int actual = LongMath.lessThanBranchFree(x, y);
          assertEquals(expected, actual);
        }
      }
    }
  }

  // Throws an ArithmeticException if "the simple implementation" of binomial coefficients overflows
  @GwtIncompatible // TODO
  private long simpleBinomial(int n, int k) {
    long accum = 1;
    for (int i = 0; i < k; i++) {
      accum = LongMath.checkedMultiply(accum, n - i);
      accum /= i + 1;

        assertWithMessage("Pearson's correlation coefficient of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
        assertWithMessage("Pearson's correlation coefficient by addAll(PairedStats) of " + values)
            .that(pearsonsCorrelationCoefficient)
            .isNaN();
      } else {
        assertWithMessage("Pearson's correlation coefficient of " + values)

    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

    return sumOfProductsOfDeltas / (count() - 1);
  }

  /**
   * Returns the <a href="http://mathworld.wolfram.com/CorrelationCoefficient.html">Pearson's or
   * product-moment correlation coefficient</a> of the values. The count must greater than one, and
   * the {@code x} and {@code y} values must both have non-zero population variance (i.e. {@code

            .size());

    // Almost force an overflow in the binomial coefficient calculation
    assertEquals(
        1391975640 /*C(34,14)*/,
        Collections2.orderedPermutations(concat(nCopies(20, 1), nCopies(14, 2))).size());
    // Do force an overflow in the binomial coefficient calculation
    assertEquals(
        Integer.MAX_VALUE,

        int m = (end + start) >>> 1;
        return listProduct(nums, start, m).multiply(listProduct(nums, m, end));
    }
  }

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, that is, {@code n! / (k! (n - k)!)}.
   *
   * <p><b>Warning:</b> the result can take as much as <i>O(k log n)</i> space.
   *

    1L * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 17 * 18 * 19 * 20
  };

  /**
   * Returns {@code n} choose {@code k}, also known as the binomial coefficient of {@code n} and
   * {@code k}, or {@link Long#MAX_VALUE} if the result does not fit in a {@code long}.
   *
   * @throws IllegalArgumentException if {@code n < 0}, {@code k < 0}, or {@code k > n}
   */