Random numbers
The first chapter of Volume 2 is about generating random numbers. I decided to implement one of them here.
The linear congruent method
The first section focused on the linear congruent method which defines a sequence in terms of four chosen values \(m, a, c,\) and \(X_0\). The sequence is defined as:
$$
X_{n+1} = (a X_n + c) \mod m, \hspace{50px} n \ge 0
$$
He suggests that for ease of computation \(m\) should be chosen to be the word-size of the computer. Since my implementation is in JavaScript, I've arbitrarily chosen my \(m\) to be \(2^{16}\) since it is similar to the sorts of numbers we would see in a real implementation but small enough to be simple. The book goes into great detail describing the number theory behind choosing good values for \(a\) and \(c\). Rather than get bogged down in this I've decided to make \(a\) and \(c\) user inputs for the purpose of this implementation. As for \(X_0\), I figured that the unix timestamp when this page loads (\(\mod m\) of course) would be a reasonable way to prevent my generator from being totally predictable.
Lastly I'm providing a max input so that the generator can be used to get random numbers in a range other than \(0\) — \(2^{16}\). The random number that is output is simply taken \(\mod max\).
![[paper clip]](/courses/source/images/paper_clip_tilt.png)
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