|Category: functors||Component type: concept|
|Argument type||The type of the Random Number Generator's argument. This must be an integral type.|
|Result type||The type returned when the Random Number Generator is called. It must be the same as the argument type.|
|F||A type that is a model of Random Number Generator.|
|Integer||The argument type of F.|
|f||Object of type F.|
|N||Object of type Integer|
The range of a Random Number Generator is the set of nonnegative integers that are less than the Random Number Generator's argument.
|Function call||f(N)||N is positive.||Returns a pseudo-random number of type Integer. ||The return value is less than N, and greater than or equal to 0.|
|Uniformity||In the limit as f is called many times with the same argument N, every integer in the range [0, N) will appear an equal number of times.|
 Uniform distribution means that all of the numbers in the range [0, N) appear with equal frequency. Or, to put it differently, the probability for obtaining any particular value is 1/N.
 Random number generators are a very subtle subject: a good random number generator must satisfy many statistical properties beyond uniform distribution. See section 3.4 of Knuth for a discussion of what it means for a sequence to be random, and section 3.2 for several algorithms that may be used to write random number generators. (D. E. Knuth, The Art of Computer Programming. Volume 2: Seminumerical Algorithms, third edition. Addison-Wesley, 1998.)
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