scala.math.Ordering.scala Maven / Gradle / Ivy
/* __ *\
** ________ ___ / / ___ Scala API **
** / __/ __// _ | / / / _ | (c) 2003-2010, LAMP/EPFL **
** __\ \/ /__/ __ |/ /__/ __ | http://scala-lang.org/ **
** /____/\___/_/ |_/____/_/ | | **
** |/ **
\* */
package scala.math
import java.util.Comparator
/** A trait for representing total orderings. It is important to
* distinguish between a type that has a total order and a representation
* of total ordering on some type. This trait is for representing the
* latter.
*
* A total ordering
* is a binary relation on a type T that is also an equivalence relation
* and partial ordering on values of type T. This relation is exposed as
* the compare method of the Ordering trait.
* This relation must be:
*
* - reflexive:
compare(x, x) == 0, for any x of
* type T.
* - symmetry:
compare(x, y) == z and compare(y, x) == w
* then math.signum(z) == -math.signum(w), for any x and y of
* type T and z and w of type Int.
* - transitive: if
compare(x, y) == z and compare(y, w) == v
* and math.signum(z) >= 0 and math.signum(v) >= 0 then
* compare(x, w) == u and math.signum(z + v) == math.signum(u),
* for any x, y,
* and w of type T and z, v, and u
* of type Int.
*
*
* @author Geoffrey Washburn
* @version 0.9.5, 2008-04-15
* @since 2.7
*/
@serializable
trait Ordering[T] extends Comparator[T] with PartialOrdering[T] {
outer =>
/** An Ordering is defined at all x and y. */
def tryCompare(x: T, y: T) = Some(compare(x, y))
/** Returns a negative integer iff x comes before
* y in the ordering, returns 0 iff x
* is the same in the ordering as y, and returns a
* positive number iff x comes after
* y in the ordering.
*/
def compare(x: T, y: T): Int
/** Returns true iff x comes before
* y in the ordering.
*/
override def lteq(x: T, y: T): Boolean = compare(x, y) <= 0
/** Returns true iff y comes before
* x in the ordering.
*/
override def gteq(x: T, y: T): Boolean = compare(x, y) >= 0
/** Returns true iff x comes before
* y in the ordering and is not the same as y.
*/
override def lt(x: T, y: T): Boolean = compare(x, y) < 0
/** Returns true iff y comes before
* x in the ordering and is not the same as x.
*/
override def gt(x: T, y: T): Boolean = compare(x, y) > 0
/** Returns true iff x is equivalent to
* y in the ordering.
*/
override def equiv(x: T, y: T): Boolean = compare(x, y) == 0
/** Returns the argument which comes later in the ordering. */
def max(x: T, y: T): T = if (gteq(x, y)) x else y
/** Returns the argument which comes earlier in the ordering. */
def min(x: T, y: T): T = if (lteq(x, y)) x else y
override def reverse: Ordering[T] = new Ordering[T]{
override def reverse = outer
def compare(x: T, y: T) = outer.compare(y, x)
}
/** Given a function U => T, creates Ordering[U]. */
def on[U](f: U => T): Ordering[U] = new Ordering[U] {
def compare(x: U, y: U) = outer.compare(f(x), f(y))
}
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)
}
implicit def mkOrderingOps(lhs: T): Ops = new Ops(lhs)
}
/** 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.
*/
trait LowPriorityOrderingImplicits {
implicit def ordered[A <: Ordered[A]]: Ordering[A] = new Ordering[A] {
def compare(x: A, y: A) = x.compare(y)
}
}
object Ordering extends LowPriorityOrderingImplicits {
def apply[T](implicit ord : Ordering[T]) = ord
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)
}
def by[T, S: Ordering](f: T => S): Ordering[T] = fromLessThan((x, y) => implicitly[Ordering[S]].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] {
def compare(x: Float, y: Float) = java.lang.Float.compare(x, y)
}
implicit object Float extends FloatOrdering
trait DoubleOrdering extends Ordering[Double] {
def compare(x: Double, y: Double) = java.lang.Double.compare(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
implicit def Option[T](implicit ord: Ordering[T]) : Ordering[Option[T]] =
new Ordering[Option[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)) => ord.compare(x, y)
}
}
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
}
}
}
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