implement-rand10-using-rand7-test.cpp

/*
 * Copyright (c) 2018 Christopher Friedt
 *
 * SPDX-License-Identifier: MIT
 */

#include <gtest/gtest.h>

#include "implement-rand10-using-rand7.cpp"

#include <array>
#include <functional>
#include <map>
#include <numeric>
#include <random>
#include <sstream>
#include <string>

string to_string(const map<int, size_t> &x) {
  stringstream ss;
  ss << "{ ";
  for (auto &kv : x) {
    auto &k = kv.first;
    auto &v = kv.second;
    ss << "{ " + to_string(k) + ", " + to_string(v) + " }, ";
  }
  ss << "}";
  return ss.str();
}

int rand7() {

  // Very c++11-ish way of generating random values.
  // In a pinch, I would probably just use random().

  static random_device rd;
  static mt19937 gen(rd());
  static uniform_int_distribution<> dis(1, 7);

  return dis(gen);
}

template <size_t N> static float mean(array<int, N> &samples) {
  float u = accumulate(samples.begin(), samples.end(), 0);
  u /= samples.size();
  return u;
}

template <size_t N> static float variance(array<int, N> &samples) {
  float var = 0;
  for (auto &s : samples) {
    var += ::powf(s, 2);
  }
  var /= samples.size();
  var -= ::powf(mean(samples), 2);
  return var;
}

template <size_t N>
static void sample(array<int, N> &samples, function<float()> &func) {
  for (auto &s : samples) {
    s = func();
  }
}

#define MEAN_OK 0.1 // this is pretty high actually, for 1M samples!!!
#define VAR_OK 0.5  // this is pretty high actually, for 1M samples!!!

TEST(ImplementRand10UsingRand7, Test_rand7) {

  size_t n = 7;
  array<int, 1000000> samples;
  function<float()> func(rand7);

  sample(samples, func);

  float u = mean(samples);
  float var = variance(samples);

  EXPECT_NEAR(u, float(1 + n) / 2, MEAN_OK);
  EXPECT_NEAR(var, (::powf(n - 1 + 1, 2) - 1) / 12, VAR_OK);

#if 0
	// output clearly shows that this is uniformly distributed
	map<int,size_t> hist;
	for( auto & s: samples ) {
		hist[ s ]++;
	}

	cerr << to_string( hist ) << std::endl;
#endif
}

TEST(ImplementRand10UsingRand7, Test_rand10) {

  size_t n = 10;
  array<int, 1000000> samples;
  function<float()> func(bind(&Solution::rand10, Solution()));

  sample(samples, func);

  float u = mean(samples);
  float var = variance(samples);

  EXPECT_NEAR(u, float(1 + n) / 2, MEAN_OK);
  EXPECT_NEAR(var, (::powf(n - 1 + 1, 2) - 1) / 12, VAR_OK);

#if 0
	// output shows that this is uniformly distributed
	map<int,size_t> hist;
	for( auto & s: samples ) {
		hist[ s ]++;
	}

	cerr << to_string( hist ) << std::endl;
#endif
}