Question

i know insertion sort isn’t that great…but even still…what are two more simple improvements that could be made to the sort below?

public static void insertion_sort_with_moves(int[] arr){
    for (int i = 1; i <= arr.length; i++){
        int v = arr[i-1];
        int j = i-1;
        for (/*declared j outside loop*/; j > 0; j--) {
            //compswap(a[j-1], a[j]);
            if (v < arr[j-1]) arr[j] = arr[j-1];
            else break;
        }
        arr[j] = v;
    }
}

Answer 1

A few micro-optimizations are:

1,2,3)

    int len = arr.length; 
...

    for (int i = 0; i < len; ++i){
            int v = arr[i];
            int j = i;

Saves you from computing i-1 two times and ++i is faster than i++.
Not sure about the length thing (could save the offset addition when accessing a class member).

4,5)

for (/*declared j outside loop*/; j != 0; --j) {

j!=0 should be faster than j>0 (really don’t expect much) and –j is faster than j–.

Well most of them may be platform dependent and may make no difference at all.