* higher value than you need can waste space and time, and a significantly lower value can lead
   * to thread contention. But overestimates and underestimates within an order of magnitude do not
   * usually have much noticeable impact. A value of one permits only one thread to modify the cache
   * at a time, but since read operations and cache loading computations can proceed concurrently,

        // The BigInteger implementation is tested separately, use it as the reference.
        // Promote the int value (rather than using intValue() on the expected value) to avoid
        // any risk of truncation which could lead to a false positive.
        assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(IntMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(int, FLOOR). */

   *
   * <p><b>Note:</b> The current implementation eagerly allocates storage for {@code size} elements.
   * As a consequence, passing values like {@code Integer.MAX_VALUE} can lead to {@link
   * OutOfMemoryError}.
   *
   * <p><b>Note:</b> if {@code iterable} is a {@link List}, use {@link Lists#partition(List, int)}
   * instead.
   *

      for (RoundingMode mode : ALL_SAFE_ROUNDING_MODES) {
        // Promote the long value (rather than using longValue() on the expected value) to avoid
        // any risk of truncation which could lead to a false positive.
        assertEquals(BigIntegerMath.sqrt(valueOf(x), mode), valueOf(LongMath.sqrt(x, mode)));
      }
    }
  }

  /* Relies on the correctness of sqrt(long, FLOOR). */

   *
   * <p><b>Note:</b> serializing the returned list is implemented by serializing {@code fromList},
   * its contents, and {@code function} -- <i>not</i> by serializing the transformed values. This
   * can lead to surprising behavior, so serializing the returned list is <b>not recommended</b>.
   * Instead, copy the list using {@link ImmutableList#copyOf(Collection)} (for example), then

  }

  /**
   * Support removal operations when filtering a filtered multimap. Since a filtered multimap has
   * iterators that don't support remove, passing one to the FilteredEntryMultimap constructor would
   * lead to a multimap whose removal operations would fail. This method combines the predicates to
   * avoid that problem.
   */
  private static <K extends @Nullable Object, V extends @Nullable Object>

  }

  /**
   * Support removal operations when filtering a filtered multimap. Since a filtered multimap has
   * iterators that don't support remove, passing one to the FilteredEntryMultimap constructor would
   * lead to a multimap whose removal operations would fail. This method combines the predicates to
   * avoid that problem.
   */
  private static <K extends @Nullable Object, V extends @Nullable Object>

     * nullness annotations in ImmutableMap and those in its own Map type. In response, it considers
     * the parameter and return type both to be platform types. As a result, Kotlin permits calls
     * that can lead to NullPointerException. That's unfortunate. But hopefully most Kotlin callers
     * use `get(key) ?: defaultValue` instead of this method, anyway.
     */
    V result = get(key);

   *
   * <p><b>Note:</b> The current implementation eagerly allocates storage for {@code size} elements.
   * As a consequence, passing values like {@code Integer.MAX_VALUE} can lead to {@link
   * OutOfMemoryError}.
   *
   * <p><b>Note:</b> if {@code iterable} is a {@link List}, use {@link Lists#partition(List, int)}
   * instead.
   *

    66,
    64,
    63,
    62,
    62,
    61,
    61,
    61
  };

  // These values were generated by using checkedMultiply to see when the simple multiply/divide
  // algorithm would lead to an overflow.

  static boolean fitsInInt(long x) {
    return (int) x == x;
  }

  /**
   * Returns the arithmetic mean of {@code x} and {@code y}, rounded toward negative infinity. This