } + + public static func >>= (lhs: inout BInt, rhs: RHS) { + lhs = lhs >> Int(rhs) + } +} + +extension BInt : ExpressibleByIntegerLiteral { + + /// Constructs a BInt from a StaticBigInt + /// + /// - Parameters: + /// - value: extended-precision integer literal + /// - Precondition: + /// Size of words must be 64 bits. + public init(integerLiteral value: StaticBigInt) { + let isNegative = value.signum() < 0 + let bitWidth = value.bitWidth + if bitWidth < Int.bitWidth { + self.init(Int(bitPattern: value[0])) + } else { + precondition(value[0].bitWidth == 64, "Requires 64-bit Ints!") + let noOfWords = (bitWidth / 64) + 1 // must be 64-bit system + var words = Limbs() + for index in 0..(_ lhs: Self, rhs: T) -> Self`) +which works with *all* `BinaryIntegers`, including BigInt's instead of +just Ints or a single integer type. + +Additionally, with support for StaticBigInt, initialization can now +use unlimited precision instead of requiring quoted numbers: + +```swift +let huge = BInt(12_345_678_901_234_567_890_123_456_789_012_345_678_901_234_567_890_123_456_789) +let hugeHex = BInt(0x1234_5678_9ABC_DEF0_1234_5678_9ABC_DEF0_1234_5678_9ABC_DEF0_1234_5678_9ABC_DEF0) +let hugeOctal = BInt(0o123_456_701_123_456_701_123_456_701_123_456_701_123_456_701_123_456_701) +let hugeBinary = BInt(0b10010101_01010101_01010101_01010010_10101000_01010111_11100101_01010101_01001010_10101010) +print(huge, "0x"+hugeHex.asString(radix: 16, uppercase: true), "0o"+hugeOctal.asString(radix: 8), + "0b"+hugeBinary.asString(radix: 2)) +``` +produces: + +``` +12345678901234567890123456789012345678901234567890123456789 +0x123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0123456789ABCDEF0 +0o123456701123456701123456701123456701123456701123456701 +0b10010101010101010101010101010010101010000101011111100101010101010100101010101010 +``` + +Finally, protocol support allows simplified extensions to the BigDecimal +package available [here](https://github.com/mgriebling/BigDecimal.git). +It contains a complete arbitrary-precision Decimal number implementation +with support for standard 32-, 64-, and 128-bit decimal number formats. + diff --git a/Sources/BigInt/BigInt.docc/BigInt.md b/Sources/BigInt/BigInt.docc/BigInt.md index ffd5e59..5f7d222 100644 --- a/Sources/BigInt/BigInt.docc/BigInt.md +++ b/Sources/BigInt/BigInt.docc/BigInt.md @@ -5,13 +5,15 @@ Signed integers and fractions of unbounded size ## > Important: -**Please note:** Due to a bug in GitHub Pages, -> clicking on certain `BInt` and `BFraction` operators in GitHub Pages (f.ex. < and | ) will show the message +**Please note:** Due to a bug in the DocC plugin that generated this documentation, +> clicking on certain `BInt` and `BFraction` operators in GitHub Pages (e.g., `<` and `|` ) will show the message > +> ``` > The page you're looking for can't be found. +> ``` > > The *BigInt.doccarchive* file contains the correct documentation. -> It is emphasized that it is only the documentation that's in error. +> It is emphasized that it is *only* the documentation that's in error. > The operators themselves work correctly. ## Overview @@ -30,13 +32,17 @@ The BigInt package provides arbitrary-precision integer and fraction arithmetic Please, see +* **Protocol and Extension Support** + + Please, see + ### Usage To use BigInt, in your project Package.swift file add a dependency like ```swift dependencies: [ - package(url: "https://github.com/leif-ibsen/BigInt", from: "1.21.0"), + package(url: "https://github.com/mgriebling/BigInt.git", from: "2.2.0"), ] ``` @@ -68,3 +74,4 @@ BigInt requires Swift 5.0. It also requires that the `Int` and `UInt` types be 6 - - - +- diff --git a/Sources/BigInt/BigInt.docc/Extensions/BInt.md b/Sources/BigInt/BigInt.docc/Extensions/BInt.md index 470039a..a72a946 100644 --- a/Sources/BigInt/BigInt.docc/Extensions/BInt.md +++ b/Sources/BigInt/BigInt.docc/Extensions/BInt.md @@ -153,9 +153,11 @@ Please, see ### Shift Operations - ``<<(_:_:)`` -- ``<<=(_:_:)`` +- ``<<=(_:_:)-9gfzo`` +- ``<<=(_:_:)-12hp5`` - ``>>(_:_:)`` -- ``>>=(_:_:)`` +- ``>>=(_:_:)-40hci`` +- ``>>=(_:_:)-3hxjp`` ### Bit Operations diff --git a/Sources/BigInt/BigInt.swift b/Sources/BigInt/BigInt.swift index af7f512..b9829e1 100755 --- a/Sources/BigInt/BigInt.swift +++ b/Sources/BigInt/BigInt.swift @@ -28,7 +28,7 @@ precedencegroup ExponentiationPrecedence { infix operator ** : ExponentiationPrecedence -public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { +public struct BInt: CustomStringConvertible, Comparable, Codable, Sendable, Equatable, Hashable { // MARK: - Constants @@ -64,8 +64,8 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - magnitude: Magnitude of value /// - isNegative: `true` means negative value, `false` means 0 or positive value, default is `false` public init(_ magnitude: Limbs, _ isNegative : Bool = false) { - self.magnitude = magnitude - self.magnitude.normalize() + self._magnitude = magnitude + self._magnitude.normalize() self.isNegative = isNegative if self.isZero { self.isNegative = false @@ -249,22 +249,22 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { } let chunks = bb.count / 8 let remaining = bb.count - chunks * 8 - self.magnitude = Limbs(repeating: 0, count: chunks + (remaining == 0 ? 0 : 1)) + self._magnitude = Limbs(repeating: 0, count: chunks + (remaining == 0 ? 0 : 1)) var bi = 0 - var li = self.magnitude.count + var li = self._magnitude.count if remaining > 0 { li -= 1 } for _ in 0 ..< remaining { - self.magnitude[li] <<= 8 - self.magnitude[li] |= Limb(bb[bi]) + self._magnitude[li] <<= 8 + self._magnitude[li] |= Limb(bb[bi]) bi += 1 } for _ in 0 ..< chunks { li -= 1 for _ in 0 ..< 8 { - self.magnitude[li] <<= 8 - self.magnitude[li] |= Limb(bb[bi]) + self._magnitude[li] <<= 8 + self._magnitude[li] |= Limb(bb[bi]) bi += 1 } } @@ -277,19 +277,19 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public internal(set) var isNegative: Bool /// The magnitude limb array - public internal(set) var magnitude: Limbs + public internal(set) var _magnitude: Limbs // MARK: Computed properties /// The absolute value of `self` public var abs: BInt { - return BInt(self.magnitude) + return BInt(self._magnitude) } /// The number of bits in the binary representation of the magnitude of `self`. 0 if `self` = 0 public var bitWidth: Int { - return self.magnitude.bitWidth + return self._magnitude.bitWidth } /// Base 10 string value of `self` @@ -299,22 +299,22 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// Is `true` if `self` is even, `false` if `self` is odd public var isEven: Bool { - return self.magnitude[0] & 1 == 0 + return self._magnitude[0] & 1 == 0 } /// Is `false` if `self` = 0, `true` otherwise public var isNotZero: Bool { - return self.magnitude.count > 1 || self.magnitude[0] > 0 + return self._magnitude.count > 1 || self._magnitude[0] > 0 } /// Is `true` if `self` is odd, `false` if `self` is even public var isOdd: Bool { - return self.magnitude[0] & 1 == 1 + return self._magnitude[0] & 1 == 1 } /// Is `true` if `self` = 1, `false` otherwise public var isOne: Bool { - return self.magnitude.count == 1 && self.magnitude[0] == 1 && !self.isNegative + return self._magnitude.count == 1 && self._magnitude[0] == 1 && !self.isNegative } /// Is `true` if `self` > 0, `false` otherwise @@ -324,23 +324,23 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// Is `true` if `self` is a power of 2: 1, 2, 4, 8 ..., `false` otherwise public var isPow2: Bool { - return !self.isNegative && self.bitWidth == self.magnitude.trailingZeroBitCount() + 1 + return !self.isNegative && self.bitWidth == self._magnitude.trailingZeroBitCount() + 1 } /// Is `true` if `self` = 0, `false` otherwise public var isZero: Bool { - return self.magnitude.count == 1 && self.magnitude[0] == 0 + return self._magnitude.count == 1 && self._magnitude[0] == 0 } /// The number of leading zero bits in the magnitude of `self`. 0 if `self` = 0 public var leadingZeroBitCount: Int { - return self.isZero ? 0 : self.magnitude.last!.leadingZeroBitCount + return self.isZero ? 0 : self._magnitude.last!.leadingZeroBitCount } /// The number of 1 bits in the magnitude of `self` public var population: Int { var p = 0 - for m in self.magnitude { + for m in self._magnitude { p += BInt.population(m) } return p @@ -353,7 +353,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// The number of trailing zero bits in the magnitude of `self`. 0 if `self` = 0 public var trailingZeroBitCount: Int { - return self.magnitude.trailingZeroBitCount() + return self._magnitude.trailingZeroBitCount() } /* @@ -384,7 +384,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Returns: `self` as a `Double` or `Infinity` if `self` is not representable as a `Double` public func asDouble() -> Double { var d = 0.0 - for m in self.magnitude.reversed() { + for m in self._magnitude.reversed() { d *= BInt.d264 d += Double(m) } @@ -395,10 +395,10 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// /// - Returns: `self` as an `Int` or `nil` if `self` is not representable as an `Int` public func asInt() -> Int? { - if self.magnitude.count > 1 { + if self._magnitude.count > 1 { return nil } - let mag0 = self.magnitude[0] + let mag0 = self._magnitude[0] if self.isNegative { return mag0 > 0x8000000000000000 ? nil : (mag0 == 0x8000000000000000 ? Int.min : -Int(mag0)) } else { @@ -472,7 +472,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// * BInt(1).asSignedBytes() = [1] /// * BInt(-1).asSignedBytes() = [255] public func asSignedBytes() -> Bytes { - var xl = self.magnitude + var xl = self._magnitude if self.isNegative { var carry = true for i in 0 ..< xl.count { @@ -529,7 +529,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { } let d = BInt.limbRadix[radix] var digitGroups = [String]() - var tmp = self.magnitude + var tmp = self._magnitude while !tmp.equalTo(0) { let (q, r) = tmp.divMod(d) digitGroups.append(String(r, radix: radix, uppercase: uppercase)) @@ -546,8 +546,8 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { } static func toSignedLimbsPair(_ x: BInt, _ y: BInt) -> (bx: Limbs, by: Limbs) { - var bx = x.magnitude - var by = y.magnitude + var bx = x._magnitude + var by = y._magnitude if x.isNegative { invert(&bx) if bx.last! & 0x8000000000000000 == 0 { @@ -689,21 +689,21 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// /// - Parameter n: The bit number public mutating func clearBit(_ n: Int) { - self.magnitude.clearBitAt(n) + self._magnitude.clearBitAt(n) } /// Invert a specified bit - a no-op if bit number < 0 /// /// - Parameter n: The bit number public mutating func flipBit(_ n: Int) { - self.magnitude.flipBitAt(n) + self._magnitude.flipBitAt(n) } /// Set a specified bit - a no-op if bit number < 0 /// /// - Parameter n: The bit number public mutating func setBit(_ n: Int) { - self.magnitude.setBitAt(n) + self._magnitude.setBitAt(n) } /// Test a specified bit - `false` if bit number < 0 @@ -711,7 +711,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Parameter n: The bit number /// - Returns: `true` if bit is set, `false` otherwise public func testBit(_ n: Int) -> Bool { - return self.magnitude.testBitAt(n) + return self._magnitude.testBitAt(n) } @@ -768,9 +768,9 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - y: Right hand addend public static func +=(x: inout BInt, y: BInt) { if x.isNegative == y.isNegative { - x.magnitude.add(y.magnitude) + x._magnitude.add(y._magnitude) } else { - let cmp = x.magnitude.difference(y.magnitude) + let cmp = x._magnitude.difference(y._magnitude) if cmp < 0 { x.isNegative = !x.isNegative } else if cmp == 0 { @@ -791,18 +791,18 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if y > 0 { if x.isNegative { - if x.magnitude.difference(Limb(y)) <= 0 { + if x._magnitude.difference(Limb(y)) <= 0 { x.setSign(false) } } else { - x.magnitude.add(Limb(y)) + x._magnitude.add(Limb(y)) } } else if y < 0 { let yy = y == Int.min ? 0x8000000000000000 : Limb(-y) if x.isNegative { - x.magnitude.add(yy) + x._magnitude.add(yy) } else { - if x.magnitude.difference(yy) < 0 { + if x._magnitude.difference(yy) < 0 { x.setSign(true) } } @@ -875,14 +875,14 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - y: Right hand subtrahend public static func -=(x: inout BInt, y: BInt) { if x.isNegative == y.isNegative { - let cmp = x.magnitude.difference(y.magnitude) + let cmp = x._magnitude.difference(y._magnitude) if cmp < 0 { x.isNegative = !x.isNegative } else if cmp == 0 { x.isNegative = false } } else { - x.magnitude.add(y.magnitude) + x._magnitude.add(y._magnitude) } } @@ -898,18 +898,18 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if y > 0 { if x.isNegative { - x.magnitude.add(Limb(y)) + x._magnitude.add(Limb(y)) } else { - if x.magnitude.difference(Limb(y)) < 0 { + if x._magnitude.difference(Limb(y)) < 0 { x.setSign(true) } } } else if y < 0 { let yy = y == Int.min ? 0x8000000000000000 : Limb(-y) if x.isPositive { - x.magnitude.add(yy) + x._magnitude.add(yy) } else { - if x.magnitude.difference(yy) <= 0 { + if x._magnitude.difference(yy) <= 0 { x.setSign(false) } } @@ -961,7 +961,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - x: Left hand multiplier /// - y: Right hand multiplicand public static func *=(x: inout BInt, y: BInt) { - x.magnitude.multiply(y.magnitude) + x._magnitude.multiply(y._magnitude) x.setSign(x.isNegative != y.isNegative) } @@ -972,12 +972,12 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - y: Right hand multiplicand public static func *=(x: inout BInt, y: Int) { if y > 0 { - x.magnitude.multiply(Limb(y)) + x._magnitude.multiply(Limb(y)) } else if y < 0 { if y == Int.min { - x.magnitude.shiftLeft(63) + x._magnitude.shiftLeft(63) } else { - x.magnitude.multiply(Limb(-y)) + x._magnitude.multiply(Limb(-y)) } x.setSign(!x.isNegative) } else { @@ -996,10 +996,10 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public func quotientAndRemainder(dividingBy x: BInt) -> (quotient: BInt, remainder: BInt) { var quotient = BInt.ZERO var remainder = BInt.ZERO - if x.magnitude.count > Limbs.BZ_DIV_LIMIT && self.magnitude.count > x.magnitude.count + Limbs.BZ_DIV_LIMIT { - (quotient.magnitude, remainder.magnitude) = self.magnitude.bzDivMod(x.magnitude) + if x._magnitude.count > Limbs.BZ_DIV_LIMIT && self._magnitude.count > x._magnitude.count + Limbs.BZ_DIV_LIMIT { + (quotient._magnitude, remainder._magnitude) = self._magnitude.bzDivMod(x._magnitude) } else { - (quotient.magnitude, remainder.magnitude) = self.magnitude.divMod(x.magnitude) + (quotient._magnitude, remainder._magnitude) = self._magnitude.divMod(x._magnitude) } quotient.setSign(self.isNegative != x.isNegative) remainder.setSign(self.isNegative) @@ -1031,7 +1031,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { } var quotient = BInt.ZERO var r: Limb - (quotient.magnitude, r) = self.magnitude.divMod(divisor) + (quotient._magnitude, r) = self._magnitude.divMod(divisor) quotient.setSign(self.isNegative && x > 0 || self.isPositive && x < 0) let remainder = self.isNegative ? -Int(r) : Int(r) return (quotient, remainder) @@ -1054,7 +1054,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Parameter x: Divisor - a BInt value /// - Returns: Quotient of `self / x` - undefined if the remainder is in fact not 0 public func quotientExact(dividingBy x: BInt) -> BInt { - return BInt(self.magnitude.divExact(x.magnitude), self.isNegative != x.isNegative) + return BInt(self._magnitude.divExact(x._magnitude), self.isNegative != x.isNegative) } /// Division @@ -1187,11 +1187,11 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Returns: `self` mod `x`, a non-negative value public func mod(_ x: Int) -> Int { if x == Int.min { - let r = Int(self.magnitude[0] & 0x7fffffffffffffff) + let r = Int(self._magnitude[0] & 0x7fffffffffffffff) return self.isNegative && r > 0 ? -(Int.min + r) : r } let absx = Limb(Swift.abs(x)) - let (_, r) = self.magnitude.divMod(absx) + let (_, r) = self._magnitude.divMod(absx) return Int(self.isNegative && r > 0 ? absx - r : r) } @@ -1222,7 +1222,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { var x = BInt.ZERO var b = BInt.ONE for i in 0 ..< tb { - if b.magnitude[0] & 1 == 1 { + if b._magnitude[0] & 1 == 1 { x.setBit(i) b -= selfr } @@ -1254,7 +1254,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { // [KOC] - section 7 // Reduce mod m - let m = self.magnitude[0] & (1 << tb - 1) + let m = self._magnitude[0] & (1 << tb - 1) let selfr = self.isNegative ? -Int(m) : Int(m) var x = 0 @@ -1292,7 +1292,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Returns: `a^x` public static func **(a: BInt, x: Int) -> BInt { precondition(x >= 0, "Exponent must be non-negative") - return x == 2 ? (a.magnitude.count > 16 ? BInt(a.magnitude.squared()) : a * a) : BInt(a.magnitude.raisedTo(x), a.isNegative && (x & 1 == 1)) + return x == 2 ? (a._magnitude.count > 16 ? BInt(a._magnitude.squared()) : a * a) : BInt(a._magnitude.raisedTo(x), a.isNegative && (x & 1 == 1)) } /// Modular exponentiation - BInt version @@ -1398,7 +1398,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - y: Second operand /// - Returns: `true` if x = y, `false` otherwise public static func ==(x: BInt, y: BInt) -> Bool { - return x.magnitude == y.magnitude && x.isNegative == y.isNegative + return x._magnitude == y._magnitude && x.isNegative == y.isNegative } /// Equal @@ -1428,7 +1428,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - y: Second operand /// - Returns: `true` if x != y, `false` otherwise public static func !=(x: BInt, y: BInt) -> Bool { - return x.magnitude != y.magnitude || x.isNegative != y.isNegative + return x._magnitude != y._magnitude || x.isNegative != y.isNegative } /// Not equal @@ -1460,7 +1460,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public static func <(x: BInt, y: BInt) -> Bool { if x.isNegative { if y.isNegative { - return y.magnitude.compare(x.magnitude) < 0 + return y._magnitude.compare(x._magnitude) < 0 } else { return true } @@ -1468,7 +1468,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if y.isNegative { return false } else { - return x.magnitude.compare(y.magnitude) < 0 + return x._magnitude.compare(y._magnitude) < 0 } } } @@ -1482,7 +1482,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public static func <(x: BInt, y: Int) -> Bool { if x.isNegative { if y < 0 { - return y == Int.min ? x < BInt(y) : x.magnitude.compare(Limb(-y)) > 0 + return y == Int.min ? x < BInt(y) : x._magnitude.compare(Limb(-y)) > 0 } else { return true } @@ -1490,7 +1490,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if y < 0 { return false } else { - return x.magnitude.compare(Limb(y)) < 0 + return x._magnitude.compare(Limb(y)) < 0 } } } @@ -1504,7 +1504,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public static func <(x: Int, y: BInt) -> Bool { if y.isNegative { if x < 0 { - return x == Int.min ? BInt(x) < y : y.magnitude.compare(Limb(-x)) <= 0 + return x == Int.min ? BInt(x) < y : y._magnitude.compare(Limb(-x)) <= 0 } else { return false } @@ -1512,7 +1512,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if x < 0 { return true } else { - return y.magnitude.compare(Limb(x)) > 0 + return y._magnitude.compare(Limb(x)) > 0 } } } @@ -1625,7 +1625,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if n < 0 { return n == Int.min ? (x >> Int.max) >> 1 : x >> -n } - return BInt(n == 1 ? x.magnitude.shifted1Left() : x.magnitude.shiftedLeft(n), x.isNegative) + return BInt(n == 1 ? x._magnitude.shifted1Left() : x._magnitude.shiftedLeft(n), x.isNegative) } /// x = x << n @@ -1636,15 +1636,15 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public static func <<=(x: inout BInt, n: Int) { if n < 0 { if n == Int.min { - x.magnitude.shiftRight(Int.max) - x.magnitude.shift1Right() + x._magnitude.shiftRight(Int.max) + x._magnitude.shift1Right() } else { - x.magnitude.shiftRight(-n) + x._magnitude.shiftRight(-n) } } else if n == 1 { - x.magnitude.shift1Left() + x._magnitude.shift1Left() } else { - x.magnitude.shiftLeft(n) + x._magnitude.shiftLeft(n) } } @@ -1663,7 +1663,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if n < 0 { return n == Int.min ? (x << Int.max) << 1 : x << -n } - return BInt(n == 1 ? x.magnitude.shifted1Right() : x.magnitude.shiftedRight(n), x.isNegative) + return BInt(n == 1 ? x._magnitude.shifted1Right() : x._magnitude.shiftedRight(n), x.isNegative) } /// x = x >> n @@ -1674,15 +1674,15 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { public static func >>=(x: inout BInt, n: Int) { if n < 0 { if n == Int.min { - x.magnitude.shiftLeft(Int.max) - x.magnitude.shift1Left() + x._magnitude.shiftLeft(Int.max) + x._magnitude.shift1Left() } else { - x.magnitude.shiftLeft(-n) + x._magnitude.shiftLeft(-n) } } else if n == 1 { - x.magnitude.shift1Right() + x._magnitude.shift1Right() } else { - x.magnitude.shiftRight(n) + x._magnitude.shiftRight(n) } if x.isZero { x.isNegative = false @@ -2021,16 +2021,16 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Returns: `root` = the integer part of the square root of `self` and `rem` = `self` - `root^2` public func sqrtRemainder() -> (root: BInt, rem: BInt) { precondition(!self.isNegative, "Square root of negative number") - let l = (self.magnitude.count - 1) >> 2 + let l = (self._magnitude.count - 1) >> 2 if l == 0 { let sq = self.basicSqrt() return (sq, self - sq ** 2) } let shifts = l * 64 - let a0 = BInt(Limbs(self.magnitude[0 ..< l])) - let a1 = BInt(Limbs(self.magnitude[l ..< 2 * l])) - let a2 = BInt(Limbs(self.magnitude[2 * l ..< 3 * l])) - let a3 = BInt(Limbs(self.magnitude[3 * l ..< self.magnitude.count])) + let a0 = BInt(Limbs(self._magnitude[0 ..< l])) + let a1 = BInt(Limbs(self._magnitude[l ..< 2 * l])) + let a2 = BInt(Limbs(self._magnitude[2 * l ..< 3 * l])) + let a3 = BInt(Limbs(self._magnitude[3 * l ..< self._magnitude.count])) let (s1, r1) = (a3 << shifts + a2).sqrtRemainder() let (q, u) = (r1 << shifts + a1).quotientAndRemainder(dividingBy: s1 << 1) var s = s1 << shifts + q @@ -2067,7 +2067,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if self.isNegative { return false } else { - return BInt.maybeSquare[Int(self.magnitude[0] & 0xff)] ? self.sqrtRemainder().rem.isZero : false + return BInt.maybeSquare[Int(self._magnitude[0] & 0xff)] ? self.sqrtRemainder().rem.isZero : false } } @@ -2301,7 +2301,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Parameter x: Operand /// - Returns: Greatest common divisor of `self` and `x` public func gcd(_ x: BInt) -> BInt { - if self.magnitude.count > BInt.RECURSIVE_GCD_LIMIT && x.magnitude.count > BInt.RECURSIVE_GCD_LIMIT { + if self._magnitude.count > BInt.RECURSIVE_GCD_LIMIT && x._magnitude.count > BInt.RECURSIVE_GCD_LIMIT { return self.recursiveGCD(x) } else { return self.lehmerGCD(x) @@ -2325,7 +2325,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { /// - Parameter x: Operand /// - Returns: Greatest common divisor `g` of `self` and `x`, and `a` and `b` such that `a` * `self` + `b` * `x` = `g` public func gcdExtended(_ x: BInt) -> (g: BInt, a: BInt, b: BInt) { - if self.magnitude.count > BInt.RECURSIVE_GCD_EXT_LIMIT && x.magnitude.count > BInt.RECURSIVE_GCD_EXT_LIMIT { + if self._magnitude.count > BInt.RECURSIVE_GCD_EXT_LIMIT && x._magnitude.count > BInt.RECURSIVE_GCD_EXT_LIMIT { return self.recursiveGCDext(x) } else { return self.lehmerGCDext(x) @@ -2357,7 +2357,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { while a.isNotZero { while a.isEven { a >>= 1 - let x = m1.magnitude[0] & 7 + let x = m1._magnitude[0] & 7 if x == 3 || x == 5 { t = -t } @@ -2365,7 +2365,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { let x = a a = m1 m1 = x - if a.magnitude[0] & 3 == 3 && m1.magnitude[0] & 3 == 3 { + if a._magnitude[0] & 3 == 3 && m1._magnitude[0] & 3 == 3 { t = -t } a = a.mod(m1) @@ -2416,7 +2416,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if self.isEven { return 0 } else { - let r = self.magnitude[0] & 7 + let r = self._magnitude[0] & 7 return r == 1 || r == 7 ? self.kroneckerSymbol(m >> 1) : -self.kroneckerSymbol(m >> 1) } } @@ -2440,7 +2440,7 @@ public struct BInt: CustomStringConvertible, Comparable, Equatable, Hashable { if self.isEven { return 0 } else { - let r = self.magnitude[0] & 7 + let r = self._magnitude[0] & 7 return r == 1 || r == 7 ? self.kroneckerSymbol(m >> 1) : -self.kroneckerSymbol(m >> 1) } } diff --git a/Sources/BigInt/BitSieve.swift b/Sources/BigInt/BitSieve.swift index 87a187d..52bb6d0 100755 --- a/Sources/BigInt/BitSieve.swift +++ b/Sources/BigInt/BitSieve.swift @@ -63,7 +63,7 @@ class BitSieve { // Construct the large sieve at an even offset specified by base repeat { // Calculate base mod convertedStep - let (_, r) = self.base.magnitude.divMod(UInt64(convertedStep)) + let (_, r) = self.base._magnitude.divMod(UInt64(convertedStep)) start = Int(r) // Take each multiple of step out of sieve diff --git a/Sources/BigInt/ExpMod.swift b/Sources/BigInt/ExpMod.swift index 97246f4..aa5dc11 100755 --- a/Sources/BigInt/ExpMod.swift +++ b/Sources/BigInt/ExpMod.swift @@ -14,8 +14,8 @@ extension BInt { let base: Limbs init(_ a: BInt, _ modulus: BInt) { - self.modulus = modulus.magnitude - self.base = a.magnitude.divMod(self.modulus).remainder + self.modulus = modulus._magnitude + self.base = a._magnitude.divMod(self.modulus).remainder } func reduce(_ t: inout Limbs) { diff --git a/Sources/BigInt/GCD.swift b/Sources/BigInt/GCD.swift index a74c417..02de9c8 100644 --- a/Sources/BigInt/GCD.swift +++ b/Sources/BigInt/GCD.swift @@ -225,7 +225,7 @@ extension BInt { if v.isZero { return u } - if u.magnitude.count > 1 { + if u._magnitude.count > 1 { let r = u.quotientAndRemainder(dividingBy: v).remainder u = v v = r @@ -236,7 +236,7 @@ extension BInt { // u and v are one-limb values assert(u < BInt.ONE << 64) assert(v < BInt.ONE << 64) - return BInt([Limbs.binaryGcd(u.magnitude[0], v.magnitude[0])]) + return BInt([Limbs.binaryGcd(u._magnitude[0], v._magnitude[0])]) } // Lehmer's gcd algorithm - [KNUTH] chapter 4.5.2, algorithm L and exercise 18 diff --git a/Sources/BigInt/ToomCook.swift b/Sources/BigInt/ToomCook.swift index 567d9f3..e2055a7 100755 --- a/Sources/BigInt/ToomCook.swift +++ b/Sources/BigInt/ToomCook.swift @@ -13,10 +13,10 @@ extension Array where Element == Limb { // Works only when the remainder of the division is known to be 0 static func divideBy3(_ d: BInt) -> BInt { - var quotient = Limbs(repeating: 0, count: d.magnitude.count) + var quotient = Limbs(repeating: 0, count: d._magnitude.count) var remainder = Limb(0) for i in 0 ..< quotient.count { - let w = remainder > d.magnitude[i] ? remainder - d.magnitude[i] : d.magnitude[i] - remainder + let w = remainder > d._magnitude[i] ? remainder - d._magnitude[i] : d._magnitude[i] - remainder let x = w &* 0xaaaaaaaaaaaaaaab quotient[i] = x remainder = x < 0x5555555555555556 ? 0 : (x < 0xaaaaaaaaaaaaaaab ? 1 : 2) @@ -72,13 +72,13 @@ extension Array where Element == Limb { var result = Limbs(repeating: 0, count: 6 * k) var offset = k << 2 - result.add(rinf.magnitude, offset) + result.add(rinf._magnitude, offset) offset -= k - result.add(rr3.magnitude, offset) + result.add(rr3._magnitude, offset) offset -= k - result.add(rr2.magnitude, offset) - result.add(rr1.magnitude, k) - result.add(r0.magnitude, 0) + result.add(rr2._magnitude, offset) + result.add(rr1._magnitude, k) + result.add(r0._magnitude, 0) return result } @@ -105,13 +105,13 @@ extension Array where Element == Limb { var result = Limbs(repeating: 0, count: 6 * k) var offset = k << 2 - result.add(vinf.magnitude, offset) + result.add(vinf._magnitude, offset) offset -= k - result.add(t2.magnitude, offset) + result.add(t2._magnitude, offset) offset -= k - result.add(t1.magnitude, offset) - result.add(tm1.magnitude, k) - result.add(v0.magnitude, 0) + result.add(t1._magnitude, offset) + result.add(tm1._magnitude, k) + result.add(v0._magnitude, 0) return result } diff --git a/Tests/BigIntTests/BitTest.swift b/Tests/BigIntTests/BitTest.swift index 8ec1af5..08a07fd 100755 --- a/Tests/BigIntTests/BitTest.swift +++ b/Tests/BigIntTests/BitTest.swift @@ -122,11 +122,11 @@ class BitTest: XCTestCase { XCTAssertFalse(y.testBit(-1)) y = BInt(0) y.setBit(200) - XCTAssertEqual(y.magnitude.count, 4) + XCTAssertEqual(y._magnitude.count, 4) XCTAssertEqual(y, BInt.ONE << 200) XCTAssertTrue(y.testBit(200)) y.clearBit(200) - XCTAssertEqual(y.magnitude.count, 1) + XCTAssertEqual(y._magnitude.count, 1) XCTAssertFalse(y.testBit(200)) XCTAssertEqual(y, BInt.ZERO) y.flipBit(200) diff --git a/Tests/BigIntTests/ConstructorTest.swift b/Tests/BigIntTests/ConstructorTest.swift index 1c6515d..879b138 100755 --- a/Tests/BigIntTests/ConstructorTest.swift +++ b/Tests/BigIntTests/ConstructorTest.swift @@ -20,10 +20,10 @@ class ConstructorTest: XCTestCase { func test1() { let x1 = BInt("123", radix: 10)! - XCTAssertEqual(x1.magnitude.count, 1) + XCTAssertEqual(x1._magnitude.count, 1) XCTAssertFalse((x1.isNegative)) let x2 = BInt("-0", radix: 10)! - XCTAssertEqual(x2.magnitude.count, 1) + XCTAssertEqual(x2._magnitude.count, 1) XCTAssertFalse((x2.isNegative)) let b: Bytes = [0, 0, 0, 123] let x3 = BInt(signed: b) @@ -33,7 +33,7 @@ class ConstructorTest: XCTestCase { let x5 = BInt(bitWidth: 100) XCTAssertTrue(x5.bitWidth <= 100) let x6 = BInt("-123")! - XCTAssertEqual(x6.magnitude[0], 123) + XCTAssertEqual(x6._magnitude[0], 123) let x71 = BInt(bitWidth: 100) let x72 = BInt(signed: x71.asSignedBytes()) XCTAssertEqual(x71, x72) @@ -72,9 +72,9 @@ class ConstructorTest: XCTestCase { let x0 = BInt(0) let x1 = BInt(1) let xm1 = BInt(-1) - XCTAssertEqual(x0.magnitude.count, 1) - XCTAssertEqual(x1.magnitude.count, 1) - XCTAssertEqual(xm1.magnitude.count, 1) + XCTAssertEqual(x0._magnitude.count, 1) + XCTAssertEqual(x1._magnitude.count, 1) + XCTAssertEqual(xm1._magnitude.count, 1) XCTAssertFalse(x0.isNegative) XCTAssertFalse(x1.isNegative) XCTAssertTrue(xm1.isNegative) diff --git a/Tests/BigIntTests/DivModBZTest.swift b/Tests/BigIntTests/DivModBZTest.swift index cc9f9fc..652804a 100644 --- a/Tests/BigIntTests/DivModBZTest.swift +++ b/Tests/BigIntTests/DivModBZTest.swift @@ -22,8 +22,8 @@ class DivModBZTest: XCTestCase { var r1: Limbs = [] var q2: Limbs = [] var r2: Limbs = [] - (q1, r1) = dividend.magnitude.divMod(divisor.magnitude) - (q2, r2) = dividend.magnitude.bzDivMod(divisor.magnitude) + (q1, r1) = dividend._magnitude.divMod(divisor._magnitude) + (q2, r2) = dividend._magnitude.bzDivMod(divisor._magnitude) XCTAssertEqual(q1, q2) XCTAssertEqual(r1, r2) } diff --git a/Tests/BigIntTests/DivModTest.swift b/Tests/BigIntTests/DivModTest.swift index 6d34216..8b1cd66 100755 --- a/Tests/BigIntTests/DivModTest.swift +++ b/Tests/BigIntTests/DivModTest.swift @@ -108,7 +108,7 @@ class DivModTest: XCTestCase { // a BInt modulo an Int for _ in 0 ..< 100 { let x = BInt(bitWidth: 1000) - let m = x.magnitude[0] == 0 ? 1 : Int(x.magnitude[0] & 0x7fffffffffffffff) + let m = x._magnitude[0] == 0 ? 1 : Int(x._magnitude[0] & 0x7fffffffffffffff) XCTAssertEqual(x.mod(m), x.mod(BInt(m)).asInt()!) XCTAssertEqual(x.mod(-m), x.mod(-BInt(m)).asInt()!) } diff --git a/Tests/BigIntTests/ExtensionTest.swift b/Tests/BigIntTests/ExtensionTest.swift new file mode 100644 index 0000000..3c9feca --- /dev/null +++ b/Tests/BigIntTests/ExtensionTest.swift @@ -0,0 +1,39 @@ +// +// Test.swift +// BigInt +// +// Created by Mike Griebling on 11.10.2024. +// + +import XCTest +@testable import BigInt + +class ExtensionTest: XCTestCase { + + func test1() { + let x = BInt(12345678901234567890123456789) + let l = BInt(integerLiteral: 12345678901234567890123456789) + let s = BInt("12345678901234567890123456789") + XCTAssertTrue(BInt.isSigned) + XCTAssertEqual(BInt(clamping: 12345), BInt(12345)) + XCTAssertEqual(l, s) + XCTAssertEqual(l, x) + XCTAssertTrue(BInt.zero.words == [0]) + XCTAssertTrue(x.words == [5097733592125636885, 669260594]) + XCTAssertEqual(BInt(-123_890), BInt("-123890")) + let x1 = x << BInt(5) + var y1 = x; y1 <<= 5 + XCTAssertEqual(x1, y1) + let x2 = x >> BInt(5) + var y2 = x; y2 >>= 5 + XCTAssertEqual(x2, y2) + var x3 = x; x3 >>= BInt(1000) + XCTAssertEqual(x3, BInt.zero) + XCTAssertNil(BInt(exactly: 123.45)) + XCTAssertEqual(BInt(123.45), BInt(123)) + XCTAssertEqual(BInt(exactly: 123), BInt(123)) + XCTAssertEqual(BInt(truncatingIfNeeded: 1234567890), BInt(1234567890)) + XCTAssertEqual(x.magnitude, x) + } + +} diff --git a/Tests/BigIntTests/FFTTest.swift b/Tests/BigIntTests/FFTTest.swift index a6a1e86..b0b06cf 100644 --- a/Tests/BigIntTests/FFTTest.swift +++ b/Tests/BigIntTests/FFTTest.swift @@ -61,13 +61,13 @@ class FFTTest: XCTestCase { let a = BInt(bitWidth: (Limbs.FFT_THR + 1) * 64) let b = BInt(bitWidth: (Limbs.FFT_THR + 1) * 64) let p = a * b - let pTC = BInt(a.magnitude.toomCookTimes(b.magnitude)) + let pTC = BInt(a._magnitude.toomCookTimes(b._magnitude)) XCTAssertEqual(p, pTC) } for _ in 0 ..< 10 { let a = BInt(bitWidth: (Limbs.FFT_THR + 1) * 64) let p = a ** 2 - let pTC = BInt(a.magnitude.toomCookSquare()) + let pTC = BInt(a._magnitude.toomCookSquare()) XCTAssertEqual(p, pTC) } } diff --git a/Tests/BigIntTests/KaratsubaTest.swift b/Tests/BigIntTests/KaratsubaTest.swift index 1bbfd67..d953fef 100755 --- a/Tests/BigIntTests/KaratsubaTest.swift +++ b/Tests/BigIntTests/KaratsubaTest.swift @@ -61,13 +61,13 @@ class KaratsubaTest: XCTestCase { let a = BInt(bitWidth: (Limbs.KA_THR + 1) * 64) let b = BInt(bitWidth: (Limbs.KA_THR + 1) * 64) let p = a * b - let pTC = BInt(a.magnitude.toomCookTimes(b.magnitude)) + let pTC = BInt(a._magnitude.toomCookTimes(b._magnitude)) XCTAssertEqual(p, pTC) } for _ in 0 ..< 10 { let a = BInt(bitWidth: (Limbs.KA_THR + 1) * 64) let p = a ** 2 - let pTC = BInt(a.magnitude.toomCookSquare()) + let pTC = BInt(a._magnitude.toomCookSquare()) XCTAssertEqual(p, pTC) } } diff --git a/Tests/BigIntTests/MultiplicationTest.swift b/Tests/BigIntTests/MultiplicationTest.swift index 46a0a73..4217169 100755 --- a/Tests/BigIntTests/MultiplicationTest.swift +++ b/Tests/BigIntTests/MultiplicationTest.swift @@ -28,7 +28,7 @@ class MultiplicationTest: XCTestCase { let (q1, r1) = c.quotientAndRemainder(dividingBy: b) XCTAssertEqual(r1, BInt(0)) XCTAssertEqual(q1, a) - var am = a.magnitude + var am = a._magnitude am = am.times(am) XCTAssertEqual(a * a, BInt(am)) } diff --git a/Tests/BigIntTests/ToomCookTest.swift b/Tests/BigIntTests/ToomCookTest.swift index d85980c..4e56dfe 100755 --- a/Tests/BigIntTests/ToomCookTest.swift +++ b/Tests/BigIntTests/ToomCookTest.swift @@ -61,13 +61,13 @@ class ToomCookTest: XCTestCase { let a = BInt(bitWidth: (Limbs.TC_THR + 1) * 64) let b = BInt(bitWidth: (Limbs.TC_THR + 1) * 64) let p = a * b - let pK = BInt(a.magnitude.karatsubaTimes(b.magnitude)) + let pK = BInt(a._magnitude.karatsubaTimes(b._magnitude)) XCTAssertEqual(p, pK) } for _ in 0 ..< 10 { let a = BInt(bitWidth: (Limbs.TC_THR + 1) * 64) let p = a ** 2 - let pK = BInt(a.magnitude.karatsubaSquare()) + let pK = BInt(a._magnitude.karatsubaSquare()) XCTAssertEqual(p, pK) } } diff --git a/docs/data/documentation/bigint.json 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b/docs/data/documentation/bigint/protocols.json new file mode 100644 index 0000000..e0f0748 --- /dev/null +++ b/docs/data/documentation/bigint/protocols.json @@ -0,0 +1 @@ +{"sections":[],"abstract":[{"text":"BigInt supports the standard integer data type’s SignedInteger, BinaryInteger, Codable, and Numeric protocols.","type":"text"}],"kind":"article","hierarchy":{"paths":[["doc:\/\/bigint.BigInt\/documentation\/BigInt"]]},"identifier":{"interfaceLanguage":"swift","url":"doc:\/\/bigint.BigInt\/documentation\/BigInt\/Protocols"},"metadata":{"modules":[{"name":"BigInt"}],"title":"Protocols and Additions","roleHeading":"Article","role":"article"},"primaryContentSections":[{"content":[{"level":2,"type":"heading","anchor":"overview","text":"Overview"},{"type":"paragraph","inlineContent":[{"type":"text","text":"BigInt (with protocols) now includes support for StaticBigInt number initialization"},{"text":" ","type":"text"},{"type":"text","text":"with macOS 13.3+, iOS 16.4+, tvOS 16.4+, 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