/* __ *\
** ________ ___ / / ___ Scala API **
** / __/ __// _ | / / / _ | (c) 2003-2009, LAMP/EPFL **
** __\ \/ /__/ __ |/ /__/ __ | **
** /____/\___/_/ |_/____/_/ | | **
** |/ **
\* */
// $Id$
package scala
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 <a href="http://en.wikipedia.org/wiki/Total_order">total ordering</a>
* is a binary relation on a type <code>T</code> that is also an equivalence relation
* and partial ordering on values of type <code>T</code>. This relation is exposed as
* the <code>compare</code> method of the <code>Ordering</code> trait.
* This relation must be:
* <ul>
* <li>reflexive: <code>compare(x, x) == 0</code>, for any <code>x</code> of
* type <code>T</code>.</li>
* <li>symmetry: <code>compare(x, y) == z</code> and <code>compare(y, x) == w</code>
* then <code>Math.signum(z) == -Math.signum(w)</code>, for any <code>x</code> and <code>y</code> of
* type <code>T</code> and <code>z</code> and <code>w</code> of type <code>Int</code>.</li>
* <li>transitive: if <code>compare(x, y) == z</code> and <code>compare(y, w) == v</code>
* and <code>Math.signum(z) >= 0</code> and <code>Math.signum(v) >= 0</code> then
* <code>compare(x, w) == u</code> and <code>Math.signum(z + v) == Math.signum(u)</code>,
* for any <code>x</code>, <code>y</code>,
* and <code>w</code> of type <code>T</code> and <code>z</code>, <code>v</code>, and <code>u</code>
* of type <code>Int</code>.</li>
* </ul>
*
* @author Geoffrey Washburn
* @version 0.9.5, 2008-04-15
* @since 2.7
*/
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 <code>x</code> comes before
* <code>y</code> in the ordering, returns 0 iff <code>x</code>
* is the same in the ordering as <code>y</code>, and returns a
* positive number iff <code>x</code> comes after
* <code>y</code> in the ordering.
*/
def compare(x: T, y: T): Int
/** Returns <code>true</code> iff <code>x</code> comes before
* <code>y</code> in the ordering.
*/
override def lteq(x: T, y: T): Boolean = compare(x, y) <= 0
/** Returns <code>true</code> iff <code>y</code> comes before
* <code>x</code> in the ordering.
*/
override def gteq(x: T, y: T): Boolean = compare(x, y) >= 0
/** Returns <code>true</code> iff <code>x</code> comes before
* <code>y</code> in the ordering and is not the same as <code>y</code>.
*/
override def lt(x: T, y: T): Boolean = compare(x, y) < 0
/** Returns <code>true</code> iff <code>y</code> comes before
* <code>x</code> in the ordering and is not the same as <code>x</code>.
*/
override def gt(x: T, y: T): Boolean = compare(x, y) > 0
/** Returns <code>true</code> iff <code>x</code> is equivalent to
* <code>y</code> 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);
}
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)
}
object Ordering
{
def apply[T](implicit ord : Ordering[T]) = ord
def ordered[A <: Ordered[A]] : Ordering[A] = new Ordering[A] {
def compare(x : A, y : A) = x.compare(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) =
if(x < y) -1;
else if (x == y) 0;
else 1
}
implicit object Float extends FloatOrdering
trait DoubleOrdering extends Ordering[Double] {
def compare(x : Double, y : Double) =
if(x < y) -1;
else if (x == y) 0;
else 1
}
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 : Tuple2[T1, T2], y : Tuple2[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 : Tuple3[T1, T2, T3], y : Tuple3[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 : Tuple4[T1, T2, T3, T4], y : Tuple4[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 : Tuple5[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 : Tuple6[T1, T2, T3, T4, T5, T6], y : Tuple6[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 : Tuple7[T1, T2, T3, T4, T5, T6, T7], y : Tuple7[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 : Tuple8[T1, T2, T3, T4, T5, T6, T7, T8], y : Tuple8[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 : Tuple9[T1, T2, T3, T4, T5, T6, T7, T8, T9], y : Tuple9[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;
}
}
}