// x^2 >= 2^(2 * result - 1), or else we would have rounded down
      assertTrue(result == 0 || ZERO.setBit(2 * result - 1).compareTo(x2) <= 0);
    }
  }

  public void testLog2HalfDown() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      int result = BigIntegerMath.log2(x, HALF_DOWN);
      BigInteger x2 = x.pow(2);
      // x^2 <= 2^(2 * result + 1), or else we would have rounded up