// n: expected insertions
  // b: m/n, bits per insertion
  // p: expected false positive probability
  //
  // 1) Optimal k = b * ln2
  // 2) p = (1 - e ^ (-kn/m))^k
  // 3) For optimal k: p = 2 ^ (-k) ~= 0.6185^b
  // 4) For optimal k: m = -nlnp / ((ln2) ^ 2)

  /**
   * Computes the optimal number of hash functions (k) for a given false positive probability (p).
   *

                        }
                    }
                }
            }
        });

        handle.setNotificationFuture(future);
    }

    /**
     * Determine optimal polling interval based on directory activity and failure count
     *
     * Current strategy is based on failure count. In the future, this could be enhanced to consider:
     * - Recent event frequency (successful notifications)

 * from uniform), and amortized since some operations can trigger a hash table resize.
 *
 * <p>Unlike {@code java.util.HashMap}, iteration is only proportional to the actual {@code size()},
 * which is optimal, and <i>not</i> the size of the internal hashtable, which could be much larger
 * than {@code size()}. Furthermore, this structure places significantly reduced load on the garbage

    tester.testAllPublicInstanceMethods(BloomFilter.create(Funnels.unencodedCharsFunnel(), 100));
    tester.testAllPublicStaticMethods(BloomFilter.class);
  }

  /** Tests that we never get an optimal hashes number of zero. */
  public void testOptimalHashes() {
    for (int n = 1; n < 1000; n++) {
      for (double p = 0.1; p > 1e-10; p /= 10) {

 * amortized since some operations can trigger a hash table resize.
 *
 * <p>Unlike {@code java.util.HashSet}, iteration is only proportional to the actual {@code size()},
 * which is optimal, and <i>not</i> the size of the internal hashtable, which could be much larger
 * than {@code size()}. Furthermore, this structure only depends on a fixed number of arrays; {@code

 * Second, it is always backed by an array large enough to hold a value for every possible
 * combination of row and column keys. (This is rarely optimal unless the table is extremely dense.)
 * Finally, every possible combination of row and column keys is always considered to have a value
 * associated with it: It is not possible to "remove" a value, only to replace it with {@code null},

 * from uniform), and amortized since some operations can trigger a hash table resize.
 *
 * <p>Unlike {@code java.util.HashMap}, iteration is only proportional to the actual {@code size()},
 * which is optimal, and <i>not</i> the size of the internal hashtable, which could be much larger
 * than {@code size()}. Furthermore, this structure places significantly reduced load on the garbage

 * Second, it is always backed by an array large enough to hold a value for every possible
 * combination of row and column keys. (This is rarely optimal unless the table is extremely dense.)
 * Finally, every possible combination of row and column keys is always considered to have a value
 * associated with it: It is not possible to "remove" a value, only to replace it with {@code null},