Spring 2012

# 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 $$\mod max$$.

new number
http://cs.marlboro.edu/ courses/ spring2012/jims_tutorials/ sam/ Random_numbers
last modified Monday April 2 2012 7:53 pm EDT

## attachments

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lcm.js Apr 13 2012 12:52 pm 1.39kB