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class Fraction(n: Int, d: Int) {
  require(d != 0, "Division by zero")
 
  var numer = n * d.signum
  var denom = d.abs
  var reduced = false
 
  def this(n: Int) = this(n, 1)
 
  def numerator = {
    reduce()
    numer
  }
 
  def numerator_=(value: Int) = {
    reduced = false
    numer = value
  }
 
  def denominator = {
    reduce()
    denom
  } ensuring (_ > 0)
 
  def denominator_=(value: Int) = {
    require(value != 0, "Division by zero")
 
    reduced = false
    if (denom < 0) numer = -numer
    denom = value.abs
  }
 
  private def gcd(a: Int, b: Int): Int =
    if (b == 0) a else gcd(b, a % b)
 
  private def reduce() {
    if (reduced) return
 
    val g = gcd(numer.abs, denom)
    numer /= g
    denom /= g
 
    reduced = true
  }
 
  def +(that: Fraction) =
    Fraction(this.numer * that.denom + that.numer * this.denom,
             this.denom * that.denom)
 
  def -(that: Fraction) = this + (- that)
 
  def *(that: Fraction) =
    Fraction(this.numer * that.numer, this.denom * that.denom)
 
  def /(that: Fraction) = this * that.reciprocal
 
  def reciprocal = Fraction(denom, numer)
  def unary_- = Fraction(- numer, denom)
  def abs = Fraction(numer.abs, denom)
  def signum = numer.signum
 
  override def toString = {
    reduce()
 
    val sign = if (numer < 0) "-" else ""
    val dPart = if (denom == 1) "" else "/" + denom
    sign + numer.abs + dPart
  }
 
  def abs(x: Fraction): Fraction =
    Fraction(numer.abs, denom)
}
 
object Fraction {
  def apply(n: Int, d: Int) = new Fraction(n, d)
  def apply(n: Int) = new Fraction(n)
 
  def zero = new Fraction(0)
  def one = new Fraction(1)
}
 
object IntExtensions {
  class Int2Fraction(a: Int) {
    def :/(b: Int) = Fraction(a, b)
  }
 
  implicit def int2Fraction(i: Int) = new Int2Fraction(i)
}
 
object Sample extends App {
  import IntExtensions._
 
  val oneThird = 1 :/ 3
  val oneSixth = 1 :/ 6
 
  // Fraction.one / Fraction.zero -> java.lang.IllegalArgumentException: requirement failed: Division by zero
  // oneThird.denominator = 0 -> java.lang.IllegalArgumentException: requirement failed: Division by zero
 
  println(s"one third plus one sixth is ${oneThird + oneSixth}")
}