* {@code String} and a {@code String} to a {@code long} that treat the {@code long} as an unsigned
 * number.
 *
 * <p>Users of these utilities must be <i>extremely careful</i> not to mix up signed and unsigned
 * {@code long} values. When possible, it is recommended that the {@link UnsignedLong} wrapper class
 * be used, at a small efficiency penalty, to enforce the distinction in the type system.
 *
 * <p>See the Guava User Guide article on <a

    Builder.DuplicateKey duplicateKey = null;
    if (tableSize <= BYTE_MAX_SIZE) {
      /*
       * Use 8 bits per entry. The value is unsigned to allow use up to a size of 2^8.
       *
       * The absent indicator of -1 signed becomes 2^8 - 1 unsigned, which reduces the actual max
       * size to 2^8 - 1. However, due to a load factor < 1 the limit is never approached.
       */

        "value (%s) is outside the range for an unsigned integer value",
        value);
    return fromIntBits(value.intValue());
  }

  /**
   * Returns an {@code UnsignedInteger} holding the value of the specified {@code String}, parsed as
   * an unsigned {@code int} value.
   *
   * @throws NumberFormatException if the string does not contain a parsable unsigned {@code int}
   *     value
   */

 *
 * <p>Note to maintainers: This implementation relies on signed arithmetic being bit-wise equivalent
 * to unsigned arithmetic in all cases except:
 *
 * <ul>
 *   <li>comparisons (signed values can be negative)
 *   <li>division (avoided here)
 *   <li>shifting (right shift must be unsigned)
 * </ul>
 *
 * @author ******@****.*** (Kyle Maddison)

 *
 * <p>Note to maintainers: This implementation relies on signed arithmetic being bit-wise equivalent
 * to unsigned arithmetic in all cases except:
 *
 * <ul>
 *   <li>comparisons (signed values can be negative)
 *   <li>division (avoided here)
 *   <li>shifting (right shift must be unsigned)
 * </ul>
 *
 * @author ******@****.*** (Kyle Maddison)

  @SuppressWarnings("ShortCircuitBoolean")
  public static boolean isPowerOfTwo(long x) {
    return x > 0 & (x & (x - 1)) == 0;
  }

  /**
   * Returns 1 if {@code x < y} as unsigned longs, and 0 otherwise. Assumes that x - y fits into a
   * signed long. The implementation is branch-free, and benchmarks suggest it is measurably faster
   * than the straightforward ternary expression.
   */
  @VisibleForTesting

   *
   * <p>This is designed for generating persistent fingerprints of strings. It isn't
   * cryptographically secure, but it produces a high-quality hash with few collisions. Fingerprints
   * generated using this are byte-wise identical to those created using the C++ version, but note
   * that this uses unsigned integers (see {@link com.google.common.primitives.UnsignedInts}).

    for (int i = 1; i < bytes.length; i++) {
      val |= (bytes[i] & 0xFF) << (i * 8);
    }
    return val;
  }

  /**
   * Returns a string containing each byte of {@link #asBytes}, in order, as a two-digit unsigned
   * hexadecimal number in lower case.
   *
   * <p>Note that if the output is considered to be a single hexadecimal number, whether this string

   *
   * <p>Use {@linkplain #readFrom(InputStream, Funnel)} to reconstruct the written BloomFilter.
   */
  public void writeTo(OutputStream out) throws IOException {
    // Serial form:
    // 1 signed byte for the strategy
    // 1 unsigned byte for the number of hash functions
    // 1 big endian int, the number of longs in our bitset
    // N big endian longs of our bitset
    DataOutputStream dout = new DataOutputStream(out);

        UnsignedInteger aUnsigned = UnsignedInteger.fromIntBits(a);
        UnsignedInteger bUnsigned = UnsignedInteger.fromIntBits(b);
        int expected =
            force32(aUnsigned.bigIntegerValue().multiply(bUnsigned.bigIntegerValue()).intValue());
        UnsignedInteger unsignedMul = aUnsigned.times(bUnsigned);
        assertWithMessage(aUnsigned + " * " + bUnsigned)
            .that(unsignedMul.intValue())