Q:

c++ random engines not really random

I'm playing a bit with c++ random engines, and something upsets me.
Having noticed that the values I had were roughly of the same order, I did the following test:
#include <random>
#include <functional>
#include <iostream>

int main()
{
    auto res = std::random_device()();
    std::ranlux24 generator(res);
    std::uniform_int_distribution<uint32_t> distribution;
    auto roll = std::bind(distribution, generator);

    for(int j = 0; j < 30; ++j)
    { 
        double ssum = 0;
        for(int i = 0; i< 300; ++i)
        {
            ssum += std::log10(roll());
        }
        std::cout << ssum / 300. << std::endl;
    }
    return 0;
}

and the values I printed were all about 9.2 looking more like a normal distribution, whatever the engine I used.
Is there something I have not understood correctly?
Thanks,
Guillaume

A:

Having noticed that the values I had were roughly of the same order

This is exactly what you'd expect with a uniform random number generator. There are 9 times as many integers in the range [10^(n-1),10^n) as there are in the range [0,10^(n-1)).

