static void checkRoundingUnnecessary(boolean condition) {
    if (!condition) {
      throw new ArithmeticException("mode was UNNECESSARY, but rounding was necessary");
    }
  }

  static void checkInRangeForRoundingInputs(boolean condition, double input, RoundingMode mode) {
    if (!condition) {
      throw new ArithmeticException(
          "rounded value is out of range for input " + input + " and rounding mode " + mode);
    }
  }

  private static final ImmutableMap<Class<? extends Throwable>, Predicate<Throwable>> INSTANCE_OF =
      ImmutableMap.<Class<? extends Throwable>, Predicate<Throwable>>builder()
          .put(ArithmeticException.class, e -> e instanceof ArithmeticException)
          .put(
              ArrayIndexOutOfBoundsException.class,
              e -> e instanceof ArrayIndexOutOfBoundsException)

  private static final ImmutableMap<Class<? extends Throwable>, Predicate<Throwable>> INSTANCE_OF =
      ImmutableMap.<Class<? extends Throwable>, Predicate<Throwable>>builder()
          .put(ArithmeticException.class, e -> e instanceof ArithmeticException)
          .put(
              ArrayIndexOutOfBoundsException.class,
              e -> e instanceof ArrayIndexOutOfBoundsException)

     * @param operation the operation name
     * @throws ArithmeticException if operation would overflow
     */
    public static void validateIntegerAddition(int a, int b, String operation) {
        long result = (long) a + (long) b;
        if (result > Integer.MAX_VALUE || result < Integer.MIN_VALUE) {
            throw new ArithmeticException(operation + " would cause integer overflow: " + a + " + " + b);
        }
    }

  private static final ImmutableMap<Class<? extends Throwable>, Predicate<Throwable>> INSTANCE_OF =
      ImmutableMap.<Class<? extends Throwable>, Predicate<Throwable>>builder()
          .put(ArithmeticException.class, e -> e instanceof ArithmeticException)
          .put(
              ArrayIndexOutOfBoundsException.class,
              e -> e instanceof ArrayIndexOutOfBoundsException)

   *
   * @throws IllegalArgumentException if {@code x <= 0}
   * @throws ArithmeticException of the next-higher power of two is not representable as a {@code
   *     long}, i.e. when {@code x > 2^62}
   * @since 20.0
   */
  public static long ceilingPowerOfTwo(long x) {
    checkPositive("x", x);
    if (x > MAX_SIGNED_POWER_OF_TWO) {
      throw new ArithmeticException("ceilingPowerOfTwo(" + x + ") is not representable as a long");
    }

      boolean isPowerOf2 = BigIntegerMath.isPowerOfTwo(x);
      try {
        assertEquals(x, ZERO.setBit(BigIntegerMath.log2(x, UNNECESSARY)));
        assertTrue(isPowerOf2);
      } catch (ArithmeticException e) {
        assertFalse(isPowerOf2);
      }
    }
  }

  public void testLog2HalfUp() {
    for (BigInteger x : POSITIVE_BIGINTEGER_CANDIDATES) {
      int result = BigIntegerMath.log2(x, HALF_UP);

  private static final ImmutableMap<Class<? extends Throwable>, Predicate<Throwable>> INSTANCE_OF =
      ImmutableMap.<Class<? extends Throwable>, Predicate<Throwable>>builder()
          .put(ArithmeticException.class, e -> e instanceof ArithmeticException)
          .put(
              ArrayIndexOutOfBoundsException.class,
              e -> e instanceof ArrayIndexOutOfBoundsException)

  private static final ImmutableMap<Class<? extends Throwable>, Predicate<Throwable>> INSTANCE_OF =
      ImmutableMap.<Class<? extends Throwable>, Predicate<Throwable>>builder()
          .put(ArithmeticException.class, e -> e instanceof ArithmeticException)
          .put(
              ArrayIndexOutOfBoundsException.class,
              e -> e instanceof ArrayIndexOutOfBoundsException)

  private static final ImmutableMap<Class<? extends Throwable>, Predicate<Throwable>> INSTANCE_OF =
      ImmutableMap.<Class<? extends Throwable>, Predicate<Throwable>>builder()
          .put(ArithmeticException.class, e -> e instanceof ArithmeticException)
          .put(
              ArrayIndexOutOfBoundsException.class,
              e -> e instanceof ArrayIndexOutOfBoundsException)