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| Category: functors | | Component type: concept |
Description
A Random Number Generator is a functors that can be used to generate a random sequence of integers. That is: if f is a Random Number Generator and N is a positive integer, then f(N) will return an integer less than N and greater than or equal to 0. If f is called many times with the same value of N, it will yield a sequence of numbers that is uniformly distributed [1] in the range [0, N). [2]
Refinement of
UnaryFunction
Associated types
| 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. |
Notation
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 |
Definitions
The domain of a Random Number Generator (i.e. the set of permissible values for its argument) is the set of numbers that are greater than zero and less than some maximum value.
The range of a Random Number Generator is the set of nonnegative integers that are less than the Random Number Generator's argument.
Valid expressions
None, except for those defined by UnaryFunction.
Expression semantics
| Name | Expression | Precondition | Semantics | Postcondition |
| Function call | f(N) | N is positive. | Returns a pseudo-random number of type Integer. [2] | The return value is less than N, and greater than or equal to 0. |
Complexity guarantees
Invariants
| 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. |
Models
Notes
[1] 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.
[2] 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.)
See also
