exercise2_lcg_coin.cpp

#include <iostream>
#include <ostream>
#include <vector>

typedef struct {
  unsigned int a, c, m, state;
} LCG;

void draw_samples_and_print_statistics(LCG &lcg, int n) {
  std::vector<int> headstails(100, 0);
  for (int i = 0; i < n; ++i) {
    lcg.state = (lcg.a * lcg.state + lcg.c) % lcg.m;
    // test rand() / (double)RAND_MAX  as example
    if ((lcg.state) / (double)lcg.m <
        0.33333333333333333) // We assume the PRNG is uniform between 0 and 1
    {
      headstails[0]++; // Heads
                       // std::cout << "Heads" << std::endl;
    } else {
      headstails[1]++; // Tails
                       // std::cout << "Tails" << std::endl;
    }
  }
  std::cout << "Heads: " << headstails[0] / (double)n
            << ", Tails: " << headstails[1] / (double)n << std::endl;
}

int main(int argc, char *argv[]) {

  // LCG for probabilities for the coin to appear fair
  unsigned int seed = 0;
  unsigned int a = 5;
  unsigned int c = 1;
  unsigned int m = 24;

  // LCG for inverted empirical probabilities for the coin to appear biased
  // towards heads unsigned int seed = 1; unsigned int a    = 5; unsigned int c
  // = 7; unsigned int m    = 21;

  std::cout << "Parameters: a=" << a << ", c=" << c << ", m=" << m
            << ", seed: " << seed << std::endl;

  LCG lcg = {a, c, m, static_cast<unsigned int>(seed)};

  draw_samples_and_print_statistics(lcg, 1e3);
}