abstract int sign(X x);

  /** Returns d's value as an X, rounded with the specified mode. */
  abstract X toX(double d, RoundingMode mode);

  /** Returns a - b, guaranteed that both arguments are nonnegative. */
  abstract X minus(X a, X b);

  /** Rounds {@code x} to a {@code double}. */
  final double roundToDouble(X x, RoundingMode mode) {
    checkNotNull(x, "x");
    checkNotNull(mode, "mode");

  abstract int sign(X x);

  /** Returns d's value as an X, rounded with the specified mode. */
  abstract X toX(double d, RoundingMode mode);

  /** Returns a - b, guaranteed that both arguments are nonnegative. */
  abstract X minus(X a, X b);

  /** Rounds {@code x} to a {@code double}. */
  final double roundToDouble(X x, RoundingMode mode) {
    checkNotNull(x, "x");
    checkNotNull(mode, "mode");

      long delta = a - b; // can't overflow, since a and b are nonnegative

      long minDeltaOrZero = delta & (delta >> (Long.SIZE - 1));
      // equivalent to Math.min(delta, 0)

      a = delta - minDeltaOrZero - minDeltaOrZero; // sets a to Math.abs(a - b)
      // a is now nonnegative and even

      b += minDeltaOrZero; // sets b to min(old a, b)

      long delta = a - b; // can't overflow, since a and b are nonnegative

      long minDeltaOrZero = delta & (delta >> (Long.SIZE - 1));
      // equivalent to Math.min(delta, 0)

      a = delta - minDeltaOrZero - minDeltaOrZero; // sets a to Math.abs(a - b)
      // a is now nonnegative and even

      b += minDeltaOrZero; // sets b to min(old a, b)

   * interpreted as an unsigned 32-bit value. Specifically, the sign bit of {@code bits} is
   * interpreted as a normal bit, and all other bits are treated as usual.
   *
   * <p>If the argument is nonnegative, the returned result will be equal to {@code bits},
   * otherwise, the result will be equal to {@code 2^32 + bits}.
   *
   * <p>To represent unsigned decimal constants, consider {@link #valueOf(long)} instead.
   *

   * interpreted as an unsigned 32-bit value. Specifically, the sign bit of {@code bits} is
   * interpreted as a normal bit, and all other bits are treated as usual.
   *
   * <p>If the argument is nonnegative, the returned result will be equal to {@code bits},
   * otherwise, the result will be equal to {@code 2^32 + bits}.
   *
   * <p>To represent unsigned decimal constants, consider {@link #valueOf(long)} instead.
   *

          x >>>= shift;
        } while (x != 0);
      } else {
        // Separate off the last digit using unsigned division. That will leave
        // a number that is nonnegative as a signed integer.
        long quotient;
        if ((radix & 1) == 0) {
          // Fast path for the usual case where the radix is even.
          quotient = (x >>> 1) / (radix >>> 1);
        } else {

  }

  // Query Operations

  /**
   * Returns the number of occurrences of {@code element} in this multiset.
   *
   * @param element the element to look for
   * @return the nonnegative number of occurrences of the element
   */
  @Override
  public int count(@CheckForNull Object element) {
    AtomicInteger existingCounter = safeGet(countMap, element);

    static final Comparator<Entry<?>> INSTANCE = new DecreasingCount();

    @Override
    public int compare(Entry<?> entry1, Entry<?> entry2) {
      return entry2.getCount() - entry1.getCount(); // subtracting two nonnegative integers
    }
  }

  /**
   * An {@link AbstractMultiset} with additional default implementations, some of them linear-time
   * implementations in terms of {@code elementSet} and {@code entrySet}.

    static final Comparator<Entry<?>> INSTANCE = new DecreasingCount();

    @Override
    public int compare(Entry<?> entry1, Entry<?> entry2) {
      return entry2.getCount() - entry1.getCount(); // subtracting two nonnegative integers
    }
  }

  /**
   * An {@link AbstractMultiset} with additional default implementations, some of them linear-time
   * implementations in terms of {@code elementSet} and {@code entrySet}.