Distributions and internal state

Question

On Stackoverflow there are many questions about generating uniformly distributed integers from a-priory unknown ranges. E.g.

• C++11 Generating random numbers fr

Answer 1

Interesting question.

So I was wondering if interfering with how the distribution works by constantly resetting it (i.e. recreating the distribution at every call of get_int_from_range) I get properly distributed results.

I've written code to test this with uniform_int_distribution and poisson_distribution. It's easy enough to extend this to test another distribution if you wish. The answer seems to be yes.

Boiler-plate code:

#include <random>
#include <memory>
#include <chrono>
#include <utility>

typedef std::mt19937_64 engine_type;

inline size_t get_seed()
    { return std::chrono::system_clock::now().time_since_epoch().count(); }

engine_type& engine_singleton()
{  
    static std::unique_ptr<engine_type> ptr;

    if ( !ptr ) 
        ptr.reset( new engine_type(get_seed()) );
    return *ptr;
}

// ------------------------------------------------------------------------

#include <cmath>
#include <cstdio>
#include <vector>
#include <string>
#include <algorithm>

void plot_distribution( const std::vector<double>& D, size_t mass = 200 )
{
    const size_t n = D.size();
    for ( size_t i = 0; i < n; ++i ) 
    {
        printf("%02ld: %s\n", i, 
            std::string(static_cast<size_t>(D[i]*mass),'*').c_str() );
    }
}

double maximum_difference( const std::vector<double>& x, const std::vector<double>& y )
{
    const size_t n = x.size(); 

    double m = 0.0;
    for ( size_t i = 0; i < n; ++i )
        m = std::max( m, std::abs(x[i]-y[i]) );

    return m;
}

Code for the actual tests:

#include <iostream>
#include <vector>
#include <cstdio>
#include <random>
#include <string>
#include <cmath>

void compare_uniform_distributions( int lo, int hi )
{
    const size_t sample_size = 1e5;

    // Initialize histograms
    std::vector<double> H1( hi-lo+1, 0.0 ), H2( hi-lo+1, 0.0 );

    // Initialize distribution
    auto U = std::uniform_int_distribution<int>(lo,hi);

    // Count!
    for ( size_t i = 0; i < sample_size; ++i )
    {
        engine_type E(get_seed());

        H1[ U(engine_singleton())-lo ] += 1.0;
        H2[ U(E)-lo ] += 1.0;
    }

    // Normalize histograms to obtain "densities"
    for ( size_t i = 0; i < H1.size(); ++i )
    {
        H1[i] /= sample_size; 
        H2[i] /= sample_size; 
    }

    printf("Engine singleton:\n"); plot_distribution(H1);
    printf("Engine creation :\n"); plot_distribution(H2);
    printf("Maximum difference: %.3f\n", maximum_difference(H1,H2) );
    std::cout<< std::string(50,'-') << std::endl << std::endl;
}

void compare_poisson_distributions( double mean )
{
    const size_t sample_size = 1e5;
    const size_t nbins = static_cast<size_t>(std::ceil(2*mean));

    // Initialize histograms
    std::vector<double> H1( nbins, 0.0 ), H2( nbins, 0.0 );

    // Initialize distribution
    auto U = std::poisson_distribution<int>(mean);

    // Count!
    for ( size_t i = 0; i < sample_size; ++i )
    {
        engine_type E(get_seed());
        int u1 = U(engine_singleton());
        int u2 = U(E);

        if (u1 < nbins) H1[u1] += 1.0;
        if (u2 < nbins) H2[u2] += 1.0;
    }

    // Normalize histograms to obtain "densities"
    for ( size_t i = 0; i < H1.size(); ++i )
    {
        H1[i] /= sample_size; 
        H2[i] /= sample_size; 
    }

    printf("Engine singleton:\n"); plot_distribution(H1);
    printf("Engine creation :\n"); plot_distribution(H2);
    printf("Maximum difference: %.3f\n", maximum_difference(H1,H2) );
    std::cout<< std::string(50,'-') << std::endl << std::endl;

}

// ------------------------------------------------------------------------

int main()
{
    compare_uniform_distributions( 0, 25 );
    compare_poisson_distributions( 12 );
}

Run it here.

---

Does the C++ standard make any guarantee regarding this topic?

Not that I know of. However, I would say that the standard makes an implicit recommendation not to re-create the engine every time; for any distribution Distrib, the prototype of Distrib::operator() takes a reference URNG& and not a const reference. This is understandably required because the engine might need to update its internal state, but it also implies that code looking like this

auto U = std::uniform_int_distribution(0,10);
for ( <something here> ) U(engine_type());

does not compile, which to me is a clear incentive not to write code like this.

---

I'm sure there are plenty of advice out there on how to properly use the random library. It does get complicated if you have to handle the possibility of using random_devices and allowing deterministic seeding for testing purposes, but I thought it might be useful to throw my own recommendation out there too:

#include <random>
#include <chrono>
#include <utility>
#include <functional>

inline size_t get_seed()
    { return std::chrono::system_clock::now().time_since_epoch().count(); }

template <class Distrib>
using generator_type = std::function< typename Distrib::result_type () >;

template <class Distrib, class Engine = std::mt19937_64, class... Args>
inline generator_type<Distrib> get_generator( Args&&... args )
{ 
    return std::bind( Distrib( std::forward<Args>(args)... ), Engine(get_seed()) ); 
}

// ------------------------------------------------------------------------

#include <iostream>

int main()
{
    auto U = get_generator<std::uniform_int_distribution<int>>(0,10);
    std::cout<< U() << std::endl;
}

Run it here. Hope this helps!

EDIT My first recommendation was a mistake, and I apologise for that; we can't use a singleton engine like in the tests above, because this would mean that two uniform int distributions would produce the same random sequence. Instead I rely on the fact that std::bind copies the newly-created engine locally in std::function with its own seed, and this yields the expected behaviour; different generators with the same distribution produce different random sequences.