ANSI C / rand() % 7 first value is always 3

Question

So trying to figure out what is special about rand() mod k7 in C. In another post someone said that C rand() uses http://en.wikipedia.org/wiki/Linear_congruential_generator but I don't see what makes (mod k7) k-> scalar special for the algorithm associated to ANSI C.

So I have the following code:

#include <stdio.h>
#include <time.h>
#include <stdlib.h>
#include <unistd.h>

void getRand(int* num1, int* num2, int* num3);


int main(int argc, const char * argv[])
{
    int i = 0;
    for (i = 0; i < 100; i++) {

        srand(time(NULL));
        printf("%d\n", rand() % 7 );

        sleep(1);
    }
    return 0;
}

This always prints 3. But if I use any n such that 7 does not divide n, I get a better sequence of first values. Still obviously not random but better then just 3 or some c mod 7 = 3.

I deliberately made the program this way with the seed in the loop to show that the first value always returns 3 regardless of the seed.

Yes I could get random numbers for Xn n > 0 but I want X1 % 7 != X1 % 7 for each Xo.

Answer 1

Ok, lets start with looking at more than just a few data points:

#include <stdio.h>
#include <time.h>
#include <stdlib.h>


int main(int argc, const char * argv[])
{
    size_t counters[7] = {0,0,0,0,0,0,0};
    time_t tt = time(NULL);

    //for (size_t i = 0; i < 7; i++) {
    //  printf("result: %d count: %d\n", i, counters[i]);
    //}

    for (size_t i = 0; i < 1000000; i++) {
        srand(tt + i);
        counters[rand() % 7] ++;
    }

    for (size_t i = 0; i < 7; i++) {
        printf("result: %d count: %d\n", i, counters[i]);
    }
}

with this, on Windows 7, Visual Studio 2013 compile as C++ I get

result: 0 count: 142894
result: 1 count: 142850
result: 2 count: 142848
result: 3 count: 142855
result: 4 count: 142854
result: 5 count: 142845
result: 6 count: 142854

what do you get, because I suspect you'll get a better result from a larger data set.