Random number generator

File: random.doc

Last edition: 2003-03-19

Author: Anders Wallenborg

History: 96-02-11/MK First released version.

96-10-02/MK Updated to Menta 1.20

97-08-15/MK Updated to Menta 3.0

2003-03-19/MK Updated to Menta 4.0

Description

A pseudo-random number generator based on the following multiplicative congruential algorithm due to D.H. Lehmer:

x(k+1) = (a*x(k)+c) mod m

where x, a, c and m are integers. With a proper choice of integers the numbers

r(k) = x(k)/m

have a uniform distribution in the range [0, 1].

If m = 2**n, c is odd and a is of the form 4k+1, the first m-1 terms in the sequence x(k) are a permutation of the integers from 1 to m-1, and then the sequence repeats itself.

References:

Moler Cleve: "Random thoughts". MATLAB News and Notes, Fall 1995.

Fröberg, Carl-Erik: "Numerical Mathematics - Theory and Computer Applications". Addison-Wesley (1985).

Park, S.K. and K.W. Miller: "Random number generators: Good ones are hard to find". (Comm ACM, vol. 32)

Inputs

Outputs

(Real) Random, 0-1.

Parameters

(Int) a 13

(Int) c 1

(Int) m 512

Public signals

(Real) Random

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