By R. Sedgewick
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Additional resources for Algorithms
Another interesting fact is that the calculation can be done a word at a time, rather than a bit at a time, according to the same recursion formula. In our example, if we take the bitwise “exclusive or” of two successive words, we get the word which appears three places later in the list. This leads us to a random number generator suitable for easy implementation on a general-purpose computer. Using a feedblack register with bits b and c tapped corresponds to using the recursion: a[k]==(a[k-b]+a[k-c]) mod m.
First, m should be large: it can be the computer word size, as mentioned above, but it needn’t be quite that large if that’s inconvenient (see the implementation below). It will normally be convenient to make m a power of 10 or 2. Second, b shouldn’t be too large or too small: a safe choice is to use a number with one digit less than m. Third, CHAPTER 3 b should be an arbitrary constant with no particular pattern in its digits, except that it should end with *-~21, with z even: this last requirement is admittedly peculiar, but it prevents the occurrence of some bad cases that have been uncovered by the mathematical analysis.
Often, in conversation, people use the term random when they really mean arbitrary. When one asks for an trrbitrary number, one is saying that one doesn’t really care what number one gets: almost any number will do. By contrast, a random number is a precisely defined mathematical concept: every number should be equally likely to occur. A random number will satisfy someone who needs an arbitrary number, but not the other way around. For “every number to be equally likely to occur” to make sense, we must restrict the numbers to be used to some finite domain.