Sorting distinct integer keys using in-place associative sort

In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms. The technique was explained by the analogy with the three main stages in the formation and retrieval of memory in cognitive neuroscience which are (i) practicing, (ii) storing and (iii) retrieval. In this study, the technique is specialized with two variants one for read-only integer keys and the other for modifiable integers. Hence, a novel algorithm is obtained that does not require additional memory other than a constant amount and sorts faster than all no matter how large is the list provided that m = O(n log n) where m is the range and n is the number of keys (or integers).