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  - AuraSinis # 1.24 Release Notes Lead
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  @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

  @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

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) {

 *  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.

 *
 * @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
   */

  }

  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);
  }

  /**

   * 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

  private static boolean shouldTrim(int actualUnique, int expectedUnique) {
    return actualUnique < (expectedUnique >> 1) + (expectedUnique >> 2);
  }

  // We use power-of-2 tables, and this is the highest int that's a power of 2
  static final int MAX_TABLE_SIZE = Ints.MAX_POWER_OF_TWO;

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

@GwtCompatible(emulated = true)
public class IntMathTest extends TestCase {
  public void testMaxSignedPowerOfTwo() {
    assertTrue(IntMath.isPowerOfTwo(IntMath.MAX_SIGNED_POWER_OF_TWO));

    // Extra work required to make GWT happy.
    long value = IntMath.MAX_SIGNED_POWER_OF_TWO * 2L;
    assertFalse(IntMath.isPowerOfTwo((int) value));
  }

  public void testCeilingPowerOfTwo() {
    for (int x : POSITIVE_INTEGER_CANDIDATES) {