return Double.MAX_VALUE * sign(x);
        case FLOOR:
          return (roundArbitrarily == Double.POSITIVE_INFINITY)
              ? Double.MAX_VALUE
              : Double.NEGATIVE_INFINITY;
        case CEILING:
          return (roundArbitrarily == Double.POSITIVE_INFINITY)
              ? Double.POSITIVE_INFINITY
              : -Double.MAX_VALUE;
        case UP:
          return roundArbitrarily;
        case UNNECESSARY:

import static com.google.common.truth.Truth.assertWithMessage;
import static java.math.BigInteger.ONE;
import static java.math.BigInteger.TEN;
import static java.math.BigInteger.ZERO;
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.truth.Truth.assertWithMessage;
import static java.math.BigInteger.ONE;
import static java.math.BigInteger.TEN;
import static java.math.BigInteger.ZERO;
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;

   * {@code BigInteger.valueOf(2).pow(log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @since 20.0
   */
  public static BigInteger ceilingPowerOfTwo(BigInteger x) {
    return BigInteger.ZERO.setBit(log2(x, CEILING));
  }

  /**
   * Returns the largest power of two less than or equal to {@code x}. This is equivalent to {@code

	cases := []struct {
		numerator, denominator, ceiling int64
	}{
		{0, 1, 0},
		{-1, 2, 0},
		{1, 2, 1},
		{1, 1, 1},
		{3, 2, 2},
		{54, 11, 5},
		{45, 11, 5},
		{-4, 3, -1},
		{4, -3, -1},
		{-4, -3, 2},
		{3, 0, 0},
	}
	for i, testCase := range cases {
		ceiling := ceilFrac(testCase.numerator, testCase.denominator)
		if ceiling != testCase.ceiling {

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

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

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

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

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

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

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

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

    for (E e : collection) {
      checkValid(e);
    }
    return delegate.addAll(collection);
  }

  @Override
  public @Nullable E ceiling(E e) {
    return delegate.ceiling(checkValid(e));
  }

  @Override
  public void clear() {
    delegate.clear();
  }

  @Override
  public Comparator<? super E> comparator() {

    for (E e : collection) {
      checkValid(e);
    }
    return delegate.addAll(collection);
  }

  @Override
  public @Nullable E ceiling(E e) {
    return delegate.ceiling(checkValid(e));
  }

  @Override
  public void clear() {
    delegate.clear();
  }

  @Override
  public Comparator<? super E> comparator() {

  @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
   *     int}, i.e. when {@code x > 2^30}
   * @since 20.0