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 allowed to use one static variable and at most 3 elementary steps, where each step consists of only one basic arithmetic operation of arity 1 or 2.
Example:
int myrandom(void){
static int x;
x = some_step1;
x = some_step2;
x = some_step3;
return x;
}
Basic arithmetic operations are +,-,%,and, not, xor, or, left shift, right shift, multiplication and division. Of course, no rand(), random() or similar stuff is allowed.
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.