}

    /*
     * We need the top SIGNIFICAND_BITS + 1 bits, including the "implicit" one bit. To make rounding
     * easier, we pick out the top SIGNIFICAND_BITS + 2 bits, so we have one to help us round up or
     * down. twiceSignifFloor will contain the top SIGNIFICAND_BITS + 2 bits, and signifFloor the
     * top SIGNIFICAND_BITS + 1.
     *

    if (MIN_LONG_AS_DOUBLE - x < 1.0 & x < MAX_LONG_AS_DOUBLE_PLUS_ONE) {
      return BigInteger.valueOf((long) x);
    }
    int exponent = getExponent(x);
    long significand = getSignificand(x);
    BigInteger result = BigInteger.valueOf(significand).shiftLeft(exponent - SIGNIFICAND_BITS);
    return (x < 0) ? result.negate() : result;
  }

  /**
   * Returns {@code true} if {@code x} is exactly equal to {@code 2^k} for some finite integer

    // The values here look like 111...11101...010 in binary, where the initial 111...1110 takes
    // up exactly as many bits as can be represented in the significand (24 for float, 53 for
    // double). That final 0 should be rounded up to 1 because the remaining bits make that number
    // slightly nearer.
    long floatConversionTest = 0xfffffe8000000002L;

    // The values here look like 111...11101...010 in binary, where the initial 111...1110 takes
    // up exactly as many bits as can be represented in the significand (24 for float, 53 for
    // double). That final 0 should be rounded up to 1 because the remaining bits make that number
    // slightly nearer.
    long floatConversionTest = 0xfffffe8000000002L;

     */
    BigInteger sqrt0;
    int log2 = log2(x, FLOOR);
    if (log2 < Double.MAX_EXPONENT) {
      sqrt0 = sqrtApproxWithDoubles(x);
    } else {
      int shift = (log2 - DoubleUtils.SIGNIFICAND_BITS) & ~1; // even!
      /*
       * We have that x / 2^shift < 2^54. Our initial approximation to sqrtFloor(x) will be
       * 2^(shift/2) * sqrtApproxWithDoubles(x / 2^shift).
       */

   *
   * <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.)
   *

             * 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.
             */

   */
  public abstract long asLong();

  /**
   * If this hashcode has enough bits, returns {@code asLong()}, otherwise returns a {@code long}
   * value with {@code asBytes()} as the least-significant bytes and {@code 0x00} as the remaining
   * most-significant bytes.
   *
   * @since 14.0 (since 11.0 as {@code Hashing.padToLong(HashCode)})
   */
  public abstract long padToLong();

  /**

        // 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)

 * comparator utilities, see either {@code Comparator} itself (for Java 8+), or {@code
 * com.google.common.collect.Ordering} (otherwise).
 *
 * <h3>Relationship to {@code Ordering}</h3>
 *
 * <p>In light of the significant enhancements to {@code Comparator} in Java 8, the overwhelming
 * majority of usages of {@code Ordering} can be written using only built-in JDK APIs. This class is