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

Question

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 th

Answer 1

There are exactly equal number of numbers between 0 and 2^29 and 2^29 and 2^30.

Another way of looking at the problem: consider binary representation of the random number you generate, the probability that the highest bit is 1 equals 1/2, and, therefore, you get order 29 in half cases. What you want is to see a number that would be below 2^25, but that means 5 highest bits are all zero, which happens with a low probability of 1/32. Chances are that even if you run it for a long time you will never see the order below 15 at all (the probability is something like rolling 6 6 times in a row).

Now, the part of your question about the seed. No, the seed cannot possibly determine the range the numbers are generated from, it just determines the first, initial element. Think of rand() as a sequence of all possible numbers in the range (predetermined permutation). The seed determines where you start drawing numbers from the sequence. This is why if you want (pseudo) randomness, you use current time to initialize the sequence: you do not care that the position you start from is not uniformly distributed, all that matters is that you never start from the same position.