a >>= aTwos; // divide out all 2s
    int bTwos = Integer.numberOfTrailingZeros(b);
    b >>= bTwos; // divide out all 2s
    while (a != b) { // both a, b are odd
      // The key to the binary GCD algorithm is as follows:
      // Both a and b are odd. Assume a > b; then gcd(a - b, b) = gcd(a, b).
      // But in gcd(a - b, b), a - b is even and b is odd, so we can divide out powers of two.

  public void testLog2HalfEven() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      int halfEven = BigIntegerMath.log2(x, HALF_EVEN);
      // Now figure out what rounding mode we should behave like (it depends if FLOOR was
      // odd/even).
      boolean floorWasEven = (BigIntegerMath.log2(x, FLOOR) & 1) == 0;

 *
 * 2. The supertype of this class could be `Function<@Nullable A, @Nullable B>`, since
 * Converter.apply (like Converter.convert) is capable of accepting null inputs. However, a
 * supertype of `Function<A, B>` turns out to be massively more useful to callers in practice: They
 * want their output to be non-null in operations like `stream.map(myConverter)`, and we can

   * instead.
   *
   * <p>Unfortunately, the method reference {@code Optional::toJavaUtil} will not work, because it
   * could refer to either the static or instance version of this method. Write out the lambda
   * expression {@code o -> Optional.toJavaUtil(o)} instead.
   *
   * @since 21.0
   */
  @CheckForNull
  public static <T> java.util.Optional<T> toJavaUtil(@CheckForNull Optional<T> googleOptional) {

   *
   * <p>For example, {@code Splitter.on(',').limit(3).split("a,b,c,d")} returns an iterable
   * containing {@code ["a", "b", "c,d"]}. When omitting empty strings, the omitted strings do not
   * count. Hence, {@code Splitter.on(',').limit(3).omitEmptyStrings().split("a,,,b,,,c,d")} returns
   * an iterable containing {@code ["a", "b", "c,d"]}. When trim is requested, all entries are

   *       MoreExecutors#newSequentialExecutor} wrapper around {@code directExecutor()}. More
   *       complex cases may require using thread pools or making deeper changes.)
   *   <li>If an exception propagates out of a {@code Runnable}, it is not necessarily seen by any
   *       {@code UncaughtExceptionHandler} for the thread. For example, if the callback passed to

     *
     * b) this iteration converges to floor(sqrt(x)). In fact, the number of correct digits doubles
     * with each iteration, so this algorithm takes O(log(digits)) iterations.
     *
     * We start out with a double-precision approximation, which may be higher or lower than the
     * true value. Therefore, we perform at least one Newton iteration to get a guess that's

  // Represents how tightly we can pack things, as a maximum.
  private static final double DESIRED_LOAD_FACTOR = 0.7;

  // If the set has this many elements, it will "max out" the table size
  private static final int CUTOFF = (int) (MAX_TABLE_SIZE * DESIRED_LOAD_FACTOR);

  /**
   * Returns an array size suitable for the backing array of a hash table that uses open addressing

 * always be represented by a pair of {@code Cut} instances.
 *
 * @author Kevin Bourrillion
 */
@SuppressWarnings("rawtypes") // https://github.com/google/guava/issues/989
@GwtCompatible
@ElementTypesAreNonnullByDefault
abstract class Cut<C extends Comparable> implements Comparable<Cut<C>>, Serializable {
  final C endpoint;

  Cut(C endpoint) {
    this.endpoint = endpoint;
  }

 * always be represented by a pair of {@code Cut} instances.
 *
 * @author Kevin Bourrillion
 */
@SuppressWarnings("rawtypes") // https://github.com/google/guava/issues/989
@GwtCompatible
@ElementTypesAreNonnullByDefault
abstract class Cut<C extends Comparable> implements Comparable<Cut<C>>, Serializable {
  final C endpoint;

  Cut(C endpoint) {
    this.endpoint = endpoint;
  }