// Three-byte form.
        if (index + 1 >= end) {
          return false;
        }
        int byte2 = bytes[index++];
        if (byte2 > (byte) 0xBF
            // Overlong? 5 most significant bits must not all be zero.
            || (byte1 == (byte) 0xE0 && byte2 < (byte) 0xA0)
            // Check for illegal surrogate codepoints.
            || (byte1 == (byte) 0xED && (byte) 0xA0 <= byte2)

    @Override
    public HashCode hashBytes(byte[] input, int off, int len) {
      return HashCode.fromBytes(Arrays.copyOfRange(input, off, off + len));
    }

    @Override
    public int bits() {
      throw new UnsupportedOperationException();
    }
  }

            BigInteger.ZERO.setBit(2 * BigIntegerMath.SQRT2_PRECOMPUTE_THRESHOLD + 1), FLOOR),
        BigIntegerMath.SQRT2_PRECOMPUTED_BITS);
  }

  public void testIsPowerOfTwo() {
    for (BigInteger x : ALL_BIGINTEGER_CANDIDATES) {
      // Checks for a single bit set.
      boolean expected = x.signum() > 0 & x.and(x.subtract(ONE)).equals(ZERO);
      assertEquals(expected, BigIntegerMath.isPowerOfTwo(x));
    }

            BigInteger.ZERO.setBit(2 * BigIntegerMath.SQRT2_PRECOMPUTE_THRESHOLD + 1), FLOOR),
        BigIntegerMath.SQRT2_PRECOMPUTED_BITS);
  }

  public void testIsPowerOfTwo() {
    for (BigInteger x : ALL_BIGINTEGER_CANDIDATES) {
      // Checks for a single bit set.
      boolean expected = x.signum() > 0 & x.and(x.subtract(ONE)).equals(ZERO);
      assertEquals(expected, BigIntegerMath.isPowerOfTwo(x));
    }

    // the output, so the input must be at least 32 bits, since the output has to be that long
    assertPutString(new char[] {'p', HashTestUtils.randomLowSurrogate(new Random())});
  }

  public void testPutStringWithHighSurrogate() {
    // we pad because the dummy hash function we use to test this, merely copies the input into
    // the output, so the input must be at least 32 bits, since the output has to be that long

    // the output, so the input must be at least 32 bits, since the output has to be that long
    assertPutString(new char[] {'p', HashTestUtils.randomLowSurrogate(new Random())});
  }

  public void testPutStringWithHighSurrogate() {
    // we pad because the dummy hash function we use to test this, merely copies the input into
    // the output, so the input must be at least 32 bits, since the output has to be that long

    for (int b = 0; b < 4; ++b) {
      for (int bit = 128; bit != 0; bit >>= 1) {
        expected[b][bit] = next;
        next = advanceOneBit(next);
      }
    }
    for (int b = 0; b < 4; ++b) {
      expected[b][0] = 0;
      for (int bit = 2; bit < 256; bit <<= 1) {
        for (int i = bit + 1; i < (bit << 1); i++) {
          expected[b][i] = expected[b][bit] ^ expected[b][i ^ bit];
        }
      }
    }

   * metadata} is the size that the arrays should be allocated with. Once the arrays have been
   * allocated, the value of {@code metadata} combines the number of bits in the "short hash", in
   * its bottom {@value CompactHashing#HASH_TABLE_BITS_MAX_BITS} bits, with a modification count in
   * the remaining bits that is used to detect concurrent modification during iteration.
   */
  private transient int metadata;

    for (int bits = 10; bits < 63; bits++) {
      for (int i = 0; i < 100; i++) {
        long p = BigInteger.probablePrime(bits, rand).longValue();
        assertTrue(LongMath.isPrime(p));
      }
    }
  }

  @GwtIncompatible // isPrime is GWT-incompatible
  public void testIsPrimeOnRandomComposites() {
    Random rand = new Random(1);
    for (int bits = 5; bits < 32; bits++) {

             * corresponds to the least significant nonzero byte in lw ^ rw, since lw and rw are
             * little-endian. Long.numberOfTrailingZeros(diff) tells us the least significant
             * nonzero bit, and zeroing out the first three bits of L.nTZ gives us the shift to get
             * that least significant nonzero byte.
             */
            int n = Long.numberOfTrailingZeros(lw ^ rw) & ~0x7;