Numerical stability in chisq.test

On 28 Dec 2017, at 13:08 , Kurt Hornik <Kurt.Hornik at wu.ac.at> wrote:

Jan Motl writes:

The chisq.test on line 57 contains following code:
	STATISTIC <- sum(sort((x - E)^2/E, decreasing = TRUE))

The preceding 2 lines seem relevant:

           ## Sorting before summing may look strange, but seems to be
           ## a sensible way to deal with rounding issues (PR#3486):
           STATISTIC <- sum(sort((x - E) ^ 2 / E, decreasing = TRUE))

-k

However, based on book "Accuracy and stability of numerical algorithms" available from:
	http://ftp.demec.ufpr.br/CFD/bibliografia/Higham_2002_Accuracy%20and%20Stability%20of%20Numerical%20Algorithms.pdf
Table 4.1 on page 89, it is better to sort the data in increasing order than in decreasing order, when the data are non-negative.

An example:
	x = matrix(c(rep(1.1, 10000)), 10^16, nrow = 10001, ncol = 1)    # We have a vector with 10000*1.1 and 1*10^16
	c(sum(sort(x, decreasing = TRUE)), sum(sort(x, decreasing = FALSE)))
The result:
	10000000000010996 10000000000011000
When we sort the data in the increasing order, we get the correct result. If we sort the data in the decreasing order, we get a result that is off by 4.

Shouldn't the sort be in the increasing order rather than in the decreasing order?

Best regards,
Jan Motl

PS: This post is based on discussion on https://stackoverflow.com/questions/47847295/why-does-chisq-test-sort-data-in-descending-order-before-summation and the response from the post to r-help at r-project.org.