import static com.google.common.math.MathTesting.NEGATIVE_INTEGER_CANDIDATES;
import static com.google.common.math.MathTesting.POSITIVE_FINITE_DOUBLE_CANDIDATES;
import static java.math.RoundingMode.CEILING;
import static java.math.RoundingMode.DOWN;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.HALF_DOWN;
import static java.math.RoundingMode.HALF_EVEN;

import static com.google.common.base.Preconditions.checkState;
import static com.google.common.math.IntMath.divide;
import static com.google.common.math.IntMath.log2;
import static java.math.RoundingMode.CEILING;
import static java.math.RoundingMode.FLOOR;
import static java.math.RoundingMode.UNNECESSARY;

import com.google.common.annotations.GwtCompatible;
import com.google.common.annotations.GwtIncompatible;

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

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

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

    @Override

    // The leftmost position at which the greatest of the k lower elements
    // -- the new value of threshold -- might be found.

    int iterations = 0;
    int maxIterations = IntMath.log2(right - left, RoundingMode.CEILING) * 3;
    while (left < right) {
      int pivotIndex = (left + right + 1) >>> 1;

      int pivotNewIndex = partition(left, right, pivotIndex);

      if (pivotNewIndex > k) {

      E higher = iterator.next();
      if (comparator().compare(e, higher) < 0) {
        return higher;
      }
    }
    return null;
  }

  @CheckForNull
  public E ceiling(E e) {
    ImmutableSortedSet<E> set = tailSet(e, true);
    return !set.isEmpty() ? set.first() : null;
  }

  @CheckForNull
  public E floor(E e) {
    ImmutableSortedSet<E> set = headSet(e, true);

    @Override
    NavigableSet<E> delegate() {
      return (NavigableSet<E>) super.delegate();
    }

    @Override
    @CheckForNull
    public E ceiling(E e) {
      synchronized (mutex) {
        return delegate().ceiling(e);
      }
    }

    @Override
    public Iterator<E> descendingIterator() {
      return delegate().descendingIterator(); // manually synchronized
    }

   * yield an empty iterable, but an iterable containing {@code ""}. This is the only case in which
   * {@code Iterables.size(split(input))} does not equal {@code IntMath.divide(input.length(),
   * length, CEILING)}. To avoid this behavior, use {@code omitEmptyStrings}.
   *
   * @param length the desired length of pieces after splitting, a positive integer

   * yield an empty iterable, but an iterable containing {@code ""}. This is the only case in which
   * {@code Iterables.size(split(input))} does not equal {@code IntMath.divide(input.length(),
   * length, CEILING)}. To avoid this behavior, use {@code omitEmptyStrings}.
   *
   * @param length the desired length of pieces after splitting, a positive integer

    return Math.max(
        ImmutableCollection.Builder.DEFAULT_INITIAL_CAPACITY,
        IntMath.sqrt(inputElementsIncludingAnyDuplicates, RoundingMode.CEILING));
  }

  private static final long serialVersionUID = 0xcafebabe;

  @CheckForNull
  public E floor(E e) {
    return Iterators.<@Nullable E>getNext(headSet(e, true).descendingIterator(), null);
  }

  /** @since 12.0 */
  @Override
  @CheckForNull
  public E ceiling(E e) {
    return Iterables.<@Nullable E>getFirst(tailSet(e, true), null);
  }

  /** @since 12.0 */
  @GwtIncompatible // NavigableSet
  @Override
  @CheckForNull
  public E higher(E e) {