/*
 * Copyright (C) 2008 The Guava Authors
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package com.google.common.collect;

import static com.google.common.base.Preconditions.checkNotNull;

import java.io.Serializable;
import java.util.Comparator;
import java.util.Iterator;
import java.util.NoSuchElementException;
import java.util.SortedSet;

import javax.annotation.Nullable;

import com.google.common.annotations.GwtCompatible;
import com.google.common.base.Equivalence;
import com.google.common.base.Function;
import com.google.common.base.Predicate;

/**
 * A range (or "interval") defines the <i>boundaries</i> around a contiguous
 * span of values of some {@code Comparable} type; for example, "integers from 1
 * to 100 inclusive." Note that it is not possible to <i>iterate</i> over these
 * contained values. To do so, pass this range instance and an appropriate
 * {@link DiscreteDomain} to {@link ContiguousSet#create}.
 *
 * <h3>Types of ranges</h3>
 *
 * <p>
 * Each end of the range may be bounded or unbounded. If bounded, there is an
 * associated <i>endpoint</i> value, and the range is considered to be either
 * <i>open</i> (does not include the endpoint) or <i>closed</i> (includes the
 * endpoint) on that side. With three possibilities on each side, this yields
 * nine basic types of ranges, enumerated below. (Notation: a square bracket
 * ({@code [ ]}) indicates that the range is closed on that side; a parenthesis
 * ({@code ( )}) means it is either open or unbounded. The construct {@code {x |
 * statement}} is read "the set of all <i>x</i> such that <i>statement</i>.")
 *
 * <blockquote>
 * <table>
 * <tr>
 * <td><b>Notation</b>
 * <td><b>Definition</b>
 * <td><b>Factory method</b>
 * <tr>
 * <td>{@code (a..b)}
 * <td>{@code {x | a < x < b}}
 * <td>{@link Range#open open}
 * <tr>
 * <td>{@code [a..b]}
 * <td>{@code {x | a <= x <= b}}
 * <td>{@link Range#closed closed}
 * <tr>
 * <td>{@code (a..b]}
 * <td>{@code {x | a < x <= b}}
 * <td>{@link Range#openClosed openClosed}
 * <tr>
 * <td>{@code [a..b)}
 * <td>{@code {x | a <= x < b}}
 * <td>{@link Range#closedOpen closedOpen}
 * <tr>
 * <td>{@code (a..+∞)}
 * <td>{@code {x | x > a}}
 * <td>{@link Range#greaterThan greaterThan}
 * <tr>
 * <td>{@code [a..+∞)}
 * <td>{@code {x | x >= a}}
 * <td>{@link Range#atLeast atLeast}
 * <tr>
 * <td>{@code (-∞..b)}
 * <td>{@code {x | x < b}}
 * <td>{@link Range#lessThan lessThan}
 * <tr>
 * <td>{@code (-∞..b]}
 * <td>{@code {x | x <= b}}
 * <td>{@link Range#atMost atMost}
 * <tr>
 * <td>{@code (-∞..+∞)}
 * <td>{@code {x}}
 * <td>{@link Range#all all}
 * </table>
 * </blockquote>
 *
 * <p>
 * When both endpoints exist, the upper endpoint may not be less than the lower.
 * The endpoints may be equal only if at least one of the bounds is closed:
 *
 * <ul>
 * <li>{@code [a..a]} : a singleton range
 * <li>{@code [a..a); (a..a]} : {@linkplain #isEmpty empty} ranges; also valid
 * <li>{@code (a..a)} : <b>invalid</b>; an exception will be thrown
 * </ul>
 *
 * <h3>Warnings</h3>
 *
 * <ul>
 * <li>Use immutable value types only, if at all possible. If you must use a
 * mutable type, <b>do not</b> allow the endpoint instances to mutate after the
 * range is created!
 * <li>Your value type's comparison method should be {@linkplain Comparable
 * consistent with equals} if at all possible. Otherwise, be aware that concepts
 * used throughout this documentation such as "equal", "same", "unique" and so
 * on actually refer to whether {@link Comparable#compareTo compareTo} returns
 * zero, not whether {@link Object#equals equals} returns {@code true}.
 * <li>A class which implements {@code Comparable<UnrelatedType>} is very
 * broken, and will cause undefined horrible things to happen in {@code Range}.
 * For now, the Range API does not prevent its use, because this would also rule
 * out all ungenerified (pre-JDK1.5) data types. <b>This may change in the
 * future.</b>
 * </ul>
 *
 * <h3>Other notes</h3>
 *
 * <ul>
 * <li>Instances of this type are obtained using the static factory methods in
 * this class.
 * <li>Ranges are <i>convex</i>: whenever two values are contained, all values
 * in between them must also be contained. More formally, for any
 * {@code c1 <= c2 <= c3} of type {@code C}, {@code
 *     r.contains(c1) && r.contains(c3)} implies {@code r.contains(c2)}). This
 * means that a {@code
 *     Range<Integer>} can never be used to represent, say, "all <i>prime</i>
 * numbers from 1 to 100."
 * <li>When evaluated as a {@link Predicate}, a range yields the same result as
 * invoking {@link #contains}.
 * <li>Terminology note: a range {@code a} is said to be the <i>maximal</i>
 * range having property <i>P</i> if, for all ranges {@code b} also having
 * property <i>P</i>, {@code a.encloses(b)}. Likewise, {@code a} is
 * <i>minimal</i> when {@code b.encloses(a)} for all {@code b} having property
 * <i>P</i>. See, for example, the definition of {@link #intersection
 * intersection}.
 * </ul>
 *
 * <h3>Further reading</h3>
 *
 * <p>
 * See the Guava User Guide article on <a href=
 * "http://code.google.com/p/guava-libraries/wiki/RangesExplained">{@code Range}</a>.
 *
 * @author Kevin Bourrillion
 * @author Gregory Kick
 * @since 10.0
 */
@GwtCompatible
@SuppressWarnings("rawtypes")
public final class Range<C extends Comparable> implements Predicate<C>, Serializable {

	private static final Function<Range, Cut> LOWER_BOUND_FN = new Function<Range, Cut>() {
		@Override
		public Cut apply(Range range) {
			return range.lowerBound;
		}
	};

	@SuppressWarnings("unchecked")
	static <C extends Comparable<?>> Function<Range<C>, Cut<C>> lowerBoundFn() {
		return (Function) LOWER_BOUND_FN;
	}

	private static final Function<Range, Cut> UPPER_BOUND_FN = new Function<Range, Cut>() {
		@Override
		public Cut apply(Range range) {
			return range.upperBound;
		}
	};

	@SuppressWarnings("unchecked")
	static <C extends Comparable<?>> Function<Range<C>, Cut<C>> upperBoundFn() {
		return (Function) UPPER_BOUND_FN;
	}

	static final Ordering<Range<?>> RANGE_LEX_ORDERING = new Ordering<Range<?>>() {
		@Override
		public int compare(Range<?> left, Range<?> right) {
			return ComparisonChain.start().compare(left.lowerBound, right.lowerBound)
					.compare(left.upperBound, right.upperBound).result();
		}
	};

	static <C extends Comparable<?>> Range<C> create(Cut<C> lowerBound, Cut<C> upperBound) {
		return new Range<C>(lowerBound, upperBound);
	}

	/**
	 * Returns a range that contains all values strictly greater than {@code
	 * lower} and strictly less than {@code upper}.
	 *
	 * @throws IllegalArgumentException if {@code lower} is greater than <i>or equal
	 *                                  to</i> {@code upper}
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> open(C lower, C upper) {
		return create(Cut.aboveValue(lower), Cut.belowValue(upper));
	}

	/**
	 * Returns a range that contains all values greater than or equal to
	 * {@code lower} and less than or equal to {@code upper}.
	 *
	 * @throws IllegalArgumentException if {@code lower} is greater than {@code
	 *     upper}
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> closed(C lower, C upper) {
		return create(Cut.belowValue(lower), Cut.aboveValue(upper));
	}

	/**
	 * Returns a range that contains all values greater than or equal to
	 * {@code lower} and strictly less than {@code upper}.
	 *
	 * @throws IllegalArgumentException if {@code lower} is greater than {@code
	 *     upper}
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> closedOpen(C lower, C upper) {
		return create(Cut.belowValue(lower), Cut.belowValue(upper));
	}

	/**
	 * Returns a range that contains all values strictly greater than {@code
	 * lower} and less than or equal to {@code upper}.
	 *
	 * @throws IllegalArgumentException if {@code lower} is greater than {@code
	 *     upper}
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> openClosed(C lower, C upper) {
		return create(Cut.aboveValue(lower), Cut.aboveValue(upper));
	}

	/**
	 * Returns a range that contains any value from {@code lower} to {@code
	 * upper}, where each endpoint may be either inclusive (closed) or exclusive
	 * (open).
	 *
	 * @throws IllegalArgumentException if {@code lower} is greater than {@code
	 *     upper}
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> range(C lower, BoundType lowerType, C upper, BoundType upperType) {
		checkNotNull(lowerType);
		checkNotNull(upperType);

		Cut<C> lowerBound = (lowerType == BoundType.OPEN) ? Cut.aboveValue(lower) : Cut.belowValue(lower);
		Cut<C> upperBound = (upperType == BoundType.OPEN) ? Cut.belowValue(upper) : Cut.aboveValue(upper);
		return create(lowerBound, upperBound);
	}

	/**
	 * Returns a range that contains all values strictly less than {@code
	 * endpoint}.
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> lessThan(C endpoint) {
		return create(Cut.<C>belowAll(), Cut.belowValue(endpoint));
	}

	/**
	 * Returns a range that contains all values less than or equal to
	 * {@code endpoint}.
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> atMost(C endpoint) {
		return create(Cut.<C>belowAll(), Cut.aboveValue(endpoint));
	}

	/**
	 * Returns a range with no lower bound up to the given endpoint, which may be
	 * either inclusive (closed) or exclusive (open).
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> upTo(C endpoint, BoundType boundType) {
		switch (boundType) {
		case OPEN:
			return lessThan(endpoint);
		case CLOSED:
			return atMost(endpoint);
		default:
			throw new AssertionError();
		}
	}

	/**
	 * Returns a range that contains all values strictly greater than {@code
	 * endpoint}.
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> greaterThan(C endpoint) {
		return create(Cut.aboveValue(endpoint), Cut.<C>aboveAll());
	}

	/**
	 * Returns a range that contains all values greater than or equal to
	 * {@code endpoint}.
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> atLeast(C endpoint) {
		return create(Cut.belowValue(endpoint), Cut.<C>aboveAll());
	}

	/**
	 * Returns a range from the given endpoint, which may be either inclusive
	 * (closed) or exclusive (open), with no upper bound.
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> downTo(C endpoint, BoundType boundType) {
		switch (boundType) {
		case OPEN:
			return greaterThan(endpoint);
		case CLOSED:
			return atLeast(endpoint);
		default:
			throw new AssertionError();
		}
	}

	private static final Range<Comparable> ALL = new Range<Comparable>(Cut.belowAll(), Cut.aboveAll());

	/**
	 * Returns a range that contains every value of type {@code C}.
	 *
	 * @since 14.0
	 */
	@SuppressWarnings("unchecked")
	public static <C extends Comparable<?>> Range<C> all() {
		return (Range) ALL;
	}

	/**
	 * Returns a range that {@linkplain Range#contains(Comparable) contains} only
	 * the given value. The returned range is {@linkplain BoundType#CLOSED closed}
	 * on both ends.
	 *
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> singleton(C value) {
		return closed(value, value);
	}

	/**
	 * Returns the minimal range that {@linkplain Range#contains(Comparable)
	 * contains} all of the given values. The returned range is
	 * {@linkplain BoundType#CLOSED closed} on both ends.
	 *
	 * @throws ClassCastException     if the parameters are not <i>mutually
	 *                                comparable</i>
	 * @throws NoSuchElementException if {@code values} is empty
	 * @throws NullPointerException   if any of {@code values} is null
	 * @since 14.0
	 */
	public static <C extends Comparable<?>> Range<C> encloseAll(Iterable<C> values) {
		checkNotNull(values);
		if (values instanceof ContiguousSet) {
			return ((ContiguousSet<C>) values).range();
		}
		Iterator<C> valueIterator = values.iterator();
		C min = checkNotNull(valueIterator.next());
		C max = min;
		while (valueIterator.hasNext()) {
			C value = checkNotNull(valueIterator.next());
			min = Ordering.natural().min(min, value);
			max = Ordering.natural().max(max, value);
		}
		return closed(min, max);
	}

	final Cut<C> lowerBound;
	final Cut<C> upperBound;

	private Range(Cut<C> lowerBound, Cut<C> upperBound) {
		if (lowerBound.compareTo(upperBound) > 0 || lowerBound == Cut.<C>aboveAll()
				|| upperBound == Cut.<C>belowAll()) {
			throw new IllegalArgumentException("Invalid range: " + toString(lowerBound, upperBound));
		}
		this.lowerBound = checkNotNull(lowerBound);
		this.upperBound = checkNotNull(upperBound);
	}

	/**
	 * Returns {@code true} if this range has a lower endpoint.
	 */
	public boolean hasLowerBound() {
		return lowerBound != Cut.belowAll();
	}

	/**
	 * Returns the lower endpoint of this range.
	 *
	 * @throws IllegalStateException if this range is unbounded below (that is,
	 *                               {@link #hasLowerBound()} returns {@code false})
	 */
	public C lowerEndpoint() {
		return lowerBound.endpoint();
	}

	/**
	 * Returns the type of this range's lower bound: {@link BoundType#CLOSED} if the
	 * range includes its lower endpoint, {@link BoundType#OPEN} if it does not.
	 *
	 * @throws IllegalStateException if this range is unbounded below (that is,
	 *                               {@link #hasLowerBound()} returns {@code false})
	 */
	public BoundType lowerBoundType() {
		return lowerBound.typeAsLowerBound();
	}

	/**
	 * Returns {@code true} if this range has an upper endpoint.
	 */
	public boolean hasUpperBound() {
		return upperBound != Cut.aboveAll();
	}

	/**
	 * Returns the upper endpoint of this range.
	 *
	 * @throws IllegalStateException if this range is unbounded above (that is,
	 *                               {@link #hasUpperBound()} returns {@code false})
	 */
	public C upperEndpoint() {
		return upperBound.endpoint();
	}

	/**
	 * Returns the type of this range's upper bound: {@link BoundType#CLOSED} if the
	 * range includes its upper endpoint, {@link BoundType#OPEN} if it does not.
	 *
	 * @throws IllegalStateException if this range is unbounded above (that is,
	 *                               {@link #hasUpperBound()} returns {@code false})
	 */
	public BoundType upperBoundType() {
		return upperBound.typeAsUpperBound();
	}

	/**
	 * Returns {@code true} if this range is of the form {@code [v..v)} or
	 * {@code (v..v]}. (This does not encompass ranges of the form {@code (v..v)},
	 * because such ranges are <i>invalid</i> and can't be constructed at all.)
	 *
	 * <p>
	 * Note that certain discrete ranges such as the integer range {@code (3..4)}
	 * are <b>not</b> considered empty, even though they contain no actual values.
	 * In these cases, it may be helpful to preprocess ranges with
	 * {@link #canonical(DiscreteDomain)}.
	 */
	public boolean isEmpty() {
		return lowerBound.equals(upperBound);
	}

	/**
	 * Returns {@code true} if {@code value} is within the bounds of this range. For
	 * example, on the range {@code [0..2)}, {@code contains(1)} returns
	 * {@code true}, while {@code contains(2)} returns {@code false}.
	 */
	public boolean contains(C value) {
		checkNotNull(value);
		// let this throw CCE if there is some trickery going on
		return lowerBound.isLessThan(value) && !upperBound.isLessThan(value);
	}

	/**
	 * @deprecated Provided only to satisfy the {@link Predicate} interface; use
	 *             {@link #contains} instead.
	 */
	@Deprecated
	@Override
	public boolean apply(C input) {
		return contains(input);
	}

	/**
	 * Returns {@code true} if every element in {@code values} is
	 * {@linkplain #contains contained} in this range.
	 */
	public boolean containsAll(Iterable<? extends C> values) {
		if (Iterables.isEmpty(values)) {
			return true;
		}

		// this optimizes testing equality of two range-backed sets
		if (values instanceof SortedSet) {
			SortedSet<? extends C> set = cast(values);
			Comparator<?> comparator = set.comparator();
			if (Ordering.natural().equals(comparator) || comparator == null) {
				return contains(set.first()) && contains(set.last());
			}
		}

		for (C value : values) {
			if (!contains(value)) {
				return false;
			}
		}
		return true;
	}

	/**
	 * Returns {@code true} if the bounds of {@code other} do not extend outside the
	 * bounds of this range. Examples:
	 *
	 * <ul>
	 * <li>{@code [3..6]} encloses {@code [4..5]}
	 * <li>{@code (3..6)} encloses {@code (3..6)}
	 * <li>{@code [3..6]} encloses {@code [4..4)} (even though the latter is empty)
	 * <li>{@code (3..6]} does not enclose {@code [3..6]}
	 * <li>{@code [4..5]} does not enclose {@code (3..6)} (even though it contains
	 * every value contained by the latter range)
	 * <li>{@code [3..6]} does not enclose {@code (1..1]} (even though it contains
	 * every value contained by the latter range)
	 * </ul>
	 *
	 * <p>
	 * Note that if {@code a.encloses(b)}, then {@code b.contains(v)} implies
	 * {@code a.contains(v)}, but as the last two examples illustrate, the converse
	 * is not always true.
	 *
	 * <p>
	 * Being reflexive, antisymmetric and transitive, the {@code encloses} relation
	 * defines a <i>partial order</i> over ranges. There exists a unique
	 * {@linkplain Range#all maximal} range according to this relation, and also
	 * numerous {@linkplain #isEmpty minimal} ranges. Enclosure also implies
	 * {@linkplain #isConnected connectedness}.
	 */
	public boolean encloses(Range<C> other) {
		return lowerBound.compareTo(other.lowerBound) <= 0 && upperBound.compareTo(other.upperBound) >= 0;
	}

	/**
	 * Returns {@code true} if there exists a (possibly empty) range which is
	 * {@linkplain #encloses enclosed} by both this range and {@code other}.
	 *
	 * <p>
	 * For example,
	 * <ul>
	 * <li>{@code [2, 4)} and {@code [5, 7)} are not connected
	 * <li>{@code [2, 4)} and {@code [3, 5)} are connected, because both enclose
	 * {@code [3, 4)}
	 * <li>{@code [2, 4)} and {@code [4, 6)} are connected, because both enclose the
	 * empty range {@code [4, 4)}
	 * </ul>
	 *
	 * <p>
	 * Note that this range and {@code other} have a well-defined {@linkplain #span
	 * union} and {@linkplain #intersection intersection} (as a single,
	 * possibly-empty range) if and only if this method returns {@code true}.
	 *
	 * <p>
	 * The connectedness relation is both reflexive and symmetric, but does not form
	 * an {@linkplain Equivalence equivalence relation} as it is not transitive.
	 * 
	 * <p>
	 * Note that certain discrete ranges are not considered connected, even though
	 * there are no elements "between them." For example, {@code [3, 5]} is not
	 * considered connected to {@code 
	 * [6, 10]}. In these cases, it may be desirable for both input ranges to be
	 * preprocessed with {@link #canonical(DiscreteDomain)} before testing for
	 * connectedness.
	 */
	public boolean isConnected(Range<C> other) {
		return lowerBound.compareTo(other.upperBound) <= 0 && other.lowerBound.compareTo(upperBound) <= 0;
	}

	/**
	 * Returns the maximal range {@linkplain #encloses enclosed} by both this range
	 * and {@code
	 * connectedRange}, if such a range exists.
	 *
	 * <p>
	 * For example, the intersection of {@code [1..5]} and {@code (3..7)} is
	 * {@code (3..5]}. The resulting range may be empty; for example, {@code [1..5)}
	 * intersected with {@code [5..7)} yields the empty range {@code [5..5)}.
	 *
	 * <p>
	 * The intersection exists if and only if the two ranges are
	 * {@linkplain #isConnected connected}.
	 *
	 * <p>
	 * The intersection operation is commutative, associative and idempotent, and
	 * its identity element is {@link Range#all}).
	 *
	 * @throws IllegalArgumentException if {@code isConnected(connectedRange)} is
	 *                                  {@code false}
	 */
	public Range<C> intersection(Range<C> connectedRange) {
		int lowerCmp = lowerBound.compareTo(connectedRange.lowerBound);
		int upperCmp = upperBound.compareTo(connectedRange.upperBound);
		if (lowerCmp >= 0 && upperCmp <= 0) {
			return this;
		} else if (lowerCmp <= 0 && upperCmp >= 0) {
			return connectedRange;
		} else {
			Cut<C> newLower = (lowerCmp >= 0) ? lowerBound : connectedRange.lowerBound;
			Cut<C> newUpper = (upperCmp <= 0) ? upperBound : connectedRange.upperBound;
			return create(newLower, newUpper);
		}
	}

	/**
	 * Returns the minimal range that {@linkplain #encloses encloses} both this
	 * range and {@code
	 * other}. For example, the span of {@code [1..3]} and {@code (5..7)} is
	 * {@code [1..7)}.
	 *
	 * <p>
	 * <i>If</i> the input ranges are {@linkplain #isConnected connected}, the
	 * returned range can also be called their <i>union</i>. If they are not, note
	 * that the span might contain values that are not contained in either input
	 * range.
	 *
	 * <p>
	 * Like {@link #intersection(Range) intersection}, this operation is
	 * commutative, associative and idempotent. Unlike it, it is always well-defined
	 * for any two input ranges.
	 */
	public Range<C> span(Range<C> other) {
		int lowerCmp = lowerBound.compareTo(other.lowerBound);
		int upperCmp = upperBound.compareTo(other.upperBound);
		if (lowerCmp <= 0 && upperCmp >= 0) {
			return this;
		} else if (lowerCmp >= 0 && upperCmp <= 0) {
			return other;
		} else {
			Cut<C> newLower = (lowerCmp <= 0) ? lowerBound : other.lowerBound;
			Cut<C> newUpper = (upperCmp >= 0) ? upperBound : other.upperBound;
			return create(newLower, newUpper);
		}
	}

	/**
	 * Returns the canonical form of this range in the given domain. The canonical
	 * form has the following properties:
	 *
	 * <ul>
	 * <li>equivalence: {@code a.canonical().contains(v) == a.contains(v)} for all
	 * {@code v} (in other words,
	 * {@code ContiguousSet.create(a.canonical(domain), domain).equals(
	 *     ContiguousSet.create(a, domain))}
	 * <li>uniqueness: unless {@code a.isEmpty()},
	 * {@code ContiguousSet.create(a, domain).equals(ContiguousSet.create(b, domain))}
	 * implies {@code a.canonical(domain).equals(b.canonical(domain))}
	 * <li>idempotence:
	 * {@code a.canonical(domain).canonical(domain).equals(a.canonical(domain))}
	 * </ul>
	 *
	 * <p>
	 * Furthermore, this method guarantees that the range returned will be one of
	 * the following canonical forms:
	 *
	 * <ul>
	 * <li>[start..end)
	 * <li>[start..+∞)
	 * <li>(-∞..end) (only if type {@code C} is unbounded below)
	 * <li>(-∞..+∞) (only if type {@code C} is unbounded below)
	 * </ul>
	 */
	public Range<C> canonical(DiscreteDomain<C> domain) {
		checkNotNull(domain);
		Cut<C> lower = lowerBound.canonical(domain);
		Cut<C> upper = upperBound.canonical(domain);
		return (lower == lowerBound && upper == upperBound) ? this : create(lower, upper);
	}

	/**
	 * Returns {@code true} if {@code object} is a range having the same endpoints
	 * and bound types as this range. Note that discrete ranges such as
	 * {@code (1..4)} and {@code [2..3]} are <b>not</b> equal to one another,
	 * despite the fact that they each contain precisely the same set of values.
	 * Similarly, empty ranges are not equal unless they have exactly the same
	 * representation, so {@code [3..3)}, {@code (3..3]}, {@code (4..4]} are all
	 * unequal.
	 */
	@Override
	public boolean equals(@Nullable Object object) {
		if (object instanceof Range) {
			Range<?> other = (Range<?>) object;
			return lowerBound.equals(other.lowerBound) && upperBound.equals(other.upperBound);
		}
		return false;
	}

	/** Returns a hash code for this range. */
	@Override
	public int hashCode() {
		return lowerBound.hashCode() * 31 + upperBound.hashCode();
	}

	/**
	 * Returns a string representation of this range, such as {@code "[3..5)"}
	 * (other examples are listed in the class documentation).
	 */
	@Override
	public String toString() {
		return toString(lowerBound, upperBound);
	}

	private static String toString(Cut<?> lowerBound, Cut<?> upperBound) {
		StringBuilder sb = new StringBuilder(16);
		lowerBound.describeAsLowerBound(sb);
		sb.append('\u2025');
		upperBound.describeAsUpperBound(sb);
		return sb.toString();
	}

	/**
	 * Used to avoid http://bugs.sun.com/view_bug.do?bug_id=6558557
	 */
	private static <T> SortedSet<T> cast(Iterable<T> iterable) {
		return (SortedSet<T>) iterable;
	}

	Object readResolve() {
		if (this.equals(ALL)) {
			return all();
		} else {
			return this;
		}
	}

	@SuppressWarnings("unchecked") // this method may throw CCE
	static int compareOrThrow(Comparable left, Comparable right) {
		return left.compareTo(right);
	}

	private static final long serialVersionUID = 0;
}
