Special simple random number generator

Question

How to create a function, which on every call generates a random integer number? This number must be most random as possible (according to uniform distribution). It is only

Answer 1

Linear congruential generators are one of the oldest and simplest methods:

int seed = 123456789;

int rand()
{
  seed = (a * seed + c) % m;
  return seed;
}

Only a few instruction with basic arithmetic operations, that's all you need.

Mind that this algorithm works fine only if a, c and m are chosen in a particular way!

To guarantee the longest possible period of this sequence, c and m should be coprime, a − 1 should be divisible by all prime factors of m, and also for 4 if m is divisible by 4.

Some examples of parameters are shown on Wikipedia: for example ANSI C for some compilers proposes m = 2 ³¹, a = 1103515245 and c = 12345.