A Swift translation of the Rational type from Chapter 6 of "Programming in Scala, 2nd Edition" by Martin Odersky, Lex Spoon, and Bill Venners

rational.swift

// Based upon Chapter 6 of Programming in Scala, Second Edition, by Martin Odersky, Lex Spoon, and Bill Venners

public struct Rational {
    public let numer: Int
    public let denom: Int

    public init(_ numerator: Int, _ denominator: Int = 1) {
        assert(denominator != 0)
        
        let g = Rational.gcd(abs(numerator), abs(denominator))
        numer = numerator / g
        denom = denominator / g
    }
    
    private static func gcd(a: Int, _ b: Int) -> Int {
        return b == 0 ? a : gcd(b, a % b)
    }
}


extension Rational: Printable {
    public var description: String { return "\(numer)/\(denom)" }
}


func + (lhs: Rational, rhs: Rational) -> Rational {
    return Rational(
        lhs.numer * rhs.denom + rhs.numer * lhs.denom,
        lhs.denom * rhs.denom
    )
}

func + (lhs: Rational, rhs: Int) -> Rational {
    return lhs + Rational(rhs)
}

func + (lhs: Int, rhs: Rational) -> Rational {
    return Rational(lhs) + rhs
}


func - (lhs: Rational, rhs: Rational) -> Rational {
    return Rational(
        lhs.numer * rhs.denom - rhs.numer * lhs.denom,
        lhs.denom * rhs.denom
    )
}

func - (lhs: Rational, rhs: Int) -> Rational {
    return lhs - Rational(rhs)
}

func - (lhs: Int, rhs: Rational) -> Rational {
    return Rational(lhs) - rhs
}


func * (lhs: Rational, rhs: Rational) -> Rational {
    return Rational(
        lhs.numer * rhs.numer,
        lhs.denom * rhs.denom
    )
}

func * (lhs: Rational, rhs: Int) -> Rational {
    return lhs * Rational(rhs)
}

func * (lhs: Int, rhs: Rational) -> Rational {
    return Rational(lhs) * rhs
}


func / (lhs: Rational, rhs: Rational) -> Rational {
    return Rational(
        lhs.numer * rhs.denom,
        lhs.denom * rhs.numer
    )
}

func / (lhs: Rational, rhs: Int) -> Rational {
    return lhs / Rational(rhs)
}

func / (lhs: Int, rhs: Rational) -> Rational {
    return Rational(lhs) / rhs
}


func < (lhs: Rational, rhs: Rational) -> Bool {
    return lhs.numer * rhs.denom < rhs.numer * lhs.denom
}


// Examples

let oneHalf = Rational(1, 2)
oneHalf.description                       // "1/2"

let twoThirds = Rational(2, 3)
twoThirds.description                     // "2/3"

let sum = oneHalf + twoThirds
sum.description                           // "7/6"

let product = oneHalf * twoThirds
product.description                       // "1/3"

let expr = oneHalf + oneHalf * twoThirds
expr.description                          // "5/6"

let y = Rational(3)
y.description                             // "3/1"

let frac = Rational(66, 42)
frac.description                          // "11/7"

let sumInt = oneHalf + 1
sumInt.description                        // "3/2"

let neg = Rational(1, -2)
neg.description                           // "1/-2"