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Simple random number generators

Project description

Author: Craig McQueen
Copyright: 2010 Craig McQueen

Simple pseudo-random number generators.


The simplerandom package is provided, which contains modules containing classes for various simple pseudo-random number generators.

One module provides Python iterators, which generate simple unsigned 32-bit integers identical to their C counterparts.

Another module provides random classes that are sub-classed from the class Random in the random module of the standard Python library.

Why use this package? These random number generators are very simple, which has two main advantages:

  • It is easy to port them to a different platform and/or language. It can be useful to be able to implement the identical algorithm on multiple platforms and/or languages.
  • Small and simple generators can be more appropriate for small embedded systems, with limited RAM and ROM.

An equivalent C implementation (of the Python simplerandom.iterators module) has been created. See:


Most algorithms were obtained from two newsgroup posts by George Marsaglia [1] [2]. However, some modifications have been made. From [3], it seems that the SHR3 algorithm defined in [1] is flawed and should not be used. It doesn’t actually have a period of 2**32-1 as expected, but has 64 different cycles, some with very short periods. The SHR3 in the 2003 post is very similar, but with two shift values swapped. It has a period of 2**32-1 as expected.

We still find KISS from [1] useful mainly because it uses 32-bit calculations for MWC, which can be more suitable for small embedded systems. So we define KISS that uses a MWC based on [1], but the Cong and SHR3 from [2].

From Pierre L’Ecuyer [4] [6], the Combined LFSR (Tausworthe) LFSR113 algorithm [5] and LFSR88 (aka Taus88) have been implemented.


[1](1, 2, 3, 4, 5, 6, 7)
George Marsaglia
Newsgroup post, sci.stat.math and others, Thu, 21 Jan 1999
[2](1, 2, 3, 4, 5, 6, 7)
George Marsaglia
Newsgroup post, sci.math, 26 Feb 2003
Greg Rose
Qualcomm Inc.
[4](1, 2)
Pierre L’Ecuyer
Mathematics of Computation, 68, 225 (1999), 261–269.
[5](1, 2)
[6](1, 2)
P. L’Ecuyer
Mathematics of Computation, 65, 213 (1996), 203–213.

Modules Provided

Module Description
simplerandom.iterators Iterator classes, which generate unsigned 32-bit integers.
simplerandom.random Classes that conform to standard Python random.Random API.

Random Number Generators Provided

In simplerandom.iterators, the following pseudo-random number generators are provided:

Generator Notes
MWC1 Two 32-bit MWCs combined. From [1].
MWC2 Very similar to MWC1, but slightly modified to improve its statistical properties.
Cong From [2].
SHR3 From [2].
MWC64 A single 64-bit multiply-with-carry calculation. From [2].
KISS Combination of MWC2, Cong and SHR3. Based on [1] but using Cong and SHR3 from [2], and the modified MWC.
KISS2 Combination of MWC64, Cong and SHR3. From [2].
LFSR113 Combined LFSR (Tausworthe) random number generator by L’Ecuyer. From [4] [5].
LFSR88 Combined LFSR (Tausworthe) random number generator by L’Ecuyer. From [6].

These generators are Python iterators, of infinite length (they never raise StopIteration). They implement the __next__() function to generate the next random integer. All the generators output 32-bit unsigned values, and take one or more 32-bit seed values during initialisation/seeding.

In simplerandom.random, pseudo-random number generators are provided which have the same names as those in simplerandom.iterators, but these generators implement the standard Python random.Random API. Each generator uses the iterator of the same name in simplerandom.iterators to generate the random bits used to produce the random floats. The jumpahead() function (in the style of the Python 2.x API) is implemented in all cases, even though jumpahead() has officially been removed from the Python 3.x random API.



>>> import simplerandom.iterators as sri
>>> rng = sri.KISS(123958, 34987243, 3495825239, 2398172431)
>>> next(rng)
>>> next(rng)
>>> next(rng)

Random class API

>>> import simplerandom.random as srr
>>> rng = srr.KISS(258725234)
>>> rng.random()
>>> rng.random()
>>> rng.random()

Supported Python Versions

Python 3.6 through 3.9 is supported. It may or may not run on earlier Python 3.x versions, but these versions are no longer being tested.

Use of Cython

Cython is used to make a fast implementation of simplerandom.iterators. Cython creates a .c file that can be compiled into a Python binary extension module.

The simplerandom source distribution package includes a .c file that was created with Cython, so it is not necessary to have Cython installed to install simplerandom.

The Cython .pyx file is also included, if you want to modify the Cython source code, in which case you do need to have Cython installed. But by default, builds the extension from the .c file (to ensure that the build doesn’t fail due to particular Cython version issues). If you wish to build using Cython from the included .pyx file, you must set USE_CYTHON=True in


The simplerandom package is installed using distutils. If you have the tools installed to build a Python extension module, run the following command:

python install

If you cannot build the C extension, you may install just the pure Python implementation, using the following command:

python build_py install --skip-build

Unit Testing

Unit testing of the iterators is in simplerandom.iterators.test. It duplicates the tests of the C algorithms given in the original newsgroup post [1], as well as other unit tests.

To run unit tests:

python -m simplerandom.iterators.test

A more thorough unit test suite is needed. A unit test suite for simplerandom.random is needed.


The code is released under the MIT license. See LICENSE.txt for details.

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