Simple pseudo-random number generators in C and Python
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Simple Random

Contact :

Copyright : 2010 Craig McQueen

Simple pseudo-random number generators for C and Python.


This project provides simplerandom, simple pseudo-random number generators.


  • Main API functions:
    • Seed
    • Generate "next" random value
    • "Discard" also known as "jumpahead" to skip the generator ahead by 'n' samples.
    • Mix real random data into the generator state
  • Simple algorithms that are easily ported to different languages.
  • Safe seeding. Many generators have some "bad" state values that must be avoided. The seed functions for all generators ensure that any "bad" state values are avoided, and replaced by a suitable alternative initial state.
  • Currently supported languages are:
    • C
    • Python
  • Same numeric output in each supported language. It can be useful to be able to implement the identical algorithm on muliple platforms and/or languages.
  • Simple algorithms and state size appropriate for limited RAM and ROM (e.g. in embedded systems).
  • Decent cross-platform support.
    • Various OS.
    • Various processors, 8- to 64-bit.
  • Implement target language's API idioms and/or existing random number generator API.
  • Reasonable statistical properties of pseudo-random output (though not for all generators provided).


Most algorithms were obtained from two newsgroup posts by George Marsaglia [mars1] [mars2]. However, some modifications have been made. From [rose1], it seems that the SHR3 algorithm defined in [mars1] is flawed and should not be used. It doesn't actually have a period of 232-1 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 232-1 as expected.

We still find KISS from [mars1] 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 [mars1], but the Cong and SHR3 from [mars2].

From Pierre L'Ecuyer [lecuyer1] [lecuyer2], the Combined LFSR (Tausworthe) LFSR113 algorithm [lecuyer3] and LFSR88 (aka Taus88) have been implemented.

Random Number Generators Provided

The following pseudo-random number generators are provided:

Generator Notes
MWC1 Two 32-bit MWCs combined. From [mars1].
MWC2 Very similar to MWC1, but slightly modified to improve its statistical properties.
Cong From [mars2].
SHR3 From [mars2].
MWC64 A single 64-bit multiply-with-carry calculation. From [mars2].
KISS Combination of MWC2, Cong and SHR3. Based on [mars1] but using Cong and SHR3 from [mars2], and the modified MWC.
KISS2 Combination of MWC64, Cong and SHR3. From [mars2].
LFSR113 Combined LFSR (Tausworthe) random number generator by L'Ecuyer. From [lecuyer1] [lecuyer3].
LFSR88 Combined LFSR (Tausworthe) random number generator by L'Ecuyer. From [lecuyer2].


A C implementation of simplerandom is provided. It should compile on a wide range of platforms and OS.


Note that simplerandom uses stdint.h for integer types such as uint32_t, so that must be available. The generator MWC64, and KISS2 which uses it, use 64-bit calculations with uint64_t. For platforms which do not support 64-bit integers, these generators are not included in the build. This is done via checking for the macro define UINT64_C.

Note that C++ compilers may not define the constant macros UINT32_C and UINT64_C unless the following line is used before the stdint.h include:


Build and Install for Unix

For Unix-style platforms the library can be built via autotools in the normal method. E.g.:

sudo make install

To run very basic unit tests:

make check

Optional cxxtest unit tests are provided. To run these:

./configure --with-cxxteset
make check

Build and Install for Other Platforms

For other platforms, it should not be difficult to add the source files to a project.

Include File

Include file:

#include <simplerandom.h>

A C++ simplerandom library is planned in future. C++ code should be able to use the C library, but should use a different include to use the C library instead of a C++ library:

#include <simplerandom-c.h>


Generator State Variable

First define a variable to contain the simplerandom generator state. E.g.:

static SimpleRandomCong_t rng_cong;
static SimpleRandomKISS_t rng_kiss;

By encapsulating generator state in a variable, multiple independent generators can be used at the same time. Independent output can be achieved by seeding them with different seeds, or by calling the generator's discard function to "jump-ahead" by a certain number of samples.


Seed the generator once with a suitable number of uint32_t seed values. The number of seeds depends on the generator.

simplerandom_cong_seed(&rng_cong, 2051391225u);
simplerandom_kiss_seed(&rng_kiss, 2247183469u, 99545079u, 3269400377u, 3950144837u);

Alternatively, there are seed functions which take seed data from an array of uint32_t.

uint32_t seed_array[8] = { 1, 2, 3, 4, 5, 6, 7, 8 };
simplerandom_kiss_seed_array(&rng_kiss, seed_array, 8, false);

If the last parameter mix_extras is false, then any "extra" seed values are simply ignored. So the above is equivalent to:

simplerandom_kiss_seed(&rng_kiss, 1, 2, 3, 4);

If the last parameter mix_extras is true, then any "extra" seed values are mixed into the state in the same was as is done by the mix function (see below). So:

uint32_t seed_array[8] = { 1, 2, 3, 4, 5, 6, 7, 8 };
simplerandom_kiss_seed_array(&rng_kiss, seed_array, 8, true);

is equivalent to:

simplerandom_kiss_seed(&rng_kiss, 1, 2, 3, 4);
simplerandom_kiss_mix(&rng_kiss, &seed_array[4], 4);

Generate Random Values

Call the generator's next function multiple times to generate random values. All generators output uniformly distributed uint32_t values in the full range (except for the SHR3 generator which excludes 0 as an output value).

uint32_t rng_value;
uint32_t rng_values_array[8];
rng_value = simplerandom_cong_next(&rng_cong);
for (i = 0; i < 8; ++i) {
    rng_values_array[i] = simplerandom_kiss_next(&rng_kiss);

Discard (Jumpahead) Function

Each generator has a discard function, which is equivalent to the jumpahead function in the Python package. It is named discard in the C library, to be consistent with the naming of the function in the C++11/Boost random API.

The discard function allows for a generator to be moved ahead by n samples.

simplerandom_kiss_discard(&rng_kiss, 1000000000000uLL);

Note that n is of type uintmax_t, which would probably be 64-bit on most platforms, but might be 32-bit on some small embedded platforms.

The calculation is done with time complexity O(log n), so n can be very large and jumpahead will still calculate quickly.

Mix Function

In some systems, there might be some source of random data available, although the quality may not be statistically ideal. The simplerandom library provides mix functions, to mix random data in to the generator state.

Incorporating truly random data decreases the predictability of the generator's output, which might be useful in some applications. Even if the statistical properties of the random data isn't that great, once it is mixed into the generator's state, the generator's output should still be statistically good.

uint32_t real_random_data[8];
get_real_random_data_from_somewhere(&real_random_data, 8);
simplerandom_kiss_mix(&rng_kiss, real_random_data, 8);


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.

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.

In simplerandom.iterators, the generators are provided as Python iterators, of infinite length (they never raise StopIteration). They implement the next() method (__next__() in Python 3.x) 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. The jumpahead() function (Python 2.x) is implemented for all the generators, and is also supported in Python 3.x, even though jumpahead() has officially been removed from the Python 3.x 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.

Iterators Usage

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

It is possible to "jump ahead" by n values at any time. The calculation is done with time complexity O(log n), so n can be very large and jumpahead will still calculate quickly.

>>> rng.jumpahead(1000000000000000000)
>>> next(rng)

Random class API Usage

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

The jumpahead function is supported for all generators in both Python 2.x and 3.x.

>>> rng.jumpahead(1000000000000000000)
>>> rng.random()

Supported Python Versions

Currently this has had basic testing on Ubuntu 13.04 64-bit and Windows XP 32-bit. It passes the simplerandom.iterators.test unit tests, as well as well as basic manual testing of simplerandom.random. A more thorough unit test suite is needed.

In Ubuntu, it has been tested on Python 2.7 and 3.3, and passes.

In Windows, it has been tested on Python 2.6, 2.7, 3.1, 3.2 and 3.3. It passes under these versions.

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 [mars1], 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.


Random Numbers for C: End, at last?
George Marsaglia
Newsgroup post, sci.stat.math and others, Thu, 21 Jan 1999

George Marsaglia
Newsgroup post, sci.math, 26 Feb 2003

KISS: A Bit Too Simple
Greg Rose
Qualcomm Inc.

Tables of Maximally-Equidistributed Combined LFSR Generators
Pierre L'Ecuyer
Mathematics of Computation, 68, 225 (1999), 261–269.

Maximally Equidistributed Combined Tausworthe Generators
P. L'Ecuyer
Mathematics of Computation, 65, 213 (1996), 203–213.

LFSR113 C double implementation
Pierre L'Ecuyer