Fast divisibility tests (by 2,3,4,5,.., 16)?

Question

What are the fastest divisibility tests? Say, given a little-endian architecture and a 32-bit signed integer: how to calculate very fast that a number is divisible by 2,3,4,

Answer 1

You should just use (i % N) == 0 as your test.

My compiler (a fairly old version of gcc) generated good code for all the cases I tried. Where bit tests were appropriate it did that. Where N was a constant it didn't generate the obvious "divide" for any case, it always used some "trick".

Just let the compiler generate the code for you, it will almost certainly know more about the architecture of the machine than you do :) And these are easy optimisations where you are unlikely to think up something better than the compiler does.

It's an interesting question though. I can't list the tricks used by the compiler for each constant as I have to compile on a different computer.. But I'll update this reply later on if nobody beats me to it :)