BigInteger plusHalfSquared = result.pow(2).add(result).shiftLeft(2).add(ONE);
      BigInteger x4 = x.shiftLeft(2);
      // sqrt(x) < result + 0.5, so 4 * x < (result + 0.5)^2 * 4
      // (result + 0.5)^2 * 4 = (result^2 + result)*4 + 1
      assertThat(plusHalfSquared).isGreaterThan(x4);
      BigInteger minusHalfSquared = result.pow(2).subtract(result).shiftLeft(2).add(ONE);

       * We have that x / 2^shift < 2^54. Our initial approximation to sqrtFloor(x) will be
       * 2^(shift/2) * sqrtApproxWithDoubles(x / 2^shift).
       */
      sqrt0 = sqrtApproxWithDoubles(x.shiftRight(shift)).shiftLeft(shift >> 1);
    }
    BigInteger sqrt1 = sqrt0.add(x.divide(sqrt0)).shiftRight(1);
    if (sqrt0.equals(sqrt1)) {
      return sqrt0;
    }
    do {
      sqrt0 = sqrt1;

      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
   * {@code k}.
   */

    checkBigIntegerConversion(
        "::ffff:ffff:ffff:ffff", BigInteger.ONE.shiftLeft(64).subtract(BigInteger.ONE));
    checkBigIntegerConversion(
        "ffff:ffff:ffff:ffff:ffff:ffff:ffff:ffff",
        BigInteger.ONE.shiftLeft(128).subtract(BigInteger.ONE));
  }

  public void testFromIpv4BigIntegerInputTooLarge() {
    IllegalArgumentException expected =

          .add(BigInteger.valueOf(Integer.MAX_VALUE).add(bigI))
          .add(BigInteger.valueOf(Integer.MIN_VALUE).add(bigI))
          .add(BigInteger.ONE.shiftLeft(63).add(bigI))
          .add(BigInteger.ONE.shiftLeft(64).add(bigI));
    }
    TEST_LONGS = testLongsBuilder.build();
    TEST_BIG_INTEGERS = testBigIntegersBuilder.build();
  }

  public void testAsUnsignedAndLongValueAreInverses() {

            257,
            511,
            512,
            513,
            Double.MAX_EXPONENT - 1,
            Double.MAX_EXPONENT,
            Double.MAX_EXPONENT + 1)) {
      BigInteger x = ONE.shiftLeft(exponent);
      bigValues.add(x, x.add(ONE), x.subtract(ONE));
    }
    bigValues.add(new BigInteger("218838949120258359057546633")); // sqrt(2^175) rounded up and
    // down

    static final int[] maxValueMods = new int[Character.MAX_RADIX + 1];
    static final int[] maxSafeDigits = new int[Character.MAX_RADIX + 1];

    static {
      BigInteger overflow = BigInteger.ONE.shiftLeft(64);
      for (int i = Character.MIN_RADIX; i <= Character.MAX_RADIX; i++) {
        maxValueDivs[i] = divide(MAX_VALUE, i);
        maxValueMods[i] = (int) remainder(MAX_VALUE, i);

  public void testMaxLog10ForLeadingZeros() {
    for (int i = 0; i < Integer.SIZE; i++) {
      assertEquals(
          BigIntegerMath.log10(BigInteger.ONE.shiftLeft(Integer.SIZE - i), FLOOR),
          IntMath.maxLog10ForLeadingZeros[i]);
    }
  }

  @GwtIncompatible // BigIntegerMath // TODO(cpovirk): GWT-enable BigIntegerMath
  public void testConstantsHalfPowersOf10() {

  public void testMaxLog10ForLeadingZeros() {
    for (int i = 0; i < Integer.SIZE; i++) {
      assertEquals(
          BigIntegerMath.log10(BigInteger.ONE.shiftLeft(Integer.SIZE - i), FLOOR),
          IntMath.maxLog10ForLeadingZeros[i]);
    }
  }

  @GwtIncompatible // BigIntegerMath // TODO(cpovirk): GWT-enable BigIntegerMath
  public void testConstantsHalfPowersOf10() {

  public void testMaxLog10ForLeadingZeros() {
    for (int i = 0; i < Long.SIZE; i++) {
      assertEquals(
          BigIntegerMath.log10(BigInteger.ONE.shiftLeft(Long.SIZE - i), FLOOR),
          LongMath.maxLog10ForLeadingZeros[i]);
    }
  }

  @GwtIncompatible // TODO
  public void testConstantsPowersOf10() {