You are writing: this algorithm is non periodic. Is only limited by the physical capacity of the computer's memory.
This is not true. There are 2^{53} possible double precision numbers between 0 and 1 so the period cannot possibly be longer than 2^{53}. You have not proven that the period is 2^{53} for all values of s. It is possible that the period could be as low as 1 for certain values of s. It is also possible that it can have a rho-shaped trajectory. This means for example a, b, c, d, e, f, g, h, f, g, h, f, g, h, f, g, h, ... where the letters represent different x-values.
The TESTU01 battery of tests is better than DIEHARD. You can find it here
Try to test your generator with TESTU01 with different values of s. |