Get a reverse iterator from a forward iterator without knowing the value type

I'm trying to implement some STL-style sorting algorithms. The prototype for std::sort looks something like this (from cplusplus.com):

template <class RandomAccessIterator>
void sort ( RandomAccessIterator first, RandomAccessIterator last );

The function is generally called like this (although the container type can vary):

std::vector<int> myVec;
// Populate myVec
std::sort(myVec.begin(), myVec.end());

I duplicated the prototype of std::sort for my own sorting function. To iterate through the container to be sorted, I do the following:

template <class RandomAccessIterator>
void mySort(RandomAccessIterator first, RandomAccessIterator last) {  
  RandomAccessIterator iter;
  for (iter = first; iter != last; ++iter) {
    // Do stuff
  }
}

Easy enough. But what if I want to use a reverse iterator? This would be convenient in algorithms that sort a container from both ends, e.g. cocktail sort.

Is there any way to get a reverse iterator from the iterators that are passed in as parameters? If I knew the container type in advance, I could do something like this:

template <class RandomAccessIterator>
void mySort(RandomAccessIterator first, RandomAccessIterator last) {
  std::vector<int>::reverse_iterator riter(last);
  std::vector<int>::reverse_iterator rend(first);
  for ( ; riter != rend; ++riter) {
    // Do stuff
  }
}    

Unfortunately, I don't know the container type. What I really need to do is something like this:

template <class RandomAccessIterator>
void mySort(RandomAccessIterator first, RandomAccessIterator last) {
  RandomAccessIterator riter = reverse_iterator(last);
  RandomAccessIterator rend = reverse_iterator(begin);
  for ( ; riter != rend; ++riter) {
    // Do stuff
  }
}

Is there some way to do this without having to pass in reverse iterators as additional parameters (which would solve the problem, but make the function prototype less intuitive)?

Note that I need both forward and reverse iterators in my implementation, so calling the function this way

std::vector<int> myVec;
// Populate myVec
mySort(myVec.rbegin(), myVec.rend());

will not work.