private final transient int size;

  /*
   * We have some considerable complexity in these create methods because of
   * Builder.buildKeepingLast(). The same Builder might be called with buildKeepingLast() and then
   * buildOrThrow(), or vice versa. So in particular, if we modify alternatingKeysAndValues to
   * eliminate duplicate keys (for buildKeepingLast()) then we have to ensure that a later call to

 * {@code SetMultimap} instead, two presidents would have vanished, and last names might or might
 * not appear in chronological order.
 *
 * <p><b>Warning:</b> instances of type {@code Multimap} may not implement {@link Object#equals} in
 * the way you expect. Multimaps containing the same key-value pairs, even in the same order, may or
 * may not be equal and may or may not have the same {@code hashCode}. The recommended subinterfaces

   * @param sampleKey a key of the same type as that contained by {@code multimap}. {@code multimap}
   *     may or may not have {@code sampleKey} as a key.
   * @param sampleValue a key of the same type as that contained by {@code multimap}. {@code
   *     multimap} may or may not have {@code sampleValue} as a key.
   */
  public static <K extends @Nullable Object, V extends @Nullable Object>

   * tasks. Second, the returned list will always be empty, as any submitted task is considered to
   * have started execution. This applies also to tasks given to {@code invokeAll} or {@code
   * invokeAny} which are pending serial execution, even the subset of the tasks that have not yet
   * started execution. It is unclear from the {@code ExecutorService} specification if these should

  //    guard.leave(), but that's a little odd as well because the
  //    guard doesn't have anything to do with leaving. You can't
  //    really enforce that the guard you're leaving is the same one
  //    you entered with, and it doesn't actually matter.
  //
  // 2. Since you can enter the monitor without a guard at all, some
  //    places you'll have monitor.enter()/monitor.leave() and other

      int result = BigIntegerMath.log2(x, HALF_UP);
      BigInteger x2 = x.pow(2);
      // x^2 < 2^(2 * result + 1), or else we would have rounded up
      assertTrue(ZERO.setBit(2 * result + 1).compareTo(x2) > 0);
      // x^2 >= 2^(2 * result - 1), or else we would have rounded down
      assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) <= 0);
    }
  }

  public void testLog2HalfDown() {

      int result = BigIntegerMath.log2(x, HALF_UP);
      BigInteger x2 = x.pow(2);
      // x^2 < 2^(2 * result + 1), or else we would have rounded up
      assertTrue(ZERO.setBit(2 * result + 1).compareTo(x2) > 0);
      // x^2 >= 2^(2 * result - 1), or else we would have rounded down
      assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) <= 0);
    }
  }

  public void testLog2HalfDown() {

 * second invocation, so implementors have made various choices, including:
 *
 * <ul>
 *   <li>returning the same iterator again
 *   <li>throwing an exception of some kind
 *   <li>or the usual, <i>robust</i> behavior, which all known {@link Collection} implementations
 *       have, of returning a new, independent iterator
 * </ul>
 *

  /**
   * Returns the result of applying this predicate to {@code input} (Java 8+ users, see notes in the
   * class documentation above). This method is <i>generally expected</i>, but not absolutely
   * required, to have the following properties:
   *
   * <ul>
   *   <li>Its execution does not cause any observable side effects.
   *   <li>The computation is <i>consistent with equals</i>; that is, {@link Objects#equal

   *
   * <p>The recommended solution for finding the {@code minimum} of some values depends on the type
   * of your data and the number of elements you have. Read more in the Guava User Guide article on
   * <a href="https://github.com/google/guava/wiki/CollectionUtilitiesExplained#comparators">{@code
   * Comparators}</a>.
   *