How to generate a random integer number from within a range

Question

This is a follow on from a previously posted question:

How to generate a random number in C?

I wish to be able to generate a random number from within a part

Answer 1

For those who understand the bias problem but can't stand the unpredictable run-time of rejection-based methods, this series produces a progressively less biased random integer in the [0, n-1] interval:

r = n / 2;
r = (rand() * n + r) / (RAND_MAX + 1);
r = (rand() * n + r) / (RAND_MAX + 1);
r = (rand() * n + r) / (RAND_MAX + 1);
...

It does so by synthesising a high-precision fixed-point random number of i * log_2(RAND_MAX + 1) bits (where i is the number of iterations) and performing a long multiplication by n.

When the number of bits is sufficiently large compared to n, the bias becomes immeasurably small.

It does not matter if RAND_MAX + 1 is less than n (as in this question), or if it is not a power of two, but care must be taken to avoid integer overflow if RAND_MAX * n is large.