* is not guaranteed to return zero when the dataset consists of the same value multiple times,
   * due to numerical errors. However, it is guaranteed never to return a negative result.
   *
   * <h3>Non-finite values</h3>
   *
   * <p>If the dataset contains any non-finite values ({@link Double#POSITIVE_INFINITY}, {@link

  public static int log2(double x, RoundingMode mode) {
    checkArgument(x > 0.0 && isFinite(x), "x must be positive and finite");
    int exponent = getExponent(x);
    if (!isNormal(x)) {
      return log2(x * IMPLICIT_BIT, mode) - SIGNIFICAND_BITS;
      // Do the calculation on a normal value.
    }
    // x is positive, finite, and normal
    boolean increment;
    switch (mode) {
      case UNNECESSARY:

   *
   * <p>This is guaranteed to return zero if the dataset contains a single pair of finite values. It
   * is not guaranteed to return zero when the dataset consists of the same pair of values multiple
   * times, due to numerical errors.
   *
   * <h3>Non-finite values</h3>
   *
   * <p>If the dataset contains any non-finite values ({@link Double#POSITIVE_INFINITY}, {@link

   *
   * <p>This is guaranteed to return zero if the dataset contains a single pair of finite values. It
   * is not guaranteed to return zero when the dataset consists of the same pair of values multiple
   * times, due to numerical errors.
   *
   * <h3>Non-finite values</h3>
   *
   * <p>If the dataset contains any non-finite values ({@link Double#POSITIVE_INFINITY}, {@link

     *
     * Consequently:
     * 1. If the previous mean is finite and the new value is non-finite then the new mean is that
     *    value (whether it is NaN or infinity).
     * 2. If the new value is finite and the previous mean is non-finite then the mean is unchanged
     *    (whether it is NaN or infinity).
     * 3. If both the previous mean and the new value are non-finite and...

  /**
   * Helper class for testing with non-finite values. {@link #ALL_MANY_VALUES} gives a number of
   * instances with many combinations of finite and non-finite values. All have {@link
   * #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

   *   computeInPlace;
   * - (except that, for non-finite values, we don't do all combinations exhaustively);
   * - percentiles with index and with indexes taking int-varargs, and with compute taking a
   *   double-collection and with computeInPlace.
   */

  private static final double ALLOWED_ERROR = 1.0e-10;

  /**
   * A {@link Correspondence} which accepts finite values within {@link #ALLOWED_ERROR} of each
   * other.
   */

   *   computeInPlace;
   * - (except that, for non-finite values, we don't do all combinations exhaustively);
   * - percentiles with index and with indexes taking int-varargs, and with compute taking a
   *   double-collection and with computeInPlace.
   */

  private static final double ALLOWED_ERROR = 1.0e-10;

  /**
   * A {@link Correspondence} which accepts finite values within {@link #ALLOWED_ERROR} of each
   * other.
   */

        .isWithin(ALLOWED_ERROR)
        .of(MANY_VALUES_MEAN);
    // For datasets of many double values created from an iterable, we test many combinations of
    // finite and non-finite values:
    for (ManyValues values : ALL_MANY_VALUES) {
      StatsAccumulator accumulator = new StatsAccumulator();
      StatsAccumulator accumulatorByAddAllStats = new StatsAccumulator();

    assertThat(TWO_VALUES_PAIRED_STATS.populationCovariance())
        .isWithin(ALLOWED_ERROR)
        .of(TWO_VALUES_SUM_OF_PRODUCTS_OF_DELTAS / 2);
    // For datasets of many double values, we test many combinations of finite and non-finite
    // x-values:
    for (ManyValues values : ALL_MANY_VALUES) {
      PairedStats stats = createPairedStatsOf(values.asIterable(), OTHER_MANY_VALUES);
      double populationCovariance = stats.populationCovariance();