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Art of Computer Programming, Volume 2, The: Seminumerical Algorithms by Donald E. Knuth

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3.3.4. The Spectral Test

In this section we shall study an especially important way to check the quality of linear congruential random number generators. Not only do all good generators pass this test, all generators now known to be bad actually fail it. Thus it is by far the most powerful test known, and it deserves particular attention. Our discussion will also bring out some fundamental limitations on the degree of randomness that we can expect from linear congruential sequences and their generalizations.

The spectral test embodies aspects of both the empirical and theoretical tests studied in previous sections: It is like the theoretical tests because it deals with properties of the full period of the sequence, and it is like the empirical ...

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