public static boolean isPowerOfTwo(BigInteger x) {
    checkNotNull(x);
    return x.signum() > 0 && x.getLowestSetBit() == x.bitLength() - 1;
  }

  /**
   * Returns the base-2 logarithm of {@code x}, rounded according to the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}

    if (x > 0.0 && isFinite(x)) {
      long significand = getSignificand(x);
      return (significand & (significand - 1)) == 0;
    }
    return false;
  }

  /**
   * Returns the base 2 logarithm of a double value.
   *
   * <p>Special cases:
   *
   * <ul>
   *   <li>If {@code x} is NaN or less than zero, the result is NaN.
   *   <li>If {@code x} is positive infinity, the result is positive infinity.

    // to make sure bit twiddling works as expected.
    return ~~(x - y) >>> (Integer.SIZE - 1);
  }

  /**
   * Returns the base-2 logarithm of {@code x}, rounded according to the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}

   */
  @VisibleForTesting
  static int lessThanBranchFree(long x, long y) {
    // Returns the sign bit of x - y.
    return (int) (~~(x - y) >>> (Long.SIZE - 1));
  }

  /**
   * Returns the base-2 logarithm of {@code x}, rounded according to the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code x}