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Carry

Random number generator class using George Marsaglia's multiply with carry algorithm.

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Contents

Interface
Class Carry
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Interface

C++

Class 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

$T_0 = 2^{60}$

(2)

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 :

$x_n = a \cdot x_{n-1} + \,\mathrm{carry}\, \,\mathrm{mod}\, 2^{32}$

(3)

where

$a = 2083801278$

(4)

Any other value of a can be chosen such that both

$a \cdot 2^{32} - 1 \,\mbox{and}\, 2^{31} - 1$

(5)

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

MISSING IMAGE!

1/carry-378.png cannot be found in /users/1/carry-378.png. Please contact the submission author.

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

Example 1

The following example displays 20 random floating point numbers and 20 random large integers. It uses two different generators to achieve this. The first generator uses the system timer to initialize the seed, while the second is simply initialized with a particular value. Notice that it was necessary to divide the timer with the CARRYDIV value in order to keep the seed in the (0, 1) interval. The output of the first generator will obviously vary with each execution of the program, while the output of the second will always be the same if the seed is never changed.

#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;
}

Authors

Lucian Bentea (August 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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Members of Carry

Carry

Carry( double s = 0.46875 )[constructor]

s	Default value = 0.46875

SetSeed

voidsetSeed( double s )

s	Seed must be in the (0, 1) interval (endpoints are excluded).