I need to generate 16-bit pseudo-random integers and I am wondering what the best choice is.
The obvious way that comes in my mind is something as follows:
std::random_device rd;
auto seed_data = std::array<int, std::mt19937::state_size> {};
std::generate(std::begin(seed_data), std::end(seed_data), std::ref(rd));
std::seed_seq seq(std::begin(seed_data), std::end(seed_data));
std::mt19937 generator(seq);
std::uniform_int_distribution<short> dis(std::numeric_limits<short>::min(),
std::numeric_limits<short>::max());
short n = dis(generator);
The problem I see here is that std::mt19937 produces 32-bit unsigned integers since it's defined as this:
using mt19937 = mersenne_twister_engine<unsigned int,
32, 624, 397,
31, 0x9908b0df,
11, 0xffffffff,
7, 0x9d2c5680,
15, 0xefc60000,
18, 1812433253>;
That means static casting is done and only the least significant part of these 32-bit integers is used by the distribution. So I am wondering how good are these series of pseudo-random shorts and I don't have the mathematical expertise to answer that.
I expect that a better solution would be to use your own defined mersenne_twister_engine engine for 16-bit integers. However, I haven't found any mentioned set for the template arguments (requirements can be found here for instance). Are there any?
UPDATE: I updated the code sample with proper initialization for the distribution.
Your way is indeed the correct way.
The mathematical arguments are complex (I'll try to dig out a paper), but taking the least significant bits of the Mersenne Twister, as implemented by the C++ standard library, is the correct thing to do.
If you're in any doubt as to the quality of the sequence, then run it through the diehard tests.