This was probably the first simulation I did. How naive I was!
Today I was doing some simulation and I need a uniform random bits stream.
What I tried first is to use the standard C function rand(), which should return a uniform integer
between 1 and 2^32. So I thought I could just use rand() to generate an integer and use it as
32 uniform random bits. But then I noticed the behavior of my simulation is a bit off my
expectation. In the end I wrote the following program to count how many 0's and 1's I get when I
use rand() many times.
{% highlight c %}
#include
#define INT_BITS (8 * sizeof(int))
int main(void)
{
srand(time(0)); //use current time as seed for random generator
int random_variable;
unsigned char bit;
unsigned long int k, n, total_bits, zeros;
double zero_ratio;
zeros = 0;
for(n = 0; n < 1e7; n++)
{
for(k = 0; k < INT_BITS; k++)
{
random_variable = rand();
bit = (random_variable >> k) & 1;
if(bit == 0)
{
zeros += 1;
}
}
}
total_bits = INT_BITS * n;
zero_ratio = (float)zeros/total_bits;
//printf("RAND_MAX %d\n", RAND_MAX);
printf("total zeros %lu total bits %lu average %f\n", zeros, total_bits, zero_ratio);
}
{% endhighlight %}
The result is pretty clear on my machine.
total zeros 164992607 total bits 320000000 average 0.515602
I consistently got more zeros than ones. And this bias does not vanish when I increased size. In the end I switched to Mersenne Twister pseudo-random generator. Works much better!