diff --git a/.circleci/config.yml b/.circleci/config.yml deleted file mode 100755 index be742e6a8..000000000 --- a/.circleci/config.yml +++ /dev/null @@ -1,40 +0,0 @@ -# iOS CircleCI 2.0 configuration file -# -# Check https://circleci.com/docs/2.0/ios-migrating-from-1-2/ for more details -# -version: 2 -jobs: - build: - - # Specify the Xcode version to use - macos: - xcode: "9.3" - - steps: - - checkout - - # Install CocoaPods - - run: - name: Install CocoaPods - command: pod install - - # Build the app and run tests - - run: - name: Build and run tests - command: fastlane scan - environment: - SCAN_DEVICE: iPhone 6 - SCAN_SCHEME: WebTests - - # Collect XML test results data to show in the UI, - # and save the same XML files under test-results folder - # in the Artifacts tab - - store_test_results: - path: test_output/report.xml - - store_artifacts: - path: /tmp/test-results - destination: scan-test-results - - store_artifacts: - path: ~/Library/Logs/scan - destination: scan-logs - diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml new file mode 100644 index 000000000..7b9492557 --- /dev/null +++ b/.github/workflows/ci.yml @@ -0,0 +1,57 @@ +name: "Web3swift CI" + +on: + push: + branches: + - master + - develop + - hotfix + paths: + - Packag*.swift + - web3swift.podspec + - Cartfile + - Sources/** + - 'Tests/**' + - 'web3swift*/**' + - '.github/workflows/**' + pull_request: + branches: + - master + - develop + +jobs: + spm: + name: Swift Package Manager 5.4 + runs-on: macOS-11 + concurrency: spm + env: + DEVELOPER_DIR: /Applications/Xcode_12.5.1.app/Contents/Developer + steps: + - uses: actions/checkout@v2 + - name: Resolve dependencies + run: swift package resolve + - name: Build + run: swift build --build-tests + # - name: Run local tests + # run: swift test --skip-build -c debug --filter localTests + carthage: + name: Carthage + runs-on: macOS-11 + concurrency: carthage + env: + DEVELOPER_DIR: /Applications/Xcode_12.5.1.app/Contents/Developer + strategy: + fail-fast: false + max-parallel: 2 + matrix: + destination: ['OS=14.5,name=iPhone 12'] + steps: + - uses: actions/checkout@v2 + - name: Resolving dependencies + run: carthage checkout + - name: Building dependencies + run: carthage build --no-use-binaries --platform iOS Simulator --use-xcframeworks + - name: Building framework + run: xcodebuild build-for-testing -project "web3swift.xcodeproj" -scheme "web3swift" -destination "${{matrix.destination}}" -testPlan LocalTests + # - name: Running local tests + # run: xcodebuild test-without-building -project "web3swift.xcodeproj" -scheme "web3swift" -destination "${{matrix.destination}}" -testPlan LocalTests diff --git a/.gitignore b/.gitignore index 1b8c7945d..06b69c170 100755 --- a/.gitignore +++ b/.gitignore @@ -5,7 +5,7 @@ ## Build generated build/ DerivedData/ -.build + ## Various settings *.pbxuser !default.pbxuser @@ -35,9 +35,11 @@ playground.xcworkspace # Swift Package Manager # # Add this line if you want to avoid checking in source code from Swift Package Manager dependencies. -# Packages/ -# Package.pins +Packages/ +Package.pins .build/ +.swiftpm/** +*/.swiftpm/** # CocoaPods # diff --git a/.travis.yml b/.travis.yml deleted file mode 100755 index 2ccd46853..000000000 --- a/.travis.yml +++ /dev/null @@ -1,15 +0,0 @@ -language: swift -osx_image: xcode10.2 -cache: bundler -xcode_project: web3swift.xcworkspace -xcode_scheme: web3swift-iOS -xcode_destination: platform=iOS Simulator, OS=12.2, name=iPhone X -#before_install: -# - brew install carthage || true -# - brew outdated carthage || brew upgrade carthage -#before_script: -# - carthage bootstrap --platform iOS --no-use-binaries --cache-builds -script: - - xcodebuild -scheme web3swift -project web3swift.xcodeproj -sdk iphonesimulator build test -after_success: - - bash <(curl -s https://codecov.io/bash) diff --git a/Cartfile b/Cartfile index 32101928a..67b90518f 100755 --- a/Cartfile +++ b/Cartfile @@ -1,5 +1,5 @@ -github "attaswift/BigInt" ~> 5.0 +github "attaswift/BigInt" ~> 5.3.0 github "attaswift/SipHash" ~> 1.2.2 -github "daltoniam/Starscream" ~> 3.1.0 -github "krzyzanowskim/CryptoSwift" ~> 1.0.0 -github "mxcl/PromiseKit" ~> 6.8.4 +github "daltoniam/Starscream" ~> 4.0.4 +github "krzyzanowskim/CryptoSwift" ~> 1.4.2 +github "mxcl/PromiseKit" ~> 6.16.2 diff --git a/Cartfile.resolved b/Cartfile.resolved index 75cdfc0d0..09eb96893 100644 --- a/Cartfile.resolved +++ b/Cartfile.resolved @@ -1,5 +1,5 @@ -github "attaswift/BigInt" "v5.2.0" +github "attaswift/BigInt" "v5.3.0" github "attaswift/SipHash" "v1.2.2" -github "daltoniam/Starscream" "3.1.1" -github "krzyzanowskim/CryptoSwift" "1.3.2" -github "mxcl/PromiseKit" "6.13.3" +github "daltoniam/Starscream" "4.0.4" +github "krzyzanowskim/CryptoSwift" "1.4.2" +github "mxcl/PromiseKit" "6.16.2" diff --git a/Carthage/Checkouts/BigInt/.github/workflows/jazzy.yml b/Carthage/Checkouts/BigInt/.github/workflows/jazzy.yml new file mode 100644 index 000000000..4ae6fb70b --- /dev/null +++ b/Carthage/Checkouts/BigInt/.github/workflows/jazzy.yml @@ -0,0 +1,29 @@ +name: Swift + +on: + push: + tags: + - '*' + +jobs: + macos: + runs-on: macos-latest + steps: + - uses: actions/checkout@v2 + - name: Install jazzy + run: gem install jazzy + - name: Generate documentation + run: | + jazzy \ + --clean \ + --github-file-prefix "https://github.com/attaswift/$module/tree/${GITHUB_REF}" \ + --module-version "${{ github.event.release.tag_name }}" \ + --copyright "© $(date '+%Y') [Károly Lőrentey](https://twitter.com/lorentey). (Last updated: $(date '+%Y-%m-%d'))" \ + --config .jazzy.yml + - name: Commit docs + run: | + git config --local user.email "bot@github.com" + git config --local user.name "GitHub Actions" + git add ./docs + git commit -m "Update docs" + git push origin HEAD:master diff --git a/Carthage/Checkouts/BigInt/.github/workflows/swift.yml b/Carthage/Checkouts/BigInt/.github/workflows/swift.yml new file mode 100644 index 000000000..3b977ac3a --- /dev/null +++ b/Carthage/Checkouts/BigInt/.github/workflows/swift.yml @@ -0,0 +1,47 @@ +name: Swift + +on: + push: + branches: [ master ] + pull_request: + branches: [ master ] + +jobs: + macos: + runs-on: macos-latest + steps: + - uses: actions/checkout@v2 + - name: Build + run: swift build --build-tests + - name: Run tests + run: swift test + xcode: + runs-on: macos-latest + strategy: + matrix: + scheme: [BigInt-macOS, BigInt-iOS, BigInt-watchOS, BigInt-tvOS] + steps: + - uses: actions/checkout@v2 + - name: Build + run: xcrun xcodebuild -workspace BigInt.xcworkspace -scheme ${{ matrix.scheme }} + linux: + container: + image: swift:${{ matrix.linux }} + runs-on: ubuntu-latest + strategy: + matrix: + linux: [bionic, xenial, focal] + steps: + - uses: actions/checkout@v2 + - name: Build + run: swift build --build-tests --enable-test-discovery + - name: Test + run: swift test --enable-test-discovery + codecov: + runs-on: macos-latest + steps: + - uses: actions/checkout@v2 + - name: Test and generate code coverage report + run: xcrun xcodebuild -workspace BigInt.xcworkspace -scheme BigInt-macOS test + - name: Upload coverage to Codecov + uses: codecov/codecov-action@v1 diff --git a/Carthage/Checkouts/BigInt/.jazzy.yml b/Carthage/Checkouts/BigInt/.jazzy.yml new file mode 100644 index 000000000..3698439d3 --- /dev/null +++ b/Carthage/Checkouts/BigInt/.jazzy.yml @@ -0,0 +1,8 @@ +module: BigInt +author: Károly Lőrentey +theme: fullwidth +output: ./docs +author_url: "https://twitter.com/lorentey" +github_url: "https://github.com/attaswift/BigInt" +root_url: "https://attaswift.github.io/BigInt/reference/" +xcodebuild_arguments: ["-workspace", "BigInt.xcworkspace", "-scheme", "BigInt-macOS"] \ No newline at end of file diff --git a/Carthage/Checkouts/BigInt/BigInt.podspec b/Carthage/Checkouts/BigInt/BigInt.podspec index 758a53727..cdb493eb9 100644 --- a/Carthage/Checkouts/BigInt/BigInt.podspec +++ b/Carthage/Checkouts/BigInt/BigInt.podspec @@ -1,7 +1,7 @@ Pod::Spec.new do |spec| spec.name = 'BigInt' - spec.version = '5.2.0' + spec.version = '5.3.0' spec.ios.deployment_target = "8.0" spec.osx.deployment_target = "10.9" spec.tvos.deployment_target = "9.0" diff --git a/Carthage/Checkouts/BigInt/BigInt.xcodeproj/project.pbxproj b/Carthage/Checkouts/BigInt/BigInt.xcodeproj/project.pbxproj index 9e27c6bf6..2402d2b9a 100644 --- a/Carthage/Checkouts/BigInt/BigInt.xcodeproj/project.pbxproj +++ b/Carthage/Checkouts/BigInt/BigInt.xcodeproj/project.pbxproj @@ -174,7 +174,6 @@ BB241C6A1DDB70B00067F917 /* BigInt Benchmark.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "BigInt Benchmark.xctest"; sourceTree = BUILT_PRODUCTS_DIR; }; BB241CE81DDB7B620067F917 /* CHANGELOG.md */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = net.daringfireball.markdown; path = CHANGELOG.md; sourceTree = ""; }; BB241CE91DDB7B620067F917 /* Demo.playground */ = {isa = PBXFileReference; lastKnownFileType = file.playground; path = Demo.playground; sourceTree = ""; }; - BB241CEA1DDB7B620067F917 /* generate-docs.sh */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text.script.sh; path = "generate-docs.sh"; sourceTree = ""; }; BB241CF01DDB84210067F917 /* .codecov.yml */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = text; path = .codecov.yml; sourceTree = ""; }; BB4273F41F24AFC800065766 /* Tools.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Tools.swift; sourceTree = ""; }; BB9889A41F3E5C3100014740 /* Strideable.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Strideable.swift; sourceTree = ""; }; @@ -191,7 +190,6 @@ BBB55AF11C8F8BE00050DDA9 /* BigInt.framework */ = {isa = PBXFileReference; explicitFileType = wrapper.framework; includeInIndex = 0; path = BigInt.framework; sourceTree = BUILT_PRODUCTS_DIR; }; BBB55AFE1C8F8CBB0050DDA9 /* BigInt.framework */ = {isa = PBXFileReference; explicitFileType = wrapper.framework; includeInIndex = 0; path = BigInt.framework; sourceTree = BUILT_PRODUCTS_DIR; }; BBB55B071C8F8CBB0050DDA9 /* BigInt-Test.xctest */ = {isa = PBXFileReference; explicitFileType = wrapper.cfbundle; includeInIndex = 0; path = "BigInt-Test.xctest"; sourceTree = BUILT_PRODUCTS_DIR; }; - BBB55B1C1C8F90F60050DDA9 /* .travis.yml */ = {isa = PBXFileReference; lastKnownFileType = text; path = .travis.yml; sourceTree = ""; }; BBB55B1D1C8F9E850050DDA9 /* LICENSE.md */ = {isa = PBXFileReference; lastKnownFileType = net.daringfireball.markdown; path = LICENSE.md; sourceTree = ""; }; BBB55B1E1C8F9E920050DDA9 /* README.md */ = {isa = PBXFileReference; lastKnownFileType = net.daringfireball.markdown; path = README.md; sourceTree = ""; }; BBE4CA4D1F3DA5AB0062A281 /* Codable.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = Codable.swift; sourceTree = ""; }; @@ -277,10 +275,8 @@ BB241CE81DDB7B620067F917 /* CHANGELOG.md */, BB241BC51DD9F6490067F917 /* Package.swift */, BB241BC71DD9F7D60067F917 /* BigInt.podspec */, - BBB55B1C1C8F90F60050DDA9 /* .travis.yml */, BB241CF01DDB84210067F917 /* .codecov.yml */, BBB55ACC1C8F80660050DDA9 /* version.xcconfig */, - BB241CEA1DDB7B620067F917 /* generate-docs.sh */, BB241CE91DDB7B620067F917 /* Demo.playground */, BBB55AB41C8F80020050DDA9 /* Sources */, BBB55AC01C8F80020050DDA9 /* Tests */, @@ -533,7 +529,7 @@ isa = PBXProject; attributes = { LastSwiftUpdateCheck = 0730; - LastUpgradeCheck = 1100; + LastUpgradeCheck = 1300; ORGANIZATIONNAME = "Károly Lőrentey"; TargetAttributes = { BBB55AB11C8F80020050DDA9 = { @@ -888,6 +884,7 @@ CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES; CLANG_WARN_OBJC_LITERAL_CONVERSION = YES; CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR; + CLANG_WARN_QUOTED_INCLUDE_IN_FRAMEWORK_HEADER = YES; CLANG_WARN_RANGE_LOOP_ANALYSIS = YES; CLANG_WARN_STRICT_PROTOTYPES = YES; CLANG_WARN_SUSPICIOUS_MOVE = YES; @@ -949,6 +946,7 @@ CLANG_WARN_OBJC_IMPLICIT_RETAIN_SELF = YES; CLANG_WARN_OBJC_LITERAL_CONVERSION = YES; CLANG_WARN_OBJC_ROOT_CLASS = YES_ERROR; + CLANG_WARN_QUOTED_INCLUDE_IN_FRAMEWORK_HEADER = YES; CLANG_WARN_RANGE_LOOP_ANALYSIS = YES; CLANG_WARN_STRICT_PROTOTYPES = YES; CLANG_WARN_SUSPICIOUS_MOVE = YES; diff --git a/Carthage/Checkouts/BigInt/BigInt.xcodeproj/xcshareddata/xcschemes/BigInt Benchmark.xcscheme b/Carthage/Checkouts/BigInt/BigInt.xcodeproj/xcshareddata/xcschemes/BigInt Benchmark.xcscheme index ee198da4d..5b99a9330 100644 --- a/Carthage/Checkouts/BigInt/BigInt.xcodeproj/xcshareddata/xcschemes/BigInt Benchmark.xcscheme +++ b/Carthage/Checkouts/BigInt/BigInt.xcodeproj/xcshareddata/xcschemes/BigInt Benchmark.xcscheme @@ -1,6 +1,6 @@ API Documentation -Generated API docs are available at http://attaswift.github.io/BigInt/. +Generated API docs are available at https://attaswift.github.io/BigInt/. ## License @@ -105,7 +106,7 @@ The last version with support for Swift 2 was BigInt 1.3.0.) | 3.x | 2.1.0 | | 4.0 | 3.1.0 | | 4.2 | 4.0.0 | -| 5.0 | 5.0.0 | +| 5.x | 5.3.0 | BigInt deploys to macOS 10.10, iOS 9, watchOS 2 and tvOS 9. It has been tested on the latest OS releases only---however, as the module uses very few platform-provided APIs, @@ -121,19 +122,19 @@ Setup instructions: Add this to the dependency section of your `Package.swift` manifest: ```Swift - .package(url: "https://github.com/attaswift/BigInt.git", from: "5.0.0") + .package(url: "https://github.com/attaswift/BigInt.git", from: "5.3.0") ``` - **CocoaPods:** Put this in your `Podfile`: ```Ruby - pod 'BigInt', '~> 5.0' + pod 'BigInt', '~> 5.3' ``` - **Carthage:** Put this in your `Cartfile`: ``` - github "attaswift/BigInt" ~> 5.0 + github "attaswift/BigInt" ~> 5.3 ``` ## Implementation notes @@ -143,7 +144,7 @@ digit at index 0. As a convenience, [`BigUInt`][BigUInt] allows you to subscript or above its `count`. [The subscript operator][subscript] returns 0 for out-of-bound `get`s and automatically extends the array on out-of-bound `set`s. This makes memory management simpler. -[`BigInt`][BigInt] is just a tiny wrapper around a `BigUInt` [absolute value][abs] and a +[`BigInt`][BigInt] is just a tiny wrapper around a `BigUInt` [absolute value][magnitude] and a [sign bit][negative], both of which are accessible as public read-write properties. ### Why is there no generic `BigInt` type? diff --git a/Carthage/Checkouts/BigInt/Sources/BigInt.swift b/Carthage/Checkouts/BigInt/Sources/BigInt.swift index 11318ffcc..8119bad50 100644 --- a/Carthage/Checkouts/BigInt/Sources/BigInt.swift +++ b/Carthage/Checkouts/BigInt/Sources/BigInt.swift @@ -23,7 +23,7 @@ /// primality test for signed integers. When you need to call one of these, just extract the absolute value: /// /// ```Swift -/// BigInt(255).abs.isPrime() // Returns false +/// BigInt(255).magnitude.isPrime() // Returns false /// ``` /// public struct BigInt: SignedInteger { diff --git a/Carthage/Checkouts/BigInt/Sources/BigUInt.swift b/Carthage/Checkouts/BigInt/Sources/BigUInt.swift index 81aa9a837..759f2aa74 100644 --- a/Carthage/Checkouts/BigInt/Sources/BigUInt.swift +++ b/Carthage/Checkouts/BigInt/Sources/BigUInt.swift @@ -68,7 +68,7 @@ extension BigUInt { /// Return true iff this integer is zero. /// /// - Complexity: O(1) - var isZero: Bool { + public var isZero: Bool { switch kind { case .inline(0, 0): return true case .array: return storage.isEmpty diff --git a/Carthage/Checkouts/BigInt/Sources/Comparable.swift b/Carthage/Checkouts/BigInt/Sources/Comparable.swift index d9ab87e7e..a5c98ffe3 100644 --- a/Carthage/Checkouts/BigInt/Sources/Comparable.swift +++ b/Carthage/Checkouts/BigInt/Sources/Comparable.swift @@ -39,7 +39,7 @@ extension BigUInt: Comparable { } } -extension BigInt { +extension BigInt: Comparable { /// Return true iff `a` is equal to `b`. public static func ==(a: BigInt, b: BigInt) -> Bool { return a.sign == b.sign && a.magnitude == b.magnitude diff --git a/Carthage/Checkouts/BigInt/Sources/Division.swift b/Carthage/Checkouts/BigInt/Sources/Division.swift index 4393f52e9..4b30dbb56 100644 --- a/Carthage/Checkouts/BigInt/Sources/Division.swift +++ b/Carthage/Checkouts/BigInt/Sources/Division.swift @@ -8,7 +8,8 @@ //MARK: Full-width multiplication and division -extension FixedWidthInteger where Magnitude == Self { +// TODO: Return to `where Magnitude == Self` when SR-13491 is resolved +extension FixedWidthInteger { private var halfShift: Self { return Self(Self.bitWidth / 2) @@ -91,13 +92,13 @@ extension FixedWidthInteger where Magnitude == Self { let w = Self(Self.bitWidth) - z let vn = self << z - let un32 = (z == 0 ? dividend.high : (dividend.high &<< z) | (dividend.low &>> w)) // No bits are lost + let un32 = (z == 0 ? dividend.high : (dividend.high &<< z) | ((dividend.low as! Self) &>> w)) // No bits are lost let un10 = dividend.low &<< z let (un1, un0) = un10.split // Divide `(un32,un10)` by `vn`, splitting the full 4/2 division into two 3/2 ones. - let (q1, un21) = quotientAndRemainder(dividing: (un32, un1), by: vn) - let (q0, rn) = quotientAndRemainder(dividing: (un21, un0), by: vn) + let (q1, un21) = quotientAndRemainder(dividing: (un32, (un1 as! Self)), by: vn) + let (q0, rn) = quotientAndRemainder(dividing: (un21, (un0 as! Self)), by: vn) // Undo normalization of the remainder and combine the two halves of the quotient. let mod = rn >> z @@ -120,7 +121,7 @@ extension FixedWidthInteger where Magnitude == Self { r = s } else { - (q, r) = y.0.fastDividingFullWidth((x.0, x.1)) + (q, r) = y.0.fastDividingFullWidth((x.0, (x.1 as! Magnitude))) } // Now refine q by considering x.2 and y.1. // Note that since y is normalized, q * y - x is between 0 and 2. @@ -130,7 +131,7 @@ extension FixedWidthInteger where Magnitude == Self { let (r1, ro) = r.addingReportingOverflow(y.0) if ro { return q - 1 } - let (pl1, so) = pl.subtractingReportingOverflow(y.1) + let (pl1, so) = pl.subtractingReportingOverflow((y.1 as! Magnitude)) let ph1 = (so ? ph - 1 : ph) if ph1 < r1 || (ph1 == r1 && pl1 <= x.2) { return q - 1 } diff --git a/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigIntTests.swift b/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigIntTests.swift index 651ce8f75..51e46e3aa 100644 --- a/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigIntTests.swift +++ b/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigIntTests.swift @@ -634,50 +634,5 @@ class BigIntTests: XCTestCase { test((BigInt(0x01) << 64 + BigInt(0x0203040506070809)) * BigInt(-1), [0x01, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 09]) } - - // - // you have to manually register linux tests here :-( - // - static var allTests = [ - ("testSigns", testSigns), - ("testInit", testInit), - ("testInit_FloatingPoint", testInit_FloatingPoint), - ("testInit_Buffer", testInit_Buffer), - ("testConversionToFloatingPoint", testConversionToFloatingPoint), - ("testTwosComplement", testTwosComplement), - ("testSign", testSign), - ("testBitWidth", testBitWidth), - ("testTrailingZeroBitCount", testTrailingZeroBitCount), - ("testWords", testWords), - ("testComplement", testComplement), - ("testBinaryAnd", testBinaryAnd), - ("testBinaryOr", testBinaryOr), - ("testBinaryXor", testBinaryXor), - ("testConversionToString", testConversionToString), - ("testComparable", testComparable), - ("testHashable", testHashable), - ("testStrideable", testStrideable), - ("testAddition", testAddition), - ("testNegation", testNegation), - ("testSubtraction", testSubtraction), - ("testMultiplication", testMultiplication), - ("testQuotientAndRemainder", testQuotientAndRemainder), - ("testDivision", testDivision), - ("testRemainder", testRemainder), - ("testModulo", testModulo), - ("testStrideableRequirements", testStrideableRequirements), - ("testAbsoluteValuableRequirements", testAbsoluteValuableRequirements), - ("testIntegerArithmeticRequirements", testIntegerArithmeticRequirements), - ("testAssignmentOperators", testAssignmentOperators), - ("testExponentiation", testExponentiation), - ("testModularExponentiation", testModularExponentiation), - ("testSquareRoot", testSquareRoot), - ("testGCD", testGCD), - ("testInverse", testInverse), - ("testPrimes", testPrimes), - ("testShifts", testShifts), - ("testShiftAssignments", testShiftAssignments), - ("testCodable", testCodable), - ("testConversionToData", testConversionToData) - ] + } diff --git a/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigUIntTests.swift b/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigUIntTests.swift index 92c01813a..d11e38075 100644 --- a/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigUIntTests.swift +++ b/Carthage/Checkouts/BigInt/Tests/BigIntTests/BigUIntTests.swift @@ -269,34 +269,34 @@ class BigUIntTests: XCTestCase { XCTAssertEqual(BigUInt(words: 1 ..< 10).extract(2 ..< 5).capacity, 0) var words: [Word] = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] words.reserveCapacity(100) - XCTAssertEqual(BigUInt(words: words).capacity, 100) + XCTAssertGreaterThanOrEqual(BigUInt(words: words).capacity, 100) } func testReserveCapacity() { var a = BigUInt() a.reserveCapacity(100) check(a, .array, []) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) a = BigUInt(word: 1) a.reserveCapacity(100) check(a, .array, [1]) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) a = BigUInt(low: 1, high: 2) a.reserveCapacity(100) check(a, .array, [1, 2]) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) a = BigUInt(words: [1, 2, 3, 4]) a.reserveCapacity(100) check(a, .array, [1, 2, 3, 4]) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) a = BigUInt(words: [1, 2, 3, 4, 5, 6], from: 1, to: 5) a.reserveCapacity(100) check(a, .array, [2, 3, 4, 5]) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) } func testLoad() { @@ -305,15 +305,15 @@ class BigUIntTests: XCTestCase { a.load(BigUInt(low: 1, high: 2)) check(a, .array, [1, 2]) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) a.load(BigUInt(words: [1, 2, 3, 4, 5, 6])) check(a, .array, [1, 2, 3, 4, 5, 6]) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) a.clear() check(a, .array, []) - XCTAssertEqual(a.capacity, 100) + XCTAssertGreaterThanOrEqual(a.capacity, 100) } func testInitFromLiterals() { @@ -1477,60 +1477,5 @@ class BigUIntTests: XCTestCase { let limit = BigUInt(UInt64.max) * BigUInt(UInt64.max) * BigUInt(UInt64.max) check { BigUInt.randomInteger(lessThan: limit, using: &$0) } } - - // - // you have to manually register linux tests here :-( - // - static var allTests = [ - ("testInit_WordBased", testInit_WordBased), - ("testInit_BinaryInteger", testInit_BinaryInteger), - ("testInit_FloatingPoint", testInit_FloatingPoint), - ("testInit_Buffer", testInit_Buffer), - ("testConversionToFloatingPoint", testConversionToFloatingPoint), - ("testInit_Misc", testInit_Misc), - ("testEnsureArray", testEnsureArray), - // ("testCapacity", testCapacity), - // ("testReserveCapacity", testReserveCapacity), - // ("testLoad", testLoad), - ("testInitFromLiterals", testInitFromLiterals), - ("testSubscriptingGetter", testSubscriptingGetter), - ("testSubscriptingSetter", testSubscriptingSetter), - ("testSlice", testSlice), - ("testSigns", testSigns), - ("testBits", testBits), - ("testStrideableRequirements", testStrideableRequirements), - ("testRightShift_ByWord", testRightShift_ByWord), - ("testLeftShift_ByWord", testLeftShift_ByWord), - ("testSplit", testSplit), - ("testLowHigh", testLowHigh), - ("testComparison", testComparison), - ("testHashing", testHashing), - ("testConversionFromBytes", testConversionFromBytes), - ("testConversionToData", testConversionToData), - ("testCodable", testCodable), - ("testAddition", testAddition), - ("testShiftedAddition", testShiftedAddition), - ("testSubtraction", testSubtraction), - ("testMultiplyByWord", testMultiplyByWord), - ("testMultiplication", testMultiplication), - ("testDivision", testDivision), - ("testFactorial", testFactorial), - ("testExponentiation", testExponentiation), - ("testModularExponentiation", testModularExponentiation), - ("testBitWidth", testBitWidth), - ("testBitwise", testBitwise), - ("testLeftShifts", testLeftShifts), - ("testRightShifts", testRightShifts), - ("testSquareRoot", testSquareRoot), - ("testGCD", testGCD), - ("testInverse", testInverse), - ("testStrongProbablePrimeTest", testStrongProbablePrimeTest), - ("testIsPrime", testIsPrime), - ("testConversionToString", testConversionToString), - ("testConversionFromString", testConversionFromString), - ("testRandomIntegerWithMaximumWidth", testRandomIntegerWithMaximumWidth), - ("testRandomIntegerWithExactWidth", testRandomIntegerWithExactWidth), - ("testRandomIntegerLessThan", testRandomIntegerLessThan), - ("testRandomFunctionsUseProvidedGenerator", testRandomFunctionsUseProvidedGenerator), - ] + } diff --git a/Carthage/Checkouts/BigInt/Tests/BigIntTests/WordTests.swift b/Carthage/Checkouts/BigInt/Tests/BigIntTests/WordTests.swift index 53204b3fc..1fc3576d1 100644 --- a/Carthage/Checkouts/BigInt/Tests/BigIntTests/WordTests.swift +++ b/Carthage/Checkouts/BigInt/Tests/BigIntTests/WordTests.swift @@ -9,11 +9,12 @@ import XCTest @testable import BigInt -struct TestDivision where Word.Magnitude == Word { +// TODO: Return to `where Word.Magnitude == Word` when SR-13491 is resolved +struct TestDivision { static func testDivision(_ u: (high: Word, low: Word.Magnitude), _ v: Word) { let (div, mod) = v.fastDividingFullWidth(u) var (ph, pl) = div.multipliedFullWidth(by: v) - let (s, o) = pl.addingReportingOverflow(mod) + let (s, o) = pl.addingReportingOverflow((mod as! Word.Magnitude)) pl = s if o { ph += Word(1) } diff --git a/Carthage/Checkouts/BigInt/docs/Extensions.html b/Carthage/Checkouts/BigInt/docs/Extensions.html index b9203ad28..7479e3581 100644 --- a/Carthage/Checkouts/BigInt/docs/Extensions.html +++ b/Carthage/Checkouts/BigInt/docs/Extensions.html @@ -14,15 +14,16 @@ +

- BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

@@ -39,7 +40,7 @@

- + Install in Dash @@ -91,7 +92,7 @@

-
+

Extensions

The following extensions are available globally.

@@ -105,9 +106,9 @@

Extensions

  • @@ -122,17 +123,13 @@

    Extensions

    Declaration

    Swift

    - 
    protocol BinaryFloatingPoint : FloatingPoint, ExpressibleByFloatLiteral
    + 
    extension BinaryFloatingPoint where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger
    • - - -
    -
    • @@ -153,7 +150,7 @@

      Declaration

      Declaration

      Swift

      - 
      struct String
      + 
      extension String
      @@ -168,8 +165,8 @@

      Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Extensions/BinaryFloatingPoint.html b/Carthage/Checkouts/BigInt/docs/Extensions/BinaryFloatingPoint.html index 648ecee7b..86bf1c39b 100644 --- a/Carthage/Checkouts/BigInt/docs/Extensions/BinaryFloatingPoint.html +++ b/Carthage/Checkouts/BigInt/docs/Extensions/BinaryFloatingPoint.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,11 +92,12 @@

    -
    +

    BinaryFloatingPoint

    - 
    protocol BinaryFloatingPoint : FloatingPoint, ExpressibleByFloatLiteral
    + + 
    extension BinaryFloatingPoint where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger
    @@ -107,13 +108,22 @@

    BinaryFloatingPoint

    +
    + + +
    + +

    Available where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger

    +

    +
    +
    @@ -141,9 +151,9 @@

    Declaration

  • - + - init(_:) + init(_:)
    @@ -158,12 +168,12 @@

    Declaration

    Declaration

    Swift

    - 
    protocol BinaryFloatingPoint : FloatingPoint, ExpressibleByFloatLiteral
    + 
    public init(_ value: BigUInt)
    - Show on GitHub + Show on GitHub
    • @@ -176,8 +186,8 @@

    Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Extensions/String.html b/Carthage/Checkouts/BigInt/docs/Extensions/String.html index 3b61515d6..8e347fd34 100644 --- a/Carthage/Checkouts/BigInt/docs/Extensions/String.html +++ b/Carthage/Checkouts/BigInt/docs/Extensions/String.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,11 +92,12 @@

    -
    +

    String

    - 
    struct String
    + + 
    extension String
    @@ -111,9 +112,9 @@

    String

  • - + - init(_:) + init(_:)
    @@ -133,12 +134,12 @@

    String

    Declaration

    Swift

    - 
    public init(_ v: BigUInt)
    + 
    public init(_ v: BigUInt)
    - Show on GitHub + Show on GitHub
    • @@ -146,9 +147,9 @@

    Declaration

  • @@ -164,8 +165,7 @@

    Declaration

    Requires

    radix > 1 && radix <= 36 -
    -
    +

    Complexity

    O(count) when radix is a power of two; otherwise O(count^2). @@ -176,12 +176,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(_ v: BigUInt, radix: Int, uppercase: Bool = false)
    + 
    public init(_ v: BigUInt, radix: Int, uppercase: Bool = false)
    - Show on GitHub + Show on GitHub
    @@ -189,9 +189,9 @@

    Declaration

  • @@ -207,8 +207,7 @@

    Declaration

    Requires

    radix > 1 && radix <= 36 -
    -
    +

    Complexity

    O(count) when radix is a power of two; otherwise O(count^2). @@ -219,12 +218,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(_ value: BigInt, radix: Int = 10, uppercase: Bool = false)
    + 
    public init(_ value: BigInt, radix: Int = 10, uppercase: Bool = false)
    - Show on GitHub + Show on GitHub
    @@ -237,8 +236,8 @@

    Declaration

    • -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Structs.html b/Carthage/Checkouts/BigInt/docs/Structs.html index 366be84d2..9ae786007 100644 --- a/Carthage/Checkouts/BigInt/docs/Structs.html +++ b/Carthage/Checkouts/BigInt/docs/Structs.html @@ -14,15 +14,16 @@ +

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -39,7 +40,7 @@

    - + Install in Dash @@ -91,7 +92,7 @@

    -
    +

    Structures

    The following structures are available globally.

    @@ -115,7 +116,7 @@

    Structures

    -

    An arbitary precision unsigned integer type, also known as a big integer.

    +

    An arbitary precision unsigned integer type, also known as a “big integer”.

    Operations on big integers never overflow, but they may take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

    @@ -129,12 +130,20 @@

    Structures

    Declaration

    Swift

    - 
    public struct BigUInt: UnsignedInteger
    + 
    public struct BigUInt : UnsignedInteger
    +
    extension BigUInt: Codable
    +
    extension BigUInt: Comparable
    +
    extension BigUInt: Hashable
    +
    extension BigUInt: ExpressibleByIntegerLiteral
    +
    extension BigUInt: Strideable
    +
    extension BigUInt: ExpressibleByStringLiteral
    +
    extension BigUInt: CustomStringConvertible
    +
    extension BigUInt: CustomPlaygroundDisplayConvertible
    - Show on GitHub + Show on GitHub
    @@ -145,9 +154,11 @@

    Declaration

    - -

    BigInt

    -     +
    + +

    BigInt

    +

    +
    • @@ -163,7 +174,7 @@

      BigInt

      -

      An arbitary precision signed integer type, also known as a big integer.

      +

      An arbitary precision signed integer type, also known as a “big integer”.

      Operations on big integers never overflow, but they might take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

      @@ -185,12 +196,19 @@

      BigInt

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public struct BigInt : SignedInteger
      +
      extension BigInt: Codable
      +
      extension BigInt: Hashable
      +
      extension BigInt: ExpressibleByIntegerLiteral
      +
      extension BigInt: Strideable
      +
      extension BigInt: ExpressibleByStringLiteral
      +
      extension BigInt: CustomStringConvertible
      +
      extension BigInt: CustomPlaygroundDisplayConvertible
      - Show on GitHub + Show on GitHub
    @@ -203,8 +221,8 @@

    Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Structs/BigInt.html b/Carthage/Checkouts/BigInt/docs/Structs/BigInt.html index 7bc104afd..ef27d99fb 100644 --- a/Carthage/Checkouts/BigInt/docs/Structs/BigInt.html +++ b/Carthage/Checkouts/BigInt/docs/Structs/BigInt.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,23 @@

    -
    +

    BigInt

    - 
    public struct BigInt: SignedInteger
    + + 
    public struct BigInt : SignedInteger
    +
    extension BigInt: Codable
    +
    extension BigInt: Hashable
    +
    extension BigInt: ExpressibleByIntegerLiteral
    +
    extension BigInt: Strideable
    +
    extension BigInt: ExpressibleByStringLiteral
    +
    extension BigInt: CustomStringConvertible
    +
    extension BigInt: CustomPlaygroundDisplayConvertible
    -

    An arbitary precision signed integer type, also known as a big integer.

    +

    An arbitary precision signed integer type, also known as a “big integer”.

    Operations on big integers never overflow, but they might take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

    @@ -116,6 +124,9 @@

    BigInt

    BigInt(255).abs.isPrime()   // Returns false
    +
    + Show on GitHub +
    @@ -144,12 +155,41 @@

    BigInt

    Declaration

    Swift

    - 
    public struct BigInt: SignedInteger
    + 
    public enum Sign
    + +
    + +
    + Show on GitHub +
    + + + +
  • +
    + + + + Magnitude + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public typealias Magnitude = BigUInt
    - Show on GitHub + Show on GitHub
    @@ -174,12 +214,12 @@

    Declaration

    Declaration

    Swift

    - 
    public typealias Word = BigUInt.Word
    + 
    public typealias Word = BigUInt.Word
    - Show on GitHub + Show on GitHub
    @@ -187,9 +227,9 @@

    Declaration

  • - + - isSigned + isSigned
    @@ -203,12 +243,12 @@

    Declaration

    Declaration

    Swift

    - 
    public static var isSigned: Bool
    + 
    public static var isSigned: Bool { get }
    - Show on GitHub + Show on GitHub
    @@ -216,9 +256,9 @@

    Declaration

  • @@ -233,12 +273,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var magnitude: BigUInt
    + 
    public var magnitude: BigUInt
    - Show on GitHub + Show on GitHub
    @@ -246,9 +286,9 @@

    Declaration

  • - + - sign + sign
    @@ -263,12 +303,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var sign: Sign
    + 
    public var sign: Sign
    - Show on GitHub + Show on GitHub
    @@ -276,9 +316,9 @@

    Declaration

  • @@ -293,12 +333,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(sign: Sign, magnitude: BigUInt)
    + 
    public init(sign: Sign, magnitude: BigUInt)
    - Show on GitHub + Show on GitHub
    @@ -306,9 +346,9 @@

    Declaration

  • - + - isZero + isZero
    @@ -328,12 +368,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var isZero: Bool
    + 
    public var isZero: Bool { get }
    - Show on GitHub + Show on GitHub
    @@ -358,7 +398,7 @@

    Declaration

    Declaration

    Swift

    - 
    public func signum() -> BigInt
    + 
    public func signum() -> BigInt
    @@ -367,21 +407,17 @@

    Return Value

    The sign of this number, expressed as an integer of the same type.

    - Show on GitHub + Show on GitHub
    • - - -
    -
    • - - - ~(_:) + + + +(_:_:)
      @@ -389,18 +425,19 @@

      Return Value

      - +

      Add a to b and return the result.

      +

      Declaration

      Swift

      - 
      public static prefix func ~(x: BigInt) -> BigInt
      + 
      public static func + (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -408,9 +445,9 @@

      Declaration

    • - - - &(_:_:) + + + +=(_:_:)
      @@ -418,29 +455,42 @@

      Declaration

      -

      Undocumented

      +

      Add b to a in place.

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public static func += (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Bitwise Operations

    +

    +
    +
    +
    • - - - |(_:_:) + + + ~(_:)
      @@ -455,12 +505,12 @@

      Declaration

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public prefix static func ~ (x: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
    @@ -468,9 +518,9 @@

    Declaration

  • - - - ^(_:_:) + + + &(_:_:)
    @@ -485,12 +535,12 @@

    Declaration

    Declaration

    Swift

    - 
    public struct BigInt: SignedInteger
    + 
    public static func & (lhs: inout BigInt, rhs: BigInt) -> BigInt
    - Show on GitHub + Show on GitHub
    @@ -498,9 +548,9 @@

    Declaration

  • - - - &=(_:_:) + + + |(_:_:)
    @@ -508,18 +558,19 @@

    Declaration

    - +

    Undocumented

    +

    Declaration

    Swift

    - 
    public static func &=(lhs: inout BigInt, rhs: BigInt)
    + 
    public static func | (lhs: inout BigInt, rhs: BigInt) -> BigInt
    - Show on GitHub + Show on GitHub
    @@ -527,9 +578,9 @@

    Declaration

  • - - - |=(_:_:) + + + ^(_:_:)
    @@ -537,18 +588,19 @@

    Declaration

    - +

    Undocumented

    +

    Declaration

    Swift

    - 
    public static func |=(lhs: inout BigInt, rhs: BigInt)
    + 
    public static func ^ (lhs: inout BigInt, rhs: BigInt) -> BigInt
    - Show on GitHub + Show on GitHub
    @@ -556,9 +608,9 @@

    Declaration

  • - - - ^=(_:_:) + + + &=(_:_:)
    @@ -566,39 +618,29 @@

    Declaration

    - +

    Undocumented

    +

    Declaration

    Swift

    - 
    public static func ^=(lhs: inout BigInt, rhs: BigInt)
    + 
    public static func &= (lhs: inout BigInt, rhs: BigInt)
    - Show on GitHub + Show on GitHub
    • - - -
    -
    - - - -

    Primality Testing

    -     -
    -
    • @@ -606,19 +648,19 @@

      Primality Testing

      -

      Returns true iff this integer passes the strong probable prime test for the specified base.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func isStrongProbablePrime(_ base: BigInt) -> Bool
      + 
      public static func |= (lhs: inout BigInt, rhs: BigInt)
      - Show on GitHub + Show on GitHub
      @@ -626,9 +668,9 @@

      Declaration

    • @@ -636,43 +678,29 @@

      Declaration

      -

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      - -

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, -each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, -but you may specify your own choice.

      - -

      To speed things up, the function checks if self is divisible by the first few prime numbers before -diving into (slower) Miller-Rabin testing.

      - -

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to -return a correct result.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func isPrime(rounds: Int = 10) -> Bool
      + 
      public static func ^= (lhs: inout BigInt, rhs: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    @@ -699,9 +727,9 @@

    Declaration

  • @@ -715,26 +743,22 @@

    Declaration

    Declaration

    Swift

    - 
    public var trailingZeroBitCount: Int
    + 
    public func encode(to encoder: Encoder) throws
    - Show on GitHub + Show on GitHub
    • - - -
    -
    • - - - Words + + + ==(_:_:)
      @@ -742,19 +766,19 @@

      Declaration

      - - See more +

      Return true iff a is equal to b.

      +

      Declaration

      Swift

      - 
      public struct Words: RandomAccessCollection
      + 
      public static func == (a: BigInt, b: BigInt) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -762,9 +786,9 @@

      Declaration

    • - - - words + + + <(_:_:)
      @@ -772,18 +796,19 @@

      Declaration

      - +

      Return true iff a is less than b.

      +

      Declaration

      Swift

      - 
      public var words: Words
      + 
      public static func < (a: BigInt, b: BigInt) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -791,9 +816,9 @@

      Declaration

    • - - - init(words:) + + + init(_:)
      @@ -801,33 +826,30 @@

      Declaration

      -

      Undocumented

      +

      Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer, +where the first byte indicates sign (0 for positive, 1 for negative)

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public init(_ buffer: UnsafeRawBufferPointer)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -835,33 +857,31 @@

      Declaration

      -

      Append this BigInt to the specified hasher.

      +

      Initializes an integer from the bits stored inside a piece of Data. +The data is assumed to be in network (big-endian) byte order with a first +byte to represent the sign (0 for positive, 1 for negative)

      Declaration

      Swift

      - 
      public func appendHashes(to hasher: inout SipHasher)
      + 
      public init(_ data: Data)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -869,28 +889,42 @@

      Declaration

      - +

      Return a Data value that contains the base-256 representation of this integer, in network (big-endian) byte order and a prepended byte to indicate the sign (0 for positive, 1 for negative)

      +

      Declaration

      Swift

      - 
      public init?<T: BinaryFloatingPoint>(exactly source: T)
      + 
      public func serialize() -> Data
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Full-width multiplication and division

    +

    +
    +
    +
    • @@ -898,32 +932,42 @@

      Declaration

      - +

      Divide this integer by y and return the resulting quotient and remainder.

      +
      +

      Requires

      + y > 0 + +
      +

      Complexity

      + O(count^2) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryFloatingPoint>(_ source: T)
      + 
      public func quotientAndRemainder(dividingBy y: BigInt) -> (quotient: BigInt, remainder: BigInt)
      +
      +

      Return Value

      +

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - negate() + + + /(_:_:)
      @@ -931,18 +975,19 @@

      Declaration

      - +

      Divide a by b and return the quotient. Traps if b is zero.

      +

      Declaration

      Swift

      - 
      public mutating func negate()
      + 
      public static func / (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -950,9 +995,9 @@

      Declaration

    • - - - -(_:_:) + + + %(_:_:)
      @@ -960,19 +1005,19 @@

      Declaration

      -

      Subtract b from a and return the result.

      +

      Divide a by b and return the remainder. The result has the same sign as a.

      Declaration

      Swift

      - 
      public static func -(a: BigInt, b: BigInt) -> BigInt
      + 
      public static func % (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -980,9 +1025,9 @@

      Declaration

    • - - - -=(_:_:) + + + modulus(_:)
      @@ -990,33 +1035,29 @@

      Declaration

      -

      Subtract b from a in place.

      +

      Return the result of a mod b. The result is always a nonnegative integer that is less than the absolute value of b.

      Declaration

      Swift

      - 
      public static func -=(a: inout BigInt, b: BigInt)
      + 
      public func modulus(_ mod: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1024,33 +1065,19 @@

      Declaration

      -

      Divide this integer by y and return the resulting quotient and remainder.

      -
      -

      Requires

      - y > 0 - -
      -
      -

      Complexity

      - O(count^2) - -
      +

      Divide a by b storing the quotient in a.

      Declaration

      Swift

      - 
      public func quotientAndRemainder(dividingBy y: BigInt) -> (quotient: BigInt, remainder: BigInt)
      + 
      public static func /= (a: inout BigInt, b: BigInt)
      -
      -

      Return Value

      -

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      -
      - Show on GitHub + Show on GitHub
      @@ -1058,9 +1085,9 @@

      Return Value

    • - - - /(_:_:) + + + %=(_:_:)
      @@ -1068,19 +1095,19 @@

      Return Value

      -

      Divide a by b and return the quotient. Traps if b is zero.

      +

      Divide a by b storing the remainder in a.

      Declaration

      Swift

      - 
      public static func /(a: BigInt, b: BigInt) -> BigInt
      + 
      public static func %= (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      @@ -1088,9 +1115,9 @@

      Declaration

    • - - - %(_:_:) + + + power(_:)
      @@ -1098,19 +1125,40 @@

      Declaration

      -

      Divide a by b and return the remainder. The result has the same sign as a.

      +

      Returns this integer raised to the power exponent.

      + +

      This function calculates the result by successively squaring the base while halving the exponent.

      +
      +

      Note

      + This function can be unreasonably expensive for large exponents, which is why exponent is + a simple integer value. If you want to calculate big exponents, you’ll probably need to use + the modulo arithmetic variant. + +
      +

      See also

      + BigUInt.power(_:, modulus:) + +
      +

      Complexity

      + O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too. + +

      Declaration

      Swift

      - 
      public static func %(a: BigInt, b: BigInt) -> BigInt
      + 
      public func power(_ exponent: Int) -> BigInt
      +
      +

      Return Value

      +

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      +
      - Show on GitHub + Show on GitHub
      @@ -1118,9 +1166,9 @@

      Declaration

    • @@ -1128,33 +1176,36 @@

      Declaration

      -

      Return the result of a mod b. The result is always a nonnegative integer that is less than the absolute value of b.

      +

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      + +

      Uses the right-to-left binary method.

      +
      +

      Complexity

      + O(exponent.count * modulus.count^log2(3)) or somesuch + +

      Declaration

      Swift

      - 
      public func modulus(_ mod: BigInt) -> BigInt
      + 
      public func power(_ exponent: BigInt, modulus: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - /=(_:_:) + + + init(exactly:)
      @@ -1162,19 +1213,18 @@

      Declaration

      -

      Divide a by b storing the quotient in a.

      - +

      Declaration

      Swift

      - 
      public static func /=(a: inout BigInt, b: BigInt)
      + 
      public init?<T>(exactly source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      @@ -1182,9 +1232,9 @@

      Declaration

    • - - - %=(_:_:) + + + init(_:)
      @@ -1192,33 +1242,28 @@

      Declaration

      -

      Divide a by b storing the remainder in a.

      - +

      Declaration

      Swift

      - 
      public static func %=(a: inout BigInt, b: BigInt)
      + 
      public init<T>(_ source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1226,19 +1271,98 @@

      Declaration

      -

      Undocumented

      - -
      +

      Returns the greatest common divisor of a and b.

      +
      +

      Complexity

      + O(count^2) where count = max(a.count, b.count) + +
      + +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public func greatestCommonDivisor(with b: BigInt) -> BigInt
      + +
      +
      +
      + Show on GitHub +
      + +
    + +
  • +
    + + + + inverse(_:) + +
    +
    +
    +
    +
    +
    +

    Returns the multiplicative inverse of this integer in modulo modulus arithmetic, +or nil if there is no such number.

    +
    +

    Requires

    + modulus.magnitude > 1 + +
    +

    Complexity

    + O(count^3) + +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public func inverse(_ modulus: BigInt) -> BigInt?
    + +
    +
    +
    +

    Return Value

    +

    If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + + + hash(into:) + +
    +
    +
    +
    +
    +
    +

    Append this BigInt to the specified hasher.

    + +

    Declaration

    Swift

    - 
    public struct BigInt: SignedInteger
    + 
    public func hash(into hasher: inout Hasher)
    - Show on GitHub + Show on GitHub
    @@ -1246,9 +1370,39 @@

    Declaration

  • - + + + init() + +
    +
    +
    +
    +
    +
    +

    Undocumented

    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public init()
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + - init(_:) + init(_:)
    @@ -1263,12 +1417,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(_ integer: BigUInt)
    + 
    public init(_ integer: BigUInt)
    - Show on GitHub + Show on GitHub
    @@ -1276,9 +1430,9 @@

    Declaration

  • - + - init(_:) + init(_:)
    @@ -1292,12 +1446,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init<T>(_ source: T) where T : BinaryInteger
    + 
    public init<T>(_ source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    @@ -1305,9 +1459,9 @@

    Declaration

  • @@ -1321,12 +1475,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init?<T>(exactly source: T) where T : BinaryInteger
    + 
    public init?<T>(exactly source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    @@ -1334,9 +1488,9 @@

    Declaration

  • @@ -1350,12 +1504,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init<T>(clamping source: T) where T : BinaryInteger
    + 
    public init<T>(clamping source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    @@ -1363,9 +1517,9 @@

    Declaration

  • @@ -1379,26 +1533,22 @@

    Declaration

    Declaration

    Swift

    - 
    public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger
    + 
    public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    • - - -
    -
    - - -
    -
    • - - - ==(_:_:) + + + *(_:_:)
      @@ -1440,19 +1586,19 @@

      Declaration

      -

      Return true iff a is equal to b.

      +

      Multiply a with b and return the result.

      Declaration

      Swift

      - 
      public static func ==(a: BigInt, b: BigInt) -> Bool
      + 
      public static func * (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -1460,9 +1606,9 @@

      Declaration

    • - - - <(_:_:) + + + *=(_:_:)
      @@ -1470,19 +1616,19 @@

      Declaration

      -

      Return true iff a is less than b.

      +

      Multiply a with b in place.

      Declaration

      Swift

      - 
      public static func <(a: BigInt, b: BigInt) -> Bool
      + 
      public static func *= (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      @@ -1490,13 +1636,22 @@

      Declaration

    +
    + + +
    + +

    Primality Testing

    +

    +
    +
    • @@ -1504,43 +1659,29 @@

      Declaration

      -

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by -letters from the English alphabet.

      -
      -

      Requires

      - radix > 1 && radix < 36 - -
      +

      Returns true iff this integer passes the strong probable prime test for the specified base.

      Declaration

      Swift

      - 
      public init?<S: StringProtocol>(_ text: S, radix: Int = 10)
      + 
      public func isStrongProbablePrime(_ base: BigInt) -> Bool
      -
      -

      Return Value

      -

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1548,20 +1689,29 @@

      Return Value

      -

      Initialize a new big integer from a Unicode scalar. -The scalar must represent a decimal digit.

      +

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      + +

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, +each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, +but you may specify your own choice.

      + +

      To speed things up, the function checks if self is divisible by the first few prime numbers before +diving into (slower) Miller-Rabin testing.

      + +

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to +return a correct result.

      Declaration

      Swift

      - 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      + 
      public func isPrime(rounds: Int = 10) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -1569,9 +1719,9 @@

      Declaration

    • @@ -1579,20 +1729,19 @@

      Declaration

      -

      Initialize a new big integer from an extended grapheme cluster. -The cluster must consist of a decimal digit.

      +

      Undocumented

      Declaration

      Swift

      - 
      public init(extendedGraphemeClusterLiteral value: String)
      + 
      public static func &<< (left: BigInt, right: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -1600,9 +1749,9 @@

      Declaration

    • @@ -1610,34 +1759,29 @@

      Declaration

      -

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. -The string must contain only decimal digits.

      +

      Undocumented

      Declaration

      Swift

      - 
      public init(stringLiteral value: StringLiteralType)
      + 
      public static func &<<= (left: inout BigInt, right: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - description + + + &>>(_:_:)
      @@ -1645,33 +1789,29 @@

      Declaration

      -

      Return the decimal representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var description: String
      + 
      public static func &>> (left: BigInt, right: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1679,33 +1819,29 @@

      Declaration

      -

      Return the playground quick look representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var customPlaygroundQuickLook: PlaygroundQuickLook
      + 
      public static func &>>= (left: inout BigInt, right: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - *(_:_:) + + + <<(_:_:)
      @@ -1713,19 +1849,19 @@

      Declaration

      -

      Multiply a with b and return the result.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func *(a: BigInt, b: BigInt) -> BigInt
      + 
      public static func << <Other>(lhs: BigInt, rhs: Other) -> BigInt where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1733,9 +1869,9 @@

      Declaration

    • - - - *=(_:_:) + + + <<=(_:_:)
      @@ -1743,33 +1879,29 @@

      Declaration

      -

      Multiply a with b in place.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func *=(a: inout BigInt, b: BigInt)
      + 
      public static func <<= <Other>(lhs: inout BigInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - advanced(by:) + + + >>(_:_:)
      @@ -1777,19 +1909,19 @@

      Declaration

      -

      Returns self + n.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func advanced(by n: Stride) -> BigInt
      + 
      public static func >> <Other>(lhs: BigInt, rhs: Other) -> BigInt where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1797,9 +1929,9 @@

      Declaration

    • - - - distance(to:) + + + >>=(_:_:)
      @@ -1807,19 +1939,19 @@

      Declaration

      -

      Returns other - self.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func distance(to other: BigInt) -> Stride
      + 
      public static func >>= <Other>(lhs: inout BigInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1827,13 +1959,22 @@

      Declaration

    +
    + + +
    + +

    Square Root

    +

    +
    +
    • - - - &<<(_:_:) + + + squareRoot()
      @@ -1841,19 +1982,28 @@

      Declaration

      -

      Undocumented

      +

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      +
      +

      Requires

      + self >= 0 + +

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public func squareRoot() -> BigInt
      +
      +

      Return Value

      +

      floor(sqrt(self))

      +
      - Show on GitHub + Show on GitHub
      @@ -1861,9 +2011,9 @@

      Declaration

    • - - - &<<=(_:_:) + + + Stride
      @@ -1871,19 +2021,18 @@

      Declaration

      -

      Undocumented

      - +

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public typealias Stride = BigInt
      - Show on GitHub + Show on GitHub
      @@ -1891,9 +2040,9 @@

      Declaration

    • - - - &>>(_:_:) + + + advanced(by:)
      @@ -1901,19 +2050,19 @@

      Declaration

      -

      Undocumented

      +

      Returns self + n.

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public func advanced(by n: Stride) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -1921,9 +2070,9 @@

      Declaration

    • @@ -1931,19 +2080,19 @@

      Declaration

      -

      Undocumented

      +

      Returns other - self.

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public func distance(to other: BigInt) -> Stride
      - Show on GitHub + Show on GitHub
      @@ -1951,9 +2100,9 @@

      Declaration

    • - - - <<(_:_:) + + + init(_:radix:)
      @@ -1961,18 +2110,29 @@

      Declaration

      - +

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by +letters from the English alphabet.

      +
      +

      Requires

      + radix > 1 && radix < 36 + +
      +

      Declaration

      Swift

      - 
      public static func <<<Other: BinaryInteger>(lhs: BigInt, rhs: Other) -> BigInt
      + 
      public init?<S>(_ text: S, radix: Int = 10) where S : StringProtocol
      +
      +

      Return Value

      +

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      +
      - Show on GitHub + Show on GitHub
      @@ -1980,9 +2140,9 @@

      Declaration

    • @@ -1990,18 +2150,20 @@

      Declaration

      - +

      Initialize a new big integer from a Unicode scalar. +The scalar must represent a decimal digit.

      +

      Declaration

      Swift

      - 
      public static func <<=<Other: BinaryInteger>(lhs: inout BigInt, rhs: Other)
      + 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      - Show on GitHub + Show on GitHub
      @@ -2009,9 +2171,9 @@

      Declaration

    • @@ -2019,18 +2181,20 @@

      Declaration

      - +

      Initialize a new big integer from an extended grapheme cluster. +The cluster must consist of a decimal digit.

      +

      Declaration

      Swift

      - 
      public static func >><Other: BinaryInteger>(lhs: BigInt, rhs: Other) -> BigInt
      + 
      public init(extendedGraphemeClusterLiteral value: String)
      - Show on GitHub + Show on GitHub
      @@ -2038,9 +2202,9 @@

      Declaration

    • @@ -2048,32 +2212,30 @@

      Declaration

      - +

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. +The string must contain only decimal digits.

      +

      Declaration

      Swift

      - 
      public static func >>=<Other: BinaryInteger>(lhs: inout BigInt, rhs: Other)
      + 
      public init(stringLiteral value: StringLiteralType)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -2081,24 +2243,19 @@

      Declaration

      -

      Returns the greatest common divisor of a and b.

      -
      -

      Complexity

      - O(count^2) where count = max(a.count, b.count) - -
      +

      Return the decimal representation of this integer.

      Declaration

      Swift

      - 
      public func greatestCommonDivisor(with b: BigInt) -> BigInt
      + 
      public var description: String { get }
      - Show on GitHub + Show on GitHub
      @@ -2106,9 +2263,9 @@

      Declaration

    • @@ -2116,48 +2273,29 @@

      Declaration

      -

      Returns the multiplicative inverse of this integer in modulo modulus arithmetic, -or nil if there is no such number.

      -
      -

      Requires

      - modulus.magnitude > 1 - -
      -
      -

      Complexity

      - O(count^3) - -
      +

      Return the playground quick look representation of this integer.

      Declaration

      Swift

      - 
      public func inverse(_ modulus: BigInt) -> BigInt?
      + 
      public var playgroundDescription: Any { get }
      -
      -

      Return Value

      -

      If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - squareRoot() + + + negate()
      @@ -2165,42 +2303,29 @@

      Return Value

      -

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      -
      -

      Requires

      - self >= 0 - -
      +

      Undocumented

      Declaration

      Swift

      - 
      public func squareRoot() -> BigInt
      + 
      public mutating func negate()
      -
      -

      Return Value

      -

      floor(sqrt(self))

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - init(from:) + + + -(_:_:)
      @@ -2208,18 +2333,19 @@

      Return Value

      - +

      Subtract b from a and return the result.

      +

      Declaration

      Swift

      - 
      public init(from decoder: Decoder) throws
      + 
      public static func - (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -2227,9 +2353,9 @@

      Declaration

    • - - - encode(to:) + + + -=(_:_:)
      @@ -2237,32 +2363,29 @@

      Declaration

      - +

      Subtract b from a in place.

      +

      Declaration

      Swift

      - 
      public func encode(to encoder: Encoder) throws
      + 
      public static func -= (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - power(_:) + + + bitWidth
      @@ -2270,42 +2393,19 @@

      Declaration

      -

      Returns this integer raised to the power exponent.

      - -

      This function calculates the result by successively squaring the base while halving the exponent.

      -
      -

      Note

      - This function can be unreasonably expensive for large exponents, which is why exponent is - a simple integer value. If you want to calculate big exponents, you’ll probably need to use - the modulo arithmetic variant. - -
      -
      -

      See also

      - BigUInt.power(_:, modulus:) - -
      -
      -

      Complexity

      - O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too. - -
      +

      Undocumented

      Declaration

      Swift

      - 
      public func power(_ exponent: Int) -> BigInt
      + 
      public var bitWidth: Int { get }
      -
      -

      Return Value

      -

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      -
      - Show on GitHub + Show on GitHub
      @@ -2313,9 +2413,9 @@

      Return Value

    • @@ -2323,40 +2423,59 @@

      Return Value

      -

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      - -

      Uses the right-to-left binary method.

      -
      -

      Complexity

      - O(exponent.count * modulus.count^log2(3)) or somesuch +

      Undocumented

      -
      +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public var trailingZeroBitCount: Int { get }
      +
      +
      +
      + Show on GitHub +
      +
      +
      +
      • +
    • +
      + + + + Words + +
      +
      +
      +
      +
      +
      + + See more

      Declaration

      Swift

      - 
      public func power(_ exponent: BigInt, modulus: BigInt) -> BigInt
      + 
      public struct Words : RandomAccessCollection
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - +(_:_:) + + + words
      @@ -2364,19 +2483,19 @@

      Declaration

      -

      Add a to b and return the result.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func +(a: BigInt, b: BigInt) -> BigInt
      + 
      public var words: Words { get }
      - Show on GitHub + Show on GitHub
      @@ -2384,9 +2503,9 @@

      Declaration

    • - - - +=(_:_:) + + + init(words:)
      @@ -2394,19 +2513,19 @@

      Declaration

      -

      Add b to a in place.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func +=(a: inout BigInt, b: BigInt)
      + 
      public init<S>(words: S) where S : Sequence, S.Element == BigInt.Word
      - Show on GitHub + Show on GitHub
      @@ -2419,8 +2538,8 @@

      Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Sign.html b/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Sign.html index 2db1db2de..93984a5b3 100644 --- a/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Sign.html +++ b/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Sign.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,10 +92,20 @@

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Words.html b/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Words.html index ba949c188..d070e5056 100644 --- a/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Words.html +++ b/Carthage/Checkouts/BigInt/docs/Structs/BigInt/Words.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,19 @@

    -
    +

    Words

    - 
    public struct Words: RandomAccessCollection
    + + 
    public struct Words : RandomAccessCollection
    +
    + Show on GitHub +
    @@ -111,9 +115,38 @@

    Words

  • - + + + Indices + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public typealias Indices = CountableRange<Int>
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + - count + count
    @@ -127,12 +160,12 @@

    Words

    Declaration

    Swift

    - 
    public var count: Int
    + 
    public var count: Int { get }
    - Show on GitHub + Show on GitHub
    @@ -140,9 +173,9 @@

    Declaration

  • - + - indices + indices
    @@ -156,12 +189,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var indices: Indices
    + 
    public var indices: Indices { get }
    - Show on GitHub + Show on GitHub
    @@ -169,9 +202,9 @@

    Declaration

  • @@ -185,12 +218,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var startIndex: Int
    + 
    public var startIndex: Int { get }
    - Show on GitHub + Show on GitHub
    @@ -198,9 +231,38 @@

    Declaration

  • - + - endIndex + endIndex + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public var endIndex: Int { get }
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + + + subscript(_:)
    @@ -214,12 +276,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var endIndex: Int
    + 
    public subscript(index: Int) -> UInt { get }
    - Show on GitHub + Show on GitHub
    @@ -232,8 +294,8 @@

    Declaration

    • -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Structs/BigUInt.html b/Carthage/Checkouts/BigInt/docs/Structs/BigUInt.html index 8c502f7c2..5d164ca90 100644 --- a/Carthage/Checkouts/BigInt/docs/Structs/BigUInt.html +++ b/Carthage/Checkouts/BigInt/docs/Structs/BigUInt.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,24 @@

    -
    +

    BigUInt

    - 
    public struct BigUInt: UnsignedInteger
    + + 
    public struct BigUInt : UnsignedInteger
    +
    extension BigUInt: Codable
    +
    extension BigUInt: Comparable
    +
    extension BigUInt: Hashable
    +
    extension BigUInt: ExpressibleByIntegerLiteral
    +
    extension BigUInt: Strideable
    +
    extension BigUInt: ExpressibleByStringLiteral
    +
    extension BigUInt: CustomStringConvertible
    +
    extension BigUInt: CustomPlaygroundDisplayConvertible
    -

    An arbitary precision unsigned integer type, also known as a big integer.

    +

    An arbitary precision unsigned integer type, also known as a “big integer”.

    Operations on big integers never overflow, but they may take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

    @@ -108,6 +117,9 @@

    BigUInt

    This particular big integer type uses base-2^64 digits to represent integers; you can think of it as a wrapper around Array<UInt64>. (In fact, BigUInt only uses an array if there are more than two digits.)

    +
    + Show on GitHub +
    @@ -135,12 +147,12 @@

    BigUInt

    Declaration

    Swift

    - 
    public typealias Word = UInt
    + 
    public typealias Word = UInt
    - Show on GitHub + Show on GitHub
    @@ -165,12 +177,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init()
    + 
    public init()
    - Show on GitHub + Show on GitHub
    @@ -178,9 +190,9 @@

    Declaration

  • @@ -195,12 +207,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(words: [Word])
    + 
    public init(words: [Word])
    - Show on GitHub + Show on GitHub
    @@ -208,13 +220,22 @@

    Declaration

    +
    + + +
    + +

    Addition

    +

    +
    +
    • - - - ~(_:) + + + +(_:_:)
      @@ -222,10 +243,10 @@

      Declaration

      -

      Return the ones’ complement of a.

      +

      Add a and b together and return the result.

      Complexity

      - O(a.count) + O(max(a.count, b.count))
      @@ -234,12 +255,12 @@

      Declaration

      Declaration

      Swift

      - 
      public static prefix func ~(a: BigUInt) -> BigUInt
      + 
      public static func + (a: BigUInt, b: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -247,9 +268,9 @@

      Declaration

    • - - - |=(_:_:) + + + +=(_:_:)
      @@ -257,7 +278,7 @@

      Declaration

      -

      Calculate the bitwise OR of a and b, and store the result in a.

      +

      Add a and b together, and store the sum in a.

      Complexity

      O(max(a.count, b.count)) @@ -269,12 +290,12 @@

      Declaration

      Declaration

      Swift

      - 
      public static func |= (a: inout BigUInt, b: BigUInt)
      + 
      public static func += (a: inout BigUInt, b: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -282,9 +303,9 @@

      Declaration

    • - - - &=(_:_:) + + + isSigned
      @@ -292,24 +313,18 @@

      Declaration

      -

      Calculate the bitwise AND of a and b and return the result.

      -
      -

      Complexity

      - O(max(a.count, b.count)) - -
      - +

      Declaration

      Swift

      - 
      public static func &= (a: inout BigUInt, b: BigUInt)
      + 
      public static var isSigned: Bool { get }
      - Show on GitHub + Show on GitHub
      @@ -317,9 +332,9 @@

      Declaration

    • - - - ^=(_:_:) + + + signum()
      @@ -327,24 +342,23 @@

      Declaration

      -

      Calculate the bitwise XOR of a and b and return the result.

      -
      -

      Complexity

      - O(max(a.count, b.count)) - -
      +

      Returns 1 if this value is, positive; otherwise, 0.

      Declaration

      Swift

      - 
      public static func ^= (a: inout BigUInt, b: BigUInt)
      + 
      public func signum() -> BigUInt
      +
      +

      Return Value

      +

      The sign of this number, expressed as an integer of the same type.

      +
      - Show on GitHub + Show on GitHub
      @@ -353,19 +367,21 @@

      Declaration

    - - - -

    Random Integers

    -     + + +
    + +

    Bitwise Operations

    +

    +
    • @@ -373,10 +389,10 @@

      Random Integers

      -

      Create a big integer consisting of width uniformly distributed random bits.

      -
      -

      Note

      - This function uses arc4random_buf to generate random bits. +

      Return the ones’ complement of a.

      +
      +

      Complexity

      + O(a.count)
      @@ -385,16 +401,12 @@

      Random Integers

      Declaration

      Swift

      - 
      public static func randomInteger(withMaximumWidth width: Int) -> BigUInt
      + 
      public prefix static func ~ (a: BigUInt) -> BigUInt
      -
      -

      Return Value

      -

      A big integer less than 1 << width.

      -
      - Show on GitHub + Show on GitHub
      @@ -402,9 +414,9 @@

      Return Value

    • @@ -412,10 +424,10 @@

      Return Value

      -

      Create a big integer consisting of width-1 uniformly distributed random bits followed by a one bit.

      -
      -

      Note

      - This function uses arc4random_buf to generate random bits. +

      Calculate the bitwise OR of a and b, and store the result in a.

      +
      +

      Complexity

      + O(max(a.count, b.count))
      @@ -424,16 +436,12 @@

      Return Value

      Declaration

      Swift

      - 
      public static func randomInteger(withExactWidth width: Int) -> BigUInt
      + 
      public static func |= (a: inout BigUInt, b: BigUInt)
      -
      -

      Return Value

      -

      A random big integer whose width is width.

      -
      - Show on GitHub + Show on GitHub
      @@ -441,9 +449,9 @@

      Return Value

    • @@ -451,10 +459,10 @@

      Return Value

      -

      Create a uniformly distributed random integer that’s less than the specified limit.

      -
      -

      Note

      - This function uses arc4random_buf to generate random bits. +

      Calculate the bitwise AND of a and b and return the result.

      +
      +

      Complexity

      + O(max(a.count, b.count))
      @@ -463,37 +471,22 @@

      Return Value

      Declaration

      Swift

      - 
      public static func randomInteger(lessThan limit: BigUInt) -> BigUInt
      + 
      public static func &= (a: inout BigUInt, b: BigUInt)
      -
      -

      Return Value

      -

      A random big integer that is less than limit.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Primality Testing

    -     -
    -
    • @@ -501,19 +494,24 @@

      Primality Testing

      -

      Returns true iff this integer passes the strong probable prime test for the specified base.

      +

      Calculate the bitwise XOR of a and b and return the result.

      +
      +

      Complexity

      + O(max(a.count, b.count)) + +

      Declaration

      Swift

      - 
      public func isStrongProbablePrime(_ base: BigUInt) -> Bool
      + 
      public static func ^= (a: inout BigUInt, b: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -521,9 +519,9 @@

      Declaration

    • @@ -531,29 +529,47 @@

      Declaration

      -

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      - -

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, -each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, -but you may specify your own choice.

      - -

      To speed things up, the function checks if self is divisible by the first few prime numbers before -diving into (slower) Miller-Rabin testing.

      - -

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to -return a correct result.

      + +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public init(from decoder: Decoder) throws
      +
      +
      +
      + Show on GitHub +
      +
      +
      +
      • +
    • +
      + + + + encode(to:) + +
      +
      +
      +
      +
      +
      +

      Declaration

      Swift

      - 
      public func isPrime(rounds: Int = 10) -> Bool
      + 
      public func encode(to encoder: Encoder) throws
      - Show on GitHub + Show on GitHub
      @@ -561,13 +577,22 @@

      Declaration

    +
    + + +
    + +

    Comparison

    +

    +
    +
    • - - - bitWidth + + + compare(_:_:)
      @@ -575,10 +600,10 @@

      Declaration

      -

      The minimum number of bits required to represent this integer in binary.

      +

      Compare a to b and return an NSComparisonResult indicating their order.

      Complexity

      - O(1) + O(count)
      @@ -587,16 +612,12 @@

      Declaration

      Declaration

      Swift

      - 
      public var bitWidth: Int
      + 
      public static func compare(_ a: BigUInt, _ b: BigUInt) -> ComparisonResult
      -
      -

      Return Value

      -

      floor(log2(2 * self + 1))

      -
      - Show on GitHub + Show on GitHub
      @@ -604,9 +625,9 @@

      Return Value

    • @@ -614,21 +635,10 @@

      Return Value

      -

      The number of leading zero bits in the binary representation of this integer in base 2^(Word.bitWidth). -This is useful when you need to normalize a BigUInt such that the top bit of its most significant word is 1.

      -
      -

      Note

      - 0 is considered to have zero leading zero bits. - -
      -
      -

      See also

      - width - -
      +

      Return true iff a is equal to b.

      Complexity

      - O(1) + O(count)
      @@ -637,16 +647,12 @@

      Return Value

      Declaration

      Swift

      - 
      public var leadingZeroBitCount: Int
      + 
      public static func == (a: BigUInt, b: BigUInt) -> Bool
      -
      -

      Return Value

      -

      A value in 0...(Word.bitWidth - 1).

      -
      - Show on GitHub + Show on GitHub
      @@ -654,9 +660,9 @@

      Return Value

    • @@ -664,12 +670,7 @@

      Return Value

      -

      The number of trailing zero bits in the binary representation of this integer.

      -
      -

      Note

      - 0 is considered to have zero trailing zero bits. - -
      +

      Return true iff a is less than b.

      Complexity

      O(count) @@ -681,16 +682,12 @@

      Return Value

      Declaration

      Swift

      - 
      public var trailingZeroBitCount: Int
      + 
      public static func < (a: BigUInt, b: BigUInt) -> Bool
      -
      -

      Return Value

      -

      A value in 0...width.

      -
      - Show on GitHub + Show on GitHub
      @@ -698,13 +695,22 @@

      Return Value

    +
    + + +
    + +

    NSData Conversion

    +

    +
    +
    • - - - Words + + + init(_:)
      @@ -712,19 +718,19 @@

      Return Value

      - - See more +

      Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer

      +

      Declaration

      Swift

      - 
      public struct Words: RandomAccessCollection
      + 
      public init(_ buffer: UnsafeRawBufferPointer)
      - Show on GitHub + Show on GitHub
      @@ -732,9 +738,9 @@

      Declaration

    • - - - words + + + init(_:)
      @@ -742,18 +748,20 @@

      Declaration

      - +

      Initializes an integer from the bits stored inside a piece of Data. +The data is assumed to be in network (big-endian) byte order.

      +

      Declaration

      Swift

      - 
      public var words: Words
      + 
      public init(_ data: Data)
      - Show on GitHub + Show on GitHub
      @@ -761,9 +769,9 @@

      Declaration

    • @@ -771,19 +779,19 @@

      Declaration

      -

      Undocumented

      +

      Return a Data value that contains the base-256 representation of this integer, in network (big-endian) byte order.

      Declaration

      Swift

      - 
      public struct BigUInt: UnsignedInteger
      + 
      public func serialize() -> Data
      - Show on GitHub + Show on GitHub
      @@ -792,19 +800,21 @@

      Declaration

    - - - -

    Hashing

    -     + + +
    + +

    Division

    +

    +
    • @@ -812,33 +822,42 @@

      Hashing

      -

      Append this BigUInt to the specified hasher.

      +

      Divide this integer by y and return the resulting quotient and remainder.

      +
      +

      Requires

      + y > 0 + +
      +

      Complexity

      + O(count^2) + +

      Declaration

      Swift

      - 
      public func appendHashes(to hasher: inout SipHasher)
      + 
      public func quotientAndRemainder(dividingBy y: BigUInt) -> (quotient: BigUInt, remainder: BigUInt)
      +
      +

      Return Value

      +

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - init(exactly:) + + + /(_:_:)
      @@ -846,18 +865,24 @@

      Declaration

      - +

      Divide x by y and return the quotient.

      +
      +

      Note

      + Use divided(by:) if you also need the remainder. + +
      +

      Declaration

      Swift

      - 
      public init?<T: BinaryFloatingPoint>(exactly source: T)
      + 
      public static func / (x: BigUInt, y: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -865,9 +890,9 @@

      Declaration

    • - - - init(_:) + + + %(_:_:)
      @@ -875,39 +900,34 @@

      Declaration

      - +

      Divide x by y and return the remainder.

      +
      +

      Note

      + Use divided(by:) if you also need the remainder. + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryFloatingPoint>(_ source: T)
      + 
      public static func % (x: BigUInt, y: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Subtraction

    -     -
    -
    • @@ -915,16 +935,10 @@

      Subtraction

      -

      Subtract other from this integer in place, and return a flag indicating if the operation caused an -arithmetic overflow. other is shifted shift digits to the left before being subtracted.

      +

      Divide x by y and store the quotient in x.

      Note

      - If the result indicates an overflow, then self becomes the twos’ complement of the absolute difference. - -
      -
      -

      Complexity

      - O(count) + Use divided(by:) if you also need the remainder.
      @@ -933,12 +947,12 @@

      Subtraction

      Declaration

      Swift

      - 
      public mutating func subtractReportingOverflow(_ b: BigUInt, shiftedBy shift: Int = 0) -> Bool
      + 
      public static func /= (x: inout BigUInt, y: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -946,9 +960,9 @@

      Declaration

    • @@ -956,16 +970,10 @@

      Declaration

      -

      Subtract other from this integer, returning the difference and a flag indicating arithmetic overflow. -other is shifted shift digits to the left before being subtracted.

      +

      Divide x by y and store the remainder in x.

      Note

      - If overflow is true, then the result value is the twos’ complement of the absolute value of the difference. - -
      -
      -

      Complexity

      - O(count) + Use divided(by:) if you also need the remainder.
      @@ -974,22 +982,35 @@

      Declaration

      Declaration

      Swift

      - 
      public func subtractingReportingOverflow(_ other: BigUInt, shiftedBy shift: Int) -> (partialValue: BigUInt, overflow: Bool)
      + 
      public static func %= (x: inout BigUInt, y: BigUInt)
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Exponentiation

    +

    +
    +
    +
    • @@ -997,15 +1018,22 @@

      Declaration

      -

      Subtracts other from self, returning the result and a flag indicating arithmetic overflow.

      +

      Returns this integer raised to the power exponent.

      + +

      This function calculates the result by successively squaring the base while halving the exponent.

      Note

      - When the operation overflows, then partialValue is the twos’ complement of the absolute value of the difference. + This function can be unreasonably expensive for large exponents, which is why exponent is + a simple integer value. If you want to calculate big exponents, you’ll probably need to use + the modulo arithmetic variant. -
      -
      +
      +

      See also

      + BigUInt.power(_:, modulus:) + +

      Complexity

      - O(count) + O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too.
      @@ -1014,12 +1042,16 @@

      Declaration

      Declaration

      Swift

      - 
      public func subtractingReportingOverflow(_ other: BigUInt) -> (partialValue: BigUInt, overflow: Bool)
      + 
      public func power(_ exponent: Int) -> BigUInt
      +
      +

      Return Value

      +

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      +
      - Show on GitHub + Show on GitHub
      @@ -1027,9 +1059,9 @@

      Declaration

    • @@ -1037,16 +1069,12 @@

      Declaration

      -

      Subtract other from this integer in place. -other is shifted shift digits to the left before being subtracted.

      -
      -

      Requires

      - self >= other * 2^shift +

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      -
      +

      Uses the right-to-left binary method.

      Complexity

      - O(count) + O(exponent.count * modulus.count^log2(3)) or somesuch
      @@ -1055,12 +1083,12 @@

      Declaration

      Declaration

      Swift

      - 
      public mutating func subtract(_ other: BigUInt, shiftedBy shift: Int = 0)
      + 
      public func power(_ exponent: BigUInt, modulus: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -1068,9 +1096,9 @@

      Declaration

    • @@ -1078,30 +1106,18 @@

      Declaration

      -

      Subtract b from this integer, and return the difference. -b is shifted shift digits to the left before being subtracted.

      -
      -

      Requires

      - self >= b * 2^shift - -
      -
      -

      Complexity

      - O(count) - -
      - +

      Declaration

      Swift

      - 
      public func subtracting(_ other: BigUInt, shiftedBy shift: Int = 0) -> BigUInt
      + 
      public init?<T>(exactly source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      @@ -1109,9 +1125,9 @@

      Declaration

    • @@ -1119,39 +1135,41 @@

      Declaration

      -

      Decrement this integer by one.

      -
      -

      Requires

      - !isZero - -
      -
      -

      Complexity

      - O(count) - -
      - +

      Declaration

      Swift

      - 
      public mutating func decrement(shiftedBy shift: Int = 0)
      + 
      public init<T>(_ source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Greatest Common Divisor

    +

    +
    +
    +
    • @@ -1159,15 +1177,10 @@

      Declaration

      -

      Subtract b from a and return the result.

      -
      -

      Requires

      - a >= b - -
      +

      Returns the greatest common divisor of self and b.

      Complexity

      - O(a.count) + O(count^2) where count = max(self.count, b.count)
      @@ -1176,12 +1189,12 @@

      Declaration

      Declaration

      Swift

      - 
      public static func -(a: BigUInt, b: BigUInt) -> BigUInt
      + 
      public func greatestCommonDivisor(with b: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -1189,9 +1202,9 @@

      Declaration

    • - - - -=(_:_:) + + + inverse(_:)
      @@ -1199,15 +1212,15 @@

      Declaration

      -

      Subtract b from a and store the result in a.

      +

      Returns the multiplicative inverse of this integer in modulo modulus arithmetic, +or nil if there is no such number.

      Requires

      - a >= b + modulus > 1 -
      -
      +

      Complexity

      - O(a.count) + O(count^3)
      @@ -1216,12 +1229,16 @@

      Declaration

      Declaration

      Swift

      - 
      public static func -=(a: inout BigUInt, b: BigUInt)
      + 
      public func inverse(_ modulus: BigUInt) -> BigUInt?
      +
      +

      Return Value

      +

      If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

      +
      - Show on GitHub + Show on GitHub
      @@ -1230,19 +1247,21 @@

      Declaration

    - - - -

    Division

    -     + + +
    + +

    Hashing

    +

    +
    • @@ -1250,33 +1269,19 @@

      Division

      -

      Divide this integer by y and return the resulting quotient and remainder.

      -
      -

      Requires

      - y > 0 - -
      -
      -

      Complexity

      - O(count^2) - -
      +

      Append this BigUInt to the specified hasher.

      Declaration

      Swift

      - 
      public func quotientAndRemainder(dividingBy y: BigUInt) -> (quotient: BigUInt, remainder: BigUInt)
      + 
      public func hash(into hasher: inout Hasher)
      -
      -

      Return Value

      -

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      -
      - Show on GitHub + Show on GitHub
      @@ -1284,9 +1289,9 @@

      Return Value

    • - - - /(_:_:) + + + init(exactly:)
      @@ -1294,24 +1299,18 @@

      Return Value

      -

      Divide x by y and return the quotient.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func /(x: BigUInt, y: BigUInt) -> BigUInt
      + 
      public init?<T>(exactly source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1319,9 +1318,9 @@

      Declaration

    • - - - %(_:_:) + + + init(_:)
      @@ -1329,24 +1328,18 @@

      Declaration

      -

      Divide x by y and return the remainder.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func %(x: BigUInt, y: BigUInt) -> BigUInt
      + 
      public init<T>(_ source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1354,9 +1347,9 @@

      Declaration

    • @@ -1364,24 +1357,18 @@

      Declaration

      -

      Divide x by y and store the quotient in x.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func /=(x: inout BigUInt, y: BigUInt)
      + 
      public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1389,9 +1376,9 @@

      Declaration

    • @@ -1399,38 +1386,28 @@

      Declaration

      -

      Divide x by y and store the remainder in x.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func %=(x: inout BigUInt, y: BigUInt)
      + 
      public init<T>(clamping source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    - +
    +
    +
    + + +
    + +

    Multiplication

    +

    +
    +
    +
    • @@ -1467,18 +1458,24 @@

      Declaration

      - +

      Multiply this big integer by a single word, and store the result in place of the original big integer.

      +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryInteger>(_ source: T)
      + 
      public mutating func multiply(byWord y: Word)
      - Show on GitHub + Show on GitHub
      @@ -1486,9 +1483,9 @@

      Declaration

    • @@ -1496,18 +1493,24 @@

      Declaration

      - +

      Multiply this big integer by a single Word, and return the result.

      +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryInteger>(truncatingIfNeeded source: T)
      + 
      public func multiplied(byWord y: Word) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -1515,9 +1518,9 @@

      Declaration

    • @@ -1525,32 +1528,43 @@

      Declaration

      - +

      Multiply x by y, and add the result to this integer, optionally shifted shift words to the left.

      +
      +

      Note

      + This is the fused multiply/shift/add operation; it is more efficient than doing the components +individually. (The fused operation doesn’t need to allocate space for temporary big integers.) + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryInteger>(clamping source: T)
      + 
      public mutating func multiplyAndAdd(_ x: BigUInt, _ y: Word, shiftedBy shift: Int = 0)
      +
      +

      Return Value

      +

      self is set to self + (x * y) << (shift * 2^Word.bitWidth)

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1558,33 +1572,39 @@

      Declaration

      -

      Initialize a new big integer from an integer literal.

      - -
      -
      +

      Multiply this integer by y and return the result.

      +
      +

      Note

      + This uses the naive O(n^2) multiplication algorithm unless both arguments have more than +BigUInt.directMultiplicationLimit words. + +
      +

      Complexity

      + O(n^log2(3)) + +
      + +
      +

      Declaration

      Swift

      - 
      public init(integerLiteral value: UInt64)
      + 
      public func multiplied(by y: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1592,18 +1612,19 @@

      Declaration

      - +

      Multiplication switches to an asymptotically better recursive algorithm when arguments have more words than this limit.

      +

      Declaration

      Swift

      - 
      public static var isSigned: Bool
      + 
      public static var directMultiplicationLimit: Int
      - Show on GitHub + Show on GitHub
      @@ -1611,9 +1632,9 @@

      Declaration

    • - - - signum() + + + *(_:_:)
      @@ -1621,44 +1642,39 @@

      Declaration

      -

      Returns -1 if this value is negative and 1 if it’s positive; otherwise, 0.

      +

      Multiply a by b and return the result.

      +
      +

      Note

      + This uses the naive O(n^2) multiplication algorithm unless both arguments have more than +BigUInt.directMultiplicationLimit words. + +
      +

      Complexity

      + O(n^log2(3)) + +

      Declaration

      Swift

      - 
      public func signum() -> BigUInt
      + 
      public static func * (x: BigUInt, y: BigUInt) -> BigUInt
      -
      -

      Return Value

      -

      The sign of this number, expressed as an integer of the same type.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Collection-like members

    -     -
    -
    • - - - subscript(_:) + + + *=(_:_:)
      @@ -1666,42 +1682,19 @@

      Collection-like members

      -

      Get or set a digit at a given index.

      -
      -

      Note

      - Unlike a normal collection, it is OK for the index to be greater than or equal to endIndex. -The subscripting getter returns zero for indexes beyond the most significant digit. -Setting these extended digits automatically appends new elements to the underlying digit array. - -
      -
      -

      Requires

      - index >= 0 - -
      -
      -

      Complexity

      - The getter is O(1). The setter is O(1) if the conditions below are true; otherwise it’s O(count). - -
        -
      • The integer’s storage is not shared with another integer
        • -
      • The integer wasn’t created as a slice of another integer
        • -
      • index < count
        • -
      - -
      +

      Multiply a by b and store the result in a.

      Declaration

      Swift

      - 
      subscript(_ index: Int) -> Word
      + 
      public static func *= (a: inout BigUInt, b: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -1710,19 +1703,21 @@

      Declaration

    - - - -

    Comparison

    -     + + +
    + +

    Primality Testing

    +

    +
    • @@ -1730,24 +1725,19 @@

      Comparison

      -

      Compare a to b and return an NSComparisonResult indicating their order.

      -
      -

      Complexity

      - O(count) - -
      +

      Returns true iff this integer passes the strong probable prime test for the specified base.

      Declaration

      Swift

      - 
      public static func compare(_ a: BigUInt, _ b: BigUInt) -> ComparisonResult
      + 
      public func isStrongProbablePrime(_ base: BigUInt) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -1755,9 +1745,9 @@

      Declaration

    • @@ -1765,24 +1755,29 @@

      Declaration

      -

      Return true iff a is equal to b.

      -
      -

      Complexity

      - O(count) +

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      -
      +

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, +each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, +but you may specify your own choice.

      + +

      To speed things up, the function checks if self is divisible by the first few prime numbers before +diving into (slower) Miller-Rabin testing.

      + +

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to +return a correct result.

      Declaration

      Swift

      - 
      public static func ==(a: BigUInt, b: BigUInt) -> Bool
      + 
      public func isPrime(rounds: Int = 10) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -1790,9 +1785,9 @@

      Declaration

    • @@ -1800,45 +1795,64 @@

      Declaration

      -

      Return true iff a is less than b.

      -
      -

      Complexity

      - O(count) - -
      +

      Create a big unsigned integer consisting of width uniformly distributed random bits.

      Declaration

      Swift

      - 
      public static func <(a: BigUInt, b: BigUInt) -> Bool
      + 
      public static func randomInteger<RNG>(withMaximumWidth width: Int, using generator: inout RNG) -> BigUInt where RNG : RandomNumberGenerator
      +
      +

      Parameters

      + + + + + + + + + + + +
      + + width + + +
      +

      The maximum number of one bits in the result.

      +
      +
      + + generator + + +
      +

      The source of randomness.

      +
      +
      +
      +
      +

      Return Value

      +

      A big unsigned integer less than 1 << width.

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    String Conversion

    -     -
    -
    • @@ -1846,11 +1860,10 @@

      String Conversion

      -

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by -letters from the English alphabet.

      -
      -

      Requires

      - radix > 1 && radix < 36 +

      Create a big unsigned integer consisting of width uniformly distributed random bits.

      +
      +

      Note

      +

      I use a SystemRandomGeneratorGenerator as the source of randomness.

      @@ -1859,16 +1872,35 @@

      String Conversion

      Declaration

      Swift

      - 
      public init?(_ text: String, radix: Int = 10)
      + 
      public static func randomInteger(withMaximumWidth width: Int) -> BigUInt
      +
      +

      Parameters

      + + + + + + + +
      + + width + + +
      +

      The maximum number of one bits in the result.

      +
      +
      +

      Return Value

      -

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      +

      A big unsigned integer less than 1 << width.

      - Show on GitHub + Show on GitHub
      @@ -1876,9 +1908,9 @@

      Return Value

    • @@ -1886,33 +1918,69 @@

      Return Value

      -

      Undocumented

      +

      Create a big unsigned integer consisting of width-1 uniformly distributed random bits followed by a one bit.

      +
      +

      Note

      +

      If width is zero, the result is zero.

      + +

      Declaration

      Swift

      - 
      public struct BigUInt: UnsignedInteger
      + 
      public static func randomInteger<RNG>(withExactWidth width: Int, using generator: inout RNG) -> BigUInt where RNG : RandomNumberGenerator
      +
      +

      Parameters

      + + + + + + + + + + + +
      + + width + + +
      +

      The number of bits required to represent the answer.

      +
      +
      + + generator + + +
      +

      The source of randomness.

      +
      +
      +
      +
      +

      Return Value

      +

      A random big unsigned integer whose width is width.

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1920,20 +1988,32 @@

      Declaration

      -

      Initialize a new big integer from a Unicode scalar. -The scalar must represent a decimal digit.

      +

      Create a big unsigned integer consisting of width-1 uniformly distributed random bits followed by a one bit.

      +
      +

      Note

      + If width is zero, the result is zero. + +
      +

      Note

      +

      I use a SystemRandomGeneratorGenerator as the source of randomness.

      + +

      Declaration

      Swift

      - 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      + 
      public static func randomInteger(withExactWidth width: Int) -> BigUInt
      +
      +

      Return Value

      +

      A random big unsigned integer whose width is width.

      +
      - Show on GitHub + Show on GitHub
      @@ -1941,9 +2021,9 @@

      Declaration

    • @@ -1951,20 +2031,59 @@

      Declaration

      -

      Initialize a new big integer from an extended grapheme cluster. -The cluster must consist of a decimal digit.

      +

      Create a uniformly distributed random unsigned integer that’s less than the specified limit.

      +
      +

      Precondition

      +

      limit > 0.

      + +

      Declaration

      Swift

      - 
      public init(extendedGraphemeClusterLiteral value: String)
      + 
      public static func randomInteger<RNG>(lessThan limit: BigUInt, using generator: inout RNG) -> BigUInt where RNG : RandomNumberGenerator
      +
      +

      Parameters

      + + + + + + + + + + + +
      + + limit + + +
      +

      The upper bound on the result.

      +
      +
      + + generator + + +
      +

      The source of randomness.

      +
      +
      +
      +
      +

      Return Value

      +

      A random big unsigned integer that is less than limit.

      +
      - Show on GitHub + Show on GitHub
      @@ -1972,9 +2091,9 @@

      Declaration

    • @@ -1982,20 +2101,51 @@

      Declaration

      -

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. -The string must contain only decimal digits.

      +

      Create a uniformly distributed random unsigned integer that’s less than the specified limit.

      +
      +

      Precondition

      + limit > 0. + +
      +

      Note

      +

      I use a SystemRandomGeneratorGenerator as the source of randomness.

      + +

      Declaration

      Swift

      - 
      public init(stringLiteral value: StringLiteralType)
      + 
      public static func randomInteger(lessThan limit: BigUInt) -> BigUInt
      +
      +

      Parameters

      + + + + + + + +
      + + limit + + +
      +

      The upper bound on the result.

      +
      +
      +
      +
      +

      Return Value

      +

      A random big unsigned integer that is less than limit.

      +
      - Show on GitHub + Show on GitHub
      @@ -2003,13 +2153,22 @@

      Declaration

    +
    + + +
    + +

    Shift Operators

    +

    +
    +
    • - - - description + + + >>=(_:_:)
      @@ -2017,33 +2176,29 @@

      Declaration

      -

      Return the decimal representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var description: String
      + 
      public static func >>= <Other>(lhs: inout BigUInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -2051,40 +2206,29 @@

      Declaration

      -

      Return the playground quick look representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var customPlaygroundQuickLook: PlaygroundQuickLook
      + 
      public static func <<= <Other>(lhs: inout BigUInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    NSData Conversion

    -     -
    -
    • - - - init(_:) + + + >>(_:_:)
      @@ -2099,12 +2243,12 @@

      NSData Conversion

      Declaration

      Swift

      - 
      public struct BigUInt: UnsignedInteger
      + 
      public static func >> <Other>(lhs: BigUInt, rhs: Other) -> BigUInt where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
    @@ -2112,9 +2256,9 @@

    Declaration

  • - - - init(_:) + + + <<(_:_:)
    @@ -2122,30 +2266,42 @@

    Declaration

    -

    Initializes an integer from the bits stored inside a piece of Data. -The data is assumed to be in network (big-endian) byte order.

    +

    Undocumented

    Declaration

    Swift

    - 
    public init(_ data: Data)
    + 
    public static func << <Other>(lhs: BigUInt, rhs: Other) -> BigUInt where Other : BinaryInteger
    - Show on GitHub + Show on GitHub
    • + + +
    +
    + + +
    + +

    Square Root

    +

    +
    +
    +
    • @@ -2153,40 +2309,33 @@

      Declaration

      -

      Return a Data value that contains the base-256 representation of this integer, in network (big-endian) byte order.

      +

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      Declaration

      Swift

      - 
      public func serialize() -> Data
      + 
      public func squareRoot() -> BigUInt
      +
      +

      Return Value

      +

      floor(sqrt(self))

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Multiplication

    -     -
    -
    • @@ -2194,24 +2343,19 @@

      Multiplication

      -

      Multiply this big integer by a single word, and store the result in place of the original big integer.

      -
      -

      Complexity

      - O(count) - -
      +

      A type that can represent the distance between two values ofa BigUInt.

      Declaration

      Swift

      - 
      public mutating func multiply(byWord y: Word)
      + 
      public typealias Stride = BigInt
      - Show on GitHub + Show on GitHub
      @@ -2219,9 +2363,9 @@

      Declaration

    • @@ -2229,24 +2373,19 @@

      Declaration

      -

      Multiply this big integer by a single Word, and return the result.

      -
      -

      Complexity

      - O(count) - -
      +

      Adds n to self and returns the result. Traps if the result would be less than zero.

      Declaration

      Swift

      - 
      public func multiplied(byWord y: Word) -> BigUInt
      + 
      public func advanced(by n: BigInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -2254,9 +2393,9 @@

      Declaration

    • @@ -2264,44 +2403,42 @@

      Declaration

      -

      Multiply x by y, and add the result to this integer, optionally shifted shift words to the left.

      -
      -

      Note

      - This is the fused multiply/shift/add operation; it is more efficient than doing the components -individually. (The fused operation doesn’t need to allocate space for temporary big integers.) - -
      -
      -

      Complexity

      - O(count) - -
      +

      Returns the (potentially negative) difference between self and other as a BigInt. Never traps.

      Declaration

      Swift

      - 
      public mutating func multiplyAndAdd(_ x: BigUInt, _ y: Word, shiftedBy shift: Int = 0)
      + 
      public func distance(to other: BigUInt) -> BigInt
      -
      -

      Return Value

      -

      self is set to self + (x * y) << (shift * 2^Word.bitWidth)

      -
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    String Conversion

    +

    +
    +
    +
    • @@ -2309,16 +2446,11 @@

      Return Value

      -

      Multiply this integer by y and return the result.

      -
      -

      Note

      - This uses the naive O(n^2) multiplication algorithm unless both arguments have more than -BigUInt.directMultiplicationLimit words. - -
      -
      -

      Complexity

      - O(n^log2(3)) +

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by +letters from the English alphabet.

      +
      +

      Requires

      + radix > 1 && radix < 36
      @@ -2327,12 +2459,16 @@

      Return Value

      Declaration

      Swift

      - 
      public func multiplied(by y: BigUInt) -> BigUInt
      + 
      public init?<S>(_ text: S, radix: Int = 10) where S : StringProtocol
      +
      +

      Return Value

      +

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      +
      - Show on GitHub + Show on GitHub
      @@ -2340,9 +2476,9 @@

      Declaration

    • @@ -2350,19 +2486,20 @@

      Declaration

      -

      Multiplication switches to an asymptotically better recursive algorithm when arguments have more words than this limit.

      +

      Initialize a new big integer from a Unicode scalar. +The scalar must represent a decimal digit.

      Declaration

      Swift

      - 
      public static var directMultiplicationLimit: Int = 1024
      + 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      - Show on GitHub + Show on GitHub
      @@ -2370,9 +2507,9 @@

      Declaration

    • @@ -2380,30 +2517,20 @@

      Declaration

      -

      Multiply a by b and return the result.

      -
      -

      Note

      - This uses the naive O(n^2) multiplication algorithm unless both arguments have more than -BigUInt.directMultiplicationLimit words. - -
      -
      -

      Complexity

      - O(n^log2(3)) - -
      +

      Initialize a new big integer from an extended grapheme cluster. +The cluster must consist of a decimal digit.

      Declaration

      Swift

      - 
      public static func *(x: BigUInt, y: BigUInt) -> BigUInt
      + 
      public init(extendedGraphemeClusterLiteral value: String)
      - Show on GitHub + Show on GitHub
      @@ -2411,9 +2538,9 @@

      Declaration

    • @@ -2421,33 +2548,30 @@

      Declaration

      -

      Multiply a by b and store the result in a.

      +

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. +The string must contain only decimal digits.

      Declaration

      Swift

      - 
      public static func *=(a: inout BigUInt, b: BigUInt)
      + 
      public init(stringLiteral value: StringLiteralType)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - Stride + + + description
      @@ -2455,19 +2579,19 @@

      Declaration

      -

      A type that can represent the distance between two values ofa BigUInt.

      +

      Return the decimal representation of this integer.

      Declaration

      Swift

      - 
      public typealias Stride = BigInt
      + 
      public var description: String { get }
      - Show on GitHub + Show on GitHub
      @@ -2475,9 +2599,9 @@

      Declaration

    • @@ -2485,29 +2609,42 @@

      Declaration

      -

      Adds n to self and returns the result. Traps if the result would be less than zero.

      +

      Return the playground quick look representation of this integer.

      Declaration

      Swift

      - 
      public func advanced(by n: BigInt) -> BigUInt
      + 
      public var playgroundDescription: Any { get }
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Subtraction

    +

    +
    +
    +
    • @@ -2515,40 +2652,39 @@

      Declaration

      -

      Returns the (potentially negative) difference between self and other as a BigInt. Never traps.

      +

      Subtract other from this integer in place, and return a flag indicating if the operation caused an +arithmetic overflow. other is shifted shift digits to the left before being subtracted.

      +
      +

      Note

      + If the result indicates an overflow, then self becomes the twos’ complement of the absolute difference. + +
      +

      Complexity

      + O(count) + +

      Declaration

      Swift

      - 
      public func distance(to other: BigUInt) -> BigInt
      + 
      public mutating func subtractReportingOverflow(_ b: BigUInt, shiftedBy shift: Int = 0) -> Bool
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Shift Operators

    -     -
    -
    • @@ -2556,18 +2692,29 @@

      Shift Operators

      - +

      Subtract other from this integer, returning the difference and a flag indicating arithmetic overflow. +other is shifted shift digits to the left before being subtracted.

      +
      +

      Note

      + If overflow is true, then the result value is the twos’ complement of the absolute value of the difference. + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func >>=<Other: BinaryInteger>(lhs: inout BigUInt, rhs: Other)
      + 
      public func subtractingReportingOverflow(_ other: BigUInt, shiftedBy shift: Int) -> (partialValue: BigUInt, overflow: Bool)
      - Show on GitHub + Show on GitHub
      @@ -2575,9 +2722,9 @@

      Declaration

    • @@ -2585,18 +2732,28 @@

      Declaration

      - +

      Subtracts other from self, returning the result and a flag indicating arithmetic overflow.

      +
      +

      Note

      + When the operation overflows, then partialValue is the twos’ complement of the absolute value of the difference. + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func <<=<Other: BinaryInteger>(lhs: inout BigUInt, rhs: Other)
      + 
      public func subtractingReportingOverflow(_ other: BigUInt) -> (partialValue: BigUInt, overflow: Bool)
      - Show on GitHub + Show on GitHub
      @@ -2604,9 +2761,9 @@

      Declaration

    • @@ -2614,18 +2771,29 @@

      Declaration

      - +

      Subtract other from this integer in place. +other is shifted shift digits to the left before being subtracted.

      +
      +

      Requires

      + self >= other * 2^shift + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func >><Other: BinaryInteger>(lhs: BigUInt, rhs: Other) -> BigUInt
      + 
      public mutating func subtract(_ other: BigUInt, shiftedBy shift: Int = 0)
      - Show on GitHub + Show on GitHub
      @@ -2633,9 +2801,9 @@

      Declaration

    • @@ -2643,39 +2811,39 @@

      Declaration

      - +

      Subtract b from this integer, and return the difference. +b is shifted shift digits to the left before being subtracted.

      +
      +

      Requires

      + self >= b * 2^shift + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func <<<Other: BinaryInteger>(lhs: BigUInt, rhs: Other) -> BigUInt
      + 
      public func subtracting(_ other: BigUInt, shiftedBy shift: Int = 0) -> BigUInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Greatest Common Divisor

    -     -
    -
    • @@ -2683,10 +2851,14 @@

      Greatest Common Divisor

      -

      Returns the greatest common divisor of self and b.

      -
      +

      Decrement this integer by one.

      +
      +

      Requires

      + !isZero + +

      Complexity

      - O(count^2) where count = max(self.count, b.count) + O(count)
      @@ -2695,12 +2867,12 @@

      Greatest Common Divisor

      Declaration

      Swift

      - 
      public func greatestCommonDivisor(with b: BigUInt) -> BigUInt
      + 
      public mutating func decrement(shiftedBy shift: Int = 0)
      - Show on GitHub + Show on GitHub
      @@ -2708,9 +2880,9 @@

      Declaration

    • - - - inverse(_:) + + + -(_:_:)
      @@ -2718,16 +2890,14 @@

      Declaration

      -

      Returns the multiplicative inverse of this integer in modulo modulus arithmetic, -or nil if there is no such number.

      +

      Subtract b from a and return the result.

      Requires

      - modulus > 1 + a >= b -
      -
      +

      Complexity

      - O(count^3) + O(a.count)
      @@ -2736,30 +2906,22 @@

      Declaration

      Declaration

      Swift

      - 
      public func inverse(_ modulus: BigUInt) -> BigUInt?
      + 
      public static func - (a: BigUInt, b: BigUInt) -> BigUInt
      -
      -

      Return Value

      -

      If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - squareRoot() + + + -=(_:_:)
      @@ -2767,37 +2929,38 @@

      Return Value

      -

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      +

      Subtract b from a and store the result in a.

      +
      +

      Requires

      + a >= b + +
      +

      Complexity

      + O(a.count) + +

      Declaration

      Swift

      - 
      public func squareRoot() -> BigUInt
      + 
      public static func -= (a: inout BigUInt, b: BigUInt)
      -
      -

      Return Value

      -

      floor(sqrt(self))

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -2805,18 +2968,19 @@

      Return Value

      - +

      Undocumented

      +

      Declaration

      Swift

      - 
      public init(from decoder: Decoder) throws
      + 
      public subscript(bitAt index: Int) -> Bool { get set }
      - Show on GitHub + Show on GitHub
      @@ -2824,9 +2988,9 @@

      Declaration

    • - - - encode(to:) + + + bitWidth
      @@ -2834,39 +2998,38 @@

      Declaration

      - +

      The minimum number of bits required to represent this integer in binary.

      +
      +

      Complexity

      + O(1) + +
      +

      Declaration

      Swift

      - 
      public func encode(to encoder: Encoder) throws
      + 
      public var bitWidth: Int { get }
      +
      +

      Return Value

      +

      floor(log2(2 * self + 1))

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Exponentiation

    -     -
    -
    • @@ -2874,24 +3037,19 @@

      Exponentiation

      -

      Returns this integer raised to the power exponent.

      - -

      This function calculates the result by successively squaring the base while halving the exponent.

      +

      The number of leading zero bits in the binary representation of this integer in base 2^(Word.bitWidth). +This is useful when you need to normalize a BigUInt such that the top bit of its most significant word is 1.

      Note

      - This function can be unreasonably expensive for large exponents, which is why exponent is - a simple integer value. If you want to calculate big exponents, you’ll probably need to use - the modulo arithmetic variant. + 0 is considered to have zero leading zero bits. -
      -
      +

      See also

      - BigUInt.power(_:, modulus:) + width -
      -
      +

      Complexity

      - O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too. + O(1)
      @@ -2900,16 +3058,16 @@

      Exponentiation

      Declaration

      Swift

      - 
      public func power(_ exponent: Int) -> BigUInt
      + 
      public var leadingZeroBitCount: Int { get }

      Return Value

      -

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      +

      A value in 0...(Word.bitWidth - 1).

      - Show on GitHub + Show on GitHub
      @@ -2917,9 +3075,9 @@

      Return Value

    • @@ -2927,12 +3085,14 @@

      Return Value

      -

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      +

      The number of trailing zero bits in the binary representation of this integer.

      +
      +

      Note

      + 0 is considered to have zero trailing zero bits. -

      Uses the right-to-left binary method.

      -
      +

      Complexity

      - O(exponent.count * modulus.count^log2(3)) or somesuch + O(count)
      @@ -2941,33 +3101,26 @@

      Return Value

      Declaration

      Swift

      - 
      public func power(_ exponent: BigUInt, modulus: BigUInt) -> BigUInt
      + 
      public var trailingZeroBitCount: Int { get }
      +
      +

      Return Value

      +

      A value in 0...width.

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Addition

    -     -
    -
    • - - - +(_:_:) + + + Words
      @@ -2975,24 +3128,19 @@

      Addition

      -

      Add a and b together and return the result.

      -
      -

      Complexity

      - O(max(a.count, b.count)) - -
      - + + See more

      Declaration

      Swift

      - 
      public static func +(a: BigUInt, b: BigUInt) -> BigUInt
      + 
      public struct Words : RandomAccessCollection
      - Show on GitHub + Show on GitHub
      @@ -3000,9 +3148,9 @@

      Declaration

    • - - - +=(_:_:) + + + words
      @@ -3010,24 +3158,48 @@

      Declaration

      -

      Add a and b together, and store the sum in a.

      -
      -

      Complexity

      - O(max(a.count, b.count)) + +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public var words: Words { get }
      -
      +
      +
      +
      + Show on GitHub +
      +
      +
      +
      • +
    • +
      + + + + init(words:) + +
      +
      +
      +
      +
      +
      +

      Undocumented

      Declaration

      Swift

      - 
      public static func +=(a: inout BigUInt, b: BigUInt)
      + 
      public init<Words>(words: Words) where Words : Sequence, Words.Element == BigUInt.Word
      - Show on GitHub + Show on GitHub
      @@ -3040,8 +3212,8 @@

      Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/Structs/BigUInt/Words.html b/Carthage/Checkouts/BigInt/docs/Structs/BigUInt/Words.html index b0dda68e0..0c13a2f7a 100644 --- a/Carthage/Checkouts/BigInt/docs/Structs/BigUInt/Words.html +++ b/Carthage/Checkouts/BigInt/docs/Structs/BigUInt/Words.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,19 @@

    -
    +

    Words

    - 
    public struct Words: RandomAccessCollection
    + + 
    public struct Words : RandomAccessCollection
    +
    + Show on GitHub +
    @@ -111,9 +115,9 @@

    Words

  • @@ -127,12 +131,12 @@

    Words

    Declaration

    Swift

    - 
    public var startIndex: Int
    + 
    public var startIndex: Int { get }
    - Show on GitHub + Show on GitHub
    @@ -140,9 +144,38 @@

    Declaration

  • - + - endIndex + endIndex + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public var endIndex: Int { get }
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + + + subscript(_:)
    @@ -156,12 +189,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var endIndex: Int
    + 
    public subscript(index: Int) -> Word { get }
    - Show on GitHub + Show on GitHub
    @@ -174,8 +207,8 @@

    Declaration

    • -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/badge.svg b/Carthage/Checkouts/BigInt/docs/badge.svg index 658cf7ab0..09c230060 100644 --- a/Carthage/Checkouts/BigInt/docs/badge.svg +++ b/Carthage/Checkouts/BigInt/docs/badge.svg @@ -1 +1,28 @@ -documentationdocumentation92%92% \ No newline at end of file + + + + + + + + + + + + + + + + documentation + + + documentation + + + 85% + + + 85% + + + diff --git a/Carthage/Checkouts/BigInt/docs/css/jazzy.css b/Carthage/Checkouts/BigInt/docs/css/jazzy.css index c83db5bfc..ff59f5f86 100644 --- a/Carthage/Checkouts/BigInt/docs/css/jazzy.css +++ b/Carthage/Checkouts/BigInt/docs/css/jazzy.css @@ -63,6 +63,10 @@ a { a:hover, a:focus { outline: 0; text-decoration: underline; } + a.discouraged { + text-decoration: line-through; } + a.discouraged:hover, a.discouraged:focus { + text-decoration: underline line-through; } table { background: #fff; @@ -90,10 +94,10 @@ pre { code { font-family: Consolas, "Liberation Mono", Menlo, Courier, monospace; } -p > code, li > code { +.item-container p > code, .item-container li > code, .top-matter p > code, .top-matter li > code { background: #f7f7f7; padding: .2em; } - p > code:before, p > code:after, li > code:before, li > code:after { + .item-container p > code:before, .item-container p > code:after, .item-container li > code:before, .item-container li > code:after, .top-matter p > code:before, .top-matter p > code:after, .top-matter li > code:before, .top-matter li > code:after { letter-spacing: -.2em; content: "\00a0"; } @@ -107,7 +111,6 @@ pre code { @media (min-width: 768px) { .content-wrapper { flex-direction: row; } } - .header { display: flex; padding: 8px; @@ -153,7 +156,6 @@ pre code { word-wrap: normal; background: #fbfbfb; border-right: 1px solid #ddd; } } - .nav-groups { list-style-type: none; padding-left: 0; } @@ -184,7 +186,6 @@ pre code { order: 2; flex: 1; padding-bottom: 60px; } } - .section { padding: 0 32px; border-bottom: 1px solid #ddd; } @@ -197,6 +198,8 @@ pre code { .section-name { color: #666; display: block; } + .section-name p { + margin-bottom: inherit; } .declaration .highlight { overflow-x: initial; @@ -215,6 +218,22 @@ pre code { content: ""; display: block; } +.section-name-container { + position: relative; } + .section-name-container .section-name-link { + position: absolute; + top: 0; + left: 0; + bottom: 0; + right: 0; + margin-bottom: 0; } + .section-name-container .section-name { + position: relative; + pointer-events: none; + z-index: 1; } + .section-name-container .section-name a { + pointer-events: auto; } + .item-container { padding: 0; } @@ -225,9 +244,11 @@ pre code { .item a[name]:before { content: ""; display: block; } - .item .token { + .item .token, .item .direct-link { + display: inline-block; + text-indent: -20px; padding-left: 3px; - margin-left: 0px; + margin-left: 20px; font-size: 1rem; } .item .declaration-note { font-size: .85em; @@ -287,9 +308,9 @@ pre code { .language .aside-title { color: #4183c4; } -.aside-warning { +.aside-warning, .aside-deprecated, .aside-unavailable { border-left: 5px solid #ff6666; } - .aside-warning .aside-title { + .aside-warning .aside-title, .aside-deprecated .aside-title, .aside-unavailable .aside-title { color: #ff0000; } .graybox { @@ -325,6 +346,7 @@ pre code { html.dash .header, html.dash .breadcrumbs, html.dash .navigation { display: none; } + html.dash .height-container { display: block; } @@ -338,14 +360,17 @@ form[role=search] input { border-radius: 1em; } .loading form[role=search] input { background: white url(../img/spinner.gif) center right 4px no-repeat; } + form[role=search] .tt-menu { margin: 0; min-width: 300px; background: #fbfbfb; color: #333; border: 1px solid #ddd; } + form[role=search] .tt-highlight { font-weight: bold; } + form[role=search] .tt-suggestion { font: 16px/1.7 "Helvetica Neue", Helvetica, Arial, sans-serif; padding: 0 8px; } @@ -358,11 +383,13 @@ form[role=search] .tt-suggestion { font-weight: normal; font-size: 0.9em; padding-left: 16px; } + form[role=search] .tt-suggestion:hover, form[role=search] .tt-suggestion.tt-cursor { cursor: pointer; background-color: #4183c4; color: #fff; } + form[role=search] .tt-suggestion:hover .doc-parent-name, form[role=search] .tt-suggestion.tt-cursor .doc-parent-name { color: #fff; } diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Info.plist b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Info.plist index dbf7f7a9b..220c951b0 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Info.plist +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Info.plist @@ -16,5 +16,7 @@ DashDocSetFamily dashtoc + DashDocSetFallbackURL + https://attaswift.github.io/BigInt/reference/ diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions.html index b9203ad28..7479e3581 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions.html @@ -14,15 +14,16 @@ +

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -39,7 +40,7 @@

    - + Install in Dash @@ -91,7 +92,7 @@

    -
    +

    Extensions

    The following extensions are available globally.

    @@ -105,9 +106,9 @@

    Extensions

  • @@ -122,17 +123,13 @@

    Extensions

    Declaration

    Swift

    - 
    protocol BinaryFloatingPoint : FloatingPoint, ExpressibleByFloatLiteral
    + 
    extension BinaryFloatingPoint where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger
    • - - -
    -
    • @@ -153,7 +150,7 @@

      Declaration

      Declaration

      Swift

      - 
      struct String
      + 
      extension String
      @@ -168,8 +165,8 @@

      Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/BinaryFloatingPoint.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/BinaryFloatingPoint.html index 648ecee7b..86bf1c39b 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/BinaryFloatingPoint.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/BinaryFloatingPoint.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,11 +92,12 @@

    -
    +

    BinaryFloatingPoint

    - 
    protocol BinaryFloatingPoint : FloatingPoint, ExpressibleByFloatLiteral
    + + 
    extension BinaryFloatingPoint where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger
    @@ -107,13 +108,22 @@

    BinaryFloatingPoint

    +
    + + +
    + +

    Available where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger

    +

    +
    +
    @@ -141,9 +151,9 @@

    Declaration

  • - + - init(_:) + init(_:)
    @@ -158,12 +168,12 @@

    Declaration

    Declaration

    Swift

    - 
    protocol BinaryFloatingPoint : FloatingPoint, ExpressibleByFloatLiteral
    + 
    public init(_ value: BigUInt)
    - Show on GitHub + Show on GitHub
    • @@ -176,8 +186,8 @@

    Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/String.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/String.html index 3b61515d6..8e347fd34 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/String.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Extensions/String.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,11 +92,12 @@

    -
    +

    String

    - 
    struct String
    + + 
    extension String
    @@ -111,9 +112,9 @@

    String

  • - + - init(_:) + init(_:)
    @@ -133,12 +134,12 @@

    String

    Declaration

    Swift

    - 
    public init(_ v: BigUInt)
    + 
    public init(_ v: BigUInt)
    - Show on GitHub + Show on GitHub
    • @@ -146,9 +147,9 @@

    Declaration

  • @@ -164,8 +165,7 @@

    Declaration

    Requires

    radix > 1 && radix <= 36 -
    -
    +

    Complexity

    O(count) when radix is a power of two; otherwise O(count^2). @@ -176,12 +176,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(_ v: BigUInt, radix: Int, uppercase: Bool = false)
    + 
    public init(_ v: BigUInt, radix: Int, uppercase: Bool = false)
    - Show on GitHub + Show on GitHub
    @@ -189,9 +189,9 @@

    Declaration

  • @@ -207,8 +207,7 @@

    Declaration

    Requires

    radix > 1 && radix <= 36 -
    -
    +

    Complexity

    O(count) when radix is a power of two; otherwise O(count^2). @@ -219,12 +218,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(_ value: BigInt, radix: Int = 10, uppercase: Bool = false)
    + 
    public init(_ value: BigInt, radix: Int = 10, uppercase: Bool = false)
    - Show on GitHub + Show on GitHub
    @@ -237,8 +236,8 @@

    Declaration

    • -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html index 366be84d2..9ae786007 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs.html @@ -14,15 +14,16 @@ +

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -39,7 +40,7 @@

    - + Install in Dash @@ -91,7 +92,7 @@

    -
    +

    Structures

    The following structures are available globally.

    @@ -115,7 +116,7 @@

    Structures

    -

    An arbitary precision unsigned integer type, also known as a big integer.

    +

    An arbitary precision unsigned integer type, also known as a “big integer”.

    Operations on big integers never overflow, but they may take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

    @@ -129,12 +130,20 @@

    Structures

    Declaration

    Swift

    - 
    public struct BigUInt: UnsignedInteger
    + 
    public struct BigUInt : UnsignedInteger
    +
    extension BigUInt: Codable
    +
    extension BigUInt: Comparable
    +
    extension BigUInt: Hashable
    +
    extension BigUInt: ExpressibleByIntegerLiteral
    +
    extension BigUInt: Strideable
    +
    extension BigUInt: ExpressibleByStringLiteral
    +
    extension BigUInt: CustomStringConvertible
    +
    extension BigUInt: CustomPlaygroundDisplayConvertible
    - Show on GitHub + Show on GitHub
    @@ -145,9 +154,11 @@

    Declaration

    - -

    BigInt

    -     +
    + +

    BigInt

    +

    +
    • @@ -163,7 +174,7 @@

      BigInt

      -

      An arbitary precision signed integer type, also known as a big integer.

      +

      An arbitary precision signed integer type, also known as a “big integer”.

      Operations on big integers never overflow, but they might take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

      @@ -185,12 +196,19 @@

      BigInt

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public struct BigInt : SignedInteger
      +
      extension BigInt: Codable
      +
      extension BigInt: Hashable
      +
      extension BigInt: ExpressibleByIntegerLiteral
      +
      extension BigInt: Strideable
      +
      extension BigInt: ExpressibleByStringLiteral
      +
      extension BigInt: CustomStringConvertible
      +
      extension BigInt: CustomPlaygroundDisplayConvertible
      - Show on GitHub + Show on GitHub
    @@ -203,8 +221,8 @@

    Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt.html index 7bc104afd..ef27d99fb 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,23 @@

    -
    +

    BigInt

    - 
    public struct BigInt: SignedInteger
    + + 
    public struct BigInt : SignedInteger
    +
    extension BigInt: Codable
    +
    extension BigInt: Hashable
    +
    extension BigInt: ExpressibleByIntegerLiteral
    +
    extension BigInt: Strideable
    +
    extension BigInt: ExpressibleByStringLiteral
    +
    extension BigInt: CustomStringConvertible
    +
    extension BigInt: CustomPlaygroundDisplayConvertible
    -

    An arbitary precision signed integer type, also known as a big integer.

    +

    An arbitary precision signed integer type, also known as a “big integer”.

    Operations on big integers never overflow, but they might take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

    @@ -116,6 +124,9 @@

    BigInt

    BigInt(255).abs.isPrime()   // Returns false
    +
    + Show on GitHub +
    @@ -144,12 +155,41 @@

    BigInt

    Declaration

    Swift

    - 
    public struct BigInt: SignedInteger
    + 
    public enum Sign
    + +
    + +
    + Show on GitHub +
    + + + +
  • +
    + + + + Magnitude + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public typealias Magnitude = BigUInt
    - Show on GitHub + Show on GitHub
    @@ -174,12 +214,12 @@

    Declaration

    Declaration

    Swift

    - 
    public typealias Word = BigUInt.Word
    + 
    public typealias Word = BigUInt.Word
    - Show on GitHub + Show on GitHub
    @@ -187,9 +227,9 @@

    Declaration

  • - + - isSigned + isSigned
    @@ -203,12 +243,12 @@

    Declaration

    Declaration

    Swift

    - 
    public static var isSigned: Bool
    + 
    public static var isSigned: Bool { get }
    - Show on GitHub + Show on GitHub
    @@ -216,9 +256,9 @@

    Declaration

  • @@ -233,12 +273,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var magnitude: BigUInt
    + 
    public var magnitude: BigUInt
    - Show on GitHub + Show on GitHub
    @@ -246,9 +286,9 @@

    Declaration

  • - + - sign + sign
    @@ -263,12 +303,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var sign: Sign
    + 
    public var sign: Sign
    - Show on GitHub + Show on GitHub
    @@ -276,9 +316,9 @@

    Declaration

  • @@ -293,12 +333,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(sign: Sign, magnitude: BigUInt)
    + 
    public init(sign: Sign, magnitude: BigUInt)
    - Show on GitHub + Show on GitHub
    @@ -306,9 +346,9 @@

    Declaration

  • - + - isZero + isZero
    @@ -328,12 +368,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var isZero: Bool
    + 
    public var isZero: Bool { get }
    - Show on GitHub + Show on GitHub
    @@ -358,7 +398,7 @@

    Declaration

    Declaration

    Swift

    - 
    public func signum() -> BigInt
    + 
    public func signum() -> BigInt
    @@ -367,21 +407,17 @@

    Return Value

    The sign of this number, expressed as an integer of the same type.

    - Show on GitHub + Show on GitHub
    • - - -
    -
    • - - - ~(_:) + + + +(_:_:)
      @@ -389,18 +425,19 @@

      Return Value

      - +

      Add a to b and return the result.

      +

      Declaration

      Swift

      - 
      public static prefix func ~(x: BigInt) -> BigInt
      + 
      public static func + (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -408,9 +445,9 @@

      Declaration

    • - - - &(_:_:) + + + +=(_:_:)
      @@ -418,29 +455,42 @@

      Declaration

      -

      Undocumented

      +

      Add b to a in place.

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public static func += (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Bitwise Operations

    +

    +
    +
    +
    • - - - |(_:_:) + + + ~(_:)
      @@ -455,12 +505,12 @@

      Declaration

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public prefix static func ~ (x: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
    @@ -468,9 +518,9 @@

    Declaration

  • - - - ^(_:_:) + + + &(_:_:)
    @@ -485,12 +535,12 @@

    Declaration

    Declaration

    Swift

    - 
    public struct BigInt: SignedInteger
    + 
    public static func & (lhs: inout BigInt, rhs: BigInt) -> BigInt
    - Show on GitHub + Show on GitHub
    @@ -498,9 +548,9 @@

    Declaration

  • - - - &=(_:_:) + + + |(_:_:)
    @@ -508,18 +558,19 @@

    Declaration

    - +

    Undocumented

    +

    Declaration

    Swift

    - 
    public static func &=(lhs: inout BigInt, rhs: BigInt)
    + 
    public static func | (lhs: inout BigInt, rhs: BigInt) -> BigInt
    - Show on GitHub + Show on GitHub
    @@ -527,9 +578,9 @@

    Declaration

  • - - - |=(_:_:) + + + ^(_:_:)
    @@ -537,18 +588,19 @@

    Declaration

    - +

    Undocumented

    +

    Declaration

    Swift

    - 
    public static func |=(lhs: inout BigInt, rhs: BigInt)
    + 
    public static func ^ (lhs: inout BigInt, rhs: BigInt) -> BigInt
    - Show on GitHub + Show on GitHub
    @@ -556,9 +608,9 @@

    Declaration

  • - - - ^=(_:_:) + + + &=(_:_:)
    @@ -566,39 +618,29 @@

    Declaration

    - +

    Undocumented

    +

    Declaration

    Swift

    - 
    public static func ^=(lhs: inout BigInt, rhs: BigInt)
    + 
    public static func &= (lhs: inout BigInt, rhs: BigInt)
    - Show on GitHub + Show on GitHub
    • - - -
    -
    - - - -

    Primality Testing

    -     -
    -
    • @@ -606,19 +648,19 @@

      Primality Testing

      -

      Returns true iff this integer passes the strong probable prime test for the specified base.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func isStrongProbablePrime(_ base: BigInt) -> Bool
      + 
      public static func |= (lhs: inout BigInt, rhs: BigInt)
      - Show on GitHub + Show on GitHub
      @@ -626,9 +668,9 @@

      Declaration

    • @@ -636,43 +678,29 @@

      Declaration

      -

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      - -

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, -each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, -but you may specify your own choice.

      - -

      To speed things up, the function checks if self is divisible by the first few prime numbers before -diving into (slower) Miller-Rabin testing.

      - -

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to -return a correct result.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func isPrime(rounds: Int = 10) -> Bool
      + 
      public static func ^= (lhs: inout BigInt, rhs: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    @@ -699,9 +727,9 @@

    Declaration

  • @@ -715,26 +743,22 @@

    Declaration

    Declaration

    Swift

    - 
    public var trailingZeroBitCount: Int
    + 
    public func encode(to encoder: Encoder) throws
    - Show on GitHub + Show on GitHub
    • - - -
    -
    • - - - Words + + + ==(_:_:)
      @@ -742,19 +766,19 @@

      Declaration

      - - See more +

      Return true iff a is equal to b.

      +

      Declaration

      Swift

      - 
      public struct Words: RandomAccessCollection
      + 
      public static func == (a: BigInt, b: BigInt) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -762,9 +786,9 @@

      Declaration

    • - - - words + + + <(_:_:)
      @@ -772,18 +796,19 @@

      Declaration

      - +

      Return true iff a is less than b.

      +

      Declaration

      Swift

      - 
      public var words: Words
      + 
      public static func < (a: BigInt, b: BigInt) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -791,9 +816,9 @@

      Declaration

    • - - - init(words:) + + + init(_:)
      @@ -801,33 +826,30 @@

      Declaration

      -

      Undocumented

      +

      Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer, +where the first byte indicates sign (0 for positive, 1 for negative)

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public init(_ buffer: UnsafeRawBufferPointer)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -835,33 +857,31 @@

      Declaration

      -

      Append this BigInt to the specified hasher.

      +

      Initializes an integer from the bits stored inside a piece of Data. +The data is assumed to be in network (big-endian) byte order with a first +byte to represent the sign (0 for positive, 1 for negative)

      Declaration

      Swift

      - 
      public func appendHashes(to hasher: inout SipHasher)
      + 
      public init(_ data: Data)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -869,28 +889,42 @@

      Declaration

      - +

      Return a Data value that contains the base-256 representation of this integer, in network (big-endian) byte order and a prepended byte to indicate the sign (0 for positive, 1 for negative)

      +

      Declaration

      Swift

      - 
      public init?<T: BinaryFloatingPoint>(exactly source: T)
      + 
      public func serialize() -> Data
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Full-width multiplication and division

    +

    +
    +
    +
    • @@ -898,32 +932,42 @@

      Declaration

      - +

      Divide this integer by y and return the resulting quotient and remainder.

      +
      +

      Requires

      + y > 0 + +
      +

      Complexity

      + O(count^2) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryFloatingPoint>(_ source: T)
      + 
      public func quotientAndRemainder(dividingBy y: BigInt) -> (quotient: BigInt, remainder: BigInt)
      +
      +

      Return Value

      +

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - negate() + + + /(_:_:)
      @@ -931,18 +975,19 @@

      Declaration

      - +

      Divide a by b and return the quotient. Traps if b is zero.

      +

      Declaration

      Swift

      - 
      public mutating func negate()
      + 
      public static func / (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -950,9 +995,9 @@

      Declaration

    • - - - -(_:_:) + + + %(_:_:)
      @@ -960,19 +1005,19 @@

      Declaration

      -

      Subtract b from a and return the result.

      +

      Divide a by b and return the remainder. The result has the same sign as a.

      Declaration

      Swift

      - 
      public static func -(a: BigInt, b: BigInt) -> BigInt
      + 
      public static func % (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -980,9 +1025,9 @@

      Declaration

    • - - - -=(_:_:) + + + modulus(_:)
      @@ -990,33 +1035,29 @@

      Declaration

      -

      Subtract b from a in place.

      +

      Return the result of a mod b. The result is always a nonnegative integer that is less than the absolute value of b.

      Declaration

      Swift

      - 
      public static func -=(a: inout BigInt, b: BigInt)
      + 
      public func modulus(_ mod: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1024,33 +1065,19 @@

      Declaration

      -

      Divide this integer by y and return the resulting quotient and remainder.

      -
      -

      Requires

      - y > 0 - -
      -
      -

      Complexity

      - O(count^2) - -
      +

      Divide a by b storing the quotient in a.

      Declaration

      Swift

      - 
      public func quotientAndRemainder(dividingBy y: BigInt) -> (quotient: BigInt, remainder: BigInt)
      + 
      public static func /= (a: inout BigInt, b: BigInt)
      -
      -

      Return Value

      -

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      -
      - Show on GitHub + Show on GitHub
      @@ -1058,9 +1085,9 @@

      Return Value

    • - - - /(_:_:) + + + %=(_:_:)
      @@ -1068,19 +1095,19 @@

      Return Value

      -

      Divide a by b and return the quotient. Traps if b is zero.

      +

      Divide a by b storing the remainder in a.

      Declaration

      Swift

      - 
      public static func /(a: BigInt, b: BigInt) -> BigInt
      + 
      public static func %= (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      @@ -1088,9 +1115,9 @@

      Declaration

    • - - - %(_:_:) + + + power(_:)
      @@ -1098,19 +1125,40 @@

      Declaration

      -

      Divide a by b and return the remainder. The result has the same sign as a.

      +

      Returns this integer raised to the power exponent.

      + +

      This function calculates the result by successively squaring the base while halving the exponent.

      +
      +

      Note

      + This function can be unreasonably expensive for large exponents, which is why exponent is + a simple integer value. If you want to calculate big exponents, you’ll probably need to use + the modulo arithmetic variant. + +
      +

      See also

      + BigUInt.power(_:, modulus:) + +
      +

      Complexity

      + O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too. + +

      Declaration

      Swift

      - 
      public static func %(a: BigInt, b: BigInt) -> BigInt
      + 
      public func power(_ exponent: Int) -> BigInt
      +
      +

      Return Value

      +

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      +
      - Show on GitHub + Show on GitHub
      @@ -1118,9 +1166,9 @@

      Declaration

    • @@ -1128,33 +1176,36 @@

      Declaration

      -

      Return the result of a mod b. The result is always a nonnegative integer that is less than the absolute value of b.

      +

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      + +

      Uses the right-to-left binary method.

      +
      +

      Complexity

      + O(exponent.count * modulus.count^log2(3)) or somesuch + +

      Declaration

      Swift

      - 
      public func modulus(_ mod: BigInt) -> BigInt
      + 
      public func power(_ exponent: BigInt, modulus: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - /=(_:_:) + + + init(exactly:)
      @@ -1162,19 +1213,18 @@

      Declaration

      -

      Divide a by b storing the quotient in a.

      - +

      Declaration

      Swift

      - 
      public static func /=(a: inout BigInt, b: BigInt)
      + 
      public init?<T>(exactly source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      @@ -1182,9 +1232,9 @@

      Declaration

    • - - - %=(_:_:) + + + init(_:)
      @@ -1192,33 +1242,28 @@

      Declaration

      -

      Divide a by b storing the remainder in a.

      - +

      Declaration

      Swift

      - 
      public static func %=(a: inout BigInt, b: BigInt)
      + 
      public init<T>(_ source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1226,19 +1271,98 @@

      Declaration

      -

      Undocumented

      - -
      +

      Returns the greatest common divisor of a and b.

      +
      +

      Complexity

      + O(count^2) where count = max(a.count, b.count) + +
      + +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public func greatestCommonDivisor(with b: BigInt) -> BigInt
      + +
      +
      +
      + Show on GitHub +
      + +
    + +
  • +
    + + + + inverse(_:) + +
    +
    +
    +
    +
    +
    +

    Returns the multiplicative inverse of this integer in modulo modulus arithmetic, +or nil if there is no such number.

    +
    +

    Requires

    + modulus.magnitude > 1 + +
    +

    Complexity

    + O(count^3) + +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public func inverse(_ modulus: BigInt) -> BigInt?
    + +
    +
    +
    +

    Return Value

    +

    If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + + + hash(into:) + +
    +
    +
    +
    +
    +
    +

    Append this BigInt to the specified hasher.

    + +

    Declaration

    Swift

    - 
    public struct BigInt: SignedInteger
    + 
    public func hash(into hasher: inout Hasher)
    - Show on GitHub + Show on GitHub
    @@ -1246,9 +1370,39 @@

    Declaration

  • - + + + init() + +
    +
    +
    +
    +
    +
    +

    Undocumented

    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public init()
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + - init(_:) + init(_:)
    @@ -1263,12 +1417,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(_ integer: BigUInt)
    + 
    public init(_ integer: BigUInt)
    - Show on GitHub + Show on GitHub
    @@ -1276,9 +1430,9 @@

    Declaration

  • - + - init(_:) + init(_:)
    @@ -1292,12 +1446,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init<T>(_ source: T) where T : BinaryInteger
    + 
    public init<T>(_ source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    @@ -1305,9 +1459,9 @@

    Declaration

  • @@ -1321,12 +1475,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init?<T>(exactly source: T) where T : BinaryInteger
    + 
    public init?<T>(exactly source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    @@ -1334,9 +1488,9 @@

    Declaration

  • @@ -1350,12 +1504,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init<T>(clamping source: T) where T : BinaryInteger
    + 
    public init<T>(clamping source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    @@ -1363,9 +1517,9 @@

    Declaration

  • @@ -1379,26 +1533,22 @@

    Declaration

    Declaration

    Swift

    - 
    public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger
    + 
    public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger
    - Show on GitHub + Show on GitHub
    • - - -
    -
    - - -
    -
    • - - - ==(_:_:) + + + *(_:_:)
      @@ -1440,19 +1586,19 @@

      Declaration

      -

      Return true iff a is equal to b.

      +

      Multiply a with b and return the result.

      Declaration

      Swift

      - 
      public static func ==(a: BigInt, b: BigInt) -> Bool
      + 
      public static func * (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -1460,9 +1606,9 @@

      Declaration

    • - - - <(_:_:) + + + *=(_:_:)
      @@ -1470,19 +1616,19 @@

      Declaration

      -

      Return true iff a is less than b.

      +

      Multiply a with b in place.

      Declaration

      Swift

      - 
      public static func <(a: BigInt, b: BigInt) -> Bool
      + 
      public static func *= (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      @@ -1490,13 +1636,22 @@

      Declaration

    +
    + + +
    + +

    Primality Testing

    +

    +
    +
    • @@ -1504,43 +1659,29 @@

      Declaration

      -

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by -letters from the English alphabet.

      -
      -

      Requires

      - radix > 1 && radix < 36 - -
      +

      Returns true iff this integer passes the strong probable prime test for the specified base.

      Declaration

      Swift

      - 
      public init?<S: StringProtocol>(_ text: S, radix: Int = 10)
      + 
      public func isStrongProbablePrime(_ base: BigInt) -> Bool
      -
      -

      Return Value

      -

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1548,20 +1689,29 @@

      Return Value

      -

      Initialize a new big integer from a Unicode scalar. -The scalar must represent a decimal digit.

      +

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      + +

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, +each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, +but you may specify your own choice.

      + +

      To speed things up, the function checks if self is divisible by the first few prime numbers before +diving into (slower) Miller-Rabin testing.

      + +

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to +return a correct result.

      Declaration

      Swift

      - 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      + 
      public func isPrime(rounds: Int = 10) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -1569,9 +1719,9 @@

      Declaration

    • @@ -1579,20 +1729,19 @@

      Declaration

      -

      Initialize a new big integer from an extended grapheme cluster. -The cluster must consist of a decimal digit.

      +

      Undocumented

      Declaration

      Swift

      - 
      public init(extendedGraphemeClusterLiteral value: String)
      + 
      public static func &<< (left: BigInt, right: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -1600,9 +1749,9 @@

      Declaration

    • @@ -1610,34 +1759,29 @@

      Declaration

      -

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. -The string must contain only decimal digits.

      +

      Undocumented

      Declaration

      Swift

      - 
      public init(stringLiteral value: StringLiteralType)
      + 
      public static func &<<= (left: inout BigInt, right: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - description + + + &>>(_:_:)
      @@ -1645,33 +1789,29 @@

      Declaration

      -

      Return the decimal representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var description: String
      + 
      public static func &>> (left: BigInt, right: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1679,33 +1819,29 @@

      Declaration

      -

      Return the playground quick look representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var customPlaygroundQuickLook: PlaygroundQuickLook
      + 
      public static func &>>= (left: inout BigInt, right: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - *(_:_:) + + + <<(_:_:)
      @@ -1713,19 +1849,19 @@

      Declaration

      -

      Multiply a with b and return the result.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func *(a: BigInt, b: BigInt) -> BigInt
      + 
      public static func << <Other>(lhs: BigInt, rhs: Other) -> BigInt where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1733,9 +1869,9 @@

      Declaration

    • - - - *=(_:_:) + + + <<=(_:_:)
      @@ -1743,33 +1879,29 @@

      Declaration

      -

      Multiply a with b in place.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func *=(a: inout BigInt, b: BigInt)
      + 
      public static func <<= <Other>(lhs: inout BigInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - advanced(by:) + + + >>(_:_:)
      @@ -1777,19 +1909,19 @@

      Declaration

      -

      Returns self + n.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func advanced(by n: Stride) -> BigInt
      + 
      public static func >> <Other>(lhs: BigInt, rhs: Other) -> BigInt where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1797,9 +1929,9 @@

      Declaration

    • - - - distance(to:) + + + >>=(_:_:)
      @@ -1807,19 +1939,19 @@

      Declaration

      -

      Returns other - self.

      +

      Undocumented

      Declaration

      Swift

      - 
      public func distance(to other: BigInt) -> Stride
      + 
      public static func >>= <Other>(lhs: inout BigInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1827,13 +1959,22 @@

      Declaration

    +
    + + +
    + +

    Square Root

    +

    +
    +
    • - - - &<<(_:_:) + + + squareRoot()
      @@ -1841,19 +1982,28 @@

      Declaration

      -

      Undocumented

      +

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      +
      +

      Requires

      + self >= 0 + +

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public func squareRoot() -> BigInt
      +
      +

      Return Value

      +

      floor(sqrt(self))

      +
      - Show on GitHub + Show on GitHub
      @@ -1861,9 +2011,9 @@

      Declaration

    • - - - &<<=(_:_:) + + + Stride
      @@ -1871,19 +2021,18 @@

      Declaration

      -

      Undocumented

      - +

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public typealias Stride = BigInt
      - Show on GitHub + Show on GitHub
      @@ -1891,9 +2040,9 @@

      Declaration

    • - - - &>>(_:_:) + + + advanced(by:)
      @@ -1901,19 +2050,19 @@

      Declaration

      -

      Undocumented

      +

      Returns self + n.

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public func advanced(by n: Stride) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -1921,9 +2070,9 @@

      Declaration

    • @@ -1931,19 +2080,19 @@

      Declaration

      -

      Undocumented

      +

      Returns other - self.

      Declaration

      Swift

      - 
      public struct BigInt: SignedInteger
      + 
      public func distance(to other: BigInt) -> Stride
      - Show on GitHub + Show on GitHub
      @@ -1951,9 +2100,9 @@

      Declaration

    • - - - <<(_:_:) + + + init(_:radix:)
      @@ -1961,18 +2110,29 @@

      Declaration

      - +

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by +letters from the English alphabet.

      +
      +

      Requires

      + radix > 1 && radix < 36 + +
      +

      Declaration

      Swift

      - 
      public static func <<<Other: BinaryInteger>(lhs: BigInt, rhs: Other) -> BigInt
      + 
      public init?<S>(_ text: S, radix: Int = 10) where S : StringProtocol
      +
      +

      Return Value

      +

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      +
      - Show on GitHub + Show on GitHub
      @@ -1980,9 +2140,9 @@

      Declaration

    • @@ -1990,18 +2150,20 @@

      Declaration

      - +

      Initialize a new big integer from a Unicode scalar. +The scalar must represent a decimal digit.

      +

      Declaration

      Swift

      - 
      public static func <<=<Other: BinaryInteger>(lhs: inout BigInt, rhs: Other)
      + 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      - Show on GitHub + Show on GitHub
      @@ -2009,9 +2171,9 @@

      Declaration

    • @@ -2019,18 +2181,20 @@

      Declaration

      - +

      Initialize a new big integer from an extended grapheme cluster. +The cluster must consist of a decimal digit.

      +

      Declaration

      Swift

      - 
      public static func >><Other: BinaryInteger>(lhs: BigInt, rhs: Other) -> BigInt
      + 
      public init(extendedGraphemeClusterLiteral value: String)
      - Show on GitHub + Show on GitHub
      @@ -2038,9 +2202,9 @@

      Declaration

    • @@ -2048,32 +2212,30 @@

      Declaration

      - +

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. +The string must contain only decimal digits.

      +

      Declaration

      Swift

      - 
      public static func >>=<Other: BinaryInteger>(lhs: inout BigInt, rhs: Other)
      + 
      public init(stringLiteral value: StringLiteralType)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -2081,24 +2243,19 @@

      Declaration

      -

      Returns the greatest common divisor of a and b.

      -
      -

      Complexity

      - O(count^2) where count = max(a.count, b.count) - -
      +

      Return the decimal representation of this integer.

      Declaration

      Swift

      - 
      public func greatestCommonDivisor(with b: BigInt) -> BigInt
      + 
      public var description: String { get }
      - Show on GitHub + Show on GitHub
      @@ -2106,9 +2263,9 @@

      Declaration

    • @@ -2116,48 +2273,29 @@

      Declaration

      -

      Returns the multiplicative inverse of this integer in modulo modulus arithmetic, -or nil if there is no such number.

      -
      -

      Requires

      - modulus.magnitude > 1 - -
      -
      -

      Complexity

      - O(count^3) - -
      +

      Return the playground quick look representation of this integer.

      Declaration

      Swift

      - 
      public func inverse(_ modulus: BigInt) -> BigInt?
      + 
      public var playgroundDescription: Any { get }
      -
      -

      Return Value

      -

      If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - squareRoot() + + + negate()
      @@ -2165,42 +2303,29 @@

      Return Value

      -

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      -
      -

      Requires

      - self >= 0 - -
      +

      Undocumented

      Declaration

      Swift

      - 
      public func squareRoot() -> BigInt
      + 
      public mutating func negate()
      -
      -

      Return Value

      -

      floor(sqrt(self))

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - init(from:) + + + -(_:_:)
      @@ -2208,18 +2333,19 @@

      Return Value

      - +

      Subtract b from a and return the result.

      +

      Declaration

      Swift

      - 
      public init(from decoder: Decoder) throws
      + 
      public static func - (a: BigInt, b: BigInt) -> BigInt
      - Show on GitHub + Show on GitHub
      @@ -2227,9 +2353,9 @@

      Declaration

    • - - - encode(to:) + + + -=(_:_:)
      @@ -2237,32 +2363,29 @@

      Declaration

      - +

      Subtract b from a in place.

      +

      Declaration

      Swift

      - 
      public func encode(to encoder: Encoder) throws
      + 
      public static func -= (a: inout BigInt, b: BigInt)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - power(_:) + + + bitWidth
      @@ -2270,42 +2393,19 @@

      Declaration

      -

      Returns this integer raised to the power exponent.

      - -

      This function calculates the result by successively squaring the base while halving the exponent.

      -
      -

      Note

      - This function can be unreasonably expensive for large exponents, which is why exponent is - a simple integer value. If you want to calculate big exponents, you’ll probably need to use - the modulo arithmetic variant. - -
      -
      -

      See also

      - BigUInt.power(_:, modulus:) - -
      -
      -

      Complexity

      - O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too. - -
      +

      Undocumented

      Declaration

      Swift

      - 
      public func power(_ exponent: Int) -> BigInt
      + 
      public var bitWidth: Int { get }
      -
      -

      Return Value

      -

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      -
      - Show on GitHub + Show on GitHub
      @@ -2313,9 +2413,9 @@

      Return Value

    • @@ -2323,40 +2423,59 @@

      Return Value

      -

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      - -

      Uses the right-to-left binary method.

      -
      -

      Complexity

      - O(exponent.count * modulus.count^log2(3)) or somesuch +

      Undocumented

      -
      +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public var trailingZeroBitCount: Int { get }
      +
      +
      +
      + Show on GitHub +
      +
      +
      +
      • +
    • +
      + + + + Words + +
      +
      +
      +
      +
      +
      + + See more

      Declaration

      Swift

      - 
      public func power(_ exponent: BigInt, modulus: BigInt) -> BigInt
      + 
      public struct Words : RandomAccessCollection
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - +(_:_:) + + + words
      @@ -2364,19 +2483,19 @@

      Declaration

      -

      Add a to b and return the result.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func +(a: BigInt, b: BigInt) -> BigInt
      + 
      public var words: Words { get }
      - Show on GitHub + Show on GitHub
      @@ -2384,9 +2503,9 @@

      Declaration

    • - - - +=(_:_:) + + + init(words:)
      @@ -2394,19 +2513,19 @@

      Declaration

      -

      Add b to a in place.

      +

      Undocumented

      Declaration

      Swift

      - 
      public static func +=(a: inout BigInt, b: BigInt)
      + 
      public init<S>(words: S) where S : Sequence, S.Element == BigInt.Word
      - Show on GitHub + Show on GitHub
      @@ -2419,8 +2538,8 @@

      Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Sign.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Sign.html index 2db1db2de..93984a5b3 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Sign.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Sign.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,10 +92,20 @@

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Words.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Words.html index ba949c188..d070e5056 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Words.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigInt/Words.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,19 @@

    -
    +

    Words

    - 
    public struct Words: RandomAccessCollection
    + + 
    public struct Words : RandomAccessCollection
    +
    + Show on GitHub +
    @@ -111,9 +115,38 @@

    Words

  • - + + + Indices + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public typealias Indices = CountableRange<Int>
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + - count + count
    @@ -127,12 +160,12 @@

    Words

    Declaration

    Swift

    - 
    public var count: Int
    + 
    public var count: Int { get }
    - Show on GitHub + Show on GitHub
    @@ -140,9 +173,9 @@

    Declaration

  • - + - indices + indices
    @@ -156,12 +189,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var indices: Indices
    + 
    public var indices: Indices { get }
    - Show on GitHub + Show on GitHub
    @@ -169,9 +202,9 @@

    Declaration

  • @@ -185,12 +218,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var startIndex: Int
    + 
    public var startIndex: Int { get }
    - Show on GitHub + Show on GitHub
    @@ -198,9 +231,38 @@

    Declaration

  • - + - endIndex + endIndex + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public var endIndex: Int { get }
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + + + subscript(_:)
    @@ -214,12 +276,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var endIndex: Int
    + 
    public subscript(index: Int) -> UInt { get }
    - Show on GitHub + Show on GitHub
    @@ -232,8 +294,8 @@

    Declaration

    • -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt.html index 8c502f7c2..5d164ca90 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,24 @@

    -
    +

    BigUInt

    - 
    public struct BigUInt: UnsignedInteger
    + + 
    public struct BigUInt : UnsignedInteger
    +
    extension BigUInt: Codable
    +
    extension BigUInt: Comparable
    +
    extension BigUInt: Hashable
    +
    extension BigUInt: ExpressibleByIntegerLiteral
    +
    extension BigUInt: Strideable
    +
    extension BigUInt: ExpressibleByStringLiteral
    +
    extension BigUInt: CustomStringConvertible
    +
    extension BigUInt: CustomPlaygroundDisplayConvertible
    -

    An arbitary precision unsigned integer type, also known as a big integer.

    +

    An arbitary precision unsigned integer type, also known as a “big integer”.

    Operations on big integers never overflow, but they may take a long time to execute. The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.

    @@ -108,6 +117,9 @@

    BigUInt

    This particular big integer type uses base-2^64 digits to represent integers; you can think of it as a wrapper around Array<UInt64>. (In fact, BigUInt only uses an array if there are more than two digits.)

    +
    + Show on GitHub +
    @@ -135,12 +147,12 @@

    BigUInt

    Declaration

    Swift

    - 
    public typealias Word = UInt
    + 
    public typealias Word = UInt
    - Show on GitHub + Show on GitHub
    @@ -165,12 +177,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init()
    + 
    public init()
    - Show on GitHub + Show on GitHub
    @@ -178,9 +190,9 @@

    Declaration

  • @@ -195,12 +207,12 @@

    Declaration

    Declaration

    Swift

    - 
    public init(words: [Word])
    + 
    public init(words: [Word])
    - Show on GitHub + Show on GitHub
    @@ -208,13 +220,22 @@

    Declaration

    +
    + + +
    + +

    Addition

    +

    +
    +
    • - - - ~(_:) + + + +(_:_:)
      @@ -222,10 +243,10 @@

      Declaration

      -

      Return the ones’ complement of a.

      +

      Add a and b together and return the result.

      Complexity

      - O(a.count) + O(max(a.count, b.count))
      @@ -234,12 +255,12 @@

      Declaration

      Declaration

      Swift

      - 
      public static prefix func ~(a: BigUInt) -> BigUInt
      + 
      public static func + (a: BigUInt, b: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -247,9 +268,9 @@

      Declaration

    • - - - |=(_:_:) + + + +=(_:_:)
      @@ -257,7 +278,7 @@

      Declaration

      -

      Calculate the bitwise OR of a and b, and store the result in a.

      +

      Add a and b together, and store the sum in a.

      Complexity

      O(max(a.count, b.count)) @@ -269,12 +290,12 @@

      Declaration

      Declaration

      Swift

      - 
      public static func |= (a: inout BigUInt, b: BigUInt)
      + 
      public static func += (a: inout BigUInt, b: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -282,9 +303,9 @@

      Declaration

    • - - - &=(_:_:) + + + isSigned
      @@ -292,24 +313,18 @@

      Declaration

      -

      Calculate the bitwise AND of a and b and return the result.

      -
      -

      Complexity

      - O(max(a.count, b.count)) - -
      - +

      Declaration

      Swift

      - 
      public static func &= (a: inout BigUInt, b: BigUInt)
      + 
      public static var isSigned: Bool { get }
      - Show on GitHub + Show on GitHub
      @@ -317,9 +332,9 @@

      Declaration

    • - - - ^=(_:_:) + + + signum()
      @@ -327,24 +342,23 @@

      Declaration

      -

      Calculate the bitwise XOR of a and b and return the result.

      -
      -

      Complexity

      - O(max(a.count, b.count)) - -
      +

      Returns 1 if this value is, positive; otherwise, 0.

      Declaration

      Swift

      - 
      public static func ^= (a: inout BigUInt, b: BigUInt)
      + 
      public func signum() -> BigUInt
      +
      +

      Return Value

      +

      The sign of this number, expressed as an integer of the same type.

      +
      - Show on GitHub + Show on GitHub
      @@ -353,19 +367,21 @@

      Declaration

    - - - -

    Random Integers

    -     + + +
    + +

    Bitwise Operations

    +

    +
    • @@ -373,10 +389,10 @@

      Random Integers

      -

      Create a big integer consisting of width uniformly distributed random bits.

      -
      -

      Note

      - This function uses arc4random_buf to generate random bits. +

      Return the ones’ complement of a.

      +
      +

      Complexity

      + O(a.count)
      @@ -385,16 +401,12 @@

      Random Integers

      Declaration

      Swift

      - 
      public static func randomInteger(withMaximumWidth width: Int) -> BigUInt
      + 
      public prefix static func ~ (a: BigUInt) -> BigUInt
      -
      -

      Return Value

      -

      A big integer less than 1 << width.

      -
      - Show on GitHub + Show on GitHub
      @@ -402,9 +414,9 @@

      Return Value

    • @@ -412,10 +424,10 @@

      Return Value

      -

      Create a big integer consisting of width-1 uniformly distributed random bits followed by a one bit.

      -
      -

      Note

      - This function uses arc4random_buf to generate random bits. +

      Calculate the bitwise OR of a and b, and store the result in a.

      +
      +

      Complexity

      + O(max(a.count, b.count))
      @@ -424,16 +436,12 @@

      Return Value

      Declaration

      Swift

      - 
      public static func randomInteger(withExactWidth width: Int) -> BigUInt
      + 
      public static func |= (a: inout BigUInt, b: BigUInt)
      -
      -

      Return Value

      -

      A random big integer whose width is width.

      -
      - Show on GitHub + Show on GitHub
      @@ -441,9 +449,9 @@

      Return Value

    • @@ -451,10 +459,10 @@

      Return Value

      -

      Create a uniformly distributed random integer that’s less than the specified limit.

      -
      -

      Note

      - This function uses arc4random_buf to generate random bits. +

      Calculate the bitwise AND of a and b and return the result.

      +
      +

      Complexity

      + O(max(a.count, b.count))
      @@ -463,37 +471,22 @@

      Return Value

      Declaration

      Swift

      - 
      public static func randomInteger(lessThan limit: BigUInt) -> BigUInt
      + 
      public static func &= (a: inout BigUInt, b: BigUInt)
      -
      -

      Return Value

      -

      A random big integer that is less than limit.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Primality Testing

    -     -
    -
    • @@ -501,19 +494,24 @@

      Primality Testing

      -

      Returns true iff this integer passes the strong probable prime test for the specified base.

      +

      Calculate the bitwise XOR of a and b and return the result.

      +
      +

      Complexity

      + O(max(a.count, b.count)) + +

      Declaration

      Swift

      - 
      public func isStrongProbablePrime(_ base: BigUInt) -> Bool
      + 
      public static func ^= (a: inout BigUInt, b: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -521,9 +519,9 @@

      Declaration

    • @@ -531,29 +529,47 @@

      Declaration

      -

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      - -

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, -each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, -but you may specify your own choice.

      - -

      To speed things up, the function checks if self is divisible by the first few prime numbers before -diving into (slower) Miller-Rabin testing.

      - -

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to -return a correct result.

      + +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public init(from decoder: Decoder) throws
      +
      +
      +
      + Show on GitHub +
      +
      +
      +
      • +
    • +
      + + + + encode(to:) + +
      +
      +
      +
      +
      +
      +

      Declaration

      Swift

      - 
      public func isPrime(rounds: Int = 10) -> Bool
      + 
      public func encode(to encoder: Encoder) throws
      - Show on GitHub + Show on GitHub
      @@ -561,13 +577,22 @@

      Declaration

    +
    + + +
    + +

    Comparison

    +

    +
    +
    • - - - bitWidth + + + compare(_:_:)
      @@ -575,10 +600,10 @@

      Declaration

      -

      The minimum number of bits required to represent this integer in binary.

      +

      Compare a to b and return an NSComparisonResult indicating their order.

      Complexity

      - O(1) + O(count)
      @@ -587,16 +612,12 @@

      Declaration

      Declaration

      Swift

      - 
      public var bitWidth: Int
      + 
      public static func compare(_ a: BigUInt, _ b: BigUInt) -> ComparisonResult
      -
      -

      Return Value

      -

      floor(log2(2 * self + 1))

      -
      - Show on GitHub + Show on GitHub
      @@ -604,9 +625,9 @@

      Return Value

    • @@ -614,21 +635,10 @@

      Return Value

      -

      The number of leading zero bits in the binary representation of this integer in base 2^(Word.bitWidth). -This is useful when you need to normalize a BigUInt such that the top bit of its most significant word is 1.

      -
      -

      Note

      - 0 is considered to have zero leading zero bits. - -
      -
      -

      See also

      - width - -
      +

      Return true iff a is equal to b.

      Complexity

      - O(1) + O(count)
      @@ -637,16 +647,12 @@

      Return Value

      Declaration

      Swift

      - 
      public var leadingZeroBitCount: Int
      + 
      public static func == (a: BigUInt, b: BigUInt) -> Bool
      -
      -

      Return Value

      -

      A value in 0...(Word.bitWidth - 1).

      -
      - Show on GitHub + Show on GitHub
      @@ -654,9 +660,9 @@

      Return Value

    • @@ -664,12 +670,7 @@

      Return Value

      -

      The number of trailing zero bits in the binary representation of this integer.

      -
      -

      Note

      - 0 is considered to have zero trailing zero bits. - -
      +

      Return true iff a is less than b.

      Complexity

      O(count) @@ -681,16 +682,12 @@

      Return Value

      Declaration

      Swift

      - 
      public var trailingZeroBitCount: Int
      + 
      public static func < (a: BigUInt, b: BigUInt) -> Bool
      -
      -

      Return Value

      -

      A value in 0...width.

      -
      - Show on GitHub + Show on GitHub
      @@ -698,13 +695,22 @@

      Return Value

    +
    + + +
    + +

    NSData Conversion

    +

    +
    +
    • - - - Words + + + init(_:)
      @@ -712,19 +718,19 @@

      Return Value

      - - See more +

      Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer

      +

      Declaration

      Swift

      - 
      public struct Words: RandomAccessCollection
      + 
      public init(_ buffer: UnsafeRawBufferPointer)
      - Show on GitHub + Show on GitHub
      @@ -732,9 +738,9 @@

      Declaration

    • - - - words + + + init(_:)
      @@ -742,18 +748,20 @@

      Declaration

      - +

      Initializes an integer from the bits stored inside a piece of Data. +The data is assumed to be in network (big-endian) byte order.

      +

      Declaration

      Swift

      - 
      public var words: Words
      + 
      public init(_ data: Data)
      - Show on GitHub + Show on GitHub
      @@ -761,9 +769,9 @@

      Declaration

    • @@ -771,19 +779,19 @@

      Declaration

      -

      Undocumented

      +

      Return a Data value that contains the base-256 representation of this integer, in network (big-endian) byte order.

      Declaration

      Swift

      - 
      public struct BigUInt: UnsignedInteger
      + 
      public func serialize() -> Data
      - Show on GitHub + Show on GitHub
      @@ -792,19 +800,21 @@

      Declaration

    - - - -

    Hashing

    -     + + +
    + +

    Division

    +

    +
    • @@ -812,33 +822,42 @@

      Hashing

      -

      Append this BigUInt to the specified hasher.

      +

      Divide this integer by y and return the resulting quotient and remainder.

      +
      +

      Requires

      + y > 0 + +
      +

      Complexity

      + O(count^2) + +

      Declaration

      Swift

      - 
      public func appendHashes(to hasher: inout SipHasher)
      + 
      public func quotientAndRemainder(dividingBy y: BigUInt) -> (quotient: BigUInt, remainder: BigUInt)
      +
      +

      Return Value

      +

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - init(exactly:) + + + /(_:_:)
      @@ -846,18 +865,24 @@

      Declaration

      - +

      Divide x by y and return the quotient.

      +
      +

      Note

      + Use divided(by:) if you also need the remainder. + +
      +

      Declaration

      Swift

      - 
      public init?<T: BinaryFloatingPoint>(exactly source: T)
      + 
      public static func / (x: BigUInt, y: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -865,9 +890,9 @@

      Declaration

    • - - - init(_:) + + + %(_:_:)
      @@ -875,39 +900,34 @@

      Declaration

      - +

      Divide x by y and return the remainder.

      +
      +

      Note

      + Use divided(by:) if you also need the remainder. + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryFloatingPoint>(_ source: T)
      + 
      public static func % (x: BigUInt, y: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Subtraction

    -     -
    -
    • @@ -915,16 +935,10 @@

      Subtraction

      -

      Subtract other from this integer in place, and return a flag indicating if the operation caused an -arithmetic overflow. other is shifted shift digits to the left before being subtracted.

      +

      Divide x by y and store the quotient in x.

      Note

      - If the result indicates an overflow, then self becomes the twos’ complement of the absolute difference. - -
      -
      -

      Complexity

      - O(count) + Use divided(by:) if you also need the remainder.
      @@ -933,12 +947,12 @@

      Subtraction

      Declaration

      Swift

      - 
      public mutating func subtractReportingOverflow(_ b: BigUInt, shiftedBy shift: Int = 0) -> Bool
      + 
      public static func /= (x: inout BigUInt, y: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -946,9 +960,9 @@

      Declaration

    • @@ -956,16 +970,10 @@

      Declaration

      -

      Subtract other from this integer, returning the difference and a flag indicating arithmetic overflow. -other is shifted shift digits to the left before being subtracted.

      +

      Divide x by y and store the remainder in x.

      Note

      - If overflow is true, then the result value is the twos’ complement of the absolute value of the difference. - -
      -
      -

      Complexity

      - O(count) + Use divided(by:) if you also need the remainder.
      @@ -974,22 +982,35 @@

      Declaration

      Declaration

      Swift

      - 
      public func subtractingReportingOverflow(_ other: BigUInt, shiftedBy shift: Int) -> (partialValue: BigUInt, overflow: Bool)
      + 
      public static func %= (x: inout BigUInt, y: BigUInt)
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Exponentiation

    +

    +
    +
    +
    • @@ -997,15 +1018,22 @@

      Declaration

      -

      Subtracts other from self, returning the result and a flag indicating arithmetic overflow.

      +

      Returns this integer raised to the power exponent.

      + +

      This function calculates the result by successively squaring the base while halving the exponent.

      Note

      - When the operation overflows, then partialValue is the twos’ complement of the absolute value of the difference. + This function can be unreasonably expensive for large exponents, which is why exponent is + a simple integer value. If you want to calculate big exponents, you’ll probably need to use + the modulo arithmetic variant. -
      -
      +
      +

      See also

      + BigUInt.power(_:, modulus:) + +

      Complexity

      - O(count) + O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too.
      @@ -1014,12 +1042,16 @@

      Declaration

      Declaration

      Swift

      - 
      public func subtractingReportingOverflow(_ other: BigUInt) -> (partialValue: BigUInt, overflow: Bool)
      + 
      public func power(_ exponent: Int) -> BigUInt
      +
      +

      Return Value

      +

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      +
      - Show on GitHub + Show on GitHub
      @@ -1027,9 +1059,9 @@

      Declaration

    • @@ -1037,16 +1069,12 @@

      Declaration

      -

      Subtract other from this integer in place. -other is shifted shift digits to the left before being subtracted.

      -
      -

      Requires

      - self >= other * 2^shift +

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      -
      +

      Uses the right-to-left binary method.

      Complexity

      - O(count) + O(exponent.count * modulus.count^log2(3)) or somesuch
      @@ -1055,12 +1083,12 @@

      Declaration

      Declaration

      Swift

      - 
      public mutating func subtract(_ other: BigUInt, shiftedBy shift: Int = 0)
      + 
      public func power(_ exponent: BigUInt, modulus: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -1068,9 +1096,9 @@

      Declaration

    • @@ -1078,30 +1106,18 @@

      Declaration

      -

      Subtract b from this integer, and return the difference. -b is shifted shift digits to the left before being subtracted.

      -
      -

      Requires

      - self >= b * 2^shift - -
      -
      -

      Complexity

      - O(count) - -
      - +

      Declaration

      Swift

      - 
      public func subtracting(_ other: BigUInt, shiftedBy shift: Int = 0) -> BigUInt
      + 
      public init?<T>(exactly source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      @@ -1109,9 +1125,9 @@

      Declaration

    • @@ -1119,39 +1135,41 @@

      Declaration

      -

      Decrement this integer by one.

      -
      -

      Requires

      - !isZero - -
      -
      -

      Complexity

      - O(count) - -
      - +

      Declaration

      Swift

      - 
      public mutating func decrement(shiftedBy shift: Int = 0)
      + 
      public init<T>(_ source: T) where T : BinaryFloatingPoint
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Greatest Common Divisor

    +

    +
    +
    +
    • @@ -1159,15 +1177,10 @@

      Declaration

      -

      Subtract b from a and return the result.

      -
      -

      Requires

      - a >= b - -
      +

      Returns the greatest common divisor of self and b.

      Complexity

      - O(a.count) + O(count^2) where count = max(self.count, b.count)
      @@ -1176,12 +1189,12 @@

      Declaration

      Declaration

      Swift

      - 
      public static func -(a: BigUInt, b: BigUInt) -> BigUInt
      + 
      public func greatestCommonDivisor(with b: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -1189,9 +1202,9 @@

      Declaration

    • - - - -=(_:_:) + + + inverse(_:)
      @@ -1199,15 +1212,15 @@

      Declaration

      -

      Subtract b from a and store the result in a.

      +

      Returns the multiplicative inverse of this integer in modulo modulus arithmetic, +or nil if there is no such number.

      Requires

      - a >= b + modulus > 1 -
      -
      +

      Complexity

      - O(a.count) + O(count^3)
      @@ -1216,12 +1229,16 @@

      Declaration

      Declaration

      Swift

      - 
      public static func -=(a: inout BigUInt, b: BigUInt)
      + 
      public func inverse(_ modulus: BigUInt) -> BigUInt?
      +
      +

      Return Value

      +

      If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

      +
      - Show on GitHub + Show on GitHub
      @@ -1230,19 +1247,21 @@

      Declaration

    - - - -

    Division

    -     + + +
    + +

    Hashing

    +

    +
    • @@ -1250,33 +1269,19 @@

      Division

      -

      Divide this integer by y and return the resulting quotient and remainder.

      -
      -

      Requires

      - y > 0 - -
      -
      -

      Complexity

      - O(count^2) - -
      +

      Append this BigUInt to the specified hasher.

      Declaration

      Swift

      - 
      public func quotientAndRemainder(dividingBy y: BigUInt) -> (quotient: BigUInt, remainder: BigUInt)
      + 
      public func hash(into hasher: inout Hasher)
      -
      -

      Return Value

      -

      (quotient, remainder) where quotient = floor(self/y), remainder = self - quotient * y

      -
      - Show on GitHub + Show on GitHub
      @@ -1284,9 +1289,9 @@

      Return Value

    • - - - /(_:_:) + + + init(exactly:)
      @@ -1294,24 +1299,18 @@

      Return Value

      -

      Divide x by y and return the quotient.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func /(x: BigUInt, y: BigUInt) -> BigUInt
      + 
      public init?<T>(exactly source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1319,9 +1318,9 @@

      Declaration

    • - - - %(_:_:) + + + init(_:)
      @@ -1329,24 +1328,18 @@

      Declaration

      -

      Divide x by y and return the remainder.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func %(x: BigUInt, y: BigUInt) -> BigUInt
      + 
      public init<T>(_ source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1354,9 +1347,9 @@

      Declaration

    • @@ -1364,24 +1357,18 @@

      Declaration

      -

      Divide x by y and store the quotient in x.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func /=(x: inout BigUInt, y: BigUInt)
      + 
      public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      @@ -1389,9 +1376,9 @@

      Declaration

    • @@ -1399,38 +1386,28 @@

      Declaration

      -

      Divide x by y and store the remainder in x.

      -
      -

      Note

      - Use divided(by:) if you also need the remainder. - -
      - +

      Declaration

      Swift

      - 
      public static func %=(x: inout BigUInt, y: BigUInt)
      + 
      public init<T>(clamping source: T) where T : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    - +
    +
    +
    + + +
    + +

    Multiplication

    +

    +
    +
    +
    • @@ -1467,18 +1458,24 @@

      Declaration

      - +

      Multiply this big integer by a single word, and store the result in place of the original big integer.

      +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryInteger>(_ source: T)
      + 
      public mutating func multiply(byWord y: Word)
      - Show on GitHub + Show on GitHub
      @@ -1486,9 +1483,9 @@

      Declaration

    • @@ -1496,18 +1493,24 @@

      Declaration

      - +

      Multiply this big integer by a single Word, and return the result.

      +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryInteger>(truncatingIfNeeded source: T)
      + 
      public func multiplied(byWord y: Word) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -1515,9 +1518,9 @@

      Declaration

    • @@ -1525,32 +1528,43 @@

      Declaration

      - +

      Multiply x by y, and add the result to this integer, optionally shifted shift words to the left.

      +
      +

      Note

      + This is the fused multiply/shift/add operation; it is more efficient than doing the components +individually. (The fused operation doesn’t need to allocate space for temporary big integers.) + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public init<T: BinaryInteger>(clamping source: T)
      + 
      public mutating func multiplyAndAdd(_ x: BigUInt, _ y: Word, shiftedBy shift: Int = 0)
      +
      +

      Return Value

      +

      self is set to self + (x * y) << (shift * 2^Word.bitWidth)

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1558,33 +1572,39 @@

      Declaration

      -

      Initialize a new big integer from an integer literal.

      - -
      -
      +

      Multiply this integer by y and return the result.

      +
      +

      Note

      + This uses the naive O(n^2) multiplication algorithm unless both arguments have more than +BigUInt.directMultiplicationLimit words. + +
      +

      Complexity

      + O(n^log2(3)) + +
      + +
      +

      Declaration

      Swift

      - 
      public init(integerLiteral value: UInt64)
      + 
      public func multiplied(by y: BigUInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1592,18 +1612,19 @@

      Declaration

      - +

      Multiplication switches to an asymptotically better recursive algorithm when arguments have more words than this limit.

      +

      Declaration

      Swift

      - 
      public static var isSigned: Bool
      + 
      public static var directMultiplicationLimit: Int
      - Show on GitHub + Show on GitHub
      @@ -1611,9 +1632,9 @@

      Declaration

    • - - - signum() + + + *(_:_:)
      @@ -1621,44 +1642,39 @@

      Declaration

      -

      Returns -1 if this value is negative and 1 if it’s positive; otherwise, 0.

      +

      Multiply a by b and return the result.

      +
      +

      Note

      + This uses the naive O(n^2) multiplication algorithm unless both arguments have more than +BigUInt.directMultiplicationLimit words. + +
      +

      Complexity

      + O(n^log2(3)) + +

      Declaration

      Swift

      - 
      public func signum() -> BigUInt
      + 
      public static func * (x: BigUInt, y: BigUInt) -> BigUInt
      -
      -

      Return Value

      -

      The sign of this number, expressed as an integer of the same type.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Collection-like members

    -     -
    -
    • - - - subscript(_:) + + + *=(_:_:)
      @@ -1666,42 +1682,19 @@

      Collection-like members

      -

      Get or set a digit at a given index.

      -
      -

      Note

      - Unlike a normal collection, it is OK for the index to be greater than or equal to endIndex. -The subscripting getter returns zero for indexes beyond the most significant digit. -Setting these extended digits automatically appends new elements to the underlying digit array. - -
      -
      -

      Requires

      - index >= 0 - -
      -
      -

      Complexity

      - The getter is O(1). The setter is O(1) if the conditions below are true; otherwise it’s O(count). - -
        -
      • The integer’s storage is not shared with another integer
        • -
      • The integer wasn’t created as a slice of another integer
        • -
      • index < count
        • -
      - -
      +

      Multiply a by b and store the result in a.

      Declaration

      Swift

      - 
      subscript(_ index: Int) -> Word
      + 
      public static func *= (a: inout BigUInt, b: BigUInt)
      - Show on GitHub + Show on GitHub
      @@ -1710,19 +1703,21 @@

      Declaration

    - - - -

    Comparison

    -     + + +
    + +

    Primality Testing

    +

    +
    • @@ -1730,24 +1725,19 @@

      Comparison

      -

      Compare a to b and return an NSComparisonResult indicating their order.

      -
      -

      Complexity

      - O(count) - -
      +

      Returns true iff this integer passes the strong probable prime test for the specified base.

      Declaration

      Swift

      - 
      public static func compare(_ a: BigUInt, _ b: BigUInt) -> ComparisonResult
      + 
      public func isStrongProbablePrime(_ base: BigUInt) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -1755,9 +1745,9 @@

      Declaration

    • @@ -1765,24 +1755,29 @@

      Declaration

      -

      Return true iff a is equal to b.

      -
      -

      Complexity

      - O(count) +

      Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.

      -
      +

      This function performs a probabilistic Miller-Rabin Primality Test, consisting of rounds iterations, +each calculating the strong probable prime test for a random base. The number of rounds is 10 by default, +but you may specify your own choice.

      + +

      To speed things up, the function checks if self is divisible by the first few prime numbers before +diving into (slower) Miller-Rabin testing.

      + +

      Also, when self is less than 82 bits wide, isPrime does a deterministic test that is guaranteed to +return a correct result.

      Declaration

      Swift

      - 
      public static func ==(a: BigUInt, b: BigUInt) -> Bool
      + 
      public func isPrime(rounds: Int = 10) -> Bool
      - Show on GitHub + Show on GitHub
      @@ -1790,9 +1785,9 @@

      Declaration

    • @@ -1800,45 +1795,64 @@

      Declaration

      -

      Return true iff a is less than b.

      -
      -

      Complexity

      - O(count) - -
      +

      Create a big unsigned integer consisting of width uniformly distributed random bits.

      Declaration

      Swift

      - 
      public static func <(a: BigUInt, b: BigUInt) -> Bool
      + 
      public static func randomInteger<RNG>(withMaximumWidth width: Int, using generator: inout RNG) -> BigUInt where RNG : RandomNumberGenerator
      +
      +

      Parameters

      + + + + + + + + + + + +
      + + width + + +
      +

      The maximum number of one bits in the result.

      +
      +
      + + generator + + +
      +

      The source of randomness.

      +
      +
      +
      +
      +

      Return Value

      +

      A big unsigned integer less than 1 << width.

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    String Conversion

    -     -
    -
    • @@ -1846,11 +1860,10 @@

      String Conversion

      -

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by -letters from the English alphabet.

      -
      -

      Requires

      - radix > 1 && radix < 36 +

      Create a big unsigned integer consisting of width uniformly distributed random bits.

      +
      +

      Note

      +

      I use a SystemRandomGeneratorGenerator as the source of randomness.

      @@ -1859,16 +1872,35 @@

      String Conversion

      Declaration

      Swift

      - 
      public init?(_ text: String, radix: Int = 10)
      + 
      public static func randomInteger(withMaximumWidth width: Int) -> BigUInt
      +
      +

      Parameters

      + + + + + + + +
      + + width + + +
      +

      The maximum number of one bits in the result.

      +
      +
      +

      Return Value

      -

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      +

      A big unsigned integer less than 1 << width.

      - Show on GitHub + Show on GitHub
      @@ -1876,9 +1908,9 @@

      Return Value

    • @@ -1886,33 +1918,69 @@

      Return Value

      -

      Undocumented

      +

      Create a big unsigned integer consisting of width-1 uniformly distributed random bits followed by a one bit.

      +
      +

      Note

      +

      If width is zero, the result is zero.

      + +

      Declaration

      Swift

      - 
      public struct BigUInt: UnsignedInteger
      + 
      public static func randomInteger<RNG>(withExactWidth width: Int, using generator: inout RNG) -> BigUInt where RNG : RandomNumberGenerator
      +
      +

      Parameters

      + + + + + + + + + + + +
      + + width + + +
      +

      The number of bits required to represent the answer.

      +
      +
      + + generator + + +
      +

      The source of randomness.

      +
      +
      +
      +
      +

      Return Value

      +

      A random big unsigned integer whose width is width.

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -1920,20 +1988,32 @@

      Declaration

      -

      Initialize a new big integer from a Unicode scalar. -The scalar must represent a decimal digit.

      +

      Create a big unsigned integer consisting of width-1 uniformly distributed random bits followed by a one bit.

      +
      +

      Note

      + If width is zero, the result is zero. + +
      +

      Note

      +

      I use a SystemRandomGeneratorGenerator as the source of randomness.

      + +

      Declaration

      Swift

      - 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      + 
      public static func randomInteger(withExactWidth width: Int) -> BigUInt
      +
      +

      Return Value

      +

      A random big unsigned integer whose width is width.

      +
      - Show on GitHub + Show on GitHub
      @@ -1941,9 +2021,9 @@

      Declaration

    • @@ -1951,20 +2031,59 @@

      Declaration

      -

      Initialize a new big integer from an extended grapheme cluster. -The cluster must consist of a decimal digit.

      +

      Create a uniformly distributed random unsigned integer that’s less than the specified limit.

      +
      +

      Precondition

      +

      limit > 0.

      + +

      Declaration

      Swift

      - 
      public init(extendedGraphemeClusterLiteral value: String)
      + 
      public static func randomInteger<RNG>(lessThan limit: BigUInt, using generator: inout RNG) -> BigUInt where RNG : RandomNumberGenerator
      +
      +

      Parameters

      + + + + + + + + + + + +
      + + limit + + +
      +

      The upper bound on the result.

      +
      +
      + + generator + + +
      +

      The source of randomness.

      +
      +
      +
      +
      +

      Return Value

      +

      A random big unsigned integer that is less than limit.

      +
      - Show on GitHub + Show on GitHub
      @@ -1972,9 +2091,9 @@

      Declaration

    • @@ -1982,20 +2101,51 @@

      Declaration

      -

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. -The string must contain only decimal digits.

      +

      Create a uniformly distributed random unsigned integer that’s less than the specified limit.

      +
      +

      Precondition

      + limit > 0. + +
      +

      Note

      +

      I use a SystemRandomGeneratorGenerator as the source of randomness.

      + +

      Declaration

      Swift

      - 
      public init(stringLiteral value: StringLiteralType)
      + 
      public static func randomInteger(lessThan limit: BigUInt) -> BigUInt
      +
      +

      Parameters

      + + + + + + + +
      + + limit + + +
      +

      The upper bound on the result.

      +
      +
      +
      +
      +

      Return Value

      +

      A random big unsigned integer that is less than limit.

      +
      - Show on GitHub + Show on GitHub
      @@ -2003,13 +2153,22 @@

      Declaration

    +
    + + +
    + +

    Shift Operators

    +

    +
    +
    • - - - description + + + >>=(_:_:)
      @@ -2017,33 +2176,29 @@

      Declaration

      -

      Return the decimal representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var description: String
      + 
      public static func >>= <Other>(lhs: inout BigUInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -2051,40 +2206,29 @@

      Declaration

      -

      Return the playground quick look representation of this integer.

      +

      Undocumented

      Declaration

      Swift

      - 
      public var customPlaygroundQuickLook: PlaygroundQuickLook
      + 
      public static func <<= <Other>(lhs: inout BigUInt, rhs: Other) where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    NSData Conversion

    -     -
    -
    • - - - init(_:) + + + >>(_:_:)
      @@ -2099,12 +2243,12 @@

      NSData Conversion

      Declaration

      Swift

      - 
      public struct BigUInt: UnsignedInteger
      + 
      public static func >> <Other>(lhs: BigUInt, rhs: Other) -> BigUInt where Other : BinaryInteger
      - Show on GitHub + Show on GitHub
    @@ -2112,9 +2256,9 @@

    Declaration

  • - - - init(_:) + + + <<(_:_:)
    @@ -2122,30 +2266,42 @@

    Declaration

    -

    Initializes an integer from the bits stored inside a piece of Data. -The data is assumed to be in network (big-endian) byte order.

    +

    Undocumented

    Declaration

    Swift

    - 
    public init(_ data: Data)
    + 
    public static func << <Other>(lhs: BigUInt, rhs: Other) -> BigUInt where Other : BinaryInteger
    - Show on GitHub + Show on GitHub
    • + + +
    +
    + + +
    + +

    Square Root

    +

    +
    +
    +
    • @@ -2153,40 +2309,33 @@

      Declaration

      -

      Return a Data value that contains the base-256 representation of this integer, in network (big-endian) byte order.

      +

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      Declaration

      Swift

      - 
      public func serialize() -> Data
      + 
      public func squareRoot() -> BigUInt
      +
      +

      Return Value

      +

      floor(sqrt(self))

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Multiplication

    -     -
    -
    • @@ -2194,24 +2343,19 @@

      Multiplication

      -

      Multiply this big integer by a single word, and store the result in place of the original big integer.

      -
      -

      Complexity

      - O(count) - -
      +

      A type that can represent the distance between two values ofa BigUInt.

      Declaration

      Swift

      - 
      public mutating func multiply(byWord y: Word)
      + 
      public typealias Stride = BigInt
      - Show on GitHub + Show on GitHub
      @@ -2219,9 +2363,9 @@

      Declaration

    • @@ -2229,24 +2373,19 @@

      Declaration

      -

      Multiply this big integer by a single Word, and return the result.

      -
      -

      Complexity

      - O(count) - -
      +

      Adds n to self and returns the result. Traps if the result would be less than zero.

      Declaration

      Swift

      - 
      public func multiplied(byWord y: Word) -> BigUInt
      + 
      public func advanced(by n: BigInt) -> BigUInt
      - Show on GitHub + Show on GitHub
      @@ -2254,9 +2393,9 @@

      Declaration

    • @@ -2264,44 +2403,42 @@

      Declaration

      -

      Multiply x by y, and add the result to this integer, optionally shifted shift words to the left.

      -
      -

      Note

      - This is the fused multiply/shift/add operation; it is more efficient than doing the components -individually. (The fused operation doesn’t need to allocate space for temporary big integers.) - -
      -
      -

      Complexity

      - O(count) - -
      +

      Returns the (potentially negative) difference between self and other as a BigInt. Never traps.

      Declaration

      Swift

      - 
      public mutating func multiplyAndAdd(_ x: BigUInt, _ y: Word, shiftedBy shift: Int = 0)
      + 
      public func distance(to other: BigUInt) -> BigInt
      -
      -

      Return Value

      -

      self is set to self + (x * y) << (shift * 2^Word.bitWidth)

      -
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    String Conversion

    +

    +
    +
    +
    • @@ -2309,16 +2446,11 @@

      Return Value

      -

      Multiply this integer by y and return the result.

      -
      -

      Note

      - This uses the naive O(n^2) multiplication algorithm unless both arguments have more than -BigUInt.directMultiplicationLimit words. - -
      -
      -

      Complexity

      - O(n^log2(3)) +

      Initialize a big integer from an ASCII representation in a given radix. Numerals above 9 are represented by +letters from the English alphabet.

      +
      +

      Requires

      + radix > 1 && radix < 36
      @@ -2327,12 +2459,16 @@

      Return Value

      Declaration

      Swift

      - 
      public func multiplied(by y: BigUInt) -> BigUInt
      + 
      public init?<S>(_ text: S, radix: Int = 10) where S : StringProtocol
      +
      +

      Return Value

      +

      The integer represented by text, or nil if text contains a character that does not represent a numeral in radix.

      +
      - Show on GitHub + Show on GitHub
      @@ -2340,9 +2476,9 @@

      Declaration

    • @@ -2350,19 +2486,20 @@

      Declaration

      -

      Multiplication switches to an asymptotically better recursive algorithm when arguments have more words than this limit.

      +

      Initialize a new big integer from a Unicode scalar. +The scalar must represent a decimal digit.

      Declaration

      Swift

      - 
      public static var directMultiplicationLimit: Int = 1024
      + 
      public init(unicodeScalarLiteral value: UnicodeScalar)
      - Show on GitHub + Show on GitHub
      @@ -2370,9 +2507,9 @@

      Declaration

    • @@ -2380,30 +2517,20 @@

      Declaration

      -

      Multiply a by b and return the result.

      -
      -

      Note

      - This uses the naive O(n^2) multiplication algorithm unless both arguments have more than -BigUInt.directMultiplicationLimit words. - -
      -
      -

      Complexity

      - O(n^log2(3)) - -
      +

      Initialize a new big integer from an extended grapheme cluster. +The cluster must consist of a decimal digit.

      Declaration

      Swift

      - 
      public static func *(x: BigUInt, y: BigUInt) -> BigUInt
      + 
      public init(extendedGraphemeClusterLiteral value: String)
      - Show on GitHub + Show on GitHub
      @@ -2411,9 +2538,9 @@

      Declaration

    • @@ -2421,33 +2548,30 @@

      Declaration

      -

      Multiply a by b and store the result in a.

      +

      Initialize a new big integer from a decimal number represented by a string literal of arbitrary length. +The string must contain only decimal digits.

      Declaration

      Swift

      - 
      public static func *=(a: inout BigUInt, b: BigUInt)
      + 
      public init(stringLiteral value: StringLiteralType)
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - Stride + + + description
      @@ -2455,19 +2579,19 @@

      Declaration

      -

      A type that can represent the distance between two values ofa BigUInt.

      +

      Return the decimal representation of this integer.

      Declaration

      Swift

      - 
      public typealias Stride = BigInt
      + 
      public var description: String { get }
      - Show on GitHub + Show on GitHub
      @@ -2475,9 +2599,9 @@

      Declaration

    • @@ -2485,29 +2609,42 @@

      Declaration

      -

      Adds n to self and returns the result. Traps if the result would be less than zero.

      +

      Return the playground quick look representation of this integer.

      Declaration

      Swift

      - 
      public func advanced(by n: BigInt) -> BigUInt
      + 
      public var playgroundDescription: Any { get }
      - Show on GitHub + Show on GitHub
      • +
    +
    +
    +
    + + +
    + +

    Subtraction

    +

    +
    +
    +
    • @@ -2515,40 +2652,39 @@

      Declaration

      -

      Returns the (potentially negative) difference between self and other as a BigInt. Never traps.

      +

      Subtract other from this integer in place, and return a flag indicating if the operation caused an +arithmetic overflow. other is shifted shift digits to the left before being subtracted.

      +
      +

      Note

      + If the result indicates an overflow, then self becomes the twos’ complement of the absolute difference. + +
      +

      Complexity

      + O(count) + +

      Declaration

      Swift

      - 
      public func distance(to other: BigUInt) -> BigInt
      + 
      public mutating func subtractReportingOverflow(_ b: BigUInt, shiftedBy shift: Int = 0) -> Bool
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Shift Operators

    -     -
    -
    • @@ -2556,18 +2692,29 @@

      Shift Operators

      - +

      Subtract other from this integer, returning the difference and a flag indicating arithmetic overflow. +other is shifted shift digits to the left before being subtracted.

      +
      +

      Note

      + If overflow is true, then the result value is the twos’ complement of the absolute value of the difference. + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func >>=<Other: BinaryInteger>(lhs: inout BigUInt, rhs: Other)
      + 
      public func subtractingReportingOverflow(_ other: BigUInt, shiftedBy shift: Int) -> (partialValue: BigUInt, overflow: Bool)
      - Show on GitHub + Show on GitHub
      @@ -2575,9 +2722,9 @@

      Declaration

    • @@ -2585,18 +2732,28 @@

      Declaration

      - +

      Subtracts other from self, returning the result and a flag indicating arithmetic overflow.

      +
      +

      Note

      + When the operation overflows, then partialValue is the twos’ complement of the absolute value of the difference. + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func <<=<Other: BinaryInteger>(lhs: inout BigUInt, rhs: Other)
      + 
      public func subtractingReportingOverflow(_ other: BigUInt) -> (partialValue: BigUInt, overflow: Bool)
      - Show on GitHub + Show on GitHub
      @@ -2604,9 +2761,9 @@

      Declaration

    • @@ -2614,18 +2771,29 @@

      Declaration

      - +

      Subtract other from this integer in place. +other is shifted shift digits to the left before being subtracted.

      +
      +

      Requires

      + self >= other * 2^shift + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func >><Other: BinaryInteger>(lhs: BigUInt, rhs: Other) -> BigUInt
      + 
      public mutating func subtract(_ other: BigUInt, shiftedBy shift: Int = 0)
      - Show on GitHub + Show on GitHub
      @@ -2633,9 +2801,9 @@

      Declaration

    • @@ -2643,39 +2811,39 @@

      Declaration

      - +

      Subtract b from this integer, and return the difference. +b is shifted shift digits to the left before being subtracted.

      +
      +

      Requires

      + self >= b * 2^shift + +
      +

      Complexity

      + O(count) + +
      +

      Declaration

      Swift

      - 
      public static func <<<Other: BinaryInteger>(lhs: BigUInt, rhs: Other) -> BigUInt
      + 
      public func subtracting(_ other: BigUInt, shiftedBy shift: Int = 0) -> BigUInt
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Greatest Common Divisor

    -     -
    -
    • @@ -2683,10 +2851,14 @@

      Greatest Common Divisor

      -

      Returns the greatest common divisor of self and b.

      -
      +

      Decrement this integer by one.

      +
      +

      Requires

      + !isZero + +

      Complexity

      - O(count^2) where count = max(self.count, b.count) + O(count)
      @@ -2695,12 +2867,12 @@

      Greatest Common Divisor

      Declaration

      Swift

      - 
      public func greatestCommonDivisor(with b: BigUInt) -> BigUInt
      + 
      public mutating func decrement(shiftedBy shift: Int = 0)
      - Show on GitHub + Show on GitHub
      @@ -2708,9 +2880,9 @@

      Declaration

    • - - - inverse(_:) + + + -(_:_:)
      @@ -2718,16 +2890,14 @@

      Declaration

      -

      Returns the multiplicative inverse of this integer in modulo modulus arithmetic, -or nil if there is no such number.

      +

      Subtract b from a and return the result.

      Requires

      - modulus > 1 + a >= b -
      -
      +

      Complexity

      - O(count^3) + O(a.count)
      @@ -2736,30 +2906,22 @@

      Declaration

      Declaration

      Swift

      - 
      public func inverse(_ modulus: BigUInt) -> BigUInt?
      + 
      public static func - (a: BigUInt, b: BigUInt) -> BigUInt
      -
      -

      Return Value

      -

      If gcd(self, modulus) == 1, the value returned is an integer a < modulus such that (a * self) % modulus == 1. If self and modulus aren’t coprime, the return value is nil.

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • - - - squareRoot() + + + -=(_:_:)
      @@ -2767,37 +2929,38 @@

      Return Value

      -

      Returns the integer square root of a big integer; i.e., the largest integer whose square isn’t greater than value.

      +

      Subtract b from a and store the result in a.

      +
      +

      Requires

      + a >= b + +
      +

      Complexity

      + O(a.count) + +

      Declaration

      Swift

      - 
      public func squareRoot() -> BigUInt
      + 
      public static func -= (a: inout BigUInt, b: BigUInt)
      -
      -

      Return Value

      -

      floor(sqrt(self))

      -
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    • @@ -2805,18 +2968,19 @@

      Return Value

      - +

      Undocumented

      +

      Declaration

      Swift

      - 
      public init(from decoder: Decoder) throws
      + 
      public subscript(bitAt index: Int) -> Bool { get set }
      - Show on GitHub + Show on GitHub
      @@ -2824,9 +2988,9 @@

      Declaration

    • - - - encode(to:) + + + bitWidth
      @@ -2834,39 +2998,38 @@

      Declaration

      - +

      The minimum number of bits required to represent this integer in binary.

      +
      +

      Complexity

      + O(1) + +
      +

      Declaration

      Swift

      - 
      public func encode(to encoder: Encoder) throws
      + 
      public var bitWidth: Int { get }
      +
      +

      Return Value

      +

      floor(log2(2 * self + 1))

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Exponentiation

    -     -
    -
    • @@ -2874,24 +3037,19 @@

      Exponentiation

      -

      Returns this integer raised to the power exponent.

      - -

      This function calculates the result by successively squaring the base while halving the exponent.

      +

      The number of leading zero bits in the binary representation of this integer in base 2^(Word.bitWidth). +This is useful when you need to normalize a BigUInt such that the top bit of its most significant word is 1.

      Note

      - This function can be unreasonably expensive for large exponents, which is why exponent is - a simple integer value. If you want to calculate big exponents, you’ll probably need to use - the modulo arithmetic variant. + 0 is considered to have zero leading zero bits. -
      -
      +

      See also

      - BigUInt.power(_:, modulus:) + width -
      -
      +

      Complexity

      - O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too. + O(1)
      @@ -2900,16 +3058,16 @@

      Exponentiation

      Declaration

      Swift

      - 
      public func power(_ exponent: Int) -> BigUInt
      + 
      public var leadingZeroBitCount: Int { get }

      Return Value

      -

      1 if exponent == 0, otherwise self raised to exponent. (This implies that 0.power(0) == 1.)

      +

      A value in 0...(Word.bitWidth - 1).

      - Show on GitHub + Show on GitHub
      @@ -2917,9 +3075,9 @@

      Return Value

    • @@ -2927,12 +3085,14 @@

      Return Value

      -

      Returns the remainder of this integer raised to the power exponent in modulo arithmetic under modulus.

      +

      The number of trailing zero bits in the binary representation of this integer.

      +
      +

      Note

      + 0 is considered to have zero trailing zero bits. -

      Uses the right-to-left binary method.

      -
      +

      Complexity

      - O(exponent.count * modulus.count^log2(3)) or somesuch + O(count)
      @@ -2941,33 +3101,26 @@

      Return Value

      Declaration

      Swift

      - 
      public func power(_ exponent: BigUInt, modulus: BigUInt) -> BigUInt
      + 
      public var trailingZeroBitCount: Int { get }
      +
      +

      Return Value

      +

      A value in 0...width.

      +
      - Show on GitHub + Show on GitHub
      • -
    -
    -
    -
    - - - -

    Addition

    -     -
    -
    • - - - +(_:_:) + + + Words
      @@ -2975,24 +3128,19 @@

      Addition

      -

      Add a and b together and return the result.

      -
      -

      Complexity

      - O(max(a.count, b.count)) - -
      - + + See more

      Declaration

      Swift

      - 
      public static func +(a: BigUInt, b: BigUInt) -> BigUInt
      + 
      public struct Words : RandomAccessCollection
      - Show on GitHub + Show on GitHub
      @@ -3000,9 +3148,9 @@

      Declaration

    • - - - +=(_:_:) + + + words
      @@ -3010,24 +3158,48 @@

      Declaration

      -

      Add a and b together, and store the sum in a.

      -
      -

      Complexity

      - O(max(a.count, b.count)) + +
      +
      +

      Declaration

      +
      +

      Swift

      + 
      public var words: Words { get }
      -
      +
      +
      +
      + Show on GitHub +
      +
      +
      +
      • +
    • +
      + + + + init(words:) + +
      +
      +
      +
      +
      +
      +

      Undocumented

      Declaration

      Swift

      - 
      public static func +=(a: inout BigUInt, b: BigUInt)
      + 
      public init<Words>(words: Words) where Words : Sequence, Words.Element == BigUInt.Word
      - Show on GitHub + Show on GitHub
      @@ -3040,8 +3212,8 @@

      Declaration

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt/Words.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt/Words.html index b0dda68e0..0c13a2f7a 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt/Words.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/Structs/BigUInt/Words.html @@ -21,9 +21,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -40,7 +40,7 @@

    - + Install in Dash @@ -92,15 +92,19 @@

    -
    +

    Words

    - 
    public struct Words: RandomAccessCollection
    + + 
    public struct Words : RandomAccessCollection
    +
    + Show on GitHub +
    @@ -111,9 +115,9 @@

    Words

  • @@ -127,12 +131,12 @@

    Words

    Declaration

    Swift

    - 
    public var startIndex: Int
    + 
    public var startIndex: Int { get }
    - Show on GitHub + Show on GitHub
    @@ -140,9 +144,38 @@

    Declaration

  • - + - endIndex + endIndex + +
    +
    +
    +
    +
    +
    + +
    +
    +

    Declaration

    +
    +

    Swift

    + 
    public var endIndex: Int { get }
    + +
    +
    +
    + Show on GitHub +
    +
    +
    +
    • +
  • +
    + + + + subscript(_:)
    @@ -156,12 +189,12 @@

    Declaration

    Declaration

    Swift

    - 
    public var endIndex: Int
    + 
    public subscript(index: Int) -> Word { get }
    - Show on GitHub + Show on GitHub
    @@ -174,8 +207,8 @@

    Declaration

    • -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

    diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/css/jazzy.css b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/css/jazzy.css index c83db5bfc..ff59f5f86 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/css/jazzy.css +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/css/jazzy.css @@ -63,6 +63,10 @@ a { a:hover, a:focus { outline: 0; text-decoration: underline; } + a.discouraged { + text-decoration: line-through; } + a.discouraged:hover, a.discouraged:focus { + text-decoration: underline line-through; } table { background: #fff; @@ -90,10 +94,10 @@ pre { code { font-family: Consolas, "Liberation Mono", Menlo, Courier, monospace; } -p > code, li > code { +.item-container p > code, .item-container li > code, .top-matter p > code, .top-matter li > code { background: #f7f7f7; padding: .2em; } - p > code:before, p > code:after, li > code:before, li > code:after { + .item-container p > code:before, .item-container p > code:after, .item-container li > code:before, .item-container li > code:after, .top-matter p > code:before, .top-matter p > code:after, .top-matter li > code:before, .top-matter li > code:after { letter-spacing: -.2em; content: "\00a0"; } @@ -107,7 +111,6 @@ pre code { @media (min-width: 768px) { .content-wrapper { flex-direction: row; } } - .header { display: flex; padding: 8px; @@ -153,7 +156,6 @@ pre code { word-wrap: normal; background: #fbfbfb; border-right: 1px solid #ddd; } } - .nav-groups { list-style-type: none; padding-left: 0; } @@ -184,7 +186,6 @@ pre code { order: 2; flex: 1; padding-bottom: 60px; } } - .section { padding: 0 32px; border-bottom: 1px solid #ddd; } @@ -197,6 +198,8 @@ pre code { .section-name { color: #666; display: block; } + .section-name p { + margin-bottom: inherit; } .declaration .highlight { overflow-x: initial; @@ -215,6 +218,22 @@ pre code { content: ""; display: block; } +.section-name-container { + position: relative; } + .section-name-container .section-name-link { + position: absolute; + top: 0; + left: 0; + bottom: 0; + right: 0; + margin-bottom: 0; } + .section-name-container .section-name { + position: relative; + pointer-events: none; + z-index: 1; } + .section-name-container .section-name a { + pointer-events: auto; } + .item-container { padding: 0; } @@ -225,9 +244,11 @@ pre code { .item a[name]:before { content: ""; display: block; } - .item .token { + .item .token, .item .direct-link { + display: inline-block; + text-indent: -20px; padding-left: 3px; - margin-left: 0px; + margin-left: 20px; font-size: 1rem; } .item .declaration-note { font-size: .85em; @@ -287,9 +308,9 @@ pre code { .language .aside-title { color: #4183c4; } -.aside-warning { +.aside-warning, .aside-deprecated, .aside-unavailable { border-left: 5px solid #ff6666; } - .aside-warning .aside-title { + .aside-warning .aside-title, .aside-deprecated .aside-title, .aside-unavailable .aside-title { color: #ff0000; } .graybox { @@ -325,6 +346,7 @@ pre code { html.dash .header, html.dash .breadcrumbs, html.dash .navigation { display: none; } + html.dash .height-container { display: block; } @@ -338,14 +360,17 @@ form[role=search] input { border-radius: 1em; } .loading form[role=search] input { background: white url(../img/spinner.gif) center right 4px no-repeat; } + form[role=search] .tt-menu { margin: 0; min-width: 300px; background: #fbfbfb; color: #333; border: 1px solid #ddd; } + form[role=search] .tt-highlight { font-weight: bold; } + form[role=search] .tt-suggestion { font: 16px/1.7 "Helvetica Neue", Helvetica, Arial, sans-serif; padding: 0 8px; } @@ -358,11 +383,13 @@ form[role=search] .tt-suggestion { font-weight: normal; font-size: 0.9em; padding-left: 16px; } + form[role=search] .tt-suggestion:hover, form[role=search] .tt-suggestion.tt-cursor { cursor: pointer; background-color: #4183c4; color: #fff; } + form[role=search] .tt-suggestion:hover .doc-parent-name, form[role=search] .tt-suggestion.tt-cursor .doc-parent-name { color: #fff; } diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/index.html b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/index.html index 15361d37f..cb588bb2b 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/index.html +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/index.html @@ -20,9 +20,9 @@

    - BigInt Docs + BigInt v5.2.1 Docs - (92% documented) + (85% documented)

    @@ -39,7 +39,7 @@

    - + Install in Dash @@ -91,7 +91,7 @@

    -
    +

    BigInt

    @@ -115,12 +115,13 @@ -

    Swift 3 +

    Swift 5 License Platform

    -

    Build Status +

    Build Status Code Coverage +jazzy Carthage compatible Version

    Overview

    @@ -128,16 +129,16 @@

    Overview<

    This repository provides integer types of arbitrary width implemented in 100% pure Swift. The underlying representation is in base 2^64, using Array<UInt64>.

    -

    This module is handy when you need an integer type that’s wider than UIntMax, but -you don’t want to add The GNU Multiple Precision Arithmetic Library +

    This module is handy when you need an integer type that’s wider than UIntMax, but +you don’t want to add The GNU Multiple Precision Arithmetic Library as a dependency.

    -

    Two big integer types are included: BigUInt and BigInt, +

    Two big integer types are included: BigUInt and BigInt, the latter being the signed variant. -Both of these are Swift structs with copy-on-write value semantics, and they can be used much +Both of these are Swift structs with copy-on-write value semantics, and they can be used much like any other integer type.

    -

    The library provides implementations for some of the most frequently useful functions on +

    The library provides implementations for some of the most frequently useful functions on big integers, including

    -

    © 2016 Károly Lőrentey. (Last updated: 2017-10-10)

    -

    Generated by jazzy ♪♫ v0.8.4, a Realm project.

    +

    © 2020 Károly Lőrentey. (Last updated: 2020-12-15)

    +

    Generated by jazzy ♪♫ v0.13.6, a Realm project.

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hash-change, open any targetted item +function openCurrentItemIfClosed() { + if (window.jazzy.docset) { + return; } -}); + var $link = $(`a[name="${location.hash.substring(1)}"]`).nextAll('.token'); + $content = itemLinkToContent($link); + if ($content.is(':hidden')) { + toggleItem($link, $content); + } +} -// On token click, toggle its discussion and animate token.marginLeft -$(".token").click(function(event) { +$(openCurrentItemIfClosed); +$(window).on('hashchange', openCurrentItemIfClosed); + +// On item link ('token') click, toggle its discussion +$('.token').on('click', function(event) { if (window.jazzy.docset) { return; } - var link = $(this); - var animationDuration = 300; - $content = link.parent().parent().next(); - $content.slideToggle(animationDuration); + var $link = $(this); + toggleItem($link, itemLinkToContent($link)); // Keeps the document from jumping to the hash. - var href = $(this).attr('href'); + var href = $link.attr('href'); if (history.pushState) { history.pushState({}, '', href); } else { @@ -36,8 +51,20 @@ $(".token").click(function(event) { event.preventDefault(); }); -// Dumb down quotes within code blocks that delimit strings instead of quotations -// https://github.com/realm/jazzy/issues/714 -$("code q").replaceWith(function () { - return ["\"", $(this).contents(), "\""]; +// Clicks on links to the current, closed, item need to open the item +$("a:not('.token')").on('click', function() { + if (location == this.href) { + openCurrentItemIfClosed(); + } }); + +// KaTeX rendering +if ("katex" in window) { + $($('.math').each( (_, element) => { + katex.render(element.textContent, element, { + displayMode: $(element).hasClass('m-block'), + throwOnError: false, + trust: true + }); + })) +} diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jazzy.search.js b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jazzy.search.js index 54be83cf7..e3d1ab905 100644 --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jazzy.search.js +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jazzy.search.js @@ -1,9 +1,4 @@ $(function(){ - var searchIndex = lunr(function() { - this.ref('url'); - this.field('name'); - }); - var $typeahead = $('[data-typeahead]'); var $form = $typeahead.parents('form'); var searchURL = $form.attr('action'); @@ -26,21 +21,34 @@ $(function(){ $form.addClass('loading'); $.getJSON(searchURL).then(function(searchData) { - $.each(searchData, function (url, doc) { - searchIndex.add({url: url, name: doc.name}); + const searchIndex = lunr(function() { + this.ref('url'); + this.field('name'); + this.field('abstract'); + for (const [url, doc] of Object.entries(searchData)) { + this.add({url: url, name: doc.name, abstract: doc.abstract}); + } }); $typeahead.typeahead( { highlight: true, - minLength: 3 + minLength: 3, + autoselect: true }, { limit: 10, display: displayTemplate, templates: { suggestion: suggestionTemplate }, source: function(query, sync) { - var results = searchIndex.search(query).map(function(result) { + const lcSearch = query.toLowerCase(); + const results = searchIndex.query(function(q) { + q.term(lcSearch, { boost: 100 }); + q.term(lcSearch, { + boost: 10, + wildcard: lunr.Query.wildcard.TRAILING + }); + }).map(function(result) { var doc = searchData[result.ref]; doc.url = result.ref; return doc; diff --git a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jquery.min.js b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jquery.min.js old mode 100755 new mode 100644 index ab28a2472..b0614034a --- a/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jquery.min.js +++ b/Carthage/Checkouts/BigInt/docs/docsets/BigInt.docset/Contents/Resources/Documents/js/jquery.min.js @@ -1,4 +1,2 @@ -/*! jQuery v1.11.1 | (c) 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