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package spire
package algebra

/**
 * A simple ADT representing the `Sign` of an object.
 */
sealed abstract class Sign(val toInt: Int) {
  import Sign._

  def unary_-(): Sign = this match {
    case Positive => Negative
    case Negative => Positive
    case Zero => Zero
  }

  def *(that: Sign): Sign = Sign(this.toInt * that.toInt)

  def **(that: Int): Sign = Sign(spire.math.pow(this.toInt, that).toInt)
}

object Sign {
  case object Zero extends Sign(0)
  case object Positive extends Sign(1)
  case object Negative extends Sign(-1)

  implicit def sign2int(s: Sign): Int = s.toInt
  implicit def apply(i: Int): Sign =
    if (i == 0) Zero else if (i > 0) Positive else Negative

  class SignAlgebra extends CMonoid[Sign] with Signed[Sign] with Order[Sign] {
    def id: Sign = Positive
    def op(a: Sign, b: Sign): Sign = a * b

    override def sign(a: Sign): Sign = a
    def signum(a: Sign): Int = a.toInt
    def abs(a: Sign): Sign = if (a == Negative) Positive else a

    def compare(x: Sign, y: Sign): Int = java.lang.Integer.signum(x.toInt - y.toInt)
  }

  implicit final val SignAlgebra = new SignAlgebra

  implicit final val SignMultiplicativeGroup: MultiplicativeCMonoid[Sign] =
    Multiplicative(SignAlgebra)

  implicit def SignAction[A](implicit A: AdditiveGroup[A]): MultiplicativeAction[A, Sign] =
    new MultiplicativeAction[A, Sign] {
      def gtimesl(s: Sign, a: A): A = s match {
        case Positive => a
        case Negative => A.negate(a)
        case Zero => A.zero
      }
      def gtimesr(a: A, s: Sign): A = gtimesl(s, a)
    }
}