static {
    ImmutableSet.Builder<Integer> intValues = ImmutableSet.builder();
    // Add boundary values manually to avoid over/under flow (this covers 2^N for 0 and 31).
    intValues.add(Integer.MAX_VALUE - 1, Integer.MAX_VALUE);
    // Add values up to 40. This covers cases like "square of a prime" and such.
    for (int i = 1; i <= 40; i++) {
      intValues.add(i);
    }

  /**
   * 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
   *     long}, i.e. when {@code x > 2^62}
   * @since 20.0
   */

 * {@link LongMath} respectively.
 *
 * @author Louis Wasserman
 * @since 11.0
 */
@GwtCompatible
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
   */

 *  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.

    int lower = 0;
    int upper = list.size() - 1;

    while (lower <= upper) {
      int middle = (lower + upper) >>> 1;
      int c = comparator.compare(key, list.get(middle));
      if (c < 0) {
        upper = middle - 1;
      } else if (c > 0) {
        lower = middle + 1;
      } else {
        return lower
            + presentBehavior.resultIndex(

    SetBuilderImpl<E> copy() {
      return this;
    }

    @Override
    ImmutableSet<E> build() {
      return ImmutableSet.of();
    }
  }

  // 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;

 * <strong>not</strong> equal to {@code key2}, it is <strong>not</strong> guaranteed that {@code
 * striped.get(key1) != striped.get(key2)}; the elements might nevertheless be mapped to the same
 * lock. The lower the number of stripes, the higher the probability of this happening.
 *
 * <p>There are three flavors of this class: {@code Striped<Lock>}, {@code Striped<Semaphore>}, and

        String lower = permission.toLowerCase(Locale.ROOT);
        final String aclPrefix;
        if (lower.startsWith(allowPrefix)) {
            lower = lower.substring(allowPrefix.length());
            permission = permission.substring(allowPrefix.length());
            aclPrefix = StringUtil.EMPTY;
        } else if (lower.startsWith(denyPrefix)) {
            lower = lower.substring(denyPrefix.length());

      }
    }
  }

  /* Relies on the correctness of isPowerOfTwo(long). */
  public void testLog2Exact() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      // We only expect an exception if x was not a power of 2.
      boolean isPowerOf2 = LongMath.isPowerOfTwo(x);
      try {
        assertEquals(x, 1L << LongMath.log2(x, UNNECESSARY));
        assertTrue(isPowerOf2);
      } catch (ArithmeticException e) {

   * {@code upper}. Assumes that {@code lower <= upper}. Correctly handles infinities (but not
   * {@code NaN}).
   */
  private static double interpolate(double lower, double upper, double remainder, double scale) {
    if (lower == NEGATIVE_INFINITY) {
      if (upper == POSITIVE_INFINITY) {
        // Return NaN when lower == NEGATIVE_INFINITY and upper == POSITIVE_INFINITY: