Radix Sort for Negative Integers

One more solution is to separate negative integers from the array, make them positive, sort as positive values using radix, then reverse it and append with sorted non-negative array.

You can treat the sign as a special kind of digit. You sort the pile on the units, then the tens, etc. and finally on the sign. This does produce a reversed order for the negatives, you then simply reverse the contents of that bucket. It's how old mechanical card sorters worked.