* </ul>
 *
 * <h3>Understanding complex orderings</h3>
 *
 * <p>Complex chained orderings like the following example can be challenging to understand.
 *
 * <pre>{@code
 * Ordering<Foo> ordering =
 *     Ordering.natural()
 *         .nullsFirst()
 *         .onResultOf(getBarFunction)
 *         .nullsLast();
 * }</pre>
 *
 * Note that each chaining method returns a new ordering instance which is backed by the previous

 * </ul>
 *
 * <h3>Understanding complex orderings</h3>
 *
 * <p>Complex chained orderings like the following example can be challenging to understand.
 *
 * <pre>{@code
 * Ordering<Foo> ordering =
 *     Ordering.natural()
 *         .nullsFirst()
 *         .onResultOf(getBarFunction)
 *         .nullsLast();
 * }</pre>
 *
 * Note that each chaining method returns a new ordering instance which is backed by the previous

John Howard <******@****.***> 1622745909 -0700

      GeneralRange<@Nullable Integer> range = GeneralRange.downTo(ORDERING, 3, lBoundType);
      for (Integer i : IN_ORDER_VALUES) {
        assertEquals(
            ORDERING.compare(i, 3) > 0 || (ORDERING.compare(i, 3) == 0 && lBoundType == CLOSED),
            range.contains(i));
        assertEquals(
            ORDERING.compare(i, 3) < 0 || (ORDERING.compare(i, 3) == 0 && lBoundType == OPEN),
            range.tooLow(i));

  ByFunctionOrdering(Function<F, ? extends T> function, Ordering<T> ordering) {
    this.function = checkNotNull(function);
    this.ordering = checkNotNull(ordering);
  }

  @Override
  public int compare(@ParametricNullness F left, @ParametricNullness F right) {
    return ordering.compare(function.apply(left), function.apply(right));
  }

  @Override
  public boolean equals(@CheckForNull Object object) {

/** An ordering that treats {@code null} as less than all other values. */
@GwtCompatible(serializable = true)
@ElementTypesAreNonnullByDefault
final class NullsFirstOrdering<T extends @Nullable Object> extends Ordering<@Nullable T>
    implements Serializable {
  final Ordering<? super T> ordering;

  NullsFirstOrdering(Ordering<? super T> ordering) {
    this.ordering = ordering;
  }

  @Override

/** An ordering that treats {@code null} as greater than all other values. */
@GwtCompatible(serializable = true)
@ElementTypesAreNonnullByDefault
final class NullsLastOrdering<T extends @Nullable Object> extends Ordering<@Nullable T>
    implements Serializable {
  final Ordering<? super T> ordering;

  NullsLastOrdering(Ordering<? super T> ordering) {
    this.ordering = ordering;
  }

  @Override

/** An ordering that treats {@code null} as greater than all other values. */
@GwtCompatible(serializable = true)
@ElementTypesAreNonnullByDefault
final class NullsLastOrdering<T extends @Nullable Object> extends Ordering<@Nullable T>
    implements Serializable {
  final Ordering<? super T> ordering;

  NullsLastOrdering(Ordering<? super T> ordering) {
    this.ordering = ordering;
  }

  @Override

    Helpers.testComparator(arbitrary, list);
  }

  public void testUsingToString() {
    Ordering<Object> ordering = Ordering.usingToString();
    Helpers.testComparator(ordering, 1, 12, 124, 2);
    assertEquals("Ordering.usingToString()", ordering.toString());
    assertSame(ordering, reserialize(ordering));
  }

  // use an enum to get easy serializability

  ByFunctionOrdering(Function<F, ? extends T> function, Ordering<T> ordering) {
    this.function = checkNotNull(function);
    this.ordering = checkNotNull(ordering);
  }

  @Override
  public int compare(@ParametricNullness F left, @ParametricNullness F right) {
    return ordering.compare(function.apply(left), function.apply(right));
  }

  @Override
  public boolean equals(@CheckForNull Object object) {