Calypso88

UPDATE: The benchmarks on this thread were taken in the Flash 9 Debug player (which includes some crazy bloating) - I've posted an updated set of tests here using the Flash 10 Release player, which should give you a better picture of real-world savings for the majority of web users.

In case you missed my earlier post, I've had a raging Flash-on for optimization lately, and today I'm jumping into the Math class. But first! A little warmup with operators.

I've often heard that addition is fastest, followed by subtraction and multiplication, with division being the slowest but I'd never seen any proof so I threw together my own test:

Way to go subtraction, almost 12% faster than addition! Ok, on to the good stuff. From here on down I'm running 1,000,000 iterations per test, the same test code I used previously, and compiling each test individually about five times (or until I'm satisfied with an average time).

Alright - the Math class. First and foremost this class holds some handy constants so my human meat-brain doesn't have to. The downside is that the AVM doesn't play well with static properties of other classes so there's a pretty significant slowdown. Instead, just retrieve the constant from Math once and store it in a locally scoped variable.

While a lot of the Math methods are invaluable (Math.atan2 == ♥), there are also a few that aren't as complex and slow your swf down unnecessarily. A big one that's easy to work around is the pow method – unless you're doing some heavy lifting with it, you'll see a good boost by keying out your formula by hand:

Or you can replace costly comparison calls with a little logic:

Going a step further, you can take advantage of int casting to shear off any significant digits to the right of the decimal.

By substituting int as a super fast round-down, it's an easy jump to true rounding:

UPDATE: A lot of other people have posted that you can recreate Math.ceil() by using int(i)+1, which never rang true to me – it only works on non-integers. I finally came around to a fix using modulus:
 
(i % 1) ? int(i) + 1 : i;
 
I don't have a fancy graph for this one but I benched it around 75% faster than Math.ceil.

My last trick is a monstrous, ugly, hack that I'm hiding over on the code page, it's an approximation for computing sine (which means you can also use it for co-sine by adding π/2 radians). Interestingly, this method of calculating the sine of an angle is actually less efficient and less accurate than the built in method, but the lag from calling the static method pushes Math.sin over the top.

Next: I'm hoping to give arrays a little loving in the not too distant future...if I ever get some free time that is. In the meantime – steer clear of unshift!

Further reading:
Joa Ebert on optimization
Speed tests over on OS Flash
Bitwise gems at Polygonal