Added FloatingPoint stubs to Failable<FloatingPoint, T> type

Sources/Validation/Failable+Helpers/Failable+FloatingPoint.swift

@@ -0,0 +1,563 @@
+extension Failable where T: FloatingPoint {
+    
+    // MARK: - Typealiases
+    
+    /// See [`FloatingPoint.Exponent`](https://developer.apple.com/documentation/swift/floatingpoint/1848224-exponent).
+    public typealias Exponent = T.Exponent
+    
+    
+    // MARK: - Initializers
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641558-init).
+    public init(_ value: Int8)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641150-init).
+    public init(_ value: Int16)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641192-init).
+    public init(_ value: Int32)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641208-init).
+    public init(_ value: Int64)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641277-init).
+    public init(_ value: UInt8)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641505-init).
+    public init(_ value: UInt16)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641406-init).
+    public init(_ value: UInt32)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641403-init).
+    public init(_ value: UInt64)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641530-init).
+    public init(_ value: UInt)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1641560-init).
+    public init(_ value: Int)throws {
+        let t = T(value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(exactly:)`](https://developer.apple.com/documentation/swift/floatingpoint/2964416-init).
+    public init?<Source>(exactly value: Source) where Source : BinaryInteger {
+        guard let t = T(exactly: value) else { return nil }
+        try? self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(sign:exponent:significand:)`](https://developer.apple.com/documentation/swift/floatingpoint/1845755-init).
+    public init(sign: FloatingPointSign, exponent: Exponent, significand: Failable<T, Validations>)throws {
+        let t = T(sign: sign, exponent: exponent, significand: significand.value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(signOf:magnitudeOf:)`](https://developer.apple.com/documentation/swift/floatingpoint/1849294-init).
+    public init(signOf: Failable<T, Validations>, magnitudeOf: Failable<T, Validations>)throws {
+        let t = T(signOf: signOf.value, magnitudeOf: magnitudeOf.value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(sign:exponent:significand:)`](https://developer.apple.com/documentation/swift/floatingpoint/1845755-init).
+    public init<V>(sign: FloatingPointSign, exponent: Exponent, significand: Failable<T, V>)throws {
+        let t = T(sign: sign, exponent: exponent, significand: significand.value)
+        try self.init(t)
+    }
+    
+    /// See [`FloatingPoint.init(signOf:magnitudeOf:)`](https://developer.apple.com/documentation/swift/floatingpoint/1849294-init).
+    public init<V1, V2>(signOf: Failable<T, V1>, magnitudeOf: Failable<T, V2>)throws {
+        let t = T(signOf: signOf.value, magnitudeOf: magnitudeOf.value)
+        try self.init(t)
+    }
+    
+    
+    // MARK: - Properties
+    
+    /// See [`FloatingPoint.exponent`](https://developer.apple.com/documentation/swift/floatingpoint/1846275-exponent).
+    public var exponent: Exponent {
+        return self.value.exponent
+    }
+    
+    /// See [`FloatingPoint.floatingPointClass`](https://developer.apple.com/documentation/swift/floatingpoint/3017961-floatingpointclass).
+    public var floatingPointClass: FloatingPointClassification {
+        return self.value.floatingPointClass
+    }
+    
+    /// See [`FloatingPoint.isCanonical`](https://developer.apple.com/documentation/swift/floatingpoint/1847929-iscanonical).
+    public var isCanonical: Bool {
+        return self.value.isCanonical
+    }
+    
+    /// See [`FloatingPoint.isFinite`](https://developer.apple.com/documentation/swift/floatingpoint/1641190-isfinite).
+    public var isFinite: Bool {
+        return self.value.isFinite
+    }
+    
+    /// See [`FloatingPoint.isInfinite`](https://developer.apple.com/documentation/swift/floatingpoint/1641669-isinfinite).
+    public var isInfinite: Bool {
+        return self.value.isInfinite
+    }
+    
+    /// See [`FloatingPoint.isNaN`](https://developer.apple.com/documentation/swift/floatingpoint/1641763-isnan).
+    public var isNaN: Bool {
+        return self.value.isNaN
+    }
+    
+    /// See [`FloatingPoint.isNormal`](https://developer.apple.com/documentation/swift/floatingpoint/1641394-isnormal).
+    public var isNormal: Bool {
+        return self.value.isNormal
+    }
+    
+    /// See [`FloatingPoint.isSignalingNaN`](https://developer.apple.com/documentation/swift/floatingpoint/1847971-issignalingnan).
+    public var isSignalingNaN: Bool {
+        return self.value.isSignalingNaN
+    }
+    
+    /// See [`FloatingPoint.isSubnormal`](https://developer.apple.com/documentation/swift/floatingpoint/1641181-issubnormal).
+    public var isSubnormal: Bool {
+        return self.value.isSubnormal
+    }
+    
+    /// See [`FloatingPoint.isZero`](https://developer.apple.com/documentation/swift/floatingpoint/1641514-iszero).
+    public var isZero: Bool {
+        return self.value.isZero
+    }
+    
+    /// See [`FloatingPoint.nextDown`](https://developer.apple.com/documentation/swift/floatingpoint/3017979-nextdown).
+    public var nextDown: Failable<T, Validations> {
+        return try! Failable(self.value.nextDown)
+    }
+    
+    /// See [`FloatingPoint.nextUp`](https://developer.apple.com/documentation/swift/floatingpoint/1848104-nextup).
+    public var nextUp: Failable<T, Validations> {
+        return try! Failable(self.value.nextUp)
+    }
+    
+    /// See [`FloatingPoint.sign`](https://developer.apple.com/documentation/swift/floatingpoint/1847735-sign).
+    public var sign: FloatingPointSign {
+        return self.value.sign
+    }
+    
+    /// See [`FloatingPoint.significand`](https://developer.apple.com/documentation/swift/floatingpoint/1847298-significand).
+    public var significand: Failable<T, Validations> {
+        return try! Failable(self.value.significand)
+    }
+    
+    /// See [`FloatingPoint.ulp`](https://developer.apple.com/documentation/swift/floatingpoint/1847492-ulp).
+    public var ulp: Failable<T, Validations> {
+        return try! Failable(self.value.ulp)
+    }
+    
+    
+    // MARK: - Static Properties
+    
+    /// See [`FloatingPoint.greatestFiniteMagnitude`](https://developer.apple.com/documentation/swift/floatingpoint/1849534-greatestfinitemagnitude).
+    public static var greatestFiniteMagnitude: Failable<T, Validations> {
+        return try! Failable(T.greatestFiniteMagnitude)
+    }
+    
+    /// See [`FloatingPoint.infinity`](https://developer.apple.com/documentation/swift/floatingpoint/1641304-infinity).
+    public static var infinity: Failable<T, Validations> {
+        return try! Failable(T.infinity)
+    }
+    
+    /// See [`FloatingPoint.leastNonzeroMagnitude`](https://developer.apple.com/documentation/swift/floatingpoint/1848591-leastnonzeromagnitude).
+    public static var leastNonzeroMagnitude: Failable<T, Validations> {
+        return try! Failable(T.leastNonzeroMagnitude)
+    }
+    
+    /// See [`FloatingPoint.leastNormalMagnitude`](https://developer.apple.com/documentation/swift/floatingpoint/1849504-leastnormalmagnitude).
+    public static var leastNormalMagnitude: Failable<T, Validations> {
+        return try! Failable(T.leastNormalMagnitude)
+    }
+    
+    /// See [`FloatingPoint.nan`](https://developer.apple.com/documentation/swift/floatingpoint/1641652-nan).
+    public static var nan: Failable<T, Validations> {
+        return try! Failable(T.nan)
+    }
+    
+    /// See [`FloatingPoint.pi`](https://developer.apple.com/documentation/swift/floatingpoint/1845454-pi).
+    public static var pi: Failable<T, Validations> {
+        return try! Failable(T.pi)
+    }
+    
+    /// See [`FloatingPoint.radix`](https://developer.apple.com/documentation/swift/floatingpoint/1846156-radix).
+    public static var radix: Failable<T, Validations> {
+        return try! Failable(T.radix)
+    }
+    
+    /// See [`FloatingPoint.signalingNaN`](https://developer.apple.com/documentation/swift/floatingpoint/1845864-signalingnan).
+    public static var signalingNaN: Failable<T, Validations> {
+        return try! Failable(T.signalingNaN)
+    }
+    
+    /// See [`FloatingPoint.ulpOfOne`](https://developer.apple.com/documentation/swift/floatingpoint/3017999-ulpofone).
+    public static var ulpOfOne: Failable<T, Validations> {
+        return try! Failable(T.ulpOfOne)
+    }
+    
+    
+    // MARK: - Instance Methods
+    
+    /// See [`FloatingPoint.addProduct(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2295205-addproduct).
+    public mutating func addProduct(_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>) {
+        self.value.addProduct(lhs.value, rhs.value)
+    }
+    
+    /// See [`FloatingPoint.addingProduct(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017959-addingproduct).
+    public func addingProduct(_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(self.value.addingProduct(lhs.value, rhs.value))
+    }
+    
+    /// See [`FloatingPoint.formRemainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/2299459-formremainder).
+    public mutating func formRemainder(dividingBy other: Failable<T, Validations>) {
+        self.value.formRemainder(dividingBy: other.value)
+    }
+    
+    /// See [`FloatingPoint.formSquareRoot()`](https://developer.apple.com/documentation/swift/floatingpoint/2299104-formsquareroot).
+    public mutating func formSquareRoot() {
+        self.value.formSquareRoot()
+    }
+    
+    /// See [`FloatingPoint.formTruncatingRemainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/1846470-formtruncatingremainder).
+    public mutating func formTruncatingRemainder(dividingBy other: Failable<T, Validations>) {
+        self.value.formTruncatingRemainder(dividingBy: other.value)
+    }
+    
+    /// See [`FloatingPoint.isEqual(to:)`](https://developer.apple.com/documentation/swift/floatingpoint/1846385-isequal).
+    public func isEqual(to other: Failable<T, Validations>) -> Bool {
+        return self.value.isEqual(to: other.value)
+    }
+    
+    /// See [`FloatingPoint.isLess(than:)`](https://developer.apple.com/documentation/swift/floatingpoint/1849403-isless).
+    public func isLess(than other: Failable<T, Validations>) -> Bool {
+        return self.value.isLess(than: other.value)
+    }
+    
+    /// See [`FloatingPoint.isLessThanOrEqualTo(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1849007-islessthanorequalto).
+    public func isLessThanOrEqualTo(_ other: Failable<T, Validations>) -> Bool {
+        return self.value.isLessThanOrEqualTo(other.value)
+    }
+    
+    /// See [`FloatingPoint.isTotallyOrdered(belowOrEqualTo:)`](https://developer.apple.com/documentation/swift/floatingpoint/2428057-istotallyordered).
+    public func isTotallyOrdered(belowOrEqualTo other: Failable<T, Validations>) -> Bool {
+        return self.value.isTotallyOrdered(belowOrEqualTo: other.value)
+    }
+    
+    /// See [`FloatingPoint.negate()`](https://developer.apple.com/documentation/swift/floatingpoint/1849560-negate).
+    public mutating func negate() {
+        self.value.negate()
+    }
+    
+    /// See [`FloatingPoint.remainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017981-remainder).
+    public func remainder(dividingBy other: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(self.value.remainder(dividingBy: other.value))
+    }
+    
+    /// See [`FloatingPoint.round()`](https://developer.apple.com/documentation/swift/floatingpoint/2297801-round).
+    public mutating func round() {
+        self.value.round()
+    }
+    
+    /// See [`FloatingPoint.round(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2298113-round).
+    public mutating func round(_ rule: FloatingPointRoundingRule) {
+        self.value.round(rule)
+    }
+    
+    /// See [`FloatingPoint.rounded()`](https://developer.apple.com/documentation/swift/floatingpoint/2295900-rounde).
+    public func rounded()throws -> Failable<T, Validations> {
+        return try Failable(self.value.rounded())
+    }
+    
+    /// See [`FloatingPoint.rounded(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017985-rounded).
+    public func rounded(_ rule: FloatingPointRoundingRule)throws -> Failable<T, Validations> {
+        return try Failable(self.value.rounded(rule))
+    }
+    
+    /// See [`FloatingPoint.squareRoot()`](https://developer.apple.com/documentation/swift/floatingpoint/3017991-squareroot).
+    public func squareRoot()throws -> Failable<T, Validations> {
+        return try Failable(self.value.squareRoot())
+    }
+    
+    /// See [`FloatingPoint.truncatingRemainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017995-truncatingremainder).
+    public func truncatingRemainder(dividingBy other: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(self.value.truncatingRemainder(dividingBy: other.value))
+    }
+    
+    // --- Validtion Flexibility ---
+    
+    /// See [`FloatingPoint.addProduct(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2295205-addproduct).
+    public mutating func addProduct<V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>) {
+        self.value.addProduct(lhs.value, rhs.value)
+    }
+    
+    /// See [`FloatingPoint.addingProduct(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017959-addingproduct).
+    public func addingProduct<V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>)throws -> Failable<T, AppendedValidations<T, V1, V2>> {
+        return try Failable<T, AppendedValidations<T, V1, V2>>(self.value.addingProduct(lhs.value, rhs.value))
+    }
+    
+    /// See [`FloatingPoint.formRemainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/2299459-formremainder).
+    public mutating func formRemainder<V>(dividingBy other: Failable<T, V>) {
+        self.value.formRemainder(dividingBy: other.value)
+    }
+    
+    /// See [`FloatingPoint.formTruncatingRemainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/1846470-formtruncatingremainder).
+    public mutating func formTruncatingRemainder<V>(dividingBy other: Failable<T, V>) {
+        self.value.formTruncatingRemainder(dividingBy: other.value)
+    }
+    
+    /// See [`FloatingPoint.isEqual(to:)`](https://developer.apple.com/documentation/swift/floatingpoint/1846385-isequal).
+    public func isEqual<V>(to other: Failable<T, V>) -> Bool {
+        return self.value.isEqual(to: other.value)
+    }
+    
+    /// See [`FloatingPoint.isLess(than:)`](https://developer.apple.com/documentation/swift/floatingpoint/1849403-isless).
+    public func isLess<V>(than other: Failable<T, V>) -> Bool {
+        return self.value.isLess(than: other.value)
+    }
+    
+    /// See [`FloatingPoint.isLessThanOrEqualTo(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/1849007-islessthanorequalto).
+    public func isLessThanOrEqualTo<V>(_ other: Failable<T, V>) -> Bool {
+        return self.value.isLessThanOrEqualTo(other.value)
+    }
+    
+    /// See [`FloatingPoint.isTotallyOrdered(belowOrEqualTo:)`](https://developer.apple.com/documentation/swift/floatingpoint/2428057-istotallyordered).
+    public func isTotallyOrdered<V>(belowOrEqualTo other: Failable<T, V>) -> Bool {
+        return self.value.isTotallyOrdered(belowOrEqualTo: other.value)
+    }
+    
+    /// See [`FloatingPoint.remainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017981-remainder).
+    public func remainder<V>(dividingBy other: Failable<T, V>)throws -> Failable<T, AppendedValidations<T, Validations, V>> {
+        return try Failable<T, AppendedValidations<T, Validations, V>>(self.value.remainder(dividingBy: other.value))
+    }
+
+    // See [`FloatingPoint.truncatingRemainder(dividingBy:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017995-truncatingremainder).
+    public func truncatingRemainder<V>(dividingBy other: Failable<T, V>)throws -> Failable<T, AppendedValidations<T, Validations, V>> {
+        return try Failable<T, AppendedValidations<T, Validations, V>>(self.value.truncatingRemainder(dividingBy: other.value))
+    }
+    
+    
+    // MARK: - Static Methods
+    
+    /// See [`FloatingPoint.maximum(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017963-maximum).
+    public static func maximum(_ x: Failable<T, Validations>, _ y: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(T.maximum(x.value, y.value))
+    }
+    
+    /// See [`FloatingPoint.maximumMagnitude(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017967-maximummagnitude).
+    public static func maximumMagnitude(_ x: Failable<T, Validations>, _ y: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(T.maximumMagnitude(x.value, y.value))
+    }
+    
+    /// See [`FloatingPoint.minimum(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017971-minimum).
+    public static func minimum(_ x: Failable<T, Validations>, _ y: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(T.minimum(x.value, y.value))
+    }
+    
+    /// See [`FloatingPoint.minimumMagnitude(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017975-minimummagnitude).
+    public static func minimumMagnitude(_ x: Failable<T, Validations>, _ y: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(T.minimumMagnitude(x.value, y.value))
+    }
+    
+    
+    /// See [`FloatingPoint.maximum(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017963-maximum).
+    public static func maximum<V1, V2>(_ x: Failable<T, V1>, _ y: Failable<T, V2>)throws -> Failable<T, AppendedValidations<T, V1, V2>> {
+        return try Failable<T, AppendedValidations<T, V1, V2>>(T.maximum(x.value, y.value))
+    }
+    
+    /// See [`FloatingPoint.maximumMagnitude(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017967-maximummagnitude).
+    public static func maximumMagnitude<V1, V2>(_ x: Failable<T, V1>, _ y: Failable<T, V2>)throws -> Failable<T, AppendedValidations<T, V1, V2>> {
+        return try Failable<T, AppendedValidations<T, V1, V2>>(T.maximumMagnitude(x.value, y.value))
+    }
+    
+    /// See [`FloatingPoint.minimum(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017971-minimum).
+    public static func minimum<V1, V2>(_ x: Failable<T, V1>, _ y: Failable<T, V2>)throws -> Failable<T, AppendedValidations<T, V1, V2>> {
+        return try Failable<T, AppendedValidations<T, V1, V2>>(T.minimum(x.value, y.value))
+    }
+    
+    /// See [`FloatingPoint.minimumMagnitude(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/3017975-minimummagnitude).
+    public static func minimumMagnitude<V1, V2>(_ x: Failable<T, V1>, _ y: Failable<T, V2>)throws -> Failable<T, AppendedValidations<T, V1, V2>> {
+        return try Failable<T, AppendedValidations<T, V1, V2>>(T.minimumMagnitude(x.value, y.value))
+    }
+    
+    
+    // MARK: - Operators
+    
+    /// See [`FloatingPoint.<(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2883927).
+    public static func < (lhs: Failable<T, Validations>, rhs: Failable<T, Validations>) -> Bool {
+        return lhs.value < rhs.value
+    }
+    
+    /// See [`FloatingPoint.<=(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2884778).
+    public static func <= (lhs: Failable<T, Validations>, rhs: Failable<T, Validations>) -> Bool {
+        return lhs.value <= rhs.value
+    }
+    
+    /// See [`FloatingPoint.>(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2885368).
+    public static func > (lhs: Failable<T, Validations>, rhs: Failable<T, Validations>) -> Bool {
+        return lhs.value > lhs.value
+    }
+    
+    /// See [`FloatingPoint.>(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2884837).
+    public static func >= (lhs: Failable<T, Validations>, rhs: Failable<T, Validations>) -> Bool {
+        return lhs.value >= lhs.value
+    }
+    
+    /// See [`FloatingPoint.*(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2886135).
+    public static func * (_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(lhs.value * rhs.value)
+    }
+    
+    /// See [`FloatingPoint.*=(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2885700).
+    public static func *= (_ lhs: inout Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws {
+        try lhs = lhs * rhs
+    }
+    
+    /// See [`FloatingPoint.+(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2885022).
+    public static func + (_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(lhs.value + rhs.value)
+    }
+    
+    /// See [`FloatingPoint.+=(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2884273).
+    public static func += (_ lhs: inout Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws {
+        try lhs = lhs + rhs
+    }
+    
+    /// See [`FloatingPoint.-(_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2884257).
+    public prefix static func - (_ x: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(-x.value)
+    }
+    
+    /// See [`FloatingPoint.-(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2885455).
+    public static func - (_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(lhs.value - rhs.value)
+    }
+    
+    /// See [`FloatingPoint.-=(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2884054).
+    public static func -= (_ lhs: inout Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws {
+        try lhs = lhs - rhs
+    }
+    
+    /// See [`FloatingPoint./(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2884057).
+    public static func / (_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws -> Failable<T, Validations> {
+        return try Failable(lhs.value / rhs.value)
+    }
+    
+    /// See [`FloatingPoint./=(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2886632).
+    public static func /= (_ lhs: inout Failable<T, Validations>, _ rhs: Failable<T, Validations>)throws {
+        try lhs = lhs + rhs
+    }
+    
+    /// See [`FloatingPoint.==(_:_:)`](https://developer.apple.com/documentation/swift/floatingpoint/2919612).
+    public static func == (_ lhs: Failable<T, Validations>, _ rhs: Failable<T, Validations>) -> Bool {
+        return lhs.value == rhs.value
+    }
+}
+
+
+public func < <T, V1, V2>(lhs: Failable<T, V1>, rhs: Failable<T, V2>) -> Bool where T: FloatingPoint {
+    return lhs.value < rhs.value
+}
+
+public func <= <T, V1, V2>(lhs: Failable<T, V1>, rhs: Failable<T, V2>) -> Bool where T: FloatingPoint {
+    return lhs.value <= rhs.value
+}
+
+public func > <T, V1, V2>(lhs: Failable<T, V1>, rhs: Failable<T, V2>) -> Bool where T: FloatingPoint {
+    return lhs.value > lhs.value
+}
+
+public func >= <T, V1, V2>(lhs: Failable<T, V1>, rhs: Failable<T, V2>) -> Bool where T: FloatingPoint {
+    return lhs.value >= lhs.value
+}
+
+/// Multiplies two `Failable` values and produces their product, rounding to a representable value.
+///
+/// - Parameters:
+///   - lhs: The left value to multiply.
+///   - rhs: The right value to multiply.
+///
+/// - Returns: The product of the multiplcation equation, where the validation is the validations of the two values passed in.
+public func * <T, V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>)throws
+    -> Failable<T, AppendedValidations<T, V1, V2>> where T: FloatingPoint
+{
+    return try Failable(lhs.value * rhs.value)
+}
+
+/// Adds two `Failable` values and produces their sum, rounding to a representable value.
+///
+/// - Parameters:
+///   - lhs: The left value to add.
+///   - rhs: The right value to add.
+///
+/// - Returns: The sum of the addition equation, where the validation is the validations of the two values passed in.
+public func + <T, V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>)throws
+    -> Failable<T, AppendedValidations<T, V1, V2>> where T: FloatingPoint
+{
+    return try Failable(lhs.value + rhs.value)
+}
+
+/// Subtracts two `Failable` values and produces their difference, rounding to a representable value.
+///
+/// - Parameters:
+///   - lhs: The value to subtract from.
+///   - rhs: The value to subtract from the left value.
+///
+/// - Returns: The difference of the subtraction equation, where the validation is the validations of the two values passed in.
+public func - <T, V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>)throws
+    -> Failable<T, AppendedValidations<T, V1, V2>> where T: FloatingPoint
+{
+    return try Failable(lhs.value - rhs.value)
+}
+
+/// Divides two `Failable` values and produces their quotient, rounding to a representable value.
+///
+/// - Parameters:
+///   - lhs: The value to subtract from.
+///   - rhs: The value to subtract from the left value.
+///
+/// - Returns: The quotient of the division equation, where the validation is the validations of the two values passed in.
+public func / <T, V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>)throws
+    -> Failable<T, AppendedValidations<T, V1, V2>> where T: FloatingPoint
+{
+    return try Failable(lhs.value / rhs.value)
+}
+
+/// Returns a Boolean value indicating whether two values are equal.
+///
+/// - Parameters:
+///   - lhs: The left value to check for equality.
+///   - rhs: The right value to check for euqality.
+///
+/// - Returns: The boolean indicating whether the values are equal or not.
+public func == <T, V1, V2>(_ lhs: Failable<T, V1>, _ rhs: Failable<T, V2>) -> Bool where T: FloatingPoint {
+    return lhs.value == rhs.value
+}