Random number generator generating low numbers more frequently than high numbers C++

Question

So, I have made a program that simulates things and in it I noticed that the c++ function rand() seemed to generate low numbers too often, so I tried to test it.

#include <iostream>
#include <fstream>
#include <stdio.h>
#include <vector>
#include <cstdlib>
#include <time.h>
#include <cfloat>
#include <iomanip> 

using namespace std;

int main(){
    srand(time(NULL));
   
    int qwerty=0;
    for(int i=0; i<10000000;i++){
        if(rand()%10000<2800){
            qwerty++;
        }
    }
    cout << qwerty << endl;
    return 0;
}

If I ran the file with this "for tester" in it I would get consistently a number near 3400000, or 34%, which is near to the 34% I had seen appear inside my real program, the problem is that the output should be near 2800000 or 28%.

I then tried to run this "for tester" on a new project(the same I wrote here) where only the libraries and the srand(time(NULL)) were present, same output.

I then tried to copy this file inside an online compiler, this time instead of 3400000 I got the correct number 2800000.

I can't find why this is happening, anyone who knows?

Additional info: I am using dev-c++ as a IDE with the TDM-GCC 4.9.2 64bit release and the ISO C++11, If I take the executable generated by my computer and run it in another one I get the same 34% result, Windows 10 is the operating system. This problem happens also if I use different numbers.

Answer 1

For a uniformly distributed random variable E in the open interval [0, 32767] the probability of mod(E, 10000) < 2800 is around 34%. Intuitively you can think of mod(E, 10000) < 2800 as favouring the bucket of numbers in the range [30000, 32767]: that bucket modulo 10000 is always less than 2800. So that has the effect of pushing the result above 28%.

That's the behavior you are observing here.

It's not a function of the quality of the random generator, although you would get better results if you were to use a uniform generator with a larger periodicity. Using rand() out of your C++ standard library is ill-advised as the standard is too relaxed about the function requirements for it to be portable. <random> from C++11 will cause you far less trouble: you'd be able to avoid explicit % too.