02/20/2010 Update: I took this blog post and turned it into a presentation to the Atlanta Scala User Group, which I gave in January 2010. The slides from that presentation are here.

05/31/2009 Update: As Mads Andersen pointed out, in the example below, I had the Complex multiplication wrong. As I was working through the example in the book, I typed it incorrectly. I could argue that this blog post was not about my mastery of complex numbers, and was actually meant to show how operator overloading works in Scala, but in the interest of all-around correctness, I have updated the code to contain the proper implementation of complex number multiplication, and I have worked out the examples by hand using the formula on the Wikipedia page to ensure their accuracy. Now, on to the original article.

So as I’m reading the section on operator overloading, it was nice to see that even though you can override the standard mathematical operators, Scala still maintains the proper precedence that everyone is used to. By this I mean that a + b * c will execute the multiplication first, then add the product of b and c to a. The reason this is interesting is because another language that I still love, Smalltalk, does it wrong (or at least, completely differently), and not just for overloaded operators. Smalltalk has no precedence for mathematical operators at all, ever. So a + b * c will execute the + operation on a, passing in b, and then execute the * operation on that result, passing in c. Always. Thus, 2 + 3 * 5 = 25 in Smalltalk, even though it should equal 17. To get 17, you’d have to write the equation as 2 + (3 * 5). I always found that strange.

The canonical example for operator overloading is a class to represent Complex numbers. I will not break with tradition and will, in fact, steal borrow the one from the book. Here, then, is the definition of the Complex class

```class Complex(val real:Int, val imaginary:Int) {
def +(operand:Complex):Complex = {
new Complex(real + operand.real, imaginary + operand.imaginary)
}

def *(operand:Complex):Complex = {
new Complex(real * operand.real - imaginary * operand.imaginary,
real * operand.imaginary + imaginary * operand.real)
}

override def toString() = {
real + (if (imaginary &amp;lt; 0) &quot;&quot; else &quot;+&quot;) + imaginary + &quot;i&quot;
}
}```

Notice that we have overridden both the + and * operators. They each take another instance of Complex as an argument, do the proper operations and return a new instance of Complex as their result. Just as you would expect. Now, to exercise these operators, we have this

```val c1 = new Complex(1, 2)
val c2 = new Complex(2, -3)
val c3 = c1 + c2

val res = c1 + c2 * c3

printf(&quot;(%s) + (%s) * (%s) = %sn&quot;, c1, c2, c3, res)

val res1 = c1 + c2 * c3 + c1 * c2

printf(&quot;(%s) + (%s) * (%s) + (%s) * (%s) = %sn&quot;, c1, c2, c3, c1, c2, res1)
```

Lines 5 and 9 are the interesting parts. The result of running these statements looks like this

(1+2i) + (2-3i) * (3-1i) = 4-9i
(1+2i) + (2-3i) * (3-1i) + (1+2i) * (2-3i) = 12-8i

which is exactly what you’d expect.

Now, C++ people are probably saying, “But C++ has always done it right!” Indeed. But languages like Smalltalk and Scala are far more fun to work in.