Entropies benchmark

entropy_benchmark.cpp

#include <iostream>
#include <cmath>
#include <chrono>

struct BenchResult
{
    std::chrono::nanoseconds duration;
    double sum;
};

double entropyShannon(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ?  -(p * log(p) + q * log(q)) : 0.0;
}
double entropyRenyi_1_2(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ? 2.0 * log(sqrt(p) + sqrt(q)) : 0.0;
}
double entropyRenyi_1_4(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ? 4.0 / 3.0 * log(sqrt(sqrt(p)) + sqrt(sqrt(q))) : 0.0;
}
double entropyRenyi_1_8(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ? 8.0 / 7.0 * log(sqrt(sqrt(sqrt(p))) + sqrt(sqrt(sqrt(q)))) : 0.0;
}
double entropyRenyi_3_4(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ? 4.0 * log(sqrt(sqrt(p*p*p)) + sqrt(sqrt(q*q*q))) : 0.0;
}
double entropyRenyi_2(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ? -log(p*p + q*q) : 0.0;
}
double entropyRenyi_5(double p) noexcept
{
    double q = 1.0 - p;
    double pp = p*p, qq = q*q;
    return (p > 0.0 && p < 1.0) ? -0.25 * log(pp*pp*p + qq*qq*q) : 0.0;
}
double entropyRenyi_10(double p) noexcept
{
    double q = 1.0 - p;
    return (p > 0.0 && p < 1.0) ? -1.0/9.0 * log(p*p*p*p*p*p*p*p*p*p + q*q*q*q*q*q*q*q*q*q) : 0.0;
}

using ent_t =  double (*)(double) noexcept;

template<ent_t fun>
[[gnu::noinline]]
BenchResult benchmark(size_t count) noexcept
{
    auto before = std::chrono::high_resolution_clock::now();
    
    double h = 1.0 / (count - 1);
    double sum = 0.0;
    
    for (size_t i = 0; i < count; ++i) {
        sum += fun(h * i);
    }
    
    auto after = std::chrono::high_resolution_clock::now();
    return BenchResult{after - before, sum / count};
}

std::ostream& operator<<(std::ostream& stream, BenchResult result)
{
    auto ms = std::chrono::duration_cast<std::chrono::milliseconds>(result.duration).count();
    std::cout << result.duration.count() << "ns \t(" << ms << "ms)\t\t sum: " << result.sum;

    return stream;
}

int main() {

    size_t count = 1000000000;
    std::cout << "samples : " << count << std::endl;

    std::cout << "Shannon   : " << benchmark<entropyShannon>   (count) << std::endl;
    std::cout << "Renyi_1_2 : " << benchmark<entropyRenyi_1_2> (count) << std::endl;
    std::cout << "Renyi_1_4 : " << benchmark<entropyRenyi_1_4> (count) << std::endl;
    std::cout << "Renyi_1_8 : " << benchmark<entropyRenyi_1_8> (count) << std::endl;
    std::cout << "Renyi_3_4 : " << benchmark<entropyRenyi_3_4> (count) << std::endl;
    std::cout << "Renyi_2   : " << benchmark<entropyRenyi_2>   (count) << std::endl;
    std::cout << "Renyi_5   : " << benchmark<entropyRenyi_5>   (count) << std::endl;
    std::cout << "Renyi_10  : " << benchmark<entropyRenyi_10>  (count) << std::endl;

    return 0;
}

// g++ -std=c++17 -pedantic -Wall -Wextra -O3 entropy_benchmark.cpp -o entropy_benchmark.bin

// Results:
// samples : 1000000000
// Shannon   : 10249895206ns   (10249ms)   sum: 0.5
// Renyi_1_2 : 8677368472ns    (8677ms)    sum: 0.570796
// Renyi_1_4 : 10421639934ns   (10421ms)   sum: 0.624029
// Renyi_1_8 : 13235709810ns   (13235ms)   sum: 0.65659
// Renyi_3_4 : 11403406522ns   (11403ms)   sum: 0.530643
// Renyi_2   : 7245386547ns    (7245ms)    sum: 0.429204
// Renyi_5   : 7771674801ns    (7771ms)    sum: 0.363444
// Renyi_10  : 10809162384ns   (10809ms)   sum: 0.336404