Developing BigInt class

Question

I have started to develop a BigInt class and i'm stuck right now. The problem is that when I try to add two numbers with different lengths, the result is not correct. For example, 123 + 1 will return 223. I know where the problem is, but I need help on fixing it.

        public static BigInt operator +(BigInt n1, BigInt n2)
    {
        Stack<char> sNew = new Stack<char>();
        Stack<char> sTemp = new Stack<char>();
        int currentDigit1, currentDigit2, sum;
        int carry = 0;

        //insert the digits, XXXyyy + ZZZ = first insert ___yyy and then calculate XXX+ZZZ
        if (n1.GetLength() > n2.GetLength())
        {
            while (n1.GetLength() > n2.GetLength())
                sNew.Push(n1.sDigits.Pop());
        }
        else if (n2.GetLength() > n1.GetLength())
        {
            while (n2.GetLength() > n1.GetLength())
                sNew.Push(n2.sDigits.Pop());
        }

        while (n1.sDigits.Count > 0)
        {
            currentDigit1 = int.Parse(n1.sDigits.Pop().ToString());
            currentDigit2 = int.Parse(n2.sDigits.Pop().ToString());
            sum = currentDigit1 + currentDigit2 + carry;
            carry = 0;

            if (sum > 10)
            {
                carry = 1;
                sum = sum % 10;
            }

            sNew.Push(char.Parse(sum.ToString()));

        }

        //if there is a carry, for example 95+18
        if (carry > 0)
            sNew.Push(char.Parse(carry.ToString()));

        //flip the stack
        while (sNew.Count > 0)
            sTemp.Push(sNew.Pop());
        while (sTemp.Count > 0)
            sNew.Push(sTemp.Pop());

        return new BigInt(sNew);
    }

Regardless of this problem, is this pattern of the class design is effective? Is there better idea for designing this kind of class?

Answer 1

This is a rather wasteful representation, using full eight bits for a single decimal digit - roughly a 60% waste of space!

Even if you stay with this representation, you should consider switching the internal representation from a Stack<char> to a List<char>, with the least significant digit stored at position 0, the digit for the tens stored at position 1, and so on. This will let you implement addition with a single loop that adds digits at the same position if both digits are available, or adds the carry to the digit of the longer number.

A better representation would be to use a base-256 system, and store individual "digits" as an array of bytes.

Note that the addition is not the trickiest operation to implement: wait till you hit multiplication and division! To take a peek at the complexity that you would need to address, download Java's implementation of BigInteger.

I am assuming that you are doing this for fun, not as part of a real project. Otherwise, there is no excuse for not using .NET's built-in representation of BigInteger.