Why does C++ rand() seem to generate only numbers of the same order of magnitude?

In a small application written in C/C++, I am facing a problem with the rand function and maybe the seed :

I want to produce a sequence of random numbers that are of different orders, i.e. with different logarithm values (base 2). But it seems that all the numbers produced are of the same order, fluctuating just between 2^25 and 2^30.

Is it because rand() is seeded with Unix time which is by now a relatively big number? What am I forgetting ? I am seeding rand() only once at the beginning of the main().

Solution 1:

There are only 3% of numbers between 1 and 2³⁰ which are NOT between 2²⁵ and 2³⁰. So, this sounds pretty normal :)

Because 2²⁵ / 2³⁰ = 2^-5 = 1/32 = 0.03125 = 3.125%

Solution 2:

The lighter green is the region between 0 and 2²⁵; the darker green is the region between 2²⁵ and 2³⁰. The ticks are powers of 2.

Solution 3:

You need to be more precise: you want different base 2 logarithm values but what distribution do you want for this? The standard rand() functions generate a uniform distribution, you will need to transform this output using the quantile function associated with the distribution that you want.

If you tell us the distribution then we can tell you the quantile function you need.