// The alternative (x + y) / 2 fails for large values.
    // The alternative (x + y) >>> 1 fails for negative values.
    return (x & y) + ((x ^ y) >> 1);
  }

  /*
   * This bitmask is used as an optimization for cheaply testing for divisibility by 2, 3, or 5.
   * Each bit is set to 1 for all remainders that indicate divisibility by 2, 3, or 5, so