Adding two numbers w/o arithmetic operator

add.php

// my initial version
function add($x, $y)
{
	$result = 0;
	
	$i = 0; // the first bit to look at
	$max = max($x, $y);
	$msb = log($max, 2); // get the most signicant bit
	$carry = 0;

	while ($i <= $msb || $carry)
	{
		$xBit = (1 << $i) & $x; // get the bit we want to compare from x
		$yBit = (1 << $i) & $y; // get the bit we want to compare from y
		
		$xor = $xBit ^ $yBit;
		$oldXor = $xor;
		$xor = $xor ^ $carry;

		if ($oldXor == 0 || $xor == 0)
		{
		    $carry = 0;
		    if ($xBit & $yBit || $oldXor & $carry)
		    {
			$carry = 1 << ($i+1);
		    }
		}
		
		$result = $xor | $result; // set the bit for the result
		$i++;
	}

	return $result;
}

// Optimized version
function add($x, $y)
{
	if ($y==0) return $x;
	$sum = $x ^ $y;
	$carry = ($x & $y) << 1;
	return add($sum, $carry);
}