* ImmutableListMultimap}, which have well-defined {@link #equals} semantics, thus avoiding a common
 * source of bugs and confusion.
 *
 * <p><b>Note:</b> every {@link ImmutableMultimap} offers an {@link #inverse} view, so there is no
 * need for a distinct {@code ImmutableBiMultimap} type.
 *
 * <p><a id="iteration"></a>
 *

         *
         * We carry out this computation in modular arithmetic. Since times2ToThe32Mod accepts any
         * unsigned long, we don't have to do a mod on every operation, only when intermediate
         * results can exceed 2^63.
         */
        long result = times2ToThe32Mod(aHi * bHi /* < 2^62 */, m); // < m < 2^63

   * Math#min(float, float)}.
   *
   * @param array a <i>nonempty</i> array of {@code float} values
   * @return the value present in {@code array} that is less than or equal to every other value in
   *     the array
   * @throws IllegalArgumentException if {@code array} is empty
   */
  @GwtIncompatible(
      "Available in GWT! Annotation is to avoid conflict with GWT specialization of base class.")

  }

  /**
   * Returns the total number of nanoseconds the cache has spent loading new values. This can be
   * used to calculate the miss penalty. This value is increased every time {@code loadSuccessCount}
   * or {@code loadExceptionCount} is incremented.
   */
  @SuppressWarnings("GoodTime") // should return a java.time.Duration
  public long totalLoadTime() {
    return totalLoadTime;

import com.google.common.collect.Iterables;
import com.google.common.primitives.Doubles;
import java.math.BigInteger;
import java.math.RoundingMode;

/**
 * Exhaustive input sets for every integral type.
 *
 * @author Louis Wasserman
 */
@GwtCompatible
public class MathTesting {
  static final ImmutableSet<RoundingMode> ALL_ROUNDING_MODES =
      ImmutableSet.copyOf(RoundingMode.values());

    }

    // Test #entries()
    assertCollectionIsUnmodifiable(multimap.entries(), Maps.immutableEntry(sampleKey, sampleValue));
    assertMultimapRemainsUnmodified(multimap, originalEntries);

    // Iterate over every element in the entry set
    for (Entry<K, V> entry : multimap.entries()) {
      assertMapEntryIsUnmodifiable(entry);
    }
    assertMultimapRemainsUnmodified(multimap, originalEntries);

    // Test #keys()

  }

  /**
   * Returns the total number of nanoseconds the cache has spent loading new values. This can be
   * used to calculate the miss penalty. This value is increased every time {@code loadSuccessCount}
   * or {@code loadExceptionCount} is incremented.
   */
  @SuppressWarnings("GoodTime") // should return a java.time.Duration
  public long totalLoadTime() {
    return totalLoadTime;

  private void assertEntrySetNotContainsString(Set<Entry<K, V>> entrySet) {
    // Very unlikely that a buggy collection would ever return true. It might accidentally throw.
    assertFalse(entrySet.contains("foo"));
  }

  /**
   * Override this to check invariants which should hold true for a particular implementation, but
   * which are not generally applicable to every instance of Map.
   *

 *       {@code AsyncCallable}) to complete, without interrupting it (and without calling {@code
 *       cancel} on the {@code Future}). So beware: <i>Even if you cancel every preceding {@code
 *       Future} returned by this class, the next task may still have to wait.</i>.
 *   <li>Once an {@code AsyncCallable} returns a {@code Future}, this class considers that task to

        // Adding the class hashCode to avoid a clash with Pred instances.
        return Succ.class.hashCode() + node.hashCode();
      }
    }
  }

  private static final Object PRED = new Object();

  // Every value in this map must either be an instance of PredAndSucc with a successorValue of
  // type V, PRED (representing predecessor), or an instance of type V (representing successor).
  private final Map<N, Object> adjacentNodeValues;