return x.negate();
        }
      };

  /*
   * This list contains values that attempt to provoke overflow in integer operations. It contains
   * positive values on or near 2^N for N near multiples of 8 (near byte boundaries).
   */
  static final ImmutableSet<Integer> POSITIVE_INTEGER_CANDIDATES;

  static final Iterable<Integer> NEGATIVE_INTEGER_CANDIDATES;

    this.predecessor = null;
    this.successor = null;
    return result;
  }

  /*
   * For discussion of the safety of the following methods for operating on predecessors and
   * successors, see the comments near the end of CompactHashMap, noting that the methods here call
   * requirePredecessors() and requireSuccessors(), which are defined at the end of this file.
   */

  private int getPredecessor(int entry) {

   *
   * <p>For the case of {@link RoundingMode#HALF_EVEN}, this implementation uses the IEEE 754
   * default rounding mode: if the two nearest representable values are equally near, the one with
   * the least significant bit zero is chosen. (In such cases, both of the nearest representable
   * values are even integers; this method returns the one that is a multiple of a greater power of
   * two.)
   *

           * technique previously used by BigIntegerMath: maintain separate numerator and
           * denominator accumulators, multiplying the fraction into result when near overflow.
           */
          for (int i = 2; i <= k; i++, n--) {
            if (numeratorBits + nBits < Long.SIZE - 1) {
              // It's definitely safe to multiply into numerator and denominator.

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