Wichmann-Hill - 5.2 English - 68552

AOCL API Guide (68552)

Document ID
68552
Release Date
2025-12-29
Version
5.2 English

The Wichmann-Hill base generator uses a combination of four linear congruential generators (LCGs) and has the form:

\[\begin{split} \begin{align} w_i& = a_1 w_{i−1}\ mod \ m_1 \\ x_i& = a_2 x_{i−1}\ mod\ m_2 \\ y_i& = a_3 y_{i−1}\ mod\ m_3z_i \\ & = a_4 z_{i−1}\ mod\ m_4 \\ u_i& = \mathbf[\frac{w_i}{m_1} \mathbf+ \frac{x_i}{m_2} \mathbf+ \frac{y_i}{m_3} \mathbf+ \frac{z_i}{m_4}]\ mod \ 1, \end{align}\end{split}\]

where the \(u_i, i = 1, 2, · · ·\) form the required sequence. There are 273 sets of parameters, {\(a_i, m_i\) : i = 1, 2, 3, 4}, to choose from. These values have been selected so that the resulting generators are independent and have a period of approximately \(2^{80}\). [Maclaren]