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std::poisson_distribution and std::negative_binomial_distribution are terrible for small types like int8_t #56656

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ldionne opened this issue Jul 21, 2022 · 0 comments
Open

std::poisson_distribution and std::negative_binomial_distribution are terrible for small types like int8_t #56656

ldionne opened this issue Jul 21, 2022 · 0 comments
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enhancement Improving things as opposed to bug fixing, e.g. new or missing feature libc++ libc++ C++ Standard Library. Not GNU libstdc++. Not libc++abi.

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@ldionne
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ldionne commented Jul 21, 2022

The following tests fail miserably for std::negative_binomial_distribution on int8_t and uint8_t. We have similar problems for std::poisson_distribution.

Basically, I think we need to re-think the algorithm we use for std::poisson_distribution (which is what negative_binomial_distribution uses too). That might require an ABI break, however breaking the ABI of random distributions might be acceptable.

#include <random>
#include <numeric>
#include <vector>
#include <cassert>

template <class T>
T sqr(T x) {
    return x * x;
}

template <class T>
void test2() {
    typedef std::negative_binomial_distribution<T> D;
    typedef std::mt19937 G;
    G g;
    D d(30, .03125);
    const int N = 1000000;
    std::vector<typename D::result_type> u;
    for (int i = 0; i < N; ++i)
    {
        typename D::result_type v = d(g);
        assert(d.min() <= v && v <= d.max());
        u.push_back(v);
    }
    double mean = std::accumulate(u.begin(), u.end(),
                                          double(0)) / u.size();
    double var = 0;
    double skew = 0;
    double kurtosis = 0;
    for (unsigned i = 0; i < u.size(); ++i)
    {
        double dbl = (u[i] - mean);
        double d2 = sqr(dbl);
        var += d2;
        skew += dbl * d2;
        kurtosis += d2 * d2;
    }
    var /= u.size();
    double dev = std::sqrt(var);
    skew /= u.size() * dev * var;
    kurtosis /= u.size() * var * var;
    kurtosis -= 3;
    double x_mean = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
    assert(std::abs((mean - x_mean) / x_mean) < 0.01);
    assert(std::abs((var - x_var) / x_var) < 0.01);
    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.01);
}

template <class T>
void test3() {
    typedef std::negative_binomial_distribution<T> D;
    typedef std::mt19937 G;
    G g;
    D d(40, .25);
    const int N = 1000000;
    std::vector<typename D::result_type> u;
    for (int i = 0; i < N; ++i)
    {
        typename D::result_type v = d(g);
        assert(d.min() <= v && v <= d.max());
        u.push_back(v);
    }
    double mean = std::accumulate(u.begin(), u.end(),
                                          double(0)) / u.size();
    double var = 0;
    double skew = 0;
    double kurtosis = 0;
    for (unsigned i = 0; i < u.size(); ++i)
    {
        double dbl = (u[i] - mean);
        double d2 = sqr(dbl);
        var += d2;
        skew += dbl * d2;
        kurtosis += d2 * d2;
    }
    var /= u.size();
    double dev = std::sqrt(var);
    skew /= u.size() * dev * var;
    kurtosis /= u.size() * var * var;
    kurtosis -= 3;
    double x_mean = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
    assert(std::abs((mean - x_mean) / x_mean) < 0.01);
    assert(std::abs((var - x_var) / x_var) < 0.01);
    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
void test5() {
    typedef std::negative_binomial_distribution<T> D;
    typedef std::mt19937 G;
    G g;
    D d(127, 0.5);
    const int N = 1000000;
    std::vector<typename D::result_type> u;
    for (int i = 0; i < N; ++i)
    {
        typename D::result_type v = d(g);
        assert(d.min() <= v && v <= d.max());
        u.push_back(v);
    }
    double mean = std::accumulate(u.begin(), u.end(),
                                          double(0)) / u.size();
    double var = 0;
    double skew = 0;
    double kurtosis = 0;
    for (unsigned i = 0; i < u.size(); ++i)
    {
        double dbl = (u[i] - mean);
        double d2 = sqr(dbl);
        var += d2;
        skew += dbl * d2;
        kurtosis += d2 * d2;
    }
    var /= u.size();
    double dev = std::sqrt(var);
    skew /= u.size() * dev * var;
    kurtosis /= u.size() * var * var;
    kurtosis -= 3;
    double x_mean = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
    assert(std::abs((mean - x_mean) / x_mean) < 0.01);
    assert(std::abs((var - x_var) / x_var) < 0.01);
    assert(std::abs((skew - x_skew) / x_skew) < 0.04);
    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.05);
}

template <class T>
void test6() {
    typedef std::negative_binomial_distribution<T> D;
    typedef std::mt19937 G;
    G g;
    D d(1, 0.05);
    const int N = 1000000;
    std::vector<typename D::result_type> u;
    for (int i = 0; i < N; ++i)
    {
        typename D::result_type v = d(g);
        assert(d.min() <= v && v <= d.max());
        u.push_back(v);
    }
    double mean = std::accumulate(u.begin(), u.end(),
                                          double(0)) / u.size();
    double var = 0;
    double skew = 0;
    double kurtosis = 0;
    for (unsigned i = 0; i < u.size(); ++i)
    {
        double dbl = (u[i] - mean);
        double d2 = sqr(dbl);
        var += d2;
        skew += dbl * d2;
        kurtosis += d2 * d2;
    }
    var /= u.size();
    double dev = std::sqrt(var);
    skew /= u.size() * dev * var;
    kurtosis /= u.size() * var * var;
    kurtosis -= 3;
    double x_mean = d.k() * (1 - d.p()) / d.p();
    double x_var = x_mean / d.p();
    double x_skew = (2 - d.p()) / std::sqrt(d.k() * (1 - d.p()));
    double x_kurtosis = 6. / d.k() + sqr(d.p()) / (d.k() * (1 - d.p()));
    assert(std::abs((mean - x_mean) / x_mean) < 0.01);
    assert(std::abs((var - x_var) / x_var) < 0.01);
    assert(std::abs((skew - x_skew) / x_skew) < 0.01);
    assert(std::abs((kurtosis - x_kurtosis) / x_kurtosis) < 0.03);
}

template <class T>
void tests() {
    test2<T>();
    test3<T>();
    test5<T>();
    test6<T>();
}

int main(int, char**) {
    tests<int8_t>();
    tests<uint8_t>();
    return 0;
}
@ldionne ldionne added the libc++ libc++ C++ Standard Library. Not GNU libstdc++. Not libc++abi. label Jul 21, 2022
@philnik777 philnik777 added the enhancement Improving things as opposed to bug fixing, e.g. new or missing feature label Jul 15, 2023
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