scala.math.Ordering

trait Ordering[T] extends Comparator[T] with PartialOrdering[T] with Serializable

Ordering is a trait whose instances each represent a strategy for sorting instances of a type.

Ordering’s companion object defines many implicit objects to deal with subtypes of AnyVal (e.g. Int, Double), String, and others.

To sort instances by one or more member variables, you can take advantage of these built-in orderings using Ordering.by and Ordering.on:

import scala.util.Sorting
val pairs = Array(("a", 5, 2), ("c", 3, 1), ("b", 1, 3))

// sort by 2nd element
Sorting.quickSort(pairs)(Ordering.by[(String, Int, Int), Int](_._2))

// sort by the 3rd element, then 1st
Sorting.quickSort(pairs)(Ordering[(Int, String)].on(x => (x._3, x._1)))

An Ordering[T] is implemented by specifying compare(a:T, b:T), which decides how to order two instances a and b. Instances of Ordering[T] can be used by things like scala.util.Sorting to sort collections like Array[T].

For example:

import scala.util.Sorting

case class Person(name:String, age:Int)
val people = Array(Person("bob", 30), Person("ann", 32), Person("carl", 19))

// sort by age
object AgeOrdering extends Ordering[Person] {
  def compare(a:Person, b:Person) = a.age compare b.age
}
Sorting.quickSort(people)(AgeOrdering)

This trait and scala.math.Ordered both provide this same functionality, but in different ways. A type T can be given a single way to order itself by extending Ordered. Using Ordering, this same type may be sorted in many other ways. Ordered and Ordering both provide implicits allowing them to be used interchangeably.

You can import scala.math.Ordering.Implicits to gain access to other implicit orderings.

Type Members

class Ops extends AnyRef

This inner class defines comparison operators available for T .

Concrete Value Members From java.util.Comparator

def reversed(): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparing(arg0: Comparator[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparingDouble(arg0: ToDoubleFunction[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparingInt(arg0: ToIntFunction[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparingLong(arg0: ToLongFunction[_ >: T]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparing[U <: Comparable[_ >: U]](arg0: java.util.function.Function[_ >: T, _ <: U]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

def thenComparing[U](arg0: java.util.function.Function[_ >: T, _ <: U], arg1: Comparator[_ >: U]): Comparator[T]

  • Definition Classes
    • Comparator

(defined at java.util.Comparator)

Abstract Value Members From scala.math.Ordering

abstract def compare(x: T, y: T): Int

Returns an integer whose sign communicates how x compares to y.

The result sign has the following meaning:

  • negative if x < y
  • positive if x > y

  • zero otherwise (if x == y)

  • Definition Classes
    • Ordering → Comparator

(defined at scala.math.Ordering)

Concrete Value Members From scala.math.Ordering

def equiv(x: T, y: T): Boolean

Return true if x == y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering → Equiv

(defined at scala.math.Ordering)

def gt(x: T, y: T): Boolean

Return true if x > y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def gteq(x: T, y: T): Boolean

Return true if x >= y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def lt(x: T, y: T): Boolean

Return true if x < y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def lteq(x: T, y: T): Boolean

Return true if x <= y in the ordering.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def max(x: T, y: T): T

Return x if x >= y , otherwise y .

(defined at scala.math.Ordering)

def min(x: T, y: T): T

Return x if x <= y , otherwise y .

(defined at scala.math.Ordering)

implicit def mkOrderingOps(lhs: T): Ops

This implicit method augments T with the comparison operators defined in scala.math.Ordering.Ops .

(defined at scala.math.Ordering)

def on[U](f: (U) ⇒ T): Ordering[U]

Given f, a function from U into T, creates an Ordering[U] whose compare function is equivalent to:

def compare(x:U, y:U) = Ordering[T].compare(f(x), f(y))

(defined at scala.math.Ordering)

def reverse: Ordering[T]

Return the opposite ordering of this one.

  • Definition Classes
    • Ordering → PartialOrdering

(defined at scala.math.Ordering)

def tryCompare(x: T, y: T): Some[Int]

Returns whether a comparison between x and y is defined, and if so the result of compare(x, y) .

  • Definition Classes
    • Ordering → PartialOrdering (defined at scala.math.Ordering)

Full Source:

/*                     __                                               *\
**     ________ ___   / /  ___     Scala API                            **
**    / __/ __// _ | / /  / _ |    (c) 2003-2013, LAMP/EPFL             **
**  __\ \/ /__/ __ |/ /__/ __ |    http://scala-lang.org/               **
** /____/\___/_/ |_/____/_/ | |                                         **
**                          |/                                          **
\*                                                                      */

package scala
package math

import java.util.Comparator
import scala.language.{implicitConversions, higherKinds}

/** Ordering is a trait whose instances each represent a strategy for sorting
  * instances of a type.
  *
  * Ordering's companion object defines many implicit objects to deal with
  * subtypes of AnyVal (e.g. Int, Double), String, and others.
  *
  * To sort instances by one or more member variables, you can take advantage
  * of these built-in orderings using Ordering.by and Ordering.on:
  *
  * {{{
  * import scala.util.Sorting
  * val pairs = Array(("a", 5, 2), ("c", 3, 1), ("b", 1, 3))
  *
  * // sort by 2nd element
  * Sorting.quickSort(pairs)(Ordering.by[(String, Int, Int), Int](_._2))
  *
  * // sort by the 3rd element, then 1st
  * Sorting.quickSort(pairs)(Ordering[(Int, String)].on(x => (x._3, x._1)))
  * }}}
  *
  * An Ordering[T] is implemented by specifying compare(a:T, b:T), which
  * decides how to order two instances a and b. Instances of Ordering[T] can be
  * used by things like scala.util.Sorting to sort collections like Array[T].
  *
  * For example:
  *
  * {{{
  * import scala.util.Sorting
  *
  * case class Person(name:String, age:Int)
  * val people = Array(Person("bob", 30), Person("ann", 32), Person("carl", 19))
  *
  * // sort by age
  * object AgeOrdering extends Ordering[Person] {
  *   def compare(a:Person, b:Person) = a.age compare b.age
  * }
  * Sorting.quickSort(people)(AgeOrdering)
  * }}}
  *
  * This trait and scala.math.Ordered both provide this same functionality, but
  * in different ways. A type T can be given a single way to order itself by
  * extending Ordered. Using Ordering, this same type may be sorted in many
  * other ways. Ordered and Ordering both provide implicits allowing them to be
  * used interchangeably.
  *
  * You can import scala.math.Ordering.Implicits to gain access to other
  * implicit orderings.
  *
  * @author Geoffrey Washburn
  * @version 0.9.5, 2008-04-15
  * @since 2.7
  * @see [[scala.math.Ordered]], [[scala.util.Sorting]]
  */
@annotation.implicitNotFound(msg = "No implicit Ordering defined for ${T}.")
trait Ordering[T] extends Comparator[T] with PartialOrdering[T] with Serializable {
  outer =>

  /** Returns whether a comparison between `x` and `y` is defined, and if so
    * the result of `compare(x, y)`.
    */
  def tryCompare(x: T, y: T) = Some(compare(x, y))

 /** Returns an integer whose sign communicates how x compares to y.
   *
   * The result sign has the following meaning:
   *
   *  - negative if x < y
   *  - positive if x > y
   *  - zero otherwise (if x == y)
   */
  def compare(x: T, y: T): Int

  /** Return true if `x` <= `y` in the ordering. */
  override def lteq(x: T, y: T): Boolean = compare(x, y) <= 0

  /** Return true if `x` >= `y` in the ordering. */
  override def gteq(x: T, y: T): Boolean = compare(x, y) >= 0

  /** Return true if `x` < `y` in the ordering. */
  override def lt(x: T, y: T): Boolean = compare(x, y) < 0

  /** Return true if `x` > `y` in the ordering. */
  override def gt(x: T, y: T): Boolean = compare(x, y) > 0

  /** Return true if `x` == `y` in the ordering. */
  override def equiv(x: T, y: T): Boolean = compare(x, y) == 0

  /** Return `x` if `x` >= `y`, otherwise `y`. */
  def max(x: T, y: T): T = if (gteq(x, y)) x else y

  /** Return `x` if `x` <= `y`, otherwise `y`. */
  def min(x: T, y: T): T = if (lteq(x, y)) x else y

  /** Return the opposite ordering of this one. */
  override def reverse: Ordering[T] = new Ordering[T] {
    override def reverse = outer
    def compare(x: T, y: T) = outer.compare(y, x)
  }

  /** Given f, a function from U into T, creates an Ordering[U] whose compare
    * function is equivalent to:
    *
    * {{{
    * def compare(x:U, y:U) = Ordering[T].compare(f(x), f(y))
    * }}}
    */
  def on[U](f: U => T): Ordering[U] = new Ordering[U] {
    def compare(x: U, y: U) = outer.compare(f(x), f(y))
  }

  /** This inner class defines comparison operators available for `T`. */
  class Ops(lhs: T) {
    def <(rhs: T) = lt(lhs, rhs)
    def <=(rhs: T) = lteq(lhs, rhs)
    def >(rhs: T) = gt(lhs, rhs)
    def >=(rhs: T) = gteq(lhs, rhs)
    def equiv(rhs: T) = Ordering.this.equiv(lhs, rhs)
    def max(rhs: T): T = Ordering.this.max(lhs, rhs)
    def min(rhs: T): T = Ordering.this.min(lhs, rhs)
  }

  /** This implicit method augments `T` with the comparison operators defined
    * in `scala.math.Ordering.Ops`.
    */
  implicit def mkOrderingOps(lhs: T): Ops = new Ops(lhs)
}

trait LowPriorityOrderingImplicits {
  /** This would conflict with all the nice implicit Orderings
   *  available, but thanks to the magic of prioritized implicits
   *  via subclassing we can make `Ordered[A] => Ordering[A]` only
   *  turn up if nothing else works.  Since `Ordered[A]` extends
   *  `Comparable[A]` anyway, we can throw in some Java interop too.
   */
  implicit def ordered[A <% Comparable[A]]: Ordering[A] = new Ordering[A] {
    def compare(x: A, y: A): Int = x compareTo y
  }
  implicit def comparatorToOrdering[A](implicit cmp: Comparator[A]): Ordering[A] = new Ordering[A] {
    def compare(x: A, y: A) = cmp.compare(x, y)
  }
}

/** This is the companion object for the [[scala.math.Ordering]] trait.
  *
  * It contains many implicit orderings as well as well as methods to construct
  * new orderings.
  */
object Ordering extends LowPriorityOrderingImplicits {
  def apply[T](implicit ord: Ordering[T]) = ord

  trait ExtraImplicits {
    /** Not in the standard scope due to the potential for divergence:
      * For instance `implicitly[Ordering[Any]]` diverges in its presence.
      */
    implicit def seqDerivedOrdering[CC[X] <: scala.collection.Seq[X], T](implicit ord: Ordering[T]): Ordering[CC[T]] =
      new Ordering[CC[T]] {
        def compare(x: CC[T], y: CC[T]): Int = {
          val xe = x.iterator
          val ye = y.iterator

          while (xe.hasNext && ye.hasNext) {
            val res = ord.compare(xe.next(), ye.next())
            if (res != 0) return res
          }

          Ordering.Boolean.compare(xe.hasNext, ye.hasNext)
        }
      }

    /** This implicit creates a conversion from any value for which an
      * implicit `Ordering` exists to the class which creates infix operations.
      * With it imported, you can write methods as follows:
      *
      * {{{
      * def lessThan[T: Ordering](x: T, y: T) = x < y
      * }}}
      */
    implicit def infixOrderingOps[T](x: T)(implicit ord: Ordering[T]): Ordering[T]#Ops = new ord.Ops(x)
  }

  /** An object containing implicits which are not in the default scope. */
  object Implicits extends ExtraImplicits { }

  /** Construct an Ordering[T] given a function `lt`. */
  def fromLessThan[T](cmp: (T, T) => Boolean): Ordering[T] = new Ordering[T] {
    def compare(x: T, y: T) = if (cmp(x, y)) -1 else if (cmp(y, x)) 1 else 0
    // overrides to avoid multiple comparisons
    override def lt(x: T, y: T): Boolean = cmp(x, y)
    override def gt(x: T, y: T): Boolean = cmp(y, x)
    override def gteq(x: T, y: T): Boolean = !cmp(x, y)
    override def lteq(x: T, y: T): Boolean = !cmp(y, x)
  }

  /** Given f, a function from T into S, creates an Ordering[T] whose compare
    * function is equivalent to:
    *
    * {{{
    * def compare(x:T, y:T) = Ordering[S].compare(f(x), f(y))
    * }}}
    *
    * This function is an analogue to Ordering.on where the Ordering[S]
    * parameter is passed implicitly.
    */
  def by[T, S](f: T => S)(implicit ord: Ordering[S]): Ordering[T] =
    fromLessThan((x, y) => ord.lt(f(x), f(y)))

  trait UnitOrdering extends Ordering[Unit] {
    def compare(x: Unit, y: Unit) = 0
  }
  implicit object Unit extends UnitOrdering

  trait BooleanOrdering extends Ordering[Boolean] {
    def compare(x: Boolean, y: Boolean) = (x, y) match {
      case (false, true) => -1
      case (true, false) => 1
      case _ => 0
    }
  }
  implicit object Boolean extends BooleanOrdering

  trait ByteOrdering extends Ordering[Byte] {
    def compare(x: Byte, y: Byte) = x.toInt - y.toInt
  }
  implicit object Byte extends ByteOrdering

  trait CharOrdering extends Ordering[Char] {
    def compare(x: Char, y: Char) = x.toInt - y.toInt
  }
  implicit object Char extends CharOrdering

  trait ShortOrdering extends Ordering[Short] {
    def compare(x: Short, y: Short) = x.toInt - y.toInt
  }
  implicit object Short extends ShortOrdering

  trait IntOrdering extends Ordering[Int] {
    def compare(x: Int, y: Int) =
      if (x < y) -1
      else if (x == y) 0
      else 1
  }
  implicit object Int extends IntOrdering

  trait LongOrdering extends Ordering[Long] {
    def compare(x: Long, y: Long) =
      if (x < y) -1
      else if (x == y) 0
      else 1
  }
  implicit object Long extends LongOrdering

  trait FloatOrdering extends Ordering[Float] {
    outer =>

    def compare(x: Float, y: Float) = java.lang.Float.compare(x, y)

    override def lteq(x: Float, y: Float): Boolean = x <= y
    override def gteq(x: Float, y: Float): Boolean = x >= y
    override def lt(x: Float, y: Float): Boolean = x < y
    override def gt(x: Float, y: Float): Boolean = x > y
    override def equiv(x: Float, y: Float): Boolean = x == y
    override def max(x: Float, y: Float): Float = math.max(x, y)
    override def min(x: Float, y: Float): Float = math.min(x, y)

    override def reverse: Ordering[Float] = new FloatOrdering {
      override def reverse = outer
      override def compare(x: Float, y: Float) = outer.compare(y, x)

      override def lteq(x: Float, y: Float): Boolean = outer.lteq(y, x)
      override def gteq(x: Float, y: Float): Boolean = outer.gteq(y, x)
      override def lt(x: Float, y: Float): Boolean = outer.lt(y, x)
      override def gt(x: Float, y: Float): Boolean = outer.gt(y, x)
      override def min(x: Float, y: Float): Float = outer.max(x, y)
      override def max(x: Float, y: Float): Float = outer.min(x, y)

    }
  }
  implicit object Float extends FloatOrdering

  trait DoubleOrdering extends Ordering[Double] {
    outer =>

    def compare(x: Double, y: Double) = java.lang.Double.compare(x, y)

    override def lteq(x: Double, y: Double): Boolean = x <= y
    override def gteq(x: Double, y: Double): Boolean = x >= y
    override def lt(x: Double, y: Double): Boolean = x < y
    override def gt(x: Double, y: Double): Boolean = x > y
    override def equiv(x: Double, y: Double): Boolean = x == y
    override def max(x: Double, y: Double): Double = math.max(x, y)
    override def min(x: Double, y: Double): Double = math.min(x, y)

    override def reverse: Ordering[Double] = new DoubleOrdering {
      override def reverse = outer
      override def compare(x: Double, y: Double) = outer.compare(y, x)

      override def lteq(x: Double, y: Double): Boolean = outer.lteq(y, x)
      override def gteq(x: Double, y: Double): Boolean = outer.gteq(y, x)
      override def lt(x: Double, y: Double): Boolean = outer.lt(y, x)
      override def gt(x: Double, y: Double): Boolean = outer.gt(y, x)
      override def min(x: Double, y: Double): Double = outer.max(x, y)
      override def max(x: Double, y: Double): Double = outer.min(x, y)
    }
  }
  implicit object Double extends DoubleOrdering

  trait BigIntOrdering extends Ordering[BigInt] {
    def compare(x: BigInt, y: BigInt) = x.compare(y)
  }
  implicit object BigInt extends BigIntOrdering

  trait BigDecimalOrdering extends Ordering[BigDecimal] {
    def compare(x: BigDecimal, y: BigDecimal) = x.compare(y)
  }
  implicit object BigDecimal extends BigDecimalOrdering

  trait StringOrdering extends Ordering[String] {
    def compare(x: String, y: String) = x.compareTo(y)
  }
  implicit object String extends StringOrdering

  trait OptionOrdering[T] extends Ordering[Option[T]] {
    def optionOrdering: Ordering[T]
    def compare(x: Option[T], y: Option[T]) = (x, y) match {
      case (None, None)       => 0
      case (None, _)          => -1
      case (_, None)          => 1
      case (Some(x), Some(y)) => optionOrdering.compare(x, y)
    }
  }
  implicit def Option[T](implicit ord: Ordering[T]): Ordering[Option[T]] =
    new OptionOrdering[T] { val optionOrdering = ord }

  implicit def Iterable[T](implicit ord: Ordering[T]): Ordering[Iterable[T]] =
    new Ordering[Iterable[T]] {
      def compare(x: Iterable[T], y: Iterable[T]): Int = {
        val xe = x.iterator
        val ye = y.iterator

        while (xe.hasNext && ye.hasNext) {
          val res = ord.compare(xe.next(), ye.next())
          if (res != 0) return res
        }

        Boolean.compare(xe.hasNext, ye.hasNext)
      }
    }

  implicit def Tuple2[T1, T2](implicit ord1: Ordering[T1], ord2: Ordering[T2]): Ordering[(T1, T2)] =
    new Ordering[(T1, T2)]{
      def compare(x: (T1, T2), y: (T1, T2)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        0
      }
    }

  implicit def Tuple3[T1, T2, T3](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3]) : Ordering[(T1, T2, T3)] =
    new Ordering[(T1, T2, T3)]{
      def compare(x: (T1, T2, T3), y: (T1, T2, T3)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        0
      }
    }

  implicit def Tuple4[T1, T2, T3, T4](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3], ord4: Ordering[T4]) : Ordering[(T1, T2, T3, T4)] =
    new Ordering[(T1, T2, T3, T4)]{
      def compare(x: (T1, T2, T3, T4), y: (T1, T2, T3, T4)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        val compare4 = ord4.compare(x._4, y._4)
        if (compare4 != 0) return compare4
        0
      }
    }

  implicit def Tuple5[T1, T2, T3, T4, T5](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3], ord4: Ordering[T4], ord5: Ordering[T5]): Ordering[(T1, T2, T3, T4, T5)] =
    new Ordering[(T1, T2, T3, T4, T5)]{
      def compare(x: (T1, T2, T3, T4, T5), y: Tuple5[T1, T2, T3, T4, T5]): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        val compare4 = ord4.compare(x._4, y._4)
        if (compare4 != 0) return compare4
        val compare5 = ord5.compare(x._5, y._5)
        if (compare5 != 0) return compare5
        0
      }
    }

  implicit def Tuple6[T1, T2, T3, T4, T5, T6](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3], ord4: Ordering[T4], ord5: Ordering[T5], ord6: Ordering[T6]): Ordering[(T1, T2, T3, T4, T5, T6)] =
    new Ordering[(T1, T2, T3, T4, T5, T6)]{
      def compare(x: (T1, T2, T3, T4, T5, T6), y: (T1, T2, T3, T4, T5, T6)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        val compare4 = ord4.compare(x._4, y._4)
        if (compare4 != 0) return compare4
        val compare5 = ord5.compare(x._5, y._5)
        if (compare5 != 0) return compare5
        val compare6 = ord6.compare(x._6, y._6)
        if (compare6 != 0) return compare6
        0
      }
    }

  implicit def Tuple7[T1, T2, T3, T4, T5, T6, T7](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3], ord4: Ordering[T4], ord5: Ordering[T5], ord6: Ordering[T6], ord7: Ordering[T7]): Ordering[(T1, T2, T3, T4, T5, T6, T7)] =
    new Ordering[(T1, T2, T3, T4, T5, T6, T7)]{
      def compare(x: (T1, T2, T3, T4, T5, T6, T7), y: (T1, T2, T3, T4, T5, T6, T7)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        val compare4 = ord4.compare(x._4, y._4)
        if (compare4 != 0) return compare4
        val compare5 = ord5.compare(x._5, y._5)
        if (compare5 != 0) return compare5
        val compare6 = ord6.compare(x._6, y._6)
        if (compare6 != 0) return compare6
        val compare7 = ord7.compare(x._7, y._7)
        if (compare7 != 0) return compare7
        0
      }
    }

  implicit def Tuple8[T1, T2, T3, T4, T5, T6, T7, T8](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3], ord4: Ordering[T4], ord5: Ordering[T5], ord6: Ordering[T6], ord7: Ordering[T7], ord8: Ordering[T8]): Ordering[(T1, T2, T3, T4, T5, T6, T7, T8)] =
    new Ordering[(T1, T2, T3, T4, T5, T6, T7, T8)]{
      def compare(x: (T1, T2, T3, T4, T5, T6, T7, T8), y: (T1, T2, T3, T4, T5, T6, T7, T8)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        val compare4 = ord4.compare(x._4, y._4)
        if (compare4 != 0) return compare4
        val compare5 = ord5.compare(x._5, y._5)
        if (compare5 != 0) return compare5
        val compare6 = ord6.compare(x._6, y._6)
        if (compare6 != 0) return compare6
        val compare7 = ord7.compare(x._7, y._7)
        if (compare7 != 0) return compare7
        val compare8 = ord8.compare(x._8, y._8)
        if (compare8 != 0) return compare8
        0
      }
    }

  implicit def Tuple9[T1, T2, T3, T4, T5, T6, T7, T8, T9](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3], ord4: Ordering[T4], ord5: Ordering[T5], ord6: Ordering[T6], ord7: Ordering[T7], ord8 : Ordering[T8], ord9: Ordering[T9]): Ordering[(T1, T2, T3, T4, T5, T6, T7, T8, T9)] =
    new Ordering[(T1, T2, T3, T4, T5, T6, T7, T8, T9)]{
      def compare(x: (T1, T2, T3, T4, T5, T6, T7, T8, T9), y: (T1, T2, T3, T4, T5, T6, T7, T8, T9)): Int = {
        val compare1 = ord1.compare(x._1, y._1)
        if (compare1 != 0) return compare1
        val compare2 = ord2.compare(x._2, y._2)
        if (compare2 != 0) return compare2
        val compare3 = ord3.compare(x._3, y._3)
        if (compare3 != 0) return compare3
        val compare4 = ord4.compare(x._4, y._4)
        if (compare4 != 0) return compare4
        val compare5 = ord5.compare(x._5, y._5)
        if (compare5 != 0) return compare5
        val compare6 = ord6.compare(x._6, y._6)
        if (compare6 != 0) return compare6
        val compare7 = ord7.compare(x._7, y._7)
        if (compare7 != 0) return compare7
        val compare8 = ord8.compare(x._8, y._8)
        if (compare8 != 0) return compare8
        val compare9 = ord9.compare(x._9, y._9)
        if (compare9 != 0) return compare9
        0
      }
    }

}