}
  }

  // Relies on the correctness of isPowerOfTwo(BigInteger).
  public void testLog2Exact() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      // We only expect an exception if x was not a power of 2.
      boolean isPowerOf2 = BigIntegerMath.isPowerOfTwo(x);
      try {
        assertEquals(x, ZERO.setBit(BigIntegerMath.log2(x, UNNECESSARY)));
        assertTrue(isPowerOf2);

  abstract ImmutableSortedSet<E> tailSetImpl(E fromElement, boolean inclusive);

  /** @since 12.0 */
  @GwtIncompatible // NavigableSet
  @Override
  @CheckForNull
  public E lower(E e) {
    return Iterators.<@Nullable E>getNext(headSet(e, false).descendingIterator(), null);
  }

  /** @since 12.0 */
  @Override
  @CheckForNull
  public E floor(E e) {

  @VisibleForTesting static final int MAX_SIGNED_POWER_OF_TWO = 1 << (Integer.SIZE - 2);

  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code checkedPow(2, log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as an {@code

  static {
    ImmutableSet.Builder<Integer> intValues = ImmutableSet.builder();
    // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31).
    intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE);
    // Add values up to 40. This covers cases like "square of a prime" and such.
    for (int i = 1; i <= 40; i++) {
      intValues.add(i);
    }

  }

  private static final int EVEN_POWERS_OF_TWO = 0x55555555;
  private static final int ODD_POWERS_OF_TWO = 0xaaaaaaaa;

  @VisibleForTesting
  static boolean isEvenLevel(int index) {
    int oneBased = ~~(index + 1); // for GWT
    checkState(oneBased > 0, "negative index");
    return (oneBased & EVEN_POWERS_OF_TWO) > (oneBased & ODD_POWERS_OF_TWO);
  }

  /**

   * is merely copied. Only as the power set is iterated are the individual subsets created, and
   * these subsets themselves occupy only a small constant amount of memory.
   *
   * @param set the set of elements to construct a power set from
   * @return the power set, as an immutable set of immutable sets

   * (inclusive) to {@code upper} (inclusive). (These are the same values contained in {@code
   * Range.closed(lower, upper)}.)
   *
   * @throws IllegalArgumentException if {@code lower} is greater than {@code upper}
   * @since 23.0
   */
  public static ContiguousSet<Integer> closed(int lower, int upper) {
    return create(Range.closed(lower, upper), DiscreteDomain.integers());
  }

  }

  @CollectionSize.Require(SEVERAL)
  public void testLowerHole() {
    resetWithHole();
    assertEquals(null, navigableSet.lower(a));
    assertEquals(a, navigableSet.lower(b));
    assertEquals(a, navigableSet.lower(c));
  }

  @CollectionSize.Require(SEVERAL)
  public void testFloorHole() {
    resetWithHole();
    assertEquals(a, navigableSet.floor(a));

  @Override
  @CheckForNull
  public E lower(@ParametricNullness E e) {
    return delegate().lower(e);
  }

  /**
   * A sensible definition of {@link #lower} in terms of the {@code descendingIterator} method of
   * {@link #headSet(Object, boolean)}. If you override {@link #headSet(Object, boolean)}, you may
   * wish to override {@link #lower} to forward to this implementation.
   */
  @CheckForNull

  }

  @Override
  @GwtIncompatible("NavigableSet")
  ImmutableSortedSet<E> createDescendingSet() {
    throw new AssertionError("should never be called");
  }

  @Override
  @CheckForNull
  public E lower(E element) {
    return forward.higher(element);
  }

  @Override
  @CheckForNull
  public E floor(E element) {
    return forward.ceiling(element);
  }

  @Override
  @CheckForNull