Question.java

package Q16_09_Operations;

import java.util.Random;

import CtCILibrary.AssortedMethods;

public class Question {
	/* Flip a positive sign to negative, or a negative sign to pos */
	public static int negate(int a) {
		int neg = 0;
		int newSign = a < 0 ? 1 : -1;
		while (a != 0) {
			neg += newSign;
			a += newSign;
		}
	    return neg;
	}
	
	/* Flip a positive sign to negative, or a negative sign to pos */
	public static int negateOptimized(int a) {
		int neg = 0;
		int newSign = a < 0 ? 1 : -1;
		int delta = newSign;
		while (a != 0) {
			boolean differentSigns = (a + delta > 0) != (a > 0);
			if (a + delta != 0 && differentSigns) { // If delta is too big, reset it.
				delta = newSign;
			}
			neg += delta;
			a += delta;
			delta += delta; // Double the delta
		}
	    return neg;
	}	

	/* Subtract two numbers by negating b and adding them */
	public static int minus(int a, int b) {
		return a + negate(b);
	}

	/* Return absolute value */
	public static int abs(int a) {
		if (a < 0) {
			return negateOptimized(a);
		}
		else return a;
	}

	/* Multiply a by b by adding a to itself b times */
	public static int multiply(int a, int b) {
		if (a < b) {
			return multiply(b, a); // algo is faster if b < a
		}
		int sum = 0;
		for (int i = abs(b); i > 0; i = minus(i, 1)) {
			sum += a;
		}
		if (b < 0) {
			sum = negateOptimized(sum);
		}
		return sum;
	}

	/* Divide a by b by literally counting how many times b can go into
	 * a. That is, count how many times you can add b to itself until you reach a. */
	public static int divide(int a, int b) throws java.lang.ArithmeticException {
		if (b == 0) {
			throw new java.lang.ArithmeticException("ERROR: Divide by zero.");
		}
		int absa = abs(a);
		int absb = abs(b);
		
		int product = 0;
		int x = 0;
		while (product + absb <= absa) { /* don't go past a */
			product += absb;
			x++;
		}
		
		if ((a < 0 && b < 0) || (a > 0 && b > 0)) {
			return x;
		} else {
			return negateOptimized(x);
		}
	}
	
	public static void main(String[] args) {
		int minRange = -100;
		int maxRange = 100;
		int cycles = 100;
		
		for (int i = 0; i < cycles; i++) {
			int a = AssortedMethods.randomIntInRange(minRange, maxRange);
			int b = AssortedMethods.randomIntInRange(minRange, maxRange);
			int ans = minus(a, b);
			if (ans != a - b) {
				System.out.println("ERROR");
			}
			System.out.println(a + " - " + b + " = " + ans);
		}
		for (int i = 0; i < cycles; i++) {
			int a = AssortedMethods.randomIntInRange(minRange, maxRange);
			int b = AssortedMethods.randomIntInRange(minRange, maxRange);
			int ans = multiply(a, b);
			if (ans != a * b) {
				System.out.println("ERROR");
			}
			System.out.println(a + " * " + b + " = " + ans);
		}
		for (int i = 0; i < cycles; i++) {
			int a = AssortedMethods.randomIntInRange(minRange, maxRange);
			int b = AssortedMethods.randomIntInRange(minRange, maxRange);
			System.out.print(a + " / " + b + " = ");
			int ans = divide(a, b);
			if (ans != a / b) {
				System.out.println("ERROR");
			}
			System.out.println(ans);
		}
	}

}