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package algebra
package std

import util.StaticMethods

import algebra.lattice._
import algebra.ring._

package object long extends LongInstances

trait LongInstances {
  implicit val longAlgebra = new LongAlgebra

  val LongMinMaxLattice: BoundedDistributiveLattice[Long] =
    BoundedDistributiveLattice.minMax[Long](Long.MinValue, Long.MaxValue)(longAlgebra)
}

class LongAlgebra extends EuclideanRing[Long]
    with Order[Long] with Serializable {

  def compare(x: Long, y: Long): Int =
    if (x < y) -1 else if (x > y) 1 else 0

  override def eqv(x: Long, y: Long) = x == y
  override def neqv(x: Long, y: Long) = x != y
  override def gt(x: Long, y: Long) = x > y
  override def gteqv(x: Long, y: Long) = x >= y
  override def lt(x: Long, y: Long) = x < y
  override def lteqv(x: Long, y: Long) = x <= y

  def zero: Long = 0
  def one: Long = 1

  def plus(x: Long, y: Long): Long = x + y
  def negate(x: Long): Long = -x
  override def minus(x: Long, y: Long): Long = x - y

  def times(x: Long, y: Long): Long = x * y
  def quot(x: Long, y: Long) = x / y
  def mod(x: Long, y: Long) = x % y

  override def pow(x: Long, y: Int): Long = StaticMethods.pow(x, y.toLong)

  def gcd(x: Long, y: Long): Long = StaticMethods.gcd(x, y)

  override def fromInt(n: Int): Long = n.toLong
}