Two More Random Exercises

August 21, 2012

We did two tasks related to random numbers in the most recent exercise, and we have looked at high-quality random number generators in several previous exercises. In today’s exercise we look at two very low-quality random number generators, which should not be used for any production application.

The first, invented by John von Neumann in 1949, occasioned his famous quip “Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.” The middle-square method takes a number with an even number of digits, squares it, and extracts the middle digits for the next iteration; for instance, if the seed is 675248, the square is 455959861504, and the middle digits are 959861.

The second, invented by IBM in the early 1960s, caused Donald Knuth to claim “its very name RANDU is enough to bring dismay into the eyes and stomachs of many computer scientists!”. RANDU is based on the recursion xn+1 = 65539 · xn (mod 231), with x0 odd.

Your task is to write functions that generate random numbers by the middle-square and RANDU methods. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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