return x > 0 & (x & (x - 1)) == 0;
  }

  /**
   * Returns 1 if {@code x < y} as unsigned longs, and 0 otherwise. Assumes that x - y fits into a
   * signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster
   * than the straightforward ternary expression.
   */
  @VisibleForTesting
  static int lessThanBranchFree(long x, long y) {
    // Returns the sign bit of x - y.

      KeyList<K, V> keyList = requireNonNull(keyToKeyList.remove(node.key));
      keyList.count = 0;
      modCount++;
    } else {
      // requireNonNull is safe (under the conditions listed in the comment in the branch above).
      KeyList<K, V> keyList = requireNonNull(keyToKeyList.get(node.key));
      keyList.count--;

      if (node.previousSibling == null) {

 *       SHORT is always discriminable from zero time, and always allows enough time for the small
 *       amounts of computation (creating a thread, calling a few methods, etc) needed to reach a
 *       timeout point. Similarly, a SMALL is always discriminable as larger than SHORT and smaller
 *       than MEDIUM. And so on. These constants are set to conservative values, but even so, if

  /**
   * Waits for the {@link Service} to reach the {@linkplain State#TERMINATED terminated state}.
   *
   * @throws IllegalStateException if the service {@linkplain State#FAILED fails}.
   * @since 15.0
   */
  void awaitTerminated();

  /**
   * Waits for the {@link Service} to reach a terminal state (either {@link Service.State#TERMINATED

    return Platform.stringIsNullOrEmpty(string);
  }

  /**
   * Returns a string, of length at least {@code minLength}, consisting of {@code string} prepended
   * with as many copies of {@code padChar} as are necessary to reach that length. For example,
   *
   * <ul>
   *   <li>{@code padStart("7", 3, '0')} returns {@code "007"}
   *   <li>{@code padStart("2010", 3, '0')} returns {@code "2010"}
   * </ul>
   *

            TimeoutException.class,
            () -> service.startAsync().awaitRunning(1, TimeUnit.MILLISECONDS));
    assertThat(e)
        .hasMessageThat()
        .isEqualTo("Timed out waiting for Foo [STARTING] to reach the RUNNING state.");
  }

  private static class TestService extends AbstractIdleService {
    int startUpCalled = 0;
    int shutDownCalled = 0;
    final List<State> transitionStates = Lists.newArrayList();

            TimeoutException.class,
            () -> service.startAsync().awaitRunning(1, TimeUnit.MILLISECONDS));
    assertThat(e)
        .hasMessageThat()
        .isEqualTo("Timed out waiting for Foo [STARTING] to reach the RUNNING state.");
  }

  private class FakeService extends AbstractExecutionThreadService implements TearDown {

    private final ExecutorService executor = Executors.newSingleThreadExecutor();

   * space in the buffer completely. In general this is a performance problem since the buffer size
   * is permanently reduced, but with certain Reader implementations it could also cause the buffer
   * size to reach 0, causing an infinite loop.
   */
  public void testCopyWithReaderThatDoesNotFillBuffer() throws IOException {
    // need a long enough string for the buffer to hit 0 remaining before the copy completes

   * space in the buffer completely. In general this is a performance problem since the buffer size
   * is permanently reduced, but with certain Reader implementations it could also cause the buffer
   * size to reach 0, causing an infinite loop.
   */
  public void testCopyWithReaderThatDoesNotFillBuffer() throws IOException {
    // need a long enough string for the buffer to hit 0 remaining before the copy completes

    @Override
    public boolean apply(CharSequence t) {
      return pattern.matcher(t).find();
    }

    @Override
    public int hashCode() {
      // Pattern uses Object.hashCode, so we have to reach
      // inside to build a hashCode consistent with equals.

      return Objects.hashCode(pattern.pattern(), pattern.flags());
    }

    @Override
    public boolean equals(@CheckForNull Object obj) {