Why is the output from race conditions not random? - c++

Question

I set up the following race condition to generate some random bits. However, as far as I can tell, the output is NOT random. I want to understand why (for learning purposes). Here is my code:
#include <iostream>
#include <vector>
#include <atomic>
#include <thread>
#include <cmath>
using namespace std;
void compute_entropy(const vector<bool> &randoms) {
int n0 = 0, n1 = 0;
for(bool x: randoms) {
if(!x) n0++;
else n1++;
}
double f0 = n0 / ((double)n0 + n1), f1 = n1 / ((double)n0 + n1);
double entropy = - f0 * log2(f0) - f1 * log2(f1);
for(int i = 0; i < min((int)randoms.size(), 100); ++i)
cout << randoms[i];
cout << endl;
cout << endl;
cout << f0 << " " << f1 << " " << endl;
cout << entropy << endl;
return;
}
int main() {
const int N = 1e7;
bool x = false;
atomic<bool> finish1(false), finish2(false);
vector<bool> randoms;
thread t1([&]() {
for(int i = 0; !finish1; ++i)
x = false;
});
thread t2([&]() {
for(int i = 0; !finish2; ++i)
x = true;
});
thread t3([&]() {
for(int i = 0; i < N; ++i)
randoms.push_back(x);
finish1 = finish2 = true;
});
t3.join();
t1.join();
t2.join();
compute_entropy(randoms);
return 0;
}
I compile and run it like this:
$ g++ -std=c++14 threads.cpp -o threads -lpthread
$ ./threads
0101001011000111110100101101111101100100010001111000111110001001010100011101110011011000010100001110
0.473792 0.526208
0.998017
No matter how many times I run it, the results are skewed.
With 10 million numbers, the results from a proper random number generator are as one would expect:
>>> np.mean(np.random.randint(0, 2, int(1e7)))
0.5003456
>>> np.mean(np.random.randint(0, 2, int(1e7)))
0.4997095

Answer 1

Why is the output from race conditions not random?
There is no guarantee that a race condition would produce random output. It is not guaranteed to be purely random nor even pseudo random of any quality.
as far as I can tell, the output is NOT random.
There exists no test that can definitely disprove randomness.
There are tests that can show that a sequence probably doesn't contain some specific patterns - and thus a sequence passing multiple such tests is probably random. However, you haven't performed such test as far as I can tell. You seem to be measuring whether the distribution of the output is even - which is a separate property from randomness. As such, your conclusion that the output isn't random is not based on a relevant measurement.
Furthermore, your program has a data race. As such, the behaviour of the entire program is undefined and here is no guarantee that the progam would behave as one might otherwise have reasonably expected.