Carry

This class provides a very fast random number generator using George Marsaglia's multiply with carry algorithm. It produces uniformly distributed pseudo-random 32-bit values with period of

(1)

George Marsaglia's original posting can be found at this link:
http://groups-beta.google.com/group/sci.math/msg/fa034083b193adf0?hl=en&lr=&ie=UTF-8

Algorithm:

It uses the following recurrence relation :

(2)

where

(3)

Any other value of a can be chosen such that both

(4)

are prime.

To give you an idea of the running time for each of the functions, here are the results for generating 100,000,000 random numbers on a 750MHz microprocessor :

• genReal() 4 seconds
• genInt() 4 seconds

This diagram is obtained by generating two sequences of 1000 uniform floating point random numbers in the (0, 1) interval and then plotting them one versus the other. It shows that the distribution is indeed uniform.

References

• George Marsaglia's original post of the multiply with carry random number generator, http://groups-beta.google.com/group/sci.math/msg/fa034083b193adf0?hl=en&lr=&ie=UTF-8
• The Newran03 random number generator library of Robert Davies, http://www.robertnz.net/nr03doc.htm

#include <iostream>
#include <time.h>

#include <codecogs/statistics/random/carry.h>
using namespace std;

#define CARRYDIV    4294967296.0

int main() 
{
    Stats::Random::Carry A(time(0) / CARRYDIV);
    Stats::Random::Carry B(0.113);

    for (int i = 0; i < 20; ++i)
        cout << A.genReal() << endl;
    cout << endl;

    for (int i = 0; i < 20; ++i)
        cout << B.genInt() << endl;
    return 0;
}