return accum;
        case 1:
          return b * accum;
        default:
          accum *= ((k & 1) == 0) ? 1 : b;
          b *= b;
      }
    }
  }

  /**
   * Returns the square root of {@code x}, rounded with the specified rounding mode.
   *
   * @throws IllegalArgumentException if {@code x < 0}
   * @throws ArithmeticException if {@code mode} is {@link RoundingMode#UNNECESSARY} and {@code

  public void testSqrtExactMatchesFloorOrThrows() {
    for (long x : POSITIVE_LONG_CANDIDATES) {
      long sqrtFloor = LongMath.sqrt(x, FLOOR);
      // We only expect an exception if x was not a perfect square.
      boolean isPerfectSquare = (sqrtFloor * sqrtFloor == x);
      try {
        assertEquals(sqrtFloor, LongMath.sqrt(x, UNNECESSARY));
        assertTrue(isPerfectSquare);
      } catch (ArithmeticException e) {

        .isWithin(ALLOWED_ERROR * INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT);
    assertThat(longManyValuesAccumulatorByAddAllIterator.populationVariance())
        .isWithin(ALLOWED_ERROR * LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT);

        .isWithin(ALLOWED_ERROR * INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT);
    assertThat(INTEGER_MANY_VALUES_STATS_ITERABLE.populationVariance())
        .isWithin(ALLOWED_ERROR * INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT);

   *
   * <p>This fit minimizes the root-mean-square error in {@code y} as a function of {@code x}. This
   * error is defined as the square root of the mean of the squares of the differences between the
   * actual {@code y} values of the data and the values predicted by the fit for the {@code x}
   * values (i.e. it is the square root of the mean of the squares of the vertical distances between

  public void testSqrtExactMatchesFloorOrThrows() {
    for (int x : POSITIVE_INTEGER_CANDIDATES) {
      int floor = IntMath.sqrt(x, FLOOR);
      // We only expect an exception if x was not a perfect square.
      boolean isPerfectSquare = (floor * floor == x);
      try {
        assertEquals(floor, IntMath.sqrt(x, UNNECESSARY));
        assertTrue(isPerfectSquare);
      } catch (ArithmeticException e) {

   * Function<Integer, String> square = new Function<Integer, String>() {
   *     public String apply(Integer in) {
   *       return Integer.toString(in * in);
   *     }
   * };
   * Multimap<String, String> transformed =
   *     Multimaps.transformValues(multimap, square);
   *   System.out.println(transformed);
   * }</pre>
   *

        .isWithin(ALLOWED_ERROR * INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT);
    assertThat(longManyValuesAccumulatorByAddAllIterator.populationVariance())
        .isWithin(ALLOWED_ERROR * LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(LONG_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / LONG_MANY_VALUES_COUNT);

        .isWithin(ALLOWED_ERROR * INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT);
    assertThat(INTEGER_MANY_VALUES_STATS_ITERABLE.populationVariance())
        .isWithin(ALLOWED_ERROR * INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS)
        .of(INTEGER_MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS / INTEGER_MANY_VALUES_COUNT);

   * #MANY_VALUES_COUNT} values. If all the values are finite then the mean is {@link
   * #MANY_VALUES_MEAN} and the sum-of-squares-of-deltas is {@link
   * #MANY_VALUES_SUM_OF_SQUARES_OF_DELTAS}. The smallest and largest finite values are always
   * {@link #MANY_VALUES_MIN} and {@link #MANY_VALUES_MAX}, although setting non-finite values will
   * change the true min and max.
   */