Just subtract 1 and add 1 afterwards.
In most programming languages, you need to watch out when finding a “previous” value, because for negative numbers, modulo does not work as you want in this case: it returns a negative number.
Here’s the C/C++ version:
int next(int i, int m, int n) { return (i + m - 1) % n + 1; }
int prev(int i, int m, int n) { return (i - m + n - 1) % n + 1; }
However, in Perl modulo always returns a positive value (at least when the second operand is a positive integer). Basically it does what you want. So you can write the following and leave out the + $_[2]:
sub nxt { ($_[0] + $_[1] - 1) % $_[2] + 1; }
sub prv { ($_[0] - $_[1] - 1) % $_[2] + 1; }