Add approximate counting C++ sample code (#834)

* Add aproximate counting C++ sample code

* Fix test, fix the confusion between double and int

Author: mika314

contents/approximate_counting/approximate_counting.md

@@ -360,6 +360,8 @@ As we do not have any objects to count, we will instead simulate the counting wi
 {% method %}
 {% sample lang="jl" %}
 [import, lang:"julia"](code/julia/approximate_counting.jl)
+{% sample lang="cpp" %}
+[import, lang:"cpp"](code/c++/approximate_counting.cpp)
 {% endmethod %}
 
 ### Bibliography

contents/approximate_counting/code/c++/approximate_counting.cpp

@@ -0,0 +1,71 @@
+#include <cmath>
+#include <iostream>
+#include <numeric>
+#include <random>
+
+// Returns a pseudo-random number generator
+std::default_random_engine& rng() {
+  // Initialize static pseudo-random engine with non-deterministic random seed
+  static std::default_random_engine randEngine(std::random_device{}());
+  return randEngine;
+}
+
+// Returns a random double in [0, 1)
+double drand() {
+  return std::uniform_real_distribution<double>(0.0, 1.0)(rng());
+}
+
+// This function takes
+//     - v: value in register
+//     - a: a  scaling value for the logarithm based on Morris's paper
+// It returns n(v,a), the approximate count
+auto n(double v, double a) { return a * (pow((1 + 1 / a), v) - 1); }
+
+// This function takes
+//    - v: value in register
+//    - a: a scaling value for the logarithm based on Morris's paper
+// It returns a new value for v
+auto increment(int v, double a) {
+  // delta is the probability of incrementing our counter
+  const auto delta = 1 / (n(v + 1, a) - n(v, a));
+  return (drand() <= delta) ? v + 1 : v;
+}
+
+// This simulates counting and takes
+//     - n_items: number of items to count and loop over
+//     - a: a scaling value for the logarithm based on Morris's paper
+// It returns n(v,a), the approximate count
+auto approximate_count(int n_items, double a) {
+  auto v = 0;
+  for (auto i = 0; i < n_items; ++i)
+    v = increment(v, a);
+
+  return n(v, a);
+}
+
+// This function takes
+//     - n_trials: the number of counting trials
+//     - n_items: the number of items to count to
+//     - a: a scaling value for the logarithm based on Morris's paper
+//     - threshold: the maximum percent error allowed
+// It returns a "pass" / "fail" test value
+auto test_approximate_count(
+    int n_trials, int n_items, double a, double threshold) {
+  auto sum = 0.0;
+  for (auto i = 0; i < n_trials; ++i)
+    sum += approximate_count(n_items, a);
+  const auto avg = sum / n_trials;
+  return std::abs((avg - n_items) / n_items) < threshold ? "pass" : "fail";
+}
+
+int main() {
+  std::cout << "Counting Tests, 100 trials\n";
+
+  std::cout << "testing 1,000, a = 30, 1% error "
+            << test_approximate_count(100, 1000, 30, 0.1) << "\n";
+  std::cout << "testing 12,345, a = 10, 1% error "
+            << test_approximate_count(100, 12345, 10, 0.1) << "\n";
+  // Note : with a lower a, we need more trials, so a higher % error here.
+  std::cout << "testing 222,222, a = 0.5, 10% error "
+            << test_approximate_count(100, 222222, 0.5, 0.2) << "\n";
+}