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
      assertTrue(x4.compareTo(plusHalfSquared) < 0);
      BigInteger minusHalfSquared = result.pow(2).subtract(result).shiftLeft(2).add(ONE);

            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

       * 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;

    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 < Long.SIZE; i++) {
      assertEquals(
          BigIntegerMath.log10(BigInteger.ONE.shiftLeft(Long.SIZE - i), FLOOR),
          LongMath.maxLog10ForLeadingZeros[i]);
    }
  }

  @GwtIncompatible // TODO
  public void testConstantsPowersOf10() {