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Probably something stupid, but I can't figure out how to work with these large numbers, then cast the result (which will be small) to an integer. I keep getting negative numbers, which I think means I'm overflowing somewhere.
int freq = 440;
int len = 256;
long timer = 2000000.0 / (freq * len);
int roundedTimer = int(timer);
I should get 18, but I'm getting -108...
freq * long, since they are both integers, are calculated as integers.
440*256=112640 - in binary that is 1 1011 1000 0000 0000 and trimmed to 16 bits becomes 1011 1000 0000 0000 which is -18432 and that is where the heart of your problem is. Unless you explicitly say otherwise the Arduino's compiler does all calculations (except floating point) as 16-bit signed integers.
By casting the values to long it forces the compiler to 'overflow' the 16-bit limit and use a 32-bit limit instead:
long timer = 2000000 / ((long)freq * (long)len);
Another alternative is to define freq and len to be long from the outset instead of int.
freq * lenneeds to be explicitly a long too: long timer = 2000000L / ((long) freq * len); – JeffThompson Jan 25 '16 at 18:09