I did not consult any reference for this implementation, so I guess there are bugs lurking everywhere.

Constructive criticisms welcome. And yes, it is C-ish.

 
int BinarySearch(int data[], unsigned int elements, int key)
{
    if(elements==0)
    {
        cerr << "Binary search not able to perform on 0 element array";
        exit(-1);
    }
    unsigned int half_offset = elements<<31? (elements-1)/2 : elements/2;   // truncation will happen anyway.
    unsigned int current_index = elements<<31? (elements-1)/2 : elements/2; // Non portable bitwise ops.
    
        
    while(half_offset!=0)
    {
        if(data[current_index]==key)
            return current_index;
        else if(data[current_index]<key)
        {
            current_index += half_offset<<31? (half_offset+1)/2 : half_offset/2;
        }
        else if(data[current_index]>key)
        {
            current_index -= half_offset<<31? (half_offset+1)/2 : half_offset/2;
        }
        half_offset /= 2; // Truncated to floor
    }
    if(data[current_index]==key)
                return current_index;
}

Is that code snippet complete? You should be getting an error that not all paths return a value. You end the function on an if-statement. I.e., when execution drops through the IF, there's no return value.

There are several unusual things you are doing there.

I discussed binary search and how to do it better, in this article that I wrote about various searching techniques:

http://homepages.ihug.co.nz/~aurora76/Malc/Searching.htm

Corrected according to feedback:

 
unsigned int BinarySearch(int data[], unsigned int elements, int key)
{
    if(elements==0)
    {
        cerr << "Binary search not able to perform on 0 element array";
        exit(-1);
    }
    unsigned int half_offset = elements/2 /*upper half smaller when even elements*/;
    unsigned int current_index = elements/2; 
    
        
    while(half_offset!=0)
    {
        if(data[current_index]==key)
            return current_index;
        else if(data[current_index]<key)
        {
            current_index += (half_offset+1)/2;
        }
        else if(data[current_index]>key)
        {
            current_index -= (half_offset+1)/2;
        }
        half_offset /= 2; // Truncated to floor
    }
    if(data[current_index]==key)
                return current_index;
    else
        cerr << "Finished array search without any matching results";
}

    if(data[current_index]==key)
                return current_index;
    else
        cerr << "Finished array search without any matching results";
    return <fail-value>; // perhaps -1 as suggested above
}

As mentioned before, you need to add a return <value> before the closing brace.

How do I choose a failure value in an unsigned int?