}

  /**
   * Returns the {@code int} value that, when treated as unsigned, is equal to {@code value}, if
   * possible.
   *
   * @param value a value between 0 and 2<sup>32</sup>-1 inclusive
   * @return the {@code int} value that, when treated as unsigned, equals {@code value}
   * @throws IllegalArgumentException if {@code value} is negative or greater than or equal to
   *     2<sup>32</sup>
   * @since 21.0
   */

  }

  /**
   * Returns the {@code int} value that, when treated as unsigned, is equal to {@code value}, if
   * possible.
   *
   * @param value a value between 0 and 2<sup>32</sup>-1 inclusive
   * @return the {@code int} value that, when treated as unsigned, equals {@code value}
   * @throws IllegalArgumentException if {@code value} is negative or greater than or equal to
   *     2<sup>32</sup>
   * @since 21.0
   */

    }
    return hash;
  }

  @Override
  public boolean equals(@CheckForNull Object object) {
    if (object instanceof PairwiseEquivalence) {
      @SuppressWarnings("unchecked")
      PairwiseEquivalence<Object, Object> that = (PairwiseEquivalence<Object, Object>) object;
      return this.elementEquivalence.equals(that.elementEquivalence);
    }

    return false;
  }

  @Override

      assertBitEquals(x.get(i), y.get(i));
    }

    AtomicDoubleArray a = new AtomicDoubleArray(VALUES);
    AtomicDoubleArray b = serialClone(a);
    assertFalse(a.equals(b));
    assertFalse(b.equals(a));
    assertEquals(a.length(), b.length());
    for (int i = 0; i < VALUES.length; i++) {
      assertBitEquals(a.get(i), b.get(i));
    }
  }

  /** toString returns current value */

   * example, {@code [] < [1] < [1, 2] < [2]}.
   *
   * <p>The returned comparator is inconsistent with {@link Object#equals(Object)} (since arrays
   * support only identity equality), but it is consistent with {@link Arrays#equals(int[], int[])}.
   *
   * @since 2.0
   */
  public static Comparator<int[]> lexicographicalComparator() {
    return LexicographicalComparator.INSTANCE;
  }

  public int hashCode() {
    return -forwardOrder.hashCode();
  }

  @Override
  public boolean equals(@CheckForNull Object object) {
    if (object == this) {
      return true;
    }
    if (object instanceof ReverseOrdering) {
      ReverseOrdering<?> that = (ReverseOrdering<?>) object;
      return this.forwardOrder.equals(that.forwardOrder);
    }
    return false;
  }

  @Override

      // similar to putInBothMaps, but set via entry
      if (Objects.equal(value, getValue())) {
        return value;
      }
      checkArgument(!containsValue(value), "value already present: %s", value);
      V oldValue = delegate.setValue(value);
      checkState(Objects.equal(value, get(getKey())), "entry no longer in map");
      updateInverseMap(getKey(), true, oldValue, value);

{!> ../../docs_src/path_params_numeric_validations/tutorial003_an.py!}
```

////

## Number validations: greater than or equal

With `Query` and `Path` (and others you'll see later) you can declare number constraints.

Here, with `ge=1`, `item_id` will need to be an integer number "`g`reater than or `e`qual" to `1`.

//// tab | Python 3.9+

```Python hl_lines="10"

    // instead of Object[].
    return delegateList().toArray(new Object[size()]);
  }

  @Override
  public boolean equals(@Nullable Object obj) {
    return delegateList().equals(obj);
  }

  @Override
  public int hashCode() {
    return delegateList().hashCode();
  }

  @Override
  public UnmodifiableIterator<E> iterator() {

        return result;
      }
    }
    return 0;
  }

  @Override
  public boolean equals(@CheckForNull Object object) {
    if (object == this) {
      return true;
    }
    if (object instanceof CompoundOrdering) {
      CompoundOrdering<?> that = (CompoundOrdering<?>) object;
      return Arrays.equals(this.comparators, that.comparators);
    }
    return false;
  }

  @Override