c++ - 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 2,3,4,5,... up to 16?

WARNING: given code is EXAMPLE only. Every line is independent! Just obvious solution using modulo operation is slow on many processors, which don't have DIV hardware (like many ARMs). Some compilers are also cannot make such optimizations (say, if divisor is a function's argument or is dependent on something).

Divisible_by_1 = do();
Divisible_by_2 = if (!(number & 1)) do();
Divisible_by_3 = ?
Divisible_by_4 = ?
Divisible_by_5 = ?
Divisible_by_6 = ?
Divisible_by_7 = ?
Divisible_by_8 = ?
Divisible_by_9 = ?
Divisible_by_10 = ?
Divisible_by_11 = ?
Divisible_by_12 = ?
Divisible_by_13 = ?
Divisible_by_14 = ?
Divisible_by_15 = ?
Divisible_by_16 = if(!number & 0x0000000F) do();

and special cases:

Divisible_by_2k = if(number & (tk-1)) do();  //tk=2**k=(2*2*2*...) k times

Answer 1

In every case (including divisible by 2):

if (number % n == 0) do();

Anding with a mask of low order bits is just obfuscation, and with a modern compiler will not be any faster than writing the code in a readable fashion.

If you have to test all of the cases, you might improve performance by putting some of the cases in the if for another: there's no point it testing for divisibility by 4 if divisibility by 2 has already failed, for example.