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/*
 * Scala (https://www.scala-lang.org)
 *
 * Copyright EPFL and Lightbend, Inc.
 *
 * Licensed under Apache License 2.0
 * (http://www.apache.org/licenses/LICENSE-2.0).
 *
 * See the NOTICE file distributed with this work for
 * additional information regarding copyright ownership.
 */

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
  * @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.Reverse[T](this)

  /** 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 {
  private final val reverseSeed  = 41
  private final val optionSeed   = 43
  private final val iterableSeed = 47

  def apply[T](implicit ord: Ordering[T]) = ord

  /** A reverse ordering */
  private final class Reverse[T](private val outer: Ordering[T]) extends Ordering[T] {
    override def reverse: Ordering[T]       = outer
    def compare(x: T, y: T): Int            = outer.compare(y, x)
    override def lteq(x: T, y: T): Boolean  = outer.lteq(y, x)
    override def gteq(x: T, y: T): Boolean  = outer.gteq(y, x)
    override def lt(x: T, y: T): Boolean    = outer.lt(y, x)
    override def gt(x: T, y: T): Boolean    = outer.gt(y, x)
    override def equiv(x: T, y: T): Boolean = outer.equiv(y, x)
    override def max(x: T, y: T): T = outer.min(x, y)
    override def min(x: T, y: T): T = outer.max(x, y)

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Reverse[T]             => this.outer == that.outer
      case _                            => false
    }
    override def hashCode(): Int = outer.hashCode() * reverseSeed
  }
  private final val IntReverse: Ordering[Int] = new Reverse(Ordering.Int)

  private final class IterableOrdering[CC[X] <: Iterable[X], T](private val ord: Ordering[T]) extends 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
      }

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

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that  => true
      case that: IterableOrdering[CC, T] => this.ord == that.ord
      case _                             => false
    }
    override def hashCode(): Int = ord.hashCode() * iterableSeed
  }

  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 IterableOrdering[CC, T](ord)

    /** 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] = new Ordering[T] {
    def compare(x: T, y: T) = ord.compare(f(x), f(y))
    override def lt(x: T, y: T): Boolean = ord.lt(f(x), f(y))
    override def gt(x: T, y: T): Boolean = ord.gt(f(x), f(y))
    override def gteq(x: T, y: T): Boolean = ord.gteq(f(x), f(y))
    override def lteq(x: T, y: T): Boolean = ord.lteq(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) = java.lang.Boolean.compare(x, y)
  }
  implicit object Boolean extends BooleanOrdering

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

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

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

  trait IntOrdering extends Ordering[Int] {
    def compare(x: Int, y: Int) = java.lang.Integer.compare(x, y)
    override def reverse: Ordering[Int] = IntReverse
  }
  implicit object Int extends IntOrdering

  trait LongOrdering extends Ordering[Long] {
    def compare(x: Long, y: Long) = java.lang.Long.compare(x, y)
  }
  implicit object Long extends LongOrdering

  trait FloatOrdering extends Ordering[Float] {
    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)
  }
  implicit object Float extends FloatOrdering

  trait DoubleOrdering extends Ordering[Double] {
    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)
  }
  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)
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: OptionOrdering[T]      => this.optionOrdering == that.optionOrdering
      case _                            => false
    }
    override def hashCode(): Int = optionOrdering.hashCode() * optionSeed
  }
  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 IterableOrdering[Iterable, T](ord)

  implicit def Tuple2[T1, T2](implicit ord1: Ordering[T1], ord2: Ordering[T2]): Ordering[(T1, T2)] =
    new Tuple2Ordering(ord1, ord2)

  private[this] final class Tuple2Ordering[T1, T2](private val ord1: Ordering[T1],
                                                   private val ord2: Ordering[T2]) extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple2Ordering[T1, T2] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2).hashCode()
  }

  implicit def Tuple3[T1, T2, T3](implicit ord1: Ordering[T1], ord2: Ordering[T2], ord3: Ordering[T3]) : Ordering[(T1, T2, T3)] =
    new Tuple3Ordering(ord1, ord2, ord3)

  private[this] final class Tuple3Ordering[T1, T2, T3](private val ord1: Ordering[T1],
                                                       private val ord2: Ordering[T2],
                                                       private val ord3: Ordering[T3]) extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple3Ordering[T1, T2, T3] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3).hashCode()
  }

  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 Tuple4Ordering(ord1, ord2, ord3, ord4)

  private[this] final class Tuple4Ordering[T1, T2, T3, T4](private val ord1: Ordering[T1],
                                                           private val ord2: Ordering[T2],
                                                           private val ord3: Ordering[T3],
                                                           private val ord4: Ordering[T4])
    extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple4Ordering[T1, T2, T3, T4] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3 &&
        this.ord4 == that.ord4
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3, ord4).hashCode()
  }

  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 Tuple5Ordering(ord1, ord2, ord3, ord4, ord5)

  private[this] final class Tuple5Ordering[T1, T2, T3, T4, T5](private val ord1: Ordering[T1],
                                                               private val ord2: Ordering[T2],
                                                               private val ord3: Ordering[T3],
                                                               private val ord4: Ordering[T4],
                                                               private val ord5: Ordering[T5])
    extends Ordering[(T1, T2, T3, T4, T5)] {
    def compare(x: (T1, T2, T3, T4, T5), y: (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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple5Ordering[T1, T2, T3, T4, T5] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3 &&
        this.ord4 == that.ord4 &&
        this.ord5 == that.ord5
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3, ord4, ord5).hashCode()
  }

  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 Tuple6Ordering(ord1, ord2, ord3, ord4, ord5, ord6)

  private[this] final class Tuple6Ordering[T1, T2, T3, T4, T5, T6](private val ord1: Ordering[T1],
                                                                   private val ord2: Ordering[T2],
                                                                   private val ord3: Ordering[T3],
                                                                   private val ord4: Ordering[T4],
                                                                   private val ord5: Ordering[T5],
                                                                   private val ord6: Ordering[T6])
    extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple6Ordering[T1, T2, T3, T4, T5, T6] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3 &&
        this.ord4 == that.ord4 &&
        this.ord5 == that.ord5 &&
        this.ord6 == that.ord6
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3, ord4, ord5, ord6).hashCode()
  }

  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 Tuple7Ordering(ord1, ord2, ord3, ord4, ord5, ord6, ord7)

  private[this] final class Tuple7Ordering[T1, T2, T3, T4, T5, T6, T7](private val ord1: Ordering[T1],
                                                                       private val ord2: Ordering[T2],
                                                                       private val ord3: Ordering[T3],
                                                                       private val ord4: Ordering[T4],
                                                                       private val ord5: Ordering[T5],
                                                                       private val ord6: Ordering[T6],
                                                                       private val ord7: Ordering[T7])
    extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple7Ordering[T1, T2, T3, T4, T5, T6, T7] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3 &&
        this.ord4 == that.ord4 &&
        this.ord5 == that.ord5 &&
        this.ord6 == that.ord6 &&
        this.ord7 == that.ord7
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3, ord4, ord5, ord6, ord7).hashCode()
  }

  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 Tuple8Ordering(ord1, ord2, ord3, ord4, ord5, ord6, ord7, ord8)

  private[this] final class Tuple8Ordering[T1, T2, T3, T4, T5, T6, T7, T8](private val ord1: Ordering[T1],
                                                                           private val ord2: Ordering[T2],
                                                                           private val ord3: Ordering[T3],
                                                                           private val ord4: Ordering[T4],
                                                                           private val ord5: Ordering[T5],
                                                                           private val ord6: Ordering[T6],
                                                                           private val ord7: Ordering[T7],
                                                                           private val ord8: Ordering[T8])
    extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple8Ordering[T1, T2, T3, T4, T5, T6, T7, T8] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3 &&
        this.ord4 == that.ord4 &&
        this.ord5 == that.ord5 &&
        this.ord6 == that.ord6 &&
        this.ord7 == that.ord7 &&
        this.ord8 == that.ord8
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3, ord4, ord5, ord6, ord7, ord8).hashCode()
  }

  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 Tuple9Ordering(ord1, ord2, ord3, ord4, ord5, ord6, ord7, ord8, ord9)

  private[this] final class Tuple9Ordering[T1, T2, T3, T4, T5, T6, T7, T8, T9](private val ord1: Ordering[T1],
                                                                               private val ord2: Ordering[T2],
                                                                               private val ord3: Ordering[T3],
                                                                               private val ord4: Ordering[T4],
                                                                               private val ord5: Ordering[T5],
                                                                               private val ord6: Ordering[T6],
                                                                               private val ord7: Ordering[T7],
                                                                               private val ord8: Ordering[T8],
                                                                               private val ord9: Ordering[T9])
    extends 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
    }

    override def equals(obj: scala.Any): Boolean = obj match {
      case that: AnyRef if this eq that => true
      case that: Tuple9Ordering[T1, T2, T3, T4, T5, T6, T7, T8, T9] =>
        this.ord1 == that.ord1 &&
        this.ord2 == that.ord2 &&
        this.ord3 == that.ord3 &&
        this.ord4 == that.ord4 &&
        this.ord5 == that.ord5 &&
        this.ord6 == that.ord6 &&
        this.ord7 == that.ord7 &&
        this.ord8 == that.ord8 &&
        this.ord9 == that.ord9
      case _ => false
    }
    override def hashCode(): Int = (ord1, ord2, ord3, ord4, ord5, ord6, ord7, ord8, ord9).hashCode()
  }
}




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