Pseudo-random number generator

Random pseudonumber generator with graphic interface.

Multiplicative congruential algorithm

It arises from a Linear Sequential Algorithm , when $C$ = 0;

Then the equation is:

• $x_i$ + 1 = $(ax_i) mod (n) \to i = 0, 1, 2, 3, .... $

The advantage of this method is that compared to the linear algorithm, it involves one less operation.

The starting parameters of this algorithm are:

• $x_o$, $a$, $m$; which must be integers and greater than zero.

• To transform the numbers $x_i$ in the interval (0, 1), we look at the equation

• $r_i = x_i / (m - 1)$ $\to$ $m = 2 ^ g$

According to Banks, Carson, Nelson and Nicol, the conditions that must be met by the parameters for the multiplicative sequential algorithm to reach its maximum period are

• $a = 5 + 8k \to k = 1, 2, 3, ... $

$x_o$ must be an odd number and $g$ must be an integer.

From these conditions a maximum lifetime is achieved.

Example

Generate enough numbers between 0 and 1 with the parameters: $x_o = 3$, $k = 5$ and $g = 8$ to find the life cycle period.

Formulas:

• $a = 5 + 8(2)$
• $m = g ^ 8$
• $x_i + 1 = (ax_i) mod (m)$
• $r_i = x_i / (m - 1).$

Features:

• Uniformity test calculation
• Independence Test Calculation

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