private static BigInteger oldSlowFactorial(int n1, int n2) {
    assert n1 <= n2;
    if (IntMath.log2(n2, CEILING) * (n2 - n1) < Long.SIZE - 1) {
      // the result will definitely fit into a long
      long result = 1;
      for (int i = n1 + 1; i <= n2; i++) {
        result *= i;
      }
      return BigInteger.valueOf(result);
    }

    /*

  private static BigInteger oldSlowFactorial(int n1, int n2) {
    assert n1 <= n2;
    if (IntMath.log2(n2, CEILING) * (n2 - n1) < Long.SIZE - 1) {
      // the result will definitely fit into a long
      long result = 1;
      for (int i = n1 + 1; i <= n2; i++) {
        result *= i;
      }
      return BigInteger.valueOf(result);
    }

    /*

 */
final class Platform {
  static CharMatcher precomputeCharMatcher(CharMatcher matcher) {
    // CharMatcher.precomputed() produces CharMatchers that are maybe a little
    // faster (and that's debatable), but definitely more memory-hungry. We're
    // choosing to turn .precomputed() into a no-op in GWT, because it doesn't
    // seem to be a worthwhile tradeoff in a browser.
    return matcher;
  }

   *
   * The initial write to delegateRef is made definitely visible via the semantics of
   * addListener/SES.schedule. The later racy write in cancel() is not guaranteed to be observed,
   * however that is fine since the correctness is based on the atomic state in our base class. The
   * initial write to timer is never definitely visible to Fire.run since it is assigned after

      // Some Android 5.0.x Samsung devices have bugs in JDK reflection APIs that cause
      // getDeclaredField to throw a NoSuchFieldException when the field is definitely there.
      // For these users fallback to a suboptimal implementation, based on synchronized. This will
      // be a definite performance hit to those users.
      thrownReflectionFailure = reflectionFailure;
      helper = new SynchronizedAtomicHelper();
    }

        }

        @Test
        @DisplayName("Should handle extensions with special characters")
        void testSpecialCharacterExtensions() throws IOException {
            // Test extensions that are definitely not in the map
            assertEquals("application/octet-stream", mimeMap.getMimeType("file.ext"));
            assertEquals("application/octet-stream", mimeMap.getMimeType("@#$%"));

@GwtCompatible
@ReflectionSupport(value = ReflectionSupport.Level.FULL)
// Some Android 5.0.x Samsung devices have bugs in JDK reflection APIs that cause
// getDeclaredField to throw a NoSuchFieldException when the field is definitely there.
// Since this class only needs CAS on one field, we can avoid this bug by extending AtomicReference
// instead of using an AtomicReferenceFieldUpdater. This reference stores Thread instances

            Thread.sleep(5); // Small delay to ensure different timestamps
            Smb2LeaseKey key3 = limitedManager.requestLease("/share/file3.txt", Smb2LeaseState.SMB2_LEASE_READ_CACHING);

            // key3 should definitely exist (just created)
            assertNotNull(limitedManager.getLease(key3));

            // key1 should have been evicted (oldest)
            assertNull(limitedManager.getLease(key1));

     *
     * We start out with a double-precision approximation, which may be higher or lower than the
     * true value. Therefore, we perform at least one Newton iteration to get a guess that's
     * definitely >= floor(sqrt(x)), and then continue the iteration until we reach a fixed point.
     */
    BigInteger sqrt0;
    int log2 = log2(x, FLOOR);
    if (log2 < Double.MAX_EXPONENT) {

 * with one-sided error: if it claims that an element is contained in it, this might be in error,
 * but if it claims that an element is <i>not</i> contained in it, then this is definitely true.
 *
 * <p>If you are unfamiliar with Bloom filters, this nice <a
 * href="http://llimllib.github.io/bloomfilter-tutorial/">tutorial</a> may help you understand how
 * they work.
 *