Q:

Data type size impact on performance

I'm running intensive numerical simulations.  I often use long integers, but I realized it would be safe to use integers instead.  Would this improve the speed of my simulations significantly? 

A:

Depends.  If you have lots and lots of numbers consecutively in memory, they're more likely to fit in the L2 cache, so you have fewer cache misses.  L2 cache misses - depending on your platform - can be a significant performance impact, so it's definitely a good idea to make things fit in cache as much as possible (and prefetch if you can).  But don't expect your code to fly all of a sudden because your types are smaller. 
EDIT: One more thing - if you choose an awkward type (like a 16-bit integer on a 32-bit or 64-bit platform), you may end up with worse performance because the CPU will have to surgically extract the 16-bit value and turn it into something it can work with.  But typically, ints are a good choice. 