How can I build my own randi function from scratch?

I want to create a randi function from scratch on Matlab, can anyone please help me do this?

[Walter Roberson]

It is not difficult to create one using floor(). However, I have been struggling on figuring out how to make it fair when the span of integers is not one of 2, 3, 5, 53, 157, 1613, 2731, or 8191.

[David Hill]

Use sponge function of SHA-3 hash to generate bit-stream to use in generating random integers of the desired range.

[Walter Roberson]

Interesting, but SHA3 produced full numbers of bits, so it produces values 0 to 2^n-1. To produce random integers in the range A to B fairly, 2^n (number of values) would have to be divisible by (B-A+1). That can only happen if (B-A+1) is a power of 2.

Answer 1

[Jan]

What exactly is "from scratch"? Which tools are included, which one are excluded? E.g. where do you want to take your random bits from? Is using rand() okay or do you need your own pseudo random number generator?

What is the desired precision? If you use rand() as source of bits, remember that it replies values from the open interval (0,1) with 53 bit precision. So you get 2^53-2 different values (2^53 excluding 0 and 1). This is 2 * 3 * 5 * 53 * 157 * 1613 * 2731 * 8191. So if you want your input to get a random number from 1 to 7, it is not trivial to find an algorithm, which allows a perfect equi-distribution. If the small bias is a problem, you need a smart approach. This is easier, if you produce the random bits by your own.