First of all, thanks for sharing this repo and for keeping it updated, you are awesome!

After tinkering with mergeSort I noticed that its time performance sharply degrades when we pass a certain input size threshold, just like you have described on your blog post.

It seems that the main culprit is the Array.prototype.shift() method that is used when merging left and right subarrays in mergeSort.merge(). A quick inspection of the Array.prototype.shift() method specification reveals that this operation takes O(N) time. The right.shift() and left.shift() operations are nested within a while loop that runs through all elemens of the subarrays. Therefore we don't have an O(n * logn) algorithm but one that seems to be quadratic.

Instead of arrays, I propose using the working LinkedList data structure to implement a queue ADT and thus spend O(1) instead of O(N) for the same operation. Running a performance test with this approach on an unsorted array of 1M elements dropped the execution time from 8m 39.435s to 0.802s (~650x). More detailed results are here.

Moral of the story: Repeatedly calling Array.prototype.shift() on big data sets can really hurt performance.