generic number in c++

I want to make a BigInteger object (for practice). I want the overloaded operators to accept any numerical datatype. I can do this polymorphically, but since it would be impractical to overload the 20+ binary operators for each of the 20~ numerical types, I would really like to do something like this:

X & operator+(const anynum input)
{
  return this->value += input;
}

...
main()
{
  X a = 1;
  a = a + 1;
  a = a + 1L;
}

sorry, my question is: "is this possible"?

I researched this most of last night I read through the operator overloading entry on cpp.com, the list of overloadable operators on wikipedia, various posts on stack overflow.

Solution

Possible through slightly different means. See example:

#include <iostream>

class X
{
public:
    X(int val) :
            value(val)
    {

    }
// this is the important part
    template<class TYPE>
    X & operator+(TYPE input)
    {
        value += input; // just demonstrating with a simple int
                        // a real bignum will be significantly more complex
                        // and you may well find that one function does not fit all cases
                        // for your particular bignum implementation
        return *this;
    }
// end of important part
    void print()
    {
        std::cout << value << std::endl;
    }
private:
    int value; 
};

int main()
{
    short s = 1;
    unsigned short us = 1;
    int i = 1;
    long l = 1;
    long long ll = 1;
    float f = 1.0;
    double d = 1.0;
    X a(1);
    a.print();
    a + 1; // templated function is automatically implemented by compiler 
           // for the data type in the call. Use all the data types you want. 
           // The compiler will make one for each one used. 
    a.print();
    a + 1L;
    a.print();
    a + 1.0;
    a.print();
    a + s;
    a.print();
    a + us;
    a.print();
    a + i;
    a.print();
    a + l;
    a.print();
    a + ll;
    a.print();
    a + f;
    a.print();
    a + d;
    a.print();
//  a + "Hi!"; Ka BOOOOOM! Cant add a string to an integer
    a + 'A'; // it does, however, allow this through because math on characters
             // is a time-honoured tradition.
    a.print();
}

For completeness, here's the output: