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Compare Large String Contents

I'm implementing a system in which I'm handling multiple complex kind of data, and I must be able to sort the data objects given their inner value, using the IComparable interface contract.

One of these object types handles short to very long (2*10^28) strings, materialized as TextReader.

Does anyone know an effective way to compute such difference on such long objects in an optimal way? It seems I can't find any solution to determine which, between two objects, is the greatest or equal, but only text diff algorithms.

Since they are materialized as TextReaders I would probably use a method like this:

static int Compare(TextReader r1, TextReader r2)
{
     int c1 = 0, c2 = 0;

     // read one char at a time and compare them
     // until we reach end of one of the strings
     while((c1 = r1.Read()) != -1 && 
           (c2 = r2.Read()) != -1)
     {
          var result = ((char)c1).CompareTo((char)c2);
          if (result != 0) return result;
     }
     // if both are -1 then strings have the same length and 
     // consist of same chars so they are equal
     if (c1 == -1 && c2 == -1)
         return 0;
     // if r1 is subset of r2 then r2 is greater
     else if (c1 == -1)
         return -1;
     // otherwise r1 is greater
     else
         return 1;
}

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