int result = BigIntegerMath.log2(x, HALF_UP);
      BigInteger x2 = x.pow(2);
      // x^2 < 2^(2 * result + 1), or else we would have rounded up
      assertTrue(ZERO.setBit(2 * result + 1).compareTo(x2) > 0);
      // x^2 >= 2^(2 * result - 1), or else we would have rounded down
      assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) <= 0);
    }
  }

  public void testLog2HalfDown() {

   * equals()} contract.
   *
   * <p><b>Note:</b> this method is now unnecessary and should be treated as deprecated; use {@link
   * java.util.Objects#equals} instead.
   */
  @SuppressWarnings("InlineMeSuggester") // would introduce fully qualified references to Objects
  public static boolean equal(@Nullable Object a, @Nullable Object b) {
    return java.util.Objects.equals(a, b);
  }

  /**

Depending on your use case, you might prefer to use a different library, but if you asked me, I would probably suggest you try **Strawberry**.

Here's a small preview of how you could integrate Strawberry with FastAPI:

{* ../../docs_src/graphql/tutorial001.py hl[3,22,25] *}

This was designed this way mainly to allow using the same objects "yielded" by dependencies inside of background tasks, because the exit code would be executed after the background tasks were finished.

### High availability

A stand-alone MinIO server would go down if the server hosting the drives goes offline. In contrast, a distributed MinIO setup with _m_ servers and _n_ drives will have your data safe as long as _m/2_ servers or _m*n_/2 or more drives are online.

In this case, we pass a dependency function `get_current_active_user` to `Security` (the same way we would do with `Depends`).

But we also pass a `list` of scopes, in this case with just one scope: `items` (it could have more).

   * its runtime check.
   *
   * <p>An example use case for this method is in implementing an {@code Iterator<T>} whose {@code
   * next} field is lazily initialized. The type of that field would be {@code @Nullable T}, and the
   * code would be responsible for populating a "real" {@code T} (which might still be the value
   * {@code null}!) before returning it to callers. Depending on how the code is structured, a

      Stopwatch s = Stopwatch.createStarted();
      // here is where you would do something
      total += s.elapsed(NANOSECONDS);
    }
    return total;
  }

  @Benchmark
  long manual(int reps) {
    long total = 0;
    for (int i = 0; i < reps; i++) {
      long start = System.nanoTime();
      // here is where you would do something
      total += System.nanoTime() - start;
    }
    return total;
  }

    assertFalse(listener.healthyCalled);
  }

  /**
   * This covers a bug where if a listener was installed that would stop the manager if any service
   * fails and something failed during startup before service.start was called on all the services,
   * then awaitStopped would deadlock due to an IllegalStateException that was thrown when trying to
   * stop the timer(!).
   */

   * worker runs and exhausts the queue, another thread enqueues a task and fails to schedule the
   * worker, and then the first thread's call to delegate.execute() returns. Without this counter,
   * it would observe the QUEUING state and set it to QUEUED, and the worker would never be
   * scheduled again for future submissions.
   */
  @GuardedBy("queue")
  private long workerRunCount = 0;

  @RetainedWith private final QueueWorker worker = new QueueWorker();