ratio.swift

infix operator /% {associativity right precedence 100 }

public struct Rational {
  private let num, den: IntMax
}

public func /%(lhs: IntMax, rhs: IntMax) -> Rational {
  let g = gcd(lhs,rhs)
  let (n,d) = (lhs / g, rhs / g)
  if d < 0 { return Rational(num: n * -1, den: d * -1) }
  return Rational(num: n, den: d)
}

private func gcd(x: IntMax, _ y: IntMax) -> IntMax {
  var (a,b) = (x,y)
  while b != 0 { (a,b) = (b,a%b) }
  return a
}

extension Rational: CustomStringConvertible {
  public var description: String {
    if den == 1 { return String(num) }
    return String(num) + " / " + String(den)
  }
}

extension Rational: Equatable {}

public func ==(lhs: Rational, rhs: Rational) -> Bool {
  return lhs.num == rhs.num && lhs.den == rhs.den
}

public func +(lhs: Rational, rhs: Rational) -> Rational {
  let g = gcd(lhs.den, rhs.den)
  let d = (lhs.den * rhs.den) / g
  return (lhs.num * (rhs.den/g) + rhs.num * (lhs.den/g)) /% d
}

public func *(lhs: Rational, rhs: Rational) -> Rational {
  return (lhs.num*rhs.num) /% (lhs.den*rhs.den)
}

public func /(lhs: Rational, rhs: Rational) -> Rational {
  return (lhs.num*rhs.den) /% (lhs.den*rhs.num)
}

public func -(lhs: Rational, rhs: Rational) -> Rational {
  return lhs + Rational(num: rhs.num * -1, den: rhs.den)
}

extension Rational: Comparable {}

public func <(lhs: Rational, rhs: Rational) -> Bool {
  return lhs.num * rhs.den < rhs.num * lhs.den
}

extension Rational: IntegerLiteralConvertible {
  public init(integerLiteral value: IntMax) {
    self = Rational(num: value, den: 1)
  }
}

extension Rational: SignedNumberType {}

public prefix func -(x: Rational) -> Rational {
  return Rational(num: x.num * -1, den: x.den)
}

extension Rational: Strideable {
  public func distanceTo(other: Rational) -> Rational {
    return other - self
  }
  public func advancedBy(n: Rational) -> Rational {
    return self + n
  }
}

extension Rational {
  public var double: Double {
    return Double(num) / Double(den)
  }
}

infix operator ** { associativity left precedence 130 }

public func **<I: ForwardIndexType where I: IntegerLiteralConvertible>(lhs: Rational, rhs: I) -> Rational {
  return (0..<rhs).reduce(1) { (a,_) in a * lhs }
}