}

  private static final int EVEN_POWERS_OF_TWO = 0x55555555;
  private static final int ODD_POWERS_OF_TWO = 0xaaaaaaaa;

  @VisibleForTesting
  static boolean isEvenLevel(int index) {
    int oneBased = ~~(index + 1); // for GWT
    checkState(oneBased > 0, "negative index");
    return (oneBased & EVEN_POWERS_OF_TWO) > (oneBased & ODD_POWERS_OF_TWO);
  }

  /**

 *  Fix: Recover gracefully when a cache entry's certificate is corrupted.

 *  Fix: Fail permanently when there's a failure loading the bundled public suffix database.
    This is the dataset that powers `HttpUrl.topPrivateDomain()`.

 *  Fix: Immediately update the connection's flow control window instead of waiting for the
    receiving stream to process it.

  @VisibleForTesting static final long MAX_SIGNED_POWER_OF_TWO = 1L << (Long.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 a {@code

  @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

        Prefer to use the `Annotated` version if possible.

    ```Python hl_lines="9"
    {!> ../../../docs_src/query_params_str_validations/tutorial006c.py!}
    ```

!!! tip

> Modern versions of Python have support for **"asynchronous code"** using something called **"coroutines"**, with **`async` and `await`** syntax.

That should make more sense now. ✨

All that is what powers FastAPI (through Starlette) and what makes it have such an impressive performance.

## Very Technical Details

!!! warning
    You can probably skip this.

"super-admin.conf" file is now deployed. The User in `admin.conf` is now bound to a new RBAC Group `kubeadm:cluster-admins` that has `cluster-admin` `ClusterRole` access. The User in `super-admin.conf` is now bound to the `system:masters` built-in super-powers / break-glass Group that can bypass RBAC. Before this change, the default `admin.conf` was bound to `system:masters` Group, which was undesired. Executing `kubeadm init phase kubeconfig all` or just `kubeadm init` will now generate the new `super-admin.conf`...

   * is merely copied. Only as the power set is iterated are the individual subsets created, and
   * these subsets themselves occupy only a small constant amount of memory.
   *
   * @param set the set of elements to construct a power set from
   * @return the power set, as an immutable set of immutable sets

public class LongMathTest extends TestCase {
  @SuppressWarnings("ConstantOverflow")
  public void testMaxSignedPowerOfTwo() {
    assertTrue(LongMath.isPowerOfTwo(LongMath.MAX_SIGNED_POWER_OF_TWO));
    assertFalse(LongMath.isPowerOfTwo(LongMath.MAX_SIGNED_POWER_OF_TWO * 2));
  }

  public void testCeilingPowerOfTwo() {
    for (long x : POSITIVE_LONG_CANDIDATES) {

 *
 * @author Louis Wasserman
 * @since 11.0
 */
@GwtCompatible(emulated = true)
@ElementTypesAreNonnullByDefault
public final class BigIntegerMath {
  /**
   * Returns the smallest power of two greater than or equal to {@code x}. This is equivalent to
   * {@code BigInteger.valueOf(2).pow(log2(x, CEILING))}.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @since 20.0
   */