Swapping Without a Temporary

XOR lets you swap two variables without using a temporary variable. Here's how:

$a := a \wedge b$

$b := a \wedge b$

$a := a \wedge b$

After these three operations, $a$ and $b$ have swapped values. Why? After the first line, $a$ holds $a \wedge b$. In the second line, $b := (a \wedge b) \wedge b = a$ (using $x \wedge x = 0$ and $x \wedge 0 = x$). In the third line, $a := (a \wedge b) \wedge a = b$. It's a clever trick, though using a temporary is usually clearer and just as fast.