Java | Create an explicit addition function only using recursion and conditionals

Question

Preface

By finding some free time in my schedule, I quested myself into improving my recursion skills (unfortunately). As practice, I want to recreate all the operators by using recursion, the first one being addition. Although I'm kind of stuck.

Question

As implied, I want to recreate the addition operator by only using recursion and conditionals. Although I got a good portion of the code done, there is still one problem as I included a single addition operator. Here is the code (which runs fine and adds as intended in all variations of positive, negative, and zero inputs). I also included some mediocre comments as help.

public class Test {
    public static void main(String[] args) {
        // Numbers to add
        int firstNumb = -5, secondNumb = 3;
        // Call the add function and save the result
        int result = add(firstNumb, secondNumb);
        // Print result
        System.out.println(result);
    }

    /*
     * Function recursively takes a number from 'giver' one at a time and
     * "gives"/"adds" it to 'receiver'. Once nothing more to "give" (second == 0),
     * then return the number that received the value, 'receiver'.
     */
    public static int add(int receiver, int giver) {
        /*
         * Base Case since nothing more to add on. != to handle signed numbers
         * instead of using > or <
         */
        if (giver != 0) {
            /*
             * Recursive Call.
             * 
             * The new 'giver' param is the incremental value of the number
             * towards 0. Ex: -5 -> -4 , 5 -> 4 (so I guess it may decrement).
             * 
             * The new 'receiver' param is the incremental value based on the
             * opposite direction the 'giver' incremented (as to why the
             * directionalIncrement() function needs both values to determine
             * direction.
             */
            return add(directionalIncrement(receiver, giver),
                    directionalIncrement(giver, -giver));
        } else {
            // Return 'receiver' which now contains all values from 'giver'
            return receiver;
        }
    }

    // Increments (or decrements) the 'number' based on the sign of the 'direction'
    public static int directionalIncrement(int number, int direction) {
        // Get incremental value (1 or -1) by dividing 'direction' by absolute
        // value of 'direction'
        int incrementalValue = direction / abs(direction);
        // Increment (or decrement I guess)
        return number + incrementalValue;
    }

    // Calculates absolute value of a number
    public static int abs(int number) {
        // If number is positive, return number, else make it positive by multiplying by -1 then return
        number = (number > 0.0F) ? number : -number;
        return number;
    }
}

The problem is the line that contains return number + incrementalValue;. As mentioned before, the code works with this although doesn't meet my own specifications of not involving any addition operators.

I changed the line to return add(number, incrementalValue); but seems like it cannot break out of the recursion and indeed throws the title of this website, a StackOverflowException.

All help appreciated. Thanks in advance.

Note

Constraint does not include any implicit increment/decrement (i++/i--) nor does it include bitwise. Try and answer towards the specific problem I am having in my own implementation.

Answer 1

public static int add (int a, int b) {
    if (b == 0) return a;
    if (b > a) return add (b, a);
    add (++a, --b);
}

Just with ++/--.

Answer 2

public static int add(int a, int b) {
    if(b == 0) return a;
    int sum = a ^ b; //SUM of two integer is A XOR B
    int carry = (a & b) << 1;  //CARRY of two integer is A AND B
    return add(sum, carry);
}

Shamefully taken from here. All credit goes to its author.