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

Here are some tips I haven't see anyone else suggest yet:

One idea is to use a switch statement, or precompute some array. Then, any decent optimizer can simply index each case directly. For example:

// tests for (2,3,4,5,6,7)
switch (n % 8)
{
case 0: break;
case 1: break;
case 2: do(2); break;
case 3: do(3); break;
case 4: do(2); do(4) break;
case 5: do(5); break;
case 6: do(2); do(3); do(4); break;
case 7: do(7); break;
} 

Your application is a bit ambiguous, but you may only need to check prime numbers less than n=16. This is because all numbers are factors of the current or previous prime numbers. So for n=16, you might be able to get away with only checking 2, 3, 5, 7, 11, 13 somehow. Just a thought.