Hand-rolling a C string comparison

Implement your own version of a function that compares two null-terminated C strings, returning negative, zero or positive as strcmp does.

Advance both pointers while characters match and are non-null, then return the difference of the current characters. Cast to unsigned char before subtracting so characters above 127 compare correctly. This takes $O(\min(m,n))$ time and $O(1)$ space; handle the case where one string is a prefix of the other, which is caught by the terminating null.